This PR implements module docstrings in Verso syntax, as well as adding
a number of improvements and fixes to Verso docstrings in general. In
particular, they now have language server support and are parsed at
parse time rather than elaboration time, so the snapshot's syntax tree
includes the parsed documentation.
This PR adds vectored write for TCP and UDP (that helps a lot with not
copying the arrays over and over) and fix a RC issue in TCP and UDP
cancel functions with the line `lean_dec((lean_object*)udp_socket);` and
a similar one that tries to decrement the object inside of the `socket`.
This PR adds a code action for `grind` parameters. We need to use
`set_option grind.param.codeAction true` to enable the option. The PR
also adds a modifier to instruct `grind` to use the "default" pattern
inference strategy.
This PR reduces noise in the 'Equivalence classes' section of the
`grind` diagnostics. It now uses a notion of *support expressions*.
Right now, it is hard-coded, but we will probably make it extensible in
the future. The current definition is
- `match`, `ite` and `dite`-applications. They have builtin support in
`grind`.
- Cast-like applications used by `grind`: `toQ`, `toInt`, `Nat.cast`,
`Int.cast`, and `cast`
- `grind` gadget applications (e.g., `Grind.nestedDecidable`)
- Projections of constructors (e.g., `{ x := 1, y := 2}.x`)
- Auxiliary arithmetic terms constructed by solvers such as `cutsat` and
`ring`.
If an equivalence class contains at most one non-support term, it goes
into the “others” bucket. Otherwise, we display the non-support elements
and place the support terms in a child node.
**BEFORE**:
<img width="1397" height="1558" alt="image"
src="https://github.com/user-attachments/assets/4fd4de31-7300-4158-908b-247024381243"
/>
**AFTER**:
<img width="840" height="340" alt="image"
src="https://github.com/user-attachments/assets/05020f34-4ade-49bf-8ccc-9eb0ba53c861"
/>
**Remark**: No information is lost; it is just grouped differently."
This PR adds an alternative implementation of `Deriving Ord` based on
comparing `.ctorIdx` and using a dedicated matcher for comparing same
constructors (added in #10152). The new option
`deriving.ord.linear_construction_threshold` sets the constructor count
threshold (10 by default) for using the new construction.
It also (unconditionally) changes the implementation for enumeration
types to simply compare the `ctorIdx`.
This PR implements `mvcgen invariants?` for providing initial invariant
skeletons for the user to flesh out. When the loop body has an early
return, it will helpfully suggest `Invariant.withEarlyReturn ...` as a
skeleton.
```lean
def mySum (l : List Nat) : Nat := Id.run do
let mut acc := 0
for x in l do
acc := acc + x
return acc
/--
info: Try this:
invariants
· ⇓⟨xs, acc⟩ => _
-/
#guard_msgs (info) in
theorem mySum_suggest_invariant (l : List Nat) : mySum l = l.sum := by
generalize h : mySum l = r
apply Id.of_wp_run_eq h
mvcgen invariants?
all_goals admit
def nodup (l : List Int) : Bool := Id.run do
let mut seen : HashSet Int := ∅
for x in l do
if x ∈ seen then
return false
seen := seen.insert x
return true
/--
info: Try this:
invariants
· Invariant.withEarlyReturn (onReturn := fun r acc => _) (onContinue := fun xs acc => _)
-/
#guard_msgs (info) in
theorem nodup_suggest_invariant (l : List Int) : nodup l ↔ l.Nodup := by
generalize h : nodup l = r
apply Id.of_wp_run_eq h
mvcgen invariants?
all_goals admit
```
This PR fixes a potential miscompilation when using non-exposed type
definitions using the module system by turning it into a static error. A
future revision may lift the restriction by making the compiler metadata
independent of the current module.
This PR makes `mvcgen` reduce through `let`s, so that it progresses over
`(have t := 42; fun _ => foo t) 23` by reduction to `have t := 42; foo
t` and then introducing `t`.
This PR ensures that issues reported by the E-matching module are
displayed only when `set_option grind.debug true` is enabled. Users
reported that these messages are too distracting and not very useful.
They are more valuable for library developers when annotating their
libraries.
This PR adds an alternative implementation of `DerivingBEq` based on
comparing `.ctorIdx` and using a dedicated matcher for comparing same
constructors (added in #10152), to avoid the quadratic overhead of the
default match implementation. The new option
`deriving.beq.linear_construction_threshold` sets the constructor count
threshold (10 by default) for using the new construction. Such instances
also allow `deriving ReflBEq, LawfulBeq`, although these proofs for
these properties are still quadratic.
This PR adds the `reduceCtorIdx` simproc which recognizes and reduces
`ctorIdx` applications. This is not on by default yet because it does
not use the discrimination tree (yet).
This PR redefines `String` to be the type of byte arrays `b` for which
`b.IsValidUtf8`.
This moves the data model of strings much closer to the actual data
representation at runtime.
In the near future, we will
- provide variants of `String.Pos` and `Substring` that only allow for
valid positions
- redefine all `String` functions to be much closer to their C++
implementations
In the near-to-medium future we will then provide comprehensive
verification of `String` based on these refactors.
This PR adds support the Count Trailing Zeros operation `BitVec.ctz` to
the bitvector library and to `bv_decide`, relying on the existing `clz`
circuit. We also build some theory around `BitVec.ctz` (analogous to the
theory existing for `BitVec.clz`) and introduce lemmas
`BitVec.[ctz_eq_reverse_clz, clz_eq_reverse_ctz, ctz_lt_iff_ne_zero,
getLsbD_false_of_lt_ctz, getLsbD_true_ctz_of_ne_zero,
two_pow_ctz_le_toNat_of_ne_zero, reverse_reverse_eq,
reverse_eq_zero_iff]`.
`ctz` operation is common in numerous compiler intrinsics (see
[here](https://clang.llvm.org/docs/LanguageExtensions.html#intrinsics-support-within-constant-expressions))
and architectures (see
[here](https://en.wikipedia.org/wiki/Find_first_set)).
---------
Co-authored-by: Siddharth <siddu.druid@gmail.com>
This PR adds `reprove N by T`, which effectively elaborates `example
type_of% N := by T`. It supports multiple identifiers. This is useful
for testing tactics.
🤖 Generated with [Claude Code](https://claude.ai/code)
---------
Co-authored-by: Claude <noreply@anthropic.com>
This PR enables the new E-matching pattern inference heuristic for
`grind`, implemented in PR #10422.
**Important**: Users can still use the old pattern inference heuristic
by setting:
```lean
set_option backward.grind.inferPattern true
```
In PR #10422, we introduced the new modifier `@[grind!]` for enabling
the minimal indexable subexpression condition. This option can now also
be set in `grind` parameters. Example:
```lean
opaque f : Nat → Nat
opaque fInv : Nat → Nat
axiom fInv_f : fInv (f x) = x
/-- trace: [grind.ematch.pattern] fInv_f: [f #0] -/
#guard_msgs in
set_option trace.grind.ematch.pattern true in
example {x y} : f x = f y → x = y := by
/-
The modifier `!` instructs `grind` to use the minimal indexable subexpression
(i.e., `f x` in this case).
-/
grind [!fInv_f]
```
This PR refines and clarifies the `meta` phase distinction in the module
system.
* `meta import A` without `public` now has the clarified meaning of
"enable compile-time evaluation of declarations in or above `A` in the
current module, but not downstream". This is now checked statically by
enforcing that public meta defs, which therefore may be referenced from
outside, can only use public meta imports, and that global evaluating
attributes such as `@[term_parser]` can only be applied to public meta
defs.
* `meta def`s may no longer reference non-meta defs even when in the
same module. This clarifies the meta distinction as well as improves
locality of (new) error messages.
* parser references in `syntax` are now also properly tracked as meta
references.
* A `meta import` of an `import` now properly loads only the `.ir` of
the nested module for the purposes of execution instead of also making
its declarations available for general elaboration.
* `initialize` is now no longer being run on import under the module
system, which is now covered by `meta initialize`.
This PR ensures users can select the "minimal indexable subexpression"
condition in `grind` parameters. Example, they can now write `grind [!
-> thmName]`. `grind?` will include the `!` modifier whenever users had
used `@[grind!]`. This PR also fixes a missing case in the new pattern
inference procedure.
It also adjusts some `grind` annotations and tests in preparation for
setting the new pattern inference heuristic as the new default.
This PR changes the order of steps tried when proving equational
theorems for structural recursion. In order to avoid goals that `split`
cannot handle, avoid unfolding the LHS of the equation to `.brecOn` and
`.rec` until after the RHS has been split into its final cases.
Fixes: #10195
This PR lets the `split` tactic generalize discriminants that are not
free variables and proofs using `generalize`. If the only
non-fvar-discriminants are proofs, then this avoids the more elaborate
generalization strategy of `split`, which can fail with dependent
motives, thus mitigating issue #10424.
This PR changes the defeq algorithm to perform `whnf` on the `String.mk`
expression it creates for string literals.
This is currently a no-op, but will no longer be one once `String` is
redefined so that `String.mk` is a regular function instead of a
constructor.
This PR implements the new E-matching pattern inference heuristic for
`grind`. It is not enabled yet. You can activate the new behavior using
`set_option backward.grind.inferPattern false`. Here is a summary of the
new behavior.
* `[grind =]`, `[grind =_]`, `[grind _=_]`, `[grind <-=]`: no changes;
we keep the current behavior.
* `[grind ->]`, `[grind <-]`, `[grind =>]`, `[grind <=]`: we stop using
the *minimal indexable subexpression* and instead use the first
indexable one.
* `[grind! <mod>]`: behaves like `[grind <mod>]` but uses the minimal
indexable subexpression restriction. We generate an error if the user
writes `[grind! =]`, `[grind! =_]`, `[grind! _=_]`, or `[grind! <-=]`,
since there is no pattern search in these cases.
* `[grind]`: it tries `=`, `=_`, `<-`, `->`, `<=`, `=>` with and without
the minimal indexable subexpression restriction. For the ones that work,
we generate a code action to encourage users to select the one they
prefer.
* `[grind!]`: it tries `<-`, `->`, `<=`, `=>` using the minimal
indexable subexpression restriction. For the ones that work, we generate
a code action to encourage users to select the one they prefer.
* `[grind? <mod>]`: where `<mod>` is one of the modifiers above, it
behaves like `[grind <mod>]` but also displays the pattern.
Example:
```lean
/--
info: Try these:
• [grind =] for pattern: [f (g #0)]
• [grind =_] for pattern: [r #0#0]
• [grind! ←] for pattern: [g #0]
-/
#guard_msgs in
@[grind] axiom fg₇ : f (g x) = r x x
```
This PR adds a normalizer for non-commutative semirings to `grind`.
Examples:
```lean
open Lean.Grind
variable (R : Type u) [Semiring R]
example (a b c : R) : a * (b + c) = a * c + a * b := by grind
example (a b : R) : (a + 2 * b)^2 = a^2 + 2 * a * b + 2 * b * a + 4 * b^2 := by grind
example (a b : R) : b^2 + (a + 2 * b)^2 = a^2 + 2 * a * b + b * (1+1) * a * 1 + 5 * b^2 := by grind
example (a b : R) : a^3 + a^2*b + a*b*a + b*a^2 + a*b^2 + b*a*b + b^2*a + b^3 = (a+b)^3 := by grind
```
This PR adds the helper theorem `eq_normS_nc` for normalizing
non-commutative semirings. We will use this theorem to justify
normalization steps in the `grind ring` module.
This PR changes the automation in `deriving_LawfulEq_tactic_step` to use
`with_reducible` when asserting the shape of the goal using `change`, so
that we do not accidentally unfold `x == x'` calls here. Fixes#10416.
This PR adds the ability to do `deriving ReflBEq, LawfulBEq`. Both
classes have to listed in the `deriving` clause. For `ReflBEq`, a simple
`simp`-based proof is used. For `LawfulBEq`, a dedicated,
syntax-directed tactic is used that should work for derived `BEq`
instances. This is meant to work with `deriving BEq` (but you can try to
use it on hand-rolled `@[methods_specs] instance : BEq…` instances).
Does not support mutual or nested inductives.
This PR fixes a bug where definitions with nested proofs that contain
`sorry` might not report "warning: declaration uses 'sorry'" if the
proof has the same type as another nested proof from a previous
declaration. The bug only affected log messages; `#print axioms` would
still correctly report uses of `sorryAx`.
The fix is that now the abstract nested proofs procedure does not
consult the aux lemma cache if the proof contains a `sorry`.
Closes#10196
This PR gives anonymous constructor notation (`⟨x,y⟩`) an error recovery
mechanism where if there are not enough arguments then synthetic sorries
are inserted for the missing arguments and an error is logged, rather
than outright failing.
Closes#9591.
This PR fixes an issue with the `if` tactic where errors were not placed
at the correct source ranges. It also adds some error recovery to avoid
additional errors about unsolved goals on the `if` token when the tactic
has incomplete syntax.
Closes#7972
This PR adds the `reduceBEq` and `reduceOrd` simprocs. They rewrite
occurrences of `_ == _` resp. `Ord.compare _ _` if both arguments are
constructors and the corresponding instance has been marked with
`@[method_specs]` (introduced in #10302), which now by default is the
case for derived instances.
This PR introduces the `@[specs]` attribute. It can be applied to
(certain) type class instances and define “specification theorems” for
the class’ operations, by taking the equational theorems of the
implementation function mentioned in the type class instance and
rephrasing them in terms of the overloaded operations. Fixes#5295.
Example:
```
inductive L α where
| nil : L α
| cons : α → L α → L α
def L.beqImpl [BEq α] : L α → L α → Bool
| nil, nil => true
| cons x xs, cons y ys => x == y && L.beqImpl xs ys
| _, _ => false
@[method_specs] instance [BEq α] : BEq (L α) := ⟨L.beqImpl⟩
/--
info: theorem instBEqL.beq_spec_2.{u_1} : ∀ {α : Type u_1} [inst : BEq α] (x_2 : α) (xs : L α) (y : α) (ys : L α),
(L.cons x_2 xs == L.cons y ys) = (x_2 == y && xs == ys)
-/
#guard_msgs(pass trace, all) in
#print sig instBEqL.beq_spec_2
```
It also introduces the `method_specs_norm` simpset to allow registering
further normalization of the theorems. The intended use of this is to
rewrite, say, `Append.append` to the `HAppend.hAppend` (i.e. `++`) that
the user wants to see. Library annotations to follow in a separate PR.
This PR makes the builtin Verso docstring elaborators bootstrap
correctly, adds the ability to postpone checks (which is necessary for
resolving forward references and bootstrapping issues), and fixes a
minor parser bug.
This PR includes some improvements to the release process, making the
updating of `stable` branches more robust, and including `cslib` in the
release checklist.
This PR implements sanity checks in the `grind ring` module to ensure
the instances synthesized by type class resolution are definitionally
equal to the corresponding ones in the `grind` core classes. The
definitional equality test is performed with reduction restricted to
reducible definitions and instances.
This PR fixes an issue where the "eta feature" in the app elaborator,
which is invoked when positional arguments are skipped due to named
arguments, results in variables that can be captured by those named
arguments. Now the temporary local variables that implement this feature
get fresh names. The names used for the closed lambda expression still
use the original parameter names.
Closes#6373
This PR enables using `notation` items in
`infix`/`infixl`/`infixr`/`prefix`/`postfix`. The motivation for this is
to enable being able to use `pp.unicode`-aware parsers. A followup PR
can combine core parsers as such:
```lean
infixr:30 unicode(" ∨ ", " \\/ ") => Or
```
Continuation of #10373.
This PR modifies the syntax for tactic configurations. Previously just
`(ident` would commit to tactic configuration item parsing, but now it
needs to be `(ident :=`. This enables reliably using tactic
configurations before the `term` category. For example, given `syntax
"my_tac" optConfig term : tactic`, it used to be that `my_tac (x + y)`
would have an error on `+` with "expected `:=`", but now it parses the
term.
An additional rationale is that these are like named arguments; (1)
terms can't begin with named arguments so now there is no parsing
ambiguity and (2) `Parser.Term.namedArgument` indeed already includes
`:=` in the atomic part.
This PR modifies pretty printing of `fun` binders, suppressing the safe
shadowing feature among the binders in the same `fun`. For example,
rather than pretty printing as `fun x x => 0`, we now see `fun x x_1 =>
0`. The calculation is done per `fun`, so for example `fun x => id fun x
=> 0` pretty prints as-is, taking advantage of safe shadowing.
The motivation for this change is that many users have reported that
safe shadowing within the same `fun` is confusing.
This PR adds support for non-commutative ring normalization in `grind`.
The new normalizer also accounts for the `IsCharP` type class. Examples:
```lean
open Lean Grind
variable (R : Type u) [Ring R]
example (a b : R) : (a + 2 * b)^2 = a^2 + 2 * a * b + 2 * b * a + 4 * b^2 := by grind
example (a b : R) : (a + 2 * b)^2 = a^2 + 2 * a * b + -b * (-4) * a - 2*b*a + 4 * b^2 := by grind
variable [IsCharP R 4]
example (a b : R) : (a - b)^2 = a^2 - a * b - b * 5 * a + b^2 := by grind
example (a b : R) : (a - b)^2 = 13*a^2 - a * b - b * 5 * a + b*3*b*3 := by grind
```
This PR adds the options `pp.piBinderNames` and
`pp.piBinderNames.hygienic`. Enabling `pp.piBinderNames` causes
non-dependent pi binder names to be pretty printed, rather than be
omitted. When `pp.piBinderNames.hygienic` is false (the default) then
only non-hygienic such biner names are pretty printed. Setting `pp.all`
enables `pp.piBinderNames` if it is not otherwise explicitly set.
Implementation note: this is exposing the secret pretty printer option
`pp.piBinderNames` that was being used within the signature pretty
printer.
Closes#1134.
This PR fixes a few bugs in the `rw` tactic: it could "steal" goals
because they appear in the type of the rewrite, it did not do an occurs
check, and new proof goals would not be synthetic opaque. This PR also
lets the `rfl` tactic assign synthetic opaque metavariables so that it
is equivalent to `exact rfl`.
Implementation note: filtering old vs new is not sufficient. This PR
partially addresses the bug where the rw tactic creates natural
metavariables for each of the goals; now new proof goals are synthetic
opaque.
Metaprogramming API: Instead of `Lean.MVarId.rewrite` prefer
`Lean.Elab.Tactic.elabRewrite` for elaborating rewrite theorems and
applying rewrites to expressions.
Closes#10172
This PR adds a `pp.unicode` option and a `unicode("→", "->")` syntax
description alias for the lower-level `unicodeSymbol "→" "->"` parser.
The syntax is added to the `notation` command as well. When `pp.unicode`
is true (the default) then the first form is used when pretty printing,
and otherwise the second ASCII form is used. A variant, `unicode("→",
"->", preserveForPP)` causes the `->` form to be preferred; delaborators
can insert `→` directly into the syntax, which will be pretty printed
as-is; this allows notations like `fun` to use custom options such as
`pp.unicode.fun` to opt into the unicode form when pretty printing.
Additionally:
- Adds more documentation for the `symbol` and `nonReservedSymbol`
parser descriptions.
- Adds documentation for the
`infix`/`infixr`/`infixl`/`prefix`/`postfix` commands.
- The parenthesizers for symbols are improved to backtrack if the atom
doesn't match.
- Fixes a bug where `&"..."` symbols aren't validated.
This is partial progress for issue #1056. What remains is enabling
`unicode(...)` for mixfix commands and then making use of it for core
notation.
This PR explicitly imports `Lake.Util` submodules in `Lake`, ensuring
Lake utilities are consistently available by default in configuration
files.
It also simplifies the Lake globs for the core build to ensure all Lake
submodules are built (even if they are not imported).
This PR ensures that the infotree recognizes `Classical.propDecidable`
as an instance, when below a `classical` tactic.
The `classical` tactic modifies the environment that the subsequent
sequence of tactics runs in (by making `Classical.propDecidable` an
instance). However, it does not add a corresponding `InfoTree.context`
node, so its effects are not visible when we want to replay a tactic
sequence (for example when running a tactic in the tactic analysis
framework). We should add a call to `Lean.Elab.withSafeInfoContext` to
remedy this issue.
There are two potential places to add this class: in the meta-level
`Lean.Elab.Tactic.classical` wrapper, or the tactic-level
`evalClassical` tactic elaborator. I chose the latter since meta-level
does not have access to info tree operations (unless we add many
parameters to `Lean.Elab.Tactic.classical`: `[MonadNameGenerator m]
[MonadOptions m] [MonadMCtx m] [MonadResolveName m] [MonadFileMap m]`).
A testcase that uses the tactic analysis framework is available here:
https://github.com/leanprover-community/mathlib4/pull/29501
This PR adds syntax for defining compile-time initializers under the
module system, with other initializers to be restricted from running at
compile time in a follow-up PR.
This PR uses the per-constructor `noConfusion` principles (from #10315)
in the `mkNoConfusion` app builder, if possible. This means they are
used by `injection`, `grind`, `simp` and other places. This brings
notable performance improvements when dealing with inductives with a
large number of constructors.
This PR adds `T.ctor.noConfusion` declarations, which are
specializations of `T.noConfusion` to equalities between `T.ctor`. The
point is to avoid reducing the `T.noConfusionType` construction every
time we use `injection` or a similar tactic.
```lean
Vec.cons.noConfusion.{u_1, u} {α : Type u} (P : Sort u_1) {n : Nat}
(x : α) (xs : Vec α n) (x' : α) (xs' : Vec α n)
(h : Vec.cons x xs = Vec.cons x' xs')
(k : n = n → x = x' → xs ≍ xs' → P) : P
```
The constructions are not as powerful as `T.noConfusion` when the
indices of the inductive type are not just constructor parameters (or
constructor applications of these parameters), so the full
`T.noConfusion` construction is still needed as a fallback.
It may seem costly to generate these eagerly, but given that we eagerly
generate injectivity theorems already, and we will use them there, it
seems reasonable for now.
To further reduce the cost, we only generate them for constructors with
fields (for others, the `T.noConfusion` theorem doesn't provide any
information), and we use `macro_inline` to prevent the compiler from
creating code for these, given that the compiler has special support for
`T.noConfusion` that we want it to use).
An earlier version of this PR also removed trivial equations and
un-HEq-ed others, leading to
```
(k : x = x' → xs = xs' → P)
```
in the example above. I backed out of that change, as it makes it harder
for tactics like `injectivity` to know how often to `intro`, so better
to keep things uniform.
This PR adds range support to`BitVec` and the `UInt*` types. This means
that it is now possible to write, for example, `for i in (1 : UInt8)...5
do`, in order to loop over the values 1, 2, 3 and 4 of type `UInt8`.
This PR adds more lemmas about the `toList` and `toArray` functions on
ranges and iterators. It also renames `Array.mem_toArray` into
`List.mem_toArray`.
This PR adds the type `Std.Internal.Parsec.Error`, which contains the
constructors `.eof` (useful for checking if parsing failed due to not
having enough input and then retrying when more input arrives that is
useful in the HTTP server) and `.other`, which describes other errors.
It also adds documentation to many functions, along with some new
functions to the `ByteArray` Parsec, such as `peekWhen?`, `octDigit`,
`takeWhile`, `takeUntil`, `skipWhile`, and `skipUntil`.
This PR is followup to the change in grind pattern heuristics from
#10342, typically resolving the discrepancy by writing out an explicit
`grind_pattern` for the intended pattern. The new behaviour is more
aggressive, because it selects smaller patterns.
This PR allows the interpreter to jump to native code of `[export]`
declarations, which can increase performance as well as the
effectiveness of `interpreter.prefer_native=true` during bootstrapping.
This PR reimplements `mkNoConfusionType` in lean, thus removing the
remaining C code related to this construction.
Also uses the ctor elimination principles only when there are more than
three ctors.
This PR completes the review of `@[grind]` annotations without a sigil
(e.g. `=` or `←`), replacing most of them with more specific annotations
or patterns.
---------
Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
This PR implements a new E-matching pattern inference procedure that is
faithful to the behavior documented in the reference manual regarding
minimal indexable subexpressions. The old inference procedure was
failing to enforce this condition. For example, the manual documents
`[grind ->]` as follows
`[@grind →]` selects a multi-pattern from the hypotheses of the theorem.
In other words, `grind` will use the theorem for forwards reasoning.
To generate a pattern, it traverses the hypotheses of the theorem from
left to right. Each time it encounters a **minimal indexable
subexpression** which covers an argument which was not previously
covered, it adds that subexpression as a pattern, until all arguments
have been covered.
That said, the new procedure is currently disabled, and the following
option must be used to enable it.
```
set_option backward.grind.inferPattern false
```
Users can inspect differences between the old a new procedures using the
option
```
set_option backward.grind.checkInferPatternDiscrepancy true
```
Example:
```lean
/--
warning: found discrepancy between old and new `grind` pattern inference procedures, old:
[@List.length #2 (@toList _ #1#0)]
new:
[@toList #2#1#0]
use `set_option backward.grind.inferPattern true` to force old procedure
-/
#guard_msgs in
set_option backward.grind.checkInferPatternDiscrepancy true in
@[grind] theorem Vector.length_toList' (xs : Vector α n) : xs.toList.length = n := by sorry
```
This PR moves the definitions and basic facts about `Function.Injective`
and `Function.Surjective` up from Mathlib. We can do a better job of
arguing via injectivity in `grind` if these are available.
This PR updates `@[grind]` annotations which should be `@[grind =]`, for
robustness (and, presumably, in some fraction of cases the existing
heuristic for `@[grind]` is already too liberal).
This PR shares common functionality relate to equalities between same
constructors, and when these are type-correct. In particular it uses the
more complete logic from `mkInjectivityThm` also in other places, such
as `CasesOnSameCtor` and the deriving code for `BEq`, `DecidableEq`,
`Ord`, for more consistency and better error messages.
This PR implements `mkNoConfusionImp` in Lean rather than in C. This
reduces our reliance on C, and may bring performance benefits from not
reducing `noConfusionType` during elaboration time (it still gets
reduced by the kernel when type-checking).
This PR makes it possible to write custom interpolation notation which
treats interpolated `String`s specially.
Sometimes it is desirable for `let w := "world"; foo!"hello {w}"` and
`foo!"hello world"` to mean different things; for instance, if debugging
and wanting to show all interpolands with `repr`. The current approach
forces `hello` to also be rendered with `repr`, which is not desirable.
This doesn't modify any existing formatters.
Requested in [#lean4 > ✔ dbg_trace should use `Repr` instance @
💬](https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/.E2.9C.94.20dbg_trace.20should.20use.20.60Repr.60.20instance/near/495082575)
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
This PR upstreams the Verso parser and adds preliminary support for
Verso in docstrings. This will allow the compiler to check examples and
cross-references in documentation.
After a `stage0` update, a follow-up PR will add the appropriate
attributes that allow the feature to be used. The parser tests from
Verso also remain to be upstreamed, and user-facing documentation will
be added once the feature has been used on more internals.
This PR fixes a performance issue in `grind linarith`. It was creating
unnecessary `NatModule`/`IntModule` structures for commutative rings
without an order. This kind of type should be handled by `grind ring`
only.
This PR implements model-based theory combination for types `A` which
implement the `ToInt` interface. Examples:
```lean
example {C : Type} (h : Fin 4 → C) (x : Fin 4)
: 3 ≤ x → x ≤ 3 → h x = h (-1) := by
grind
example {C : Type} (h : UInt8 → C) (x y z w : UInt8)
: y + 1 + w ≤ x + w → x + w ≤ z → z ≤ y + w + 1 → h (x + w) = h (y + w + 1) := by
grind
example {C : Type} (h : Fin 8 → C) (x y w r : Fin 8)
: y + 1 + w ≤ r → r ≤ y + w + x → x = 1 → h r = h (y + w + 1) := by
grind
```
This PR removes `grind →` annotations that fire too often, unhelpfully.
It would be nice for `grind` to instantiate these lemmas, but only if
they already see `xs ++ ys` and `#[]` in the same equivalence class, not
just as soon as it sees `xs ++ ys`.
In the meantime, let's see what is using these.
This PR introduces limited functionality frontends `cutsat` and
`grobner` for `grind`. We disable theorem instantiation (and case
splitting for `grobner`), and turn off all other solvers. Both still
allow `grind` configuration options, so for example one can use `cutsat
+ring` (or `grobner +cutsat`) to solve problems that require both.
For `cutsat`, it is helpful to instantiate a limited set of theorems
(e.g. `Nat.max_def`). Currently this isn't supported, but we intend to
add this later.
This PR fixes the `grind` canonicalizer for `OfNat.ofNat` applications.
Example:
```lean
example {C : Type} (h : Fin 2 → C) :
-- `0` in the first `OfNat.ofNat` is not a raw literal
h (@OfNat.ofNat (Fin (1 + 1)) 0 Fin.instOfNat) = h 0 := by
grind
```
This PR ensures that the auxiliary temporary metavariable IDs created by
the E-matching module used in `grind` are not affected by what has been
executed before invoking `grind`. The goal is to increase `grind`’s
robustness.
For example, in the E-matching module we use `Expr.quickLt` to sort
candidates. `Expr.quickLt` depends on the `Expr` hash code, which in
turn depends on metavariable IDs. Thus, before this change, the initial
next metavariable ID at the time of `grind` invocation could affect the
order in which instances were generated, and consequently the `grind`
search.
This PR changes the string interpolation procedure to omit redundant
empty parts. For example `s!"{1}{2}"` previously elaborated to `toString
"" ++ toString 1 ++ toString "" ++ toString 2 ++ toString ""` and now
elaborates to `toString 1 ++ toString 2`.
- [x] Updated docstrings for `simp!`, `simp_all!`, `dsimp!` to use
user-friendly language
- [x] Updated docstrings for `autoUnfold` fields to use user-friendly
language
- [x] Fixed broken test by updating expected output for simp! hover
documentation
- [x] Replaced technical terms with clear language: "will unfold
applications of functions defined by pattern matching, when one of the
patterns applies"
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This PR adds missing the lemmas `ofList_eq_insertMany_empty`,
`get?_eq_some_iff`, `getElem?_eq_some_iff` and `getKey?_eq_some_iff` to
all container types.
Bumps
[actions/download-artifact](https://github.com/actions/download-artifact)
from 4 to 5.
<details>
<summary>Release notes</summary>
<p><em>Sourced from <a
href="https://github.com/actions/download-artifact/releases">actions/download-artifact's
releases</a>.</em></p>
<blockquote>
<h2>v5.0.0</h2>
<h2>What's Changed</h2>
<ul>
<li>Update README.md by <a
href="https://github.com/nebuk89"><code>@nebuk89</code></a> in <a
href="https://redirect.github.com/actions/download-artifact/pull/407">actions/download-artifact#407</a></li>
<li>BREAKING fix: inconsistent path behavior for single artifact
downloads by ID by <a
href="https://github.com/GrantBirki"><code>@GrantBirki</code></a> in <a
href="https://redirect.github.com/actions/download-artifact/pull/416">actions/download-artifact#416</a></li>
</ul>
<h2>v5.0.0</h2>
<h3>🚨 Breaking Change</h3>
<p>This release fixes an inconsistency in path behavior for single
artifact downloads by ID. <strong>If you're downloading single artifacts
by ID, the output path may change.</strong></p>
<h4>What Changed</h4>
<p>Previously, <strong>single artifact downloads</strong> behaved
differently depending on how you specified the artifact:</p>
<ul>
<li><strong>By name</strong>: <code>name: my-artifact</code> → extracted
to <code>path/</code> (direct)</li>
<li><strong>By ID</strong>: <code>artifact-ids: 12345</code> → extracted
to <code>path/my-artifact/</code> (nested)</li>
</ul>
<p>Now both methods are consistent:</p>
<ul>
<li><strong>By name</strong>: <code>name: my-artifact</code> → extracted
to <code>path/</code> (unchanged)</li>
<li><strong>By ID</strong>: <code>artifact-ids: 12345</code> → extracted
to <code>path/</code> (fixed - now direct)</li>
</ul>
<h4>Migration Guide</h4>
<h5>✅ No Action Needed If:</h5>
<ul>
<li>You download artifacts by <strong>name</strong></li>
<li>You download <strong>multiple</strong> artifacts by ID</li>
<li>You already use <code>merge-multiple: true</code> as a
workaround</li>
</ul>
<h5>⚠️ Action Required If:</h5>
<p>You download <strong>single artifacts by ID</strong> and your
workflows expect the nested directory structure.</p>
<p><strong>Before v5 (nested structure):</strong></p>
<pre lang="yaml"><code>- uses: actions/download-artifact@v4
with:
artifact-ids: 12345
path: dist
# Files were in: dist/my-artifact/
</code></pre>
<blockquote>
<p>Where <code>my-artifact</code> is the name of the artifact you
previously uploaded</p>
</blockquote>
<p><strong>To maintain old behavior (if needed):</strong></p>
<pre lang="yaml"><code></tr></table>
</code></pre>
</blockquote>
<p>... (truncated)</p>
</details>
<details>
<summary>Commits</summary>
<ul>
<li><a
href="634f93cb29"><code>634f93c</code></a>
Merge pull request <a
href="https://redirect.github.com/actions/download-artifact/issues/416">#416</a>
from actions/single-artifact-id-download-path</li>
<li><a
href="b19ff43027"><code>b19ff43</code></a>
refactor: resolve download path correctly in artifact download tests
(mainly ...</li>
<li><a
href="e262cbee4a"><code>e262cbe</code></a>
bundle dist</li>
<li><a
href="bff23f9308"><code>bff23f9</code></a>
update docs</li>
<li><a
href="fff8c148a8"><code>fff8c14</code></a>
fix download path logic when downloading a single artifact by id</li>
<li><a
href="448e3f862a"><code>448e3f8</code></a>
Merge pull request <a
href="https://redirect.github.com/actions/download-artifact/issues/407">#407</a>
from actions/nebuk89-patch-1</li>
<li><a
href="47225c44b3"><code>47225c4</code></a>
Update README.md</li>
<li>See full diff in <a
href="https://github.com/actions/download-artifact/compare/v4...v5">compare
view</a></li>
</ul>
</details>
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This PR adds missing `grind` normalization rules for `natCast` and
`intCast` Examples:
```
open Lean.Grind
variable (R : Type) (a b : R)
section CommSemiring
variable [CommSemiring R]
example (m n : Nat) : (m + n) • a = m • a + n • a := by grind
example (m n : Nat) : (m * n) • a = m • (n • a) := by grind
end CommSemiring
section CommRing
variable [CommRing R]
example (m n : Nat) : (m + n) • a = m • a + n • a := by grind
example (m n : Nat) : (m * n) • a = m • (n • a) := by grind
example (m n : Int) : (m * n) • (a * b) = (m • a) * (n • b) := by grind
end CommRing
```
This PR makes `IO.RealWorld` opaque. It also adds a new compiler -only
`lcRealWorld` constant to represent this type within the compiler. By
default, an opaque type definition is treated like `lcAny`, whereas we
want a more efficient representation. At the moment, this isn't a big
difference, but in the future we would like to completely erase
`IO.RealWorld` at runtime.
This PR offers an alternative `noConfusion` construction for the
off-diagonal use (i.e. for different constructors), based on comparing
the `.ctorIdx`. This should lead to faster type checking, as the kernel
only has to reduce `.ctorIdx` twice, instead of the complicate
`noConfusionType` construction.
This PR changes the "declaration uses 'sorry'" error to pretty print an
actual `sorry` expression in the message. The effect is that the `sorry`
is hoverable and, if it's labeled, you can "go to definition" to see
where it came from.
The implementation prefers reporting synthetic sorries. These can appear
even if there are no error messages if a declaration refers to a
declaration that has elaboration errors. Users should focus on
elaboration errors before worrying about user-written `sorry`s.
In the future we could have some more precise logic for sorry reporting.
All the sorries in a declaration should be considered to be reported,
and we should not re-report sorries in later declarations. Some
elaborators use `warn.sorry` to avoid re-reporting sorries in auxiliary
declarations.
This PR changes the implementation of a function `unfoldPredRel` used in
(co)inductive predicate machinery, that unfolds pointwise order on
predicates to quantifications and implications. Previous implementation
relied on `withDeclsDND` that could not deal with types which depend on
each other. This caused the following example to fail:
```lean4
inductive infSeq_functor1.{u} {α : Type u} (r : α → α → Prop) (call : {α : Type u} → (r : α → α → Prop) → α → Prop) : α → Prop where
| step : r a b → infSeq_functor1 r call b → infSeq_functor1 r call a
def infSeq1 (r : α → α → Prop) : α → Prop := infSeq_functor1 r (infSeq1)
coinductive_fixpoint monotonicity by sorry
#check infSeq1.coinduct
```
Closes#10234.
This test involves re-running the compiler on decls that have already
been compiled, which can cause all sorts of issues. I just hit these
issues on a PR, so it's time to retire this test like others that hit
the same issues.
This PR completes the `grind` solver extension design and ports the
`grind ac` solver to the new framework. Future PRs will document the API
and port the remaining solvers. An additional benefit of the new design
is faster build times.
The proof of the instWPMonad instance relies on the equality of any two
terms of type `IO.RealWorld`, which is only a side effect of the current
transparent definition. Ignoring the questions around the utility of
proving things about programs in `IO`, the semantic validity of this
instance in the intended model of the IO monad is also unclear.
I tried a few things to axiomatize this instance so it could be put into
the test file to preserve the one test section that relies on it, but I
was unsuccessful; everything I attempted caused errors.
This PR adds infrastructure for registering new `grind` solvers. `grind`
already includes many solvers, and this PR is the first step toward
modularizing the design and supporting user-defined solvers.
This PR prepares for a future reorganization of the import hierarchy so
that `Init.Data.String.Basic` can import `Init.Data.UInt.Bitwise` and
`Init.Data.Array.Lemmas`.
This PR moves `String.utf8EncodeChar` to the prelude to prepare for the
imminent redefinition of `String`.
The definition in the prelude uses modulo and division operations on
natural numbers. In `String.Extra`, a `csimp` lemma is provided, showing
that the new definition is equal to the previous one (which is now
called `utf8EncodeCharFast`) which uses bitwise operations on `UInt8`.
This PR implements diagnostic information for the `grind ac` module. It
now displays the basis, normalized disequalities, and additional
properties detected for each associative operator.
This PR improves the counterexamples produced by `grind linarith` for
`NatModule`s. `grind` now hides occurrences of the auxiliary function
`Grind.IntModule.OfNatModule.toQ`.
This PR implements `NatModule` normalization when the `AddRightCancel`
instance is not available. Note that in this case, the embedding into
`IntModule` is not injective. Therefore, we use a custom normalizer,
similar to the `CommSemiring` normalizer used in the `grind ring`
module. Example:
```lean
open Lean Grind
example [NatModule α] (a b c : α)
: 2•a + 2•(b + 2•c) + 3•a = 4•a + c + 2•b + 3•c + a := by
grind
```
This PR adds the auxiliary theorem `Lean.Grind.Linarith.eq_normN` for
normalizing `NatModule` equations when the instance `AddRightCancel` is
not available.
This PR changes the implementation of the linear `DecidableEq`
implementation to use `match decEq` rather than `if h : ` to compare the
constructor tags. Otherwise, the “smart unfolding” machinery will not
let `rfl` decide that different constructors are different.
This PR adds support for `NatModule` equalities and inequalities in
`grind linarith`. Examples:
```lean
open Lean Grind Std
example [NatModule α] [LE α] [LT α]
[LawfulOrderLT α] [IsLinearOrder α] [OrderedAdd α]
(x y : α) : x ≤ y → 2 • x + y ≤ 3 • y := by
grind
example [NatModule α] [AddRightCancel α] [LE α] [LT α]
[LawfulOrderLT α] [IsLinearOrder α] [OrderedAdd α]
(a b c d : α) : a ≤ b → a ≥ c + d → d ≤ 0 → d ≥ 0 → b = c → a = b := by
grind
```
This PR changes the naming of the internal functions in deriving
instances like BEq to use accessible names. This is necessary to
reasonably easily prove things about these functions. For example after
`deriving BEq` for a type `T`, the implementation of `instBEqT` is in
`instBEqT.beq`.
This PR adds a new option `maxErrors` that limits the number of errors
printed from a single `lean` run, defaulting to 100. Processing is
aborted when the limit is reached, but this is tracked only on a
per-command level.
Smaller values can be useful when making changes that break a lot of
files and would otherwise scroll the actual root failures out of the
terminal view.
This PR implements the infrastructure for supporting `NatModule` in
`grind linarith` and uses it to handle disequalities. Another PR will
add support for equalities and inequalities. Example:
```lean
open Lean Grind
variable (M : Type) [NatModule M] [AddRightCancel M]
example (x y : M) : 2 • x + 3 • y + x = 3 • (x + y) := by
grind
```
This PR fixes a panic in `grind ring` exposed by #10242. `grind ring`
should not assume that all normalizations have been applied, because
some subterms cannot be rewritten by `simp` due to typing constraints.
Moreover, `grind` uses `preprocessLight` in a few places, and it skips
the simplifier/normalizer.
Closes#10242
This PR improves the names of definitions and lemmas in the polymorphic
range API. It also introduces a recommended spelling. For example, a
left-closed, right-open range is spelled `Rco` in analogy with Mathlib's
`Ico` intervals.
This PR speeds up auto-completion by a factor of ~3.5x through various
performance improvements in the language server. On one machine, with
`import Mathlib`, completing `i` used to take 3200ms and now instead
yields a result in 920ms.
Specifically, the following improvements are made:
- The watchdog process no longer de-serializes and re-serializes most
messages from the file worker before passing them on to the user - a
fast partial de-serialization procedure is now used to determine whether
the message needs to be de-serialized in full or not.
- `escapePart` is optimized to perform better on ASCII strings that do
not need escaping.
- `Json.compress` is optimized to allocate fewer objects.
- A faster JSON compression specifically for completion responses is
implemented that skips allocating `Json` altogether.
- The JSON compression has been moved to the task where we convert a
request response to `Json` so that converting to a string won't block
the output task of the FileWorker and so the `Json` value is not marked
as multi-threaded when we compress is, which drastically increases the
cost of reference-counting.
- The JSON representation of the `data?` field of each completion item
is optimized.
- Both the completion kind and the set of completion tags for each
imported completion item is now cached.
- The filtering of duplicate completion items is optimized.
Other adjustments:
- `LT UInt8` and `LE UInt8` are moved to Prelude so that they can be
used in `Init.Meta` for the name part escaping fast path.
- `Array.usize` is exposed since it was marked as `@[simp]`.
This PR moves the `PackageConfig` definition from `Lake.Config.Package`
into its own module. This enables a significant reduction in the `meta
import` tree of the `Lake.CLI.Translate` modules.
This PR fixes a bug in the `LinearOrderPackage.ofOrd` factory. If there
is a `LawfulEqOrd` instance available, it should automatically use it
instead of requiring the user to provide the `eq_of_compare` argument to
the factory. The PR also solves a hygiene-related problem making the
factories fail when `Std` is not open.
This PR adds some test cases for `grind` working with `Fin`. There are
many still failing tests in `tests/lean/grind/grind_fin.lean` which I'm
intending to triage and work on.
This PR fixes the E-matching procedure for theorems that contain
universe parameters not referenced by any regular parameter. This kind
of theorem seldom happens in practice, but we do have instances in the
standard library. Example:
```
@[simp, grind =] theorem Std.Do.SPred.down_pure {φ : Prop} : (⌜φ⌝ : SPred []).down = φ := rfl
```
closes#10233
This PR fixes a missing case in the `grind` canonicalizer. Some types
may include terms or propositions that are internalized later in the
`grind` state.
closes#10232
This PR adds `MonoBind` for more monad transformers. This allows using
`partial_fixpoint` for more complicated monads based on `Option` and
`EIO`. Example:
```lean-4
abbrev M := ReaderT String (StateT String.Pos Option)
def parseAll (x : M α) : M (List α) := do
if (← read).atEnd (← get) then
return []
let val ← x
let list ← parseAll x
return val :: list
partial_fixpoint
```
This PR is the result of analyzing the elaborator performance regression
introduced by #10005. It makes the `workspaceSymboldNewRanges` and
`iterators` benchmarks less noisy. It also replaces some range-related
instances for `Nat` with shortcuts to the general-purpose instances.
This is a trade-off between the ergonomics and the synthesis cost of
having general-purpose instances.
This PR generalizes the monadic operations for `HashMap`, `TreeMap`, and
`HashSet` to work for `m : Type u → Type v`.
This upstreams [a workaround from
Aesop](66a992130e/Aesop/Util/Basic.lean (L57-L66)),
and seems to continue a pattern already established in other files, such
as:
```lean
Array.forM.{u, v, w} {α : Type u} {m : Type v → Type w} [Monad m] (f : α → m PUnit) (as : Array α) (start : Nat := 0)
(stop : Nat := as.size) : m PUnit
```
This PR introduces an alternative construction for `DecidableEq`
instances that avoids the quadratic overhead of the default
construction.
The usual construction uses a `match` statement that looks at each pair
of constructors, and thus is necessarily quadratic in size. For
inductive data type with dozens of constructors or more, this quickly
becomes slow to process.
The new construction first compares the constructor tags (using the
`.ctorIdx` introduced in #9951), and handles the case of a differing
constructor tag quickly. If the constructor tags match, it uses the
per-constructor-eliminators (#9952) to create a linear-size instance. It
does so by creating a custom “matcher” for a parallel match on the data
types and the `h : x1.ctorIdx = x2.ctorIdx` assumption; this behaves
(and delaborates) like a normal `match` statement, but is implemented in
a bespoke way. This same-constructor-matcher will be useful for
implementing other instances as well.
The new construction produces less efficient code at the moment, so we
use it only for inductive types with 10 or more constructors by default.
The option `deriving.decEq.linear_construction_threshold` can be used to
adjust the threshold; set it to 0 to always use the new construction.
This PR implements equality propagation from the new AC module into the
`grind` core. Examples:
```lean
example {α β : Sort u} (f : α → β) (op : α → α → α) [Std.Associative op] [Std.Commutative op]
(a b c d : α) : op a (op b b) = op d c → f (op (op b a) (op b c)) = f (op c (op d c)) := by
grind only
example (a b c : Nat) : min a (max b (max c 0)) = min (max c b) a := by
grind -cutsat only
example {α β : Sort u} (bar : α → β) (op : α → α → α) [Std.Associative op] [Std.IdempotentOp op]
(a b c d e f x y w : α) :
op d (op x c) = op a b →
op e (op f (op y w)) = op (op d a) (op b c) →
bar (op d (op x c)) = bar (op e (op f (op y w))) := by
grind only
```
This PR adds the extra critical pairs to ensure the `grind ac` procedure
is complete when the operator is associative and idempotent, but not
commutative. Example:
```lean
example {α : Sort u} (op : α → α → α) [Std.Associative op] [Std.IdempotentOp op] (a b c d e f x y w : α)
: op d (op x c) = op a b →
op e (op f (op y w)) = op a (op b c) →
op d (op x c) = op e (op f (op y w)) := by
grind only
example {α : Sort u} (op : α → α → α) [Std.Associative op] [Std.IdempotentOp op] (a b c d e f x y w : α)
: op a (op d x) = op b c →
op e (op f (op y w)) = op a (op b c) →
op a (op d x) = op e (op f (op y w)) := by
grind only
```
This PR makes `saveModuleData` throw an IO.Error instead of panicking,
if given something that cannot be serialized. This doesn't really matter
for saving modules, but is handy when writing tools to save auxiliary
date in olean files via Batteries' `pickle`.
The caller of this C++ function already is guarded in a `try`/`catch`
that promotes from a `lean::exception` to an `IO.userError`.
A simple test of this in the web editor is
```
import Batteries
#eval pickle "/tmp/foo.txt" fun x : Nat => x
```
which crashes before this change.
---------
Co-authored-by: Laurent Sartran <lsartran@google.com>
This PR adds the extra critical pairs to ensure the `grind ac` procedure
is complete when the operator is AC and idempotent. Example:
```lean
example {α : Sort u} (op : α → α → α) [Std.Associative op] [Std.Commutative op] [Std.IdempotentOp op]
(a b c d : α) : op a (op b b) = op d c → op (op b a) (op b c) = op c (op d c) := by
grind only
```
This PR adds the inverse of a dyadic rational, at a given precision, and
characterising lemmas. Also cleans up various parts of the `Int.DivMod`
and `Rat` APIs, and proves some characterising lemmas about
`Rat.toDyadic`.
---------
Co-authored-by: Rob23oba <152706811+Rob23oba@users.noreply.github.com>
This PR adds superposition for associative (but non-commutative)
operators in `grind ac`. Examples:
```lean
example {α} (op : α → α → α) [Std.Associative op] (a b c d : α)
: op a b = c →
op b a = d →
op (op c a) (op b c) = op (op a d) (op d b) := by
grind
example {α} (a b c d : List α)
: a ++ b = c →
b ++ a = d →
c ++ a ++ b ++ c = a ++ d ++ d ++ b := by
grind only
```
This PR adds superposition for associative and commutative operators in
`grind ac`. Examples:
```lean
example (a b c d e f g h : Nat) :
max a b = max c d → max b e = max d f → max b g = max d h →
max (max f d) (max c g) = max (max e (max d (max b (max c e)))) h := by
grind -cutsat only
example {α} (op : α → α → α) [Std.Associative op] [Std.Commutative op] (a b c d : α)
: op a b = op b c → op c c = op d c →
op (op d a) (op b d) = op (op a a) (op b d) := by
grind only
```
This PR almost completely rewrites the inductive predicate recursion
algorithm; in particular `IndPredBelow` to function more consistently.
Historically, the `brecOn` generation through `IndPredBelow` has been
very error-prone -- this should be fixed now since the new algorithm is
very direct and doesn't rely on tactics or meta-variables at all.
Additionally, the new structural recursion procedure for inductive
predicates shares more code with regular structural recursion and thus
allows for mutual and nested recursion in the same way it was possible
with regular structural recursion. For example, the following works now:
```lean-4
mutual
inductive Even : Nat → Prop where
| zero : Even 0
| succ (h : Odd n) : Even n.succ
inductive Odd : Nat → Prop where
| succ (h : Even n) : Odd n.succ
end
mutual
theorem Even.exists (h : Even n) : ∃ a, n = 2 * a :=
match h with
| .zero => ⟨0, rfl⟩
| .succ h =>
have ⟨a, ha⟩ := h.exists
⟨a + 1, congrArg Nat.succ ha⟩
termination_by structural h
theorem Odd.exists (h : Odd n) : ∃ a, n = 2 * a + 1 :=
match h with
| .succ h =>
have ⟨a, ha⟩ := h.exists
⟨a, congrArg Nat.succ ha⟩
termination_by structural h
end
```
Closes#1672Closes#10004
This PR implements the proof terms for the new `grind ac` module.
Examples:
```lean
example {α : Sort u} (op : α → α → α) [Std.Associative op] (a b c d : α)
: op a (op b b) = op c d → op c (op d c) = op (op a b) (op b c) := by
grind only
example {α : Sort u} (op : α → α → α) [Std.Associative op] [Std.Commutative op] (a b c d : α)
: op a (op b b) = op d c → op (op b a) (op b c) = op c (op d c) := by
grind only
example {α : Sort u} (op : α → α → α) [Std.Associative op] [Std.Commutative op]
(one : α) [Std.LawfulIdentity op one] (a b c d : α)
: op a (op (op b one) b) = op d c → op (op b a) (op (op b one) c) = op (op c one) (op d c) := by
grind only
```
The `grind ac` module is not complete yet, we still need to implement
critical pair computation and fix the support for idempotent operators.
This PR fixes `grind` instance normalization procedure.
Some modules in grind use builtin instances defined directly in core
(e.g., `cutsat`), while others synthesize them using `synthInstance`
(e.g., `ring`). This inconsistency is problematic, as it may introduce
mismatches and result in two different representations for the same
term. This PR fixes the issue.
This PR modifies macros, which implement non-atomic definitions and
```$cmd1 in $cmd2``` syntax. These macros involve implicit scopes,
introduced through ```section``` and ```namespace``` commands. Since
sections or namespaces are designed to delimit local attributes, this
has led to unintuitive behaviour when applying local attributes to
definitions appearing in the above-mentioned contexts. This has been
causing the following examples to fail:
```lean4
axiom A : Prop
namespace ex1
open Nat in
@[local simp] axiom a : A ↔ True
example : A := by simp
end ex1
namespace ex2
@[local simp] axiom Foo.a : A ↔ True
example : A := by simp
end ex2
```
This PR adds an internal-only piece of syntax,
```InternalSyntax.end_local_scope```, that influences the
```ScopedEnvExtension.addLocalEntry``` used in implementing local
attributes, to avoid delimiting local entries in the current scope. This
command is used in the above-mentioned macros.
Closes [#9445](https://github.com/leanprover/lean4/issues/9445).
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This PR changes the construction of a `CompleteLattice` instance on
predicates (maps intro `Prop`) inside of
`coinductive_fixpoint`/`inductive_fixpoint` machinery.
Consider a following endomap on predicates of the type ` α → Prop`:
```lean4
def DefFunctor (r : α → α → Prop) (infSeq : α → Prop) : α → Prop :=
λ x : α => ∃ y, r x y ∧ infSeq y
```
The following eta-reduced expression failed to elaborate:
```lean4
def def1 (r : α → α → Prop) : α → Prop := DefFunctor r (def1 r)
coinductive_fixpoint monotonicity sorry
```
At the same time, eta-expanded variant would elaborate correctly:
```lean4
def def2 (r : α → α → Prop) : α → Prop := fun x => DefFunctor r (def2 r) x
coinductive_fixpoint monotonicity sorry
```
This PR fixes the above issue, by changing the way how `CompleteLattice`
instance on the space of predicates is constructed, to allow for the
eta-reduced case, as outlined above.
This PR reviews the expected-to-fail-right-now tests for `grind`, moving
some (now passing) tests to the main test suite, updating some tests,
and adding some tests about normalisation of exponents.
Re-enables `Suggestion.messageData?` after it was deprecated in #9966
since it is needed for the workaround described in #10150. We will
hopefully be able to clean up with API once #10150 is properly fixed.
This PR adds benchmarks for deriving `DecidableEq` on inductives with
many constructors. (Although at the moment, many is “many” as we timeout
for more than 30 or 40 constructors.)
This PR ensures `where finally` tactics can access private data under
the module system even when the corresponding holes are in the public
scope as long as all of them are of proposition types.
This PR adds “non-branching case statements”: For each inductive
constructor `T.con` this adds a function `T.con.with` that is similar
`T.casesOn`, but has only one arm (the one for `con`), and an additional
`t.toCtorIdx = 12` assumption.
For example:
```lean
inductive Vec (α : Type) : Nat → Type where
| nil : Vec α 0
| cons {n} : α → Vec α n → Vec α (n + 1)
/--
info: @[reducible] protected def Vec.cons.elim.{u} : {α : Type} →
{motive : (a : Nat) → Vec α a → Sort u} →
{a : Nat} →
(t : Vec α a) →
t.ctorIdx = 1 → ({n : Nat} → (a : α) → (a_1 : Vec α n) → motive (n + 1) (Vec.cons a a_1)) → motive a t
-/
#guard_msgs in
#print sig Vec.cons.elim
```
This is a building block for non-quadratic implementations of `BEq` and
`DecidableEq` etc.
Builds on top of #9951.
The compiled code for a these functions could presumably, without
branching on the inductive value, directly access the fields. Achieving
this optimization (and achieving it without a quadratic compilation
cost) is not in scope for this PR.
Visibility is now handled implicitly for all deriving handlers by
adjusting section visibility according to the presence of private types
while removing exposition on presence of private constructors can be
opted in on a per-handler level via the new combinator
`withoutExposeFromCtors`.
Fixes#10062#10063#10064#10065
This PR adds support for pretty printing using generalized field
notation (dot notation) for private definitions on public types. It also
modifies dot notation elaboration to resolve names after removing the
private prefix, which enables using dot notation for private definitions
on private imported types.
It won't pretty print with dot notation for definitions on inaccessible
private types from other modules.
Closes#7297
This PR implements the basic infrastructure for the new procedure
handling AC operators in grind. It already supports normalizing
disequalities. Future PRs will add support for simplification using
equalities, and computing critical pairs. Examples:
```lean
example {α : Sort u} (op : α → α → α) [Std.Associative op] (a b c : α)
: op a (op b c) = op (op a b) c := by
grind only
example {α : Sort u} (op : α → α → α) (u : α) [Std.Associative op] [Std.LawfulIdentity op u] (a b c : α)
: op a (op b c) = op (op a b) (op c u) := by
grind only
example {α : Type u} (op : α → α → α) (u : α) [Std.Associative op] [Std.Commutative op]
[Std.IdempotentOp op] [Std.LawfulIdentity op u] (a b c : α)
: op (op a a) (op b c) = op (op (op b a) (op (op u b) b)) c := by
grind only
example {α} (as bs cs : List α) : as ++ (bs ++ cs) = ((as ++ []) ++ bs) ++ (cs ++ []) := by
grind only
example (a b c : Nat) : max a (max b c) = max (max b 0) (max a c) ∧ min a b = min b a := by
grind only [cases Or]
```
This PR ports more of the post-initialization C++ shell code to Lean.
All that remains is the initialization of the profiler and task manager.
As initialization tasks rather than main shell code, they were left in
C++ (where the rest of the initialization code currently is).
The `max_memory` and `timeout` Lean options used by the the `--memory`
and `--timeout` command-line options are now properly registered. The
server defaults for max memory and max heartbeats (timeout) were removed
as they were not actually used (because the `server` option that was
checked was neither set nor exists).
This PR also makes better use of the module system in `Shell.lean` and
fixes a minor bug in a previous port where the file name check was
dependent on building the `.ilean` rather than the `.c` file (as was
originally the case).
Fixes#9879.
This PR adds a private `Lean.Name.getUtf8Byte'` to `Init.Meta` for a
future PR that optimizes `Lean.Name.escapePart`.
`Lean.Name.getUtf8Byte'` should be replaced with `String.getUtf8Byte`
once the string refactor is through.
This PR implements the fast circuit for overflow detection in unsigned
multiplication used by Bitwuzla and proposed in:
https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=987767
The theorem is based on three definitions:
* `uppcRec`: the unsigned parallel prefix circuit for the bits until a
certain `i`
* `aandRec`: the conjunction between the parallel prefix circuit at of
the first operand until a certain `i` and the `i`-th bit in the second
operand
* `resRec`: the preliminary overflow flag computed with these two
definitions
To establish the correspondence between these definitiions and their
meaning in `Nat`, we rely on `clz` and `clzAuxRec` definitions.
Therefore, this PR contains the `clz`- and `clzAuxRec`-related
infrastructure that was necessary to get the proofs through.
An additional change this PR contains is the moving of `### Count
leading zeros` section in `BitVec.Lemmas` downwards. In fact, some of
the proofs I wrote required introducing `Bitvec.toNat_lt_iff` and
`BitVec.le_toNat_iff` which I believe should live in the `Inequalities`
section. Therefore, to put these in the appropriate section, I decided
to move the whole `clz` section downwards (while it's small and
relatively self contained. Specifically, the theorems I moved are:
`clzAuxRec_zero`, `clzAuxRec_succ`, `clzAuxRec_eq_clzAuxRec_of_le`,
`clzAuxRec_eq_clzAuxRec_of_getLsbD_false`.
The fast circuit is not yet the default one in the bitblaster, as it's
performance is not yet competitive due to some missing rewrites that
bitwuzla supports but are not in Lean yet.
co-authored-by: @bollu
---------
Co-authored-by: Tobias Grosser <tobias@grosser.es>
This PR lets the `ctorIdx` definition for single constructor inductives
avoid the pointless `.casesOn`, and uses `macro_inline` to avoid
compiling the function and wasting symbols.
This PR adjusts the "try this" widget to be rendered as a widget message
under 'Messages', not a separate widget under a 'Suggestions' section.
The main benefit of this is that the message of the widget is not
duplicated between 'Messages' and 'Suggestions'.
Since widget message suggestions were already implemented by @jrr6 for
the new hint infrastructure, this PR replaces the old "try this"
implementation with the new hint infrastructure. In doing so, the
`style?` field of suggestions is deprecated, since the hint
infrastructure highlights hints using diff colors, and `style?` also
never saw much use downstream. Additionally, since the message and the
suggestion are now the same component, the `messageData?` field of
suggestions is deprecated as well. Notably, the "Try this:" message
string now also contains a newline and indentation to separate the
suggestion from the rest of the message more clearly and the `postInfo?`
field of the suggestion is now part of the message.
Finally, this PR changes the diff colors used by the hint infrastructure
to be more color-blindness-friendly (insertions are now blue, not green,
and text that remains unchanged is now using the editor foreground color
instead of blue).
### Breaking changes
Tests that use `#guard_msgs` to test the "Try this:" message may need to
be adjusted for the new formatting of the message.
This PR makes the generation of functional induction principles more
robust when the user `let`-binds a variable that is then `match`'ed on.
Fixes#10132.
This PR creates the deprecated `.toCtorIdx` alias only for enumeration
types, which are the types that used to have this function. No need
generating an alias for types that never had it. Should reduce the
number of symbols in the standard library.
This PR prevents `rcases` and `obtain` from creating absurdly long case
tag names when taking single constructor types (like `Exists`) apart.
Fixes#6550
The change does not affect `cases` and `induction`, it seems (where the
user might be surprised to not address the single goal with a name),
because I make the change in Lean/`Meta/Tactic/Induction.lean`, not
`Lean/Elab/Tactic/Induction.lean`. Yes, that's confusing.
This PR defines the dyadic rationals, showing they are an ordered ring
embedding into the rationals. We will use this for future interval
arithmetic tactics.
Many thanks to @Rob23oba, who did most of the implementation work here.
---------
Co-authored-by: Rob23oba <robin.arnez@web.de>
This PR fixes an issue where private definitions recursively invoked
using generalized field notation (dot notation) would give an "invalid
field" errors. It also fixes an issue where "invalid field notation"
errors would pretty print the name of the declaration with a `_private`
prefix.
Closes#10044
this PR reorders the `DiscrTree.Key` constructors to match the order
given in the manually written `DiscrTree.Key.ctorIdx`. This allows us to
use the auto-generated one, and moreover lets this code benefit from
special compiler support for `.ctorIdx`, once that lands.
This PR normalizes the published diagnostics in the test runner so that
messages published out of order (due to parallelism) cannot cause test
failures. Clients can handle out-of-order messages just fine.
This PR generates `.ctorIdx` functions for all inductive types, not just
enumeration types. This can be a building block for other constructions
(`BEq`, `noConfusion`) that are size-efficient even for large
inductives.
It also renames it from `.toCtorIdx` to `.ctorIdx`, which is the more
idiomatic naming.
The old name exists as an alias, with a deprecation attribute to be
added after the next
stage0 update.
These functions can arguably compiled down to a rather efficient tag
lookup, rather than a `case` statement. This is future work (but
hopefully near future).
For a fair number of basic types the compiler is not able to compile a
function using `casesOn` until further definitions have been defined.
This therefore (ab)uses the `genInjectivity` flag and
`gen_injective_theorems%` command to also control the generation of this
construct.
For (slightly) more efficient kernel reduction one could use `.rec`
rather than `.casesOn`. I did not do that yet, also because it
complicates compilation.
This PR fixes a bug that caused the Lean server process tree to survive
the closing of VS Code.
The cause of this issue was that the file worker main task was blocked
on waiting for the result of `lake setup-file` because the blocking call
was lifted outside of the dedicated server task that was supposed to
contain it by the compiler.
This PR upstreams lemmas about `Rat` from `Mathlib.Data.Rat.Defs` and
`Mathlib.Algebra.Order.Ring.Unbundled.Rat`, specifically enough to get
`Lean.Grind.Field Rat` and `Lean.Grind.OrderedRing Rat`. In addition to
the lemmas, instances for `Inv Rat`, `Pow Rat Nat` and `Pow Rat Int`
have been upstreamed.
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
This PR adds support for detecting associative operators in `grind`. The
new AC module also detects whether the operator is commutative,
idempotent, and whether it has a neutral element. The information is
cached.
This PR allows for more fine-grained control over what derived instances
have exposed definitions under the module system: handlers should not
expose their implementation unless either the deriving item or a
surrounding section is marked with `@[expose]`. Built-in handlers to be
updated after a stage 0 update.
This PR adds the modules in `Lake.Util` to core's Lake configuration to
ensure all utilities are built. With the module system port, they were
no longer all transitively imported.
Specifically, `Lake.Util.Lock` is unused because Lake does not currently
use a lock file for the build.
This PR allows Lean's parser to run with a final position prior to the
end of the string, so it can be invoked on a sub-region of the input.
This has applications in Verso proper, which parses Lean syntax in
contexts such as code blocks and docstrings, and it is a prerequisite to
parsing the contents of Lean docstrings.
This PR replaces `Std.Internal.Rat` with the new public `Rat` upstreamed
from Batteries.
The time library was depending on some defeqs which are no longer true,
so I have inserted some casts.
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
Co-authored-by: Sofia Rodrigues <sofia@algebraic.dev>
This PR contains lemmas about `Int` (minor amendments for BitVec and
Nat) that are being used in preparing the dyadics. This is all work of
@Rob23oba, which I'm pulling out of #9993 early to keep that one
manageable.
This PR fixes the compilation of `noConfusion` by repairing an oversight
made when porting this code from the old compiler. The old compiler only
repeatedly expanded the major for each non-`Prop` field of the inductive
under consideration, mirroring the construction of `noConfusion` itself,
whereas the new compiler erroneously counted all fields.
Fixes#9971.
This PR improves support for `a^n` in `grind cutsat`. For example, if
`cutsat` discovers that `a` and `b` are equal to numerals, it now
propagates the equality. This PR is similar to #9996, but `a^b`.
Example:
```lean
example (n : Nat) : n = 2 → 2 ^ (n+1) = 8 := by
grind
```
With #10022, it also improves the support for `BitVec n` when `n` is not
numeral. Example:
```lean
example {n m : Nat} (x : BitVec n)
: 2 ≤ n → n ≤ m → m = 2 → x = 0 ∨ x = 1 ∨ x = 2 ∨ x = 3 := by
grind
```
This PR refactors the Lake codebase to use the new module system
throughout. Every module in `Lake` is now a `module`.
As this was already a large-scale refactor, a general cleanup of the
code has also been bundled in.
This PR also uses workarounds for currently outstanding module system
issues: #10061, #10062, #10063, #10064, #10065, #10067, and #10068.
**Breaking change:** Since the module system encourages a
`private`-by-default design, the Lake API has switched from its previous
`public`-by-default approach. As such, many definitions that were
previously public are now private. The newly private definitions are not
expected to have had significant user use, Nonetheless, important use
cases could be missed. If a key API is now inaccessible but seems like
it should be public, users are encouraged to report this as an issue on
GitHub.
This PR reverts parts of #10005 that surprisingly turned out to cause a
performance regression in the benchmarks. The slowdown seems to be
related to elaboration, not inefficiencies in the generated code. This
is just a quick fix. I will take a closer look in a week.
This PR adds a stop position field to parser input contexts, allowing
the parser to be instructed to stop parsing prior to the end of a file.
This is step 1, prior to a stage0 update, to make run-time data
structures sufficiently compatible to avoid segfaults. After the update,
the actual code to stop parsing can be merged.
This PR implements the necessary typeclasses so that range notation
works for integers. For example, `((-2)...3).toList = [-2, -1, 0, 1, 2]
: List Int`.
This PR changes macro scope numbering from per-module to per-command,
ensuring that unrelated changes to other commands do not affect macro
scopes generated by a command, which improves `prefer_native` hit rates
on bootstrapping as well as avoids further rebuilds under the module
system.
In detail, instead of always using the current module name as a macro
scope prefix, each command now introduces a new macro scope prefix
(called "context") of the shape `<main module>._hygCtx_<uniq>` where
`uniq` is a `UInt32` derived from the command but automatically
incremented in case of conflicts (which must be local to the current
module). In the current implementation, `uniq` is the hash of the
declaration name, if any, or else the hash of the full command's syntax.
Thus, it is always independent of syntactic changes to other commands
(except in case of hash conflicts, which should only happen in practice
for syntactically identical commands) and, in the case of declarations,
also independent of syntactic changes to any private parts of the
declaration.
This PR replaces the implementation of `Nat.log2` with a version that
reduces faster.
The new version can handle:
```lean-4
example : Nat.log2 (1 <<< 500) = 500 := rfl
```
This PR enables core's `LakeMain` to be a `module` when core is built
without `USE_LAKE`.
This was a problem when porting Lake to the module system (#9749).
This PR shortens the work necessary to make a type compatible with the
polymorphic range notation. In the concrete case of `Nat`, it reduces
the required lines of code from 150 to 70.
This PR adds useful declarations to the `LawfulOrderMin/Max` and
`LawfulOrderLeftLeaningMin/Max` API. In particular, it introduces
`.leftLeaningOfLE` factories for `Min` and `Max`. It also renames
`LawfulOrderMin/Max.of_le` to .of_le_min_iff` and `.of_max_le_iff` and
introduces a second variant with different arguments.
This PR changes the `toMono` pass to replace decls with their `_redArg`
equivalent, which has the consequence of not considering arguments
deemed useless by the `reduceArity` pass for the purposes of the
`noncomputable` check.
This PR adds support for correctly handling computations on fields in
`casesOn` for inductive predicates that support large elimination. In
any such predicate, the only relevant fields allowed are those that are
also used as an index, in which case we can find the supplied index and
use that term instead.
This PR improves support for `Fin n` in `grind cutsat` when `n` is not a
numeral. For example, the following goals can now be solved
automatically:
```lean
example (p d : Nat) (n : Fin (p + 1))
: 2 ≤ p → p ≤ d + 1 → d = 1 → n = 0 ∨ n = 1 ∨ n = 2 := by
grind
example (s : Nat) (i j : Fin (s + 1)) (hn : i ≠ j) (hl : ¬i < j) : j < i := by
grind
example {n : Nat} (j : Fin (n + 1)) : j ≤ j := by
grind
example {n : Nat} (x y : Fin ((n + 1) + 1)) (h₂ : ¬x = y) (h : ¬x < y) : y < x := by
grind
```
This PR adds `@[expose]` to `Lean.ParserState.setPos`. This makes it
possible to prove in-boundedness for a state produced by `setPos` for
functions like `next'` and `get'` without needing to `import all`.
This came up while porting Lake to the module system (#9749).
This PR changes the handling of overapplied constructors when lowering
LCNF to IR from a (slightly implicit) assertion failure to producing
`unreachable`. Transformations on inlined unreachable code can produce
constructor applications with additional arguments.
In the old compiler, these additional arguments were silently ignored,
but it seems more sensible to replace them with `unreachable`, just in
case they arise due to a compiler error.
Fixes#9937.
This PR derives `BEq` and `Hashable` for `Lean.Import`. Lake already did
this later, but it now done when defining `Import`.
Doing this in Lake became problematic when porting it to the module
system (#9749).
This PR exposes the bodies of `Name.append`, `Name.appendCore`, and
`Name.hasMacroScopes`. This enables proof by reflection of the
concatenation of name literals when using the module system.
```lean
example : `foo ++ `bar = `foo.bar := rfl
```
This is necessary for Lake as part of the port to using `module`
(#9749).
This PR make some minor changes to the grind annotation analysis script,
including sorting results and handling errors. Still need to add an
external UI.
This PR changes Lake to not set `LEAN_GITHASH` when in core (i.e.
`bootstrap = true`). This avoids Lake rebuilding modules when the Lake
watchdog is on one build of Lean/Lake and the command line is on a
different one.
The current reuse analysis is greedy in that every function attempts to
reuse a value. However, this means that if the last use is an owned
argument, it will be `inc`'d prior to this last use, in order to prevent
reuse from happening in the callee. In many cases, it makes more sense
to give the callee the chance to reuse it instead. The benchmark results
indicate that this is a much better default.
This PR improves support for nonlinear `/` and `%` in `grind cutsat`.
For example, given `a / b`, if `cutsat` discovers that `b = 2`, it now
propagates that `a / b = b / 2`. This PR is similar to #9996, but for
`/` and `%`. Example:
```lean
example (a b c d : Nat)
: b > 1 → d = 1 → b ≤ d + 1 → a % b = 1 → a = 2 * c → False := by
grind
```
This PR fixes a bug in `#eval` where clicking on the evaluated
expression could show errors in the Infoview. This was caused by `#eval`
not saving the temporary environment that is used when elaborating the
expression.
This PR provides factories that derive order typeclasses in bulk, given
an `Ord` instance. If present, existing instances are preferred over
those derived from `Ord`. It is possible to specify any instance
manually if desired.
This PR reduces the number of `Nat.Bitwise` grind annotations we have
the deal with distributivity. The new smaller set encourages `grind` to
rewrite into DNF. The old behaviour just resulted in saturating up to
the instantiation limits.
This PR improves support for nonlinear monomials in `grind cutsat`. For
example, given a monomial `a * b`, if `cutsat` discovers that `a = 2`,
it now propagates that `a * b = 2 * b`.
Recall that nonlinear monomials like `a * b` are treated as variables in
`cutsat`, a procedure designed for linear integer arithmetic.
Example:
```lean
example (a : Nat) (ha : a < 8) (b c : Nat) : 2 ≤ b → c = 1 → b ≤ c + 1 → a * b < 8 * b := by
grind
example (x y z w : Int) : z * x * y = 4 → x = z + w → z = 1 → w = 2 → False := by
grind
```
This PR registers a parser alias for `Lean.Parser.Command.visibility`.
This avoids having to import `Lean.Parser.Command` in simple command
macros that use visibilities.
This PR provides the means to quickly provide all the order instances
associated with some high-level order structure (preorder, partial
order, linear preorder, linear order). This can be done via the factory
functions `PreorderPackage.ofLE`, `PartialOrderPackage.ofLE`,
`LinearPreorderPackage.ofLE` and `LinearOrderPackage.ofLE`.
This PR makes `IsPreorder`, `IsPartialOrder`, `IsLinearPreorder` and
`IsLinearOrder` extend `BEq` and `Ord` as appropriate, adds the
`LawfulOrderBEq` and `LawfulOrderOrd` typeclasses relating `BEq` and
`Ord` to `LE`, and adds many lemmas and instances.
Note: This PR contains a refactoring where `Init.Data.Ord` is moved to
`Init.Data.Ord.Basic`. If I added `Init.Data.Ord` simply importing all
submodules, git would not be able to determine that `Init.Data.Ord` was
renamed to `Init.Data.Ord.Basic`. This could lead to unnecessary merge
conflicts in the future. Hence, I chose the name `Init.Data.OrdRoot`
instead of `Init.Data.Ord` temporarily. After this PR, I will rename
this module back to `Init.Data.Ord` in a separate PR.
(This is a copy of #9430: I will not touch that PR because it currently
allows to debug a CI problem and pushing commits might break the
reproducibility.)
This PR eliminates uses of `intros x y z` (with arguments) and updates
the `intros` docstring to suggest that `intro x y z` should be used
instead. The `intros` tactic is historical, and can be traced all the
way back to Lean 2, when `intro` could only introduce a single
hypothesis. Since 2020, the `intro` tactic has superceded it. The
`intros` tactic (without arguments) is currently still useful.
This PR upstreams the definition of Rat from Batteries, for use in our
planned interval arithmetic tactic.
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
This PR adds two test cases extracted from Mathlib, that `grind` cannot
solve but `omega` can. Originally the multiplication instance came from
`Nat.instSemiring` and `Int.instSemiring`, in minimizing I found that
`Distrib` is already enough.
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
This PR fixes an issue when running Mathlib's `FintypeCat` as code,
where an erased type former is passed to a polymorphic function. We were
lowering the arrow type to`object`, which conflicts with the runtime
representation of an erased value as a tagged scalar.
This PR modifies the generation of induction and partial correctness
lemmas for `mutual` blocks defined via `partial_fixpoint`. Additionally,
the generation of lattice-theoretic induction principles of functions
via `mutual` blocks is modified for consistency with `partial_fixpoint`.
The lemmas now come in two variants:
1. A conjunction variant that combines conclusions for all elements of
the mutual block. This is generated only for the first function inside
of the mutual block.
2. Projected variants for each function separately
## Example 1
```lean4
axiom A : Type
axiom B : Type
axiom A.toB : A → B
axiom B.toA : B → A
mutual
noncomputable def f : A := g.toA
partial_fixpoint
noncomputable def g : B := f.toB
partial_fixpoint
end
```
Generated `fixpoint_induct` lemmas:
```lean4
f.fixpoint_induct (motive_1 : A → Prop) (motive_2 : B → Prop) (adm_1 : admissible motive_1)
(adm_2 : admissible motive_2) (h_1 : ∀ (g : B), motive_2 g → motive_1 g.toA)
(h_2 : ∀ (f : A), motive_1 f → motive_2 f.toB) : motive_1 f
g.fixpoint_induct (motive_1 : A → Prop) (motive_2 : B → Prop) (adm_1 : admissible motive_1)
(adm_2 : admissible motive_2) (h_1 : ∀ (g : B), motive_2 g → motive_1 g.toA)
(h_2 : ∀ (f : A), motive_1 f → motive_2 f.toB) : motive_2 g
```
Mutual (conjunction) variant:
```lean4
f.mutual_fixpoint_induct (motive_1 : A → Prop) (motive_2 : B → Prop) (adm_1 : admissible motive_1) (adm_2 : admissible motive_2)
(h_1 : ∀ (g : B), motive_2 g → motive_1 g.toA) (h_2 : ∀ (f : A), motive_1 f → motive_2 f.toB) :
motive_1 f ∧ motive_2 g
```
## Example 2
```lean4
mutual
def f (n : Nat) : Option Nat :=
g (n + 1)
partial_fixpoint
def g (n : Nat) : Option Nat :=
if n = 0 then .none else f (n + 1)
partial_fixpoint
end
```
Generated `partial_correctness` lemmas (in a projected variant):
```lean4
f.partial_correctness (motive_1 motive_2 : Nat → Nat → Prop)
(h_1 :
∀ (g : Nat → Option Nat),
(∀ (n r : Nat), g n = some r → motive_2 n r) → ∀ (n r : Nat), g (n + 1) = some r → motive_1 n r)
(h_2 :
∀ (f : Nat → Option Nat),
(∀ (n r : Nat), f n = some r → motive_1 n r) →
∀ (n r : Nat), (if n = 0 then none else f (n + 1)) = some r → motive_2 n r)
(n r✝ : Nat) : f n = some r✝ → motive_1 n r✝
g.partial_correctness (motive_1 motive_2 : Nat → Nat → Prop)
(h_1 :
∀ (g : Nat → Option Nat),
(∀ (n r : Nat), g n = some r → motive_2 n r) → ∀ (n r : Nat), g (n + 1) = some r → motive_1 n r)
(h_2 :
∀ (f : Nat → Option Nat),
(∀ (n r : Nat), f n = some r → motive_1 n r) →
∀ (n r : Nat), (if n = 0 then none else f (n + 1)) = some r → motive_2 n r)
(n r✝ : Nat) : g n = some r✝ → motive_2 n r✝
```
Mutual (conjunction) variant:
```
f.mutual_partial_correctness (motive_1 motive_2 : Nat → Nat → Prop)
(h_1 :
∀ (g : Nat → Option Nat),
(∀ (n r : Nat), g n = some r → motive_2 n r) → ∀ (n r : Nat), g (n + 1) = some r → motive_1 n r)
(h_2 :
∀ (f : Nat → Option Nat),
(∀ (n r : Nat), f n = some r → motive_1 n r) →
∀ (n r : Nat), (if n = 0 then none else f (n + 1)) = some r → motive_2 n r) :
(∀ (n r : Nat), f n = some r → motive_1 n r) ∧ ∀ (n r : Nat), g n = some r → motive_2 n r
```
This PR modifies `intro` to create tactic info localized to each
hypothesis, making it possible to see how `intro` works
variable-by-variable. Additionally:
- The tactic supports `intro rfl` to introduce an equality and
immediately substitute it, like `rintro rfl` (recall: the `rfl` pattern
is like doing `intro h; subst h`). The `rintro` tactic can also now
support `HEq` in `rfl` patterns if `eq_of_heq` applies.
- In `intro (h : t)`, elaboration of `t` is interleaved with unification
with the type of `h`, which prevents default instances from causing
unification to fail.
- Tactics that change types of hypotheses (including `intro (h : t)`,
`delta`, `dsimp`) now update the local instance cache.
In `intro x y z`, tactic info ranges are `intro x`, `y`, and `z`. The
reason for including `intro` with `x` is to make sure the info range is
"monotonic" while adding the first argument to `intro`.
This PR adds lemmas for the `TreeMap` operations `filter`, `map` and
`filterMap`. These lemmas existed already for hash maps and are simply
ported over from there.
This PR allows most of the `List.lookup` lemmas to be used when
`LawfulBEq α` is not available.
`LawfulBEq` is very strong. Most of the lemmas don't actually require it
-- some only require `ReflBEq`, and only `List.lookup_eq_some_iff`
actually requires `LawfulBEq`.
This PR moves arithmetic of `String.Pos` out of the prelude.
Other `String` declarations are part of the prelude because they are
generated by macros, but this does not seem to be the case for these.
This PR cleans up `optParam`/`autoParam`/etc. annotations before
elaborating definition bodies, theorem bodies, `fun` bodies, and `let`
function bodies. Both `variable`s and binders in declaration headers are
supported.
There are no changes to `inductive`/`structure`/`axiom`/etc. processing,
just `def`/`theorem`/`example`/`instance`.
This PR ensures that equations in the `grind cutsat` module are
maintained in solved form. That is, given an equation `a*x + p = 0` used
to eliminate `x`, the linear polynomial `p` must not contain other
eliminated variables. Before this PR, equations were maintained in
triangular form. We are going to use the solved form to linearize
nonlinear terms.
This PR removes the option `grind +ringNull`. It provided an alternative
proof term construction for the `grind ring` module, but it was less
effective than the default proof construction mode and had effectively
become dead code.
This PR also optimizes semiring normalization proof terms using the
infrastructure added in #9946.
**Remark:** After updating stage0, we can remove several background
theorems from the `Init/Grind` folder.
This PR optimizes the proof terms produced by `grind linarith`. It is
similar to #9945, but for the `linarith` module in `grind`.
It removes unused entries from the context objects when generating the
final proof, significantly reducing the amount of junk in the resulting
terms.
This PR optimizes the proof terms produced by `grind cutsat`. It removes
unused entries from the context objects when generating the final proof,
significantly reducing the amount of junk in the resulting terms.
Example:
```lean
/--
trace: [grind.debug.proof] fun h h_1 h_2 h_3 h_4 h_5 h_6 h_7 h_8 =>
let ctx := RArray.leaf (f 2);
let p_1 := Poly.add 1 0 (Poly.num 0);
let p_2 := Poly.add (-1) 0 (Poly.num 1);
let p_3 := Poly.num 1;
le_unsat ctx p_3 (eagerReduce (Eq.refl true)) (le_combine ctx p_2 p_1 p_3 (eagerReduce (Eq.refl true)) h_8 h_1)
-/
#guard_msgs in -- Context should contain only `f 2`
open Lean Int Linear in
set_option trace.grind.debug.proof true in
example (f : Nat → Int) :
f 1 <= 0 → f 2 <= 0 → f 3 <= 0 → f 4 <= 0 → f 5 <= 0 →
f 6 <= 0 → f 7 <= 0 → f 8 <= 0 → -1 * f 2 + 1 <= 0 → False := by
grind
```
This PR expands `mvcgen using invariants | $n => $t` to `mvcgen; case
inv<$n> => exact $t` to avoid MVar instantiation mishaps observable in
the test case for #9581.
Closes#9581.
This PR implements extended `induction`-inspired syntax for `mvcgen`,
allowing optional `using invariants` and `with` sections.
```lean
mvcgen
using invariants
| 1 => Invariant.withEarlyReturn
(onReturn := fun ret seen => ⌜ret = false ∧ ¬l.Nodup⌝)
(onContinue := fun traversalState seen =>
⌜(∀ x, x ∈ seen ↔ x ∈ traversalState.prefix) ∧ traversalState.prefix.Nodup⌝)
with mleave -- mleave is a no-op here, but we are just testing the grammar
| vc1 => grind
| vc2 => grind
| vc3 => grind
| vc4 => grind
| vc5 => grind
```
This PR guards the `Std.Tactic.Do.MGoalEntails` delaborator by a check
ensuring that there are at least 3 arguments present, preventing
potential panics.
This PR fixes the `forIn` function, that previously caused the resulting
Promise to be dropped without a value when an exception was thrown
inside of it. It also corrects the parameter order of the `background`
function.
This PR changes `internalizeCode` to replace all substitutions with
non-param-bound fvars in `Expr`s (which are all types) with `lcAny`,
preserving the invariant that there are no such dependencies. The
violation of this invariant across files caused test failures in a
pending PR, but it is difficult to write a direct test for it. In the
future, we should probably change the LCNF checker to detect this.
This change also speeds up some compilation-heavy benchmarks much more
than I would've expected, which is a pleasant surprise. This indicates
we might get more speedups from reducing the amount of type information
we preserve in LCNF.
This PR fixes a panic in the delaborator for `Std.PRange`. It also
modifies the delaborators for both `Std.Range` and `Std.PRange` to not
use `let_expr`, which cleans up annotations and metadata, since
delaborators must follow the structures of expressions. It adds support
for `pp.notation` and `pp.explicit` options. It also adds tests for
these delaborators.
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
Co-authored-by: Kyle Miller <kmill31415@gmail.com>
This PR adds a guard for a delaborator that is causing panics in
doc-gen4. This is a band-aid solution for now, and @sgraf812 will take a
look when they're back from leave.
This PR ensures `grind cutsat` does not rely on div/mod terms to have
been normalized. The `grind` preprocessor has normalizers for them, but
sometimes they cannot be applied because of type dependencies.
Closes#9907
This PR addresses a missing check in the module system where private
names that remain in the public environment map for technical reasons
(e.g. inductive constructors generated by the kernel and relied on by
the code generator) accidentally were accessible in the public scope.
This PR reviews `grind` annotations for `Option`, preferring to use
`@[grind =]` instead of `@[grind]` (and fixing a few problems revealed
by this), and making sure `@[grind =]` theorems are "fully applied".
This PR lets the unused simp argument linter explain that the given hint
of removing `←` arguments may be too strong, and that replacing them
with `-` arguments can be needed. Fixes#9909.
This PR adds a JSON schema for `lakefile.toml`. Importantly, this schema
is *not* intended for validating `lakefile.toml`, but is instead
optimized for auto-completion and hovers using the [Even Better
TOML](https://marketplace.visualstudio.com/items?itemName=tamasfe.even-better-toml)
VS Code extension.
Once merged, I will attempt to contribute a link to this schema to the
[JSON Schema store](https://github.com/SchemaStore/schemastore). When
that is done, we can integrate the Lean 4 VS Code extension with Even
Better TOML, providing us with language server support in
`lakefile.toml`.
The schema contributed by this PR has the following known deficiencies:
- Superfluous properties do not produce an error.
- The structure of complicated structures (e.g. path or version
patterns) is deliberately not accurately reflected in the schema. Even
Better TOML doesn't seem to handle these structures well in
auto-completion.
- Due to the lack of an accurate declarative spec of the lakefile.toml
format and several deviations from the format to provide better
auto-completions, this schema will have to be kept in sync manually with
the code in Lake, at least for now.
This PR ensures that `Nat.cast` and `Int.cast` of numerals are
normalized by `grind`.
It also adds a `simp` flag for controlling how bitvector literals are
represented. By default, the bitvector simprocs use `BitVec.ofNat`. This
representation is problematic for the `grind ring` and `grind cutsat`
modules. The new flag allows the use of `OfNat.ofNat` and `Neg.neg` to
represent literals, consistent with how they are represented for other
commutative rings.
Closes#9321
This PR improves the heuristic used to select patterns for local
`forall` expressions occurring in the goal being solved by `grind`. It
now considers all singleton patterns in addition to the selected
multi-patterns. Example:
```lean
example (p : Nat → Prop) (h₁ : x < n) (h₂ : ¬ p x) : ∃ i, i < n ∧ ¬ p i := by
grind
```
This PR makes `mvcgen` aggressively eta-expand before trying to apply a
spec. This ensures that `mspec` will be able to frame hypotheses
involving uninstantiated loop invariants in goals for the inductive step
of a loop instead of losing them in a destructive world update.
This PR moves `List.range'_elim` to `List.eq_of_range'_eq_append_cons`
and adds a couple of `grind` annotations for `List.range'`. This will
make it more convenient to work with proof obligations produced by
`mvcgen`.
This PR is initially motivated by noticing `Lean.Grind.Preorder.toLE`
appearing in long Mathlib typeclass searches; this change will prevent
these searches. These changes are also helpful preparation for
potentially dropping the custom `Lean.Grind.*` typeclasses, and unifying
with the new typeclasses introduced in #9729.
This PR adds improved support for proof-by-reflection to the kernel type
checker. It addresses the performance issue exposed by #9854. With this
PR, whenever the kernel type-checks an argument of the form `eagerReduce
_`, it enters "eager-reduction" mode. In this mode, the kernel is more
eager to reduce terms. The new `eagerReduce _` hint is often used to
wrap `Eq.refl true`. The new hint should not negatively impact any
existing Lean package.
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This PR adds new variants of `Array.getInternal` and
`Array.get!Internal` that return their argument borrowed, i.e. without a
reference count increment. These are intended for use by the compiler in
cases where it can determine that the array will continue to hold a
valid reference to the element for the returned value's lifetime.
In the future, this will likely be replaced by a return value borrow
annotation, in which case the special variant of the functions could be
removed, with the compiler inserting an extra `inc` in the non-borrow
cases.
This PR ensures `grind` can E-match patterns containing universe
polymorphic ground sub-patterns. For example, given
```
set_option pp.universes true in
attribute [grind?] Id.run_pure
```
the pattern
```
Id.run_pure.{u_1}: [@Id.run.{u_1} #1 (@pure.{u_1, u_1} `[Id.{u_1}] `[Applicative.toPure.{u_1, u_1}] _ #0)]
```
contains two nested universe polymorphic ground patterns
- `Id.{u_1}`
- `Applicative.toPure.{u_1, u_1}`
This kind of pattern is not common, but it occurs in core.
This PR removes the `inShareCommon` quick filter used in `grind`
preprocessing steps. `shareCommon` is no longer used only for fully
preprocessed terms.
closes#9830
This PR makes `mvcgen` produce deterministic case labels for the
generated VCs. Invariants will be named `inv<n>` and every other VC will
be named `vc<n>.*`, where the `*` part serves as a loose indication of
provenance.
This PR introduces a canonical way to endow a type with an order
structure. The basic operations (`LE`, `LT`, `Min`, `Max`, and in later
PRs `BEq`, `Ord`, ...) and any higher-level property (a preorder, a
partial order, a linear order etc.) are then put in relation to `LE` as
necessary. The PR provides `IsLinearOrder` instances for many core types
and updates the signatures of some lemmas.
**BREAKING CHANGES:**
* The requirements of the `lt_of_le_of_lt`/`le_trans` lemmas for
`Vector`, `List` and `Array` are simplified. They now require an
`IsLinearOrder` instance. The new requirements are logically equivalent
to the old ones, but the `IsLinearOrder` instance is not automatically
inferred from the smaller typeclasses.
* Hypotheses of type `Std.Total (¬ · < · : α → α → Prop)` are replaced
with the equivalent class `Std.Asymm (· < · : α → α → Prop)`. Breakage
should be limited because there is now an instance that derives the
latter from the former.
* In `Init.Data.List.MinMax`, multiple theorem signatures are modified,
replacing explicit parameters for antisymmetry, totality, `min_ex_or`
etc. with corresponding instance parameters.
This PR migrates the ⌜p⌝ notation for embedding pure p : Prop into SPred
σs to expand into a simple, first-order expression SPred.pure p that can
be supported by e-matching in grind.
Doing so deprives ⌜p⌝ notation of its idiom-bracket-like support for
#selector and ‹Nat›ₛ syntax which is thus removed.
This PR replaces some `HashSet Expr`-typed collections of facts in
`omega`'s implementation with plain lists. This change makes some
`omega` calls faster, some slower, but the advantage is that `omega`'s
performance is more independent the state of the name generator that
produces fvar IDs.
I've created this PR for discussion and am happy to hear opinions on
whether this should be merged or not. A good reason *not* to merge is
that it causes regressions in some places and `grind` is expected to
supersede `omega` either way. A good reason to merge is that `omega` is
used all over the place and its flaky performance increases the noise in
future benchmarks.
This PR fixes a bug in `mvcgen` triggered by excess state arguments to
the `wp` application, a situation which arises when working with
`StateT` primitives.
This PR improves the delta deriving handler, giving it the ability to
process definitions with binders, as well as the ability to recursively
unfold definitions. Furthermore, delta deriving now tries all explicit
non-out-param arguments to a class, and it can handle "mixin" instance
arguments. The `deriving` syntax has been changed to accept general
terms, which makes it possible to derive specific instances with for
example `deriving OfNat _ 1` or `deriving Module R`. The class is
allowed to be a pi type, to add additional hypotheses; here is a Mathlib
example:
```lean
def Sym (α : Type*) (n : ℕ) :=
{ s : Multiset α // Multiset.card s = n }
deriving [DecidableEq α] → DecidableEq _
```
This underscore stands for where `Sym α n` may be inserted, which is
necessary when `→` is used. The `deriving instance` command can refer to
scoped variables when delta deriving as well. Breaking change: the
derived instance's name uses the `instance` command's name generator,
and the new instance is added to the current namespace.
This closes
[mathlib4#380](https://github.com/leanprover-community/mathlib4/issues/380).
This PR reorganizes the directory structure of Lake's module test and
renames some of the files to be more descriptive.
Originally, this was meant to be combined with a fix, but that fix
appears to be incorrect, so this is just a refactor.
This PR fixes a bug where the `DecidableEq` deriving handler did not
take universe levels into account for enumerations (inductive types
whose constructors all have no fields). Closes#9541.
This PR adds a script for analyzing `grind` E-matching annotations. The
script is useful for detecting matching loops. We plan to add
user-facing commands for running the script in the future.
This PR allows trailing comma in the argument list of `simp?`, `dsimp?`,
`simpa`, etc... Previously, it was only allowed in the non `?` variants
of `simp`, `dsimp`, `simp_all`.
Closes#7383.
This PR improves the API for invariants and postconditions and as such
introduces a few breaking changes to the existing pre-release API around
`Std.Do`. It also adds Markus Himmel's `pairsSumToZero` example as a
test case.
This PR changes the IR RC pass to take "implied borrows" from
projections into account. If a projected value's lifetime is contained
in that of its parent (or any projection ancestor), then it does not
need its reference count incremented (or later decremented).
I believe that this same technique should generalize to both the
reset/reuse and borrow signature inference passes.
This PR splits out an implementation detail of
MVarId.getMVarDependencies into a top-level function. Aesop was relying
on the function defined in the where clause, which is no longer possible
after #9759.
This PR modifies the pretty printing of anonymous metavariables to use
the index rather than the internal name. This leads to smaller numerical
suffixes in `?m.123` since the indices are numbered within a given
metavariable context rather than across an entire file, hence each
command gets its own numbering. This does not yet affect pretty printing
of universe level metavariables.
For debugging purposes, metavariables that are not defined now pretty
print as `?_mvar.123` rather than cause pretty printing to fail.
This PR combines the simplification and unfold-reducible-constants steps
in `grind` to ensure that no potential normalization steps are missed.
Closes#9610
This PR fixes a bug in the projection over constructor propagator used
in `grind`. It may construct type incorrect terms when a equivalence
class contains heterogeneous equalities.
closes#9769
We compute the liveness information for the join point body, so the only
thing that updateJPLiveVarMap should be adding is the binding of the
params, which we can easily do ourselves.
If we supported recursive join points, I believe this would actually be
a correctness issue, but as-is it doesn't affect the output.
This PR fixes the documentation of the pipe operator |>, which is
currently (emphasis mine):
> Haskell-like pipe operator `|>`. `x |> f` means **the same as the same
as** `f x`,
> and it chains such that `x |> f |> g` is interpreted as `g (f x)`.
This PR implements the option `mvcgen +jp` to employ a slightly lossy VC
encoding for join points that prevents exponential VC blowup incurred by
naïve splitting on control flow.
```lean
def ifs_pure (n : Nat) : Id Nat := do
let mut x := 0
if n > 0 then x := x + 1 else x := x + 2
if n > 1 then x := x + 3 else x := x + 4
if n > 2 then x := x + 1 else x := x + 2
if n > 3 then x := x + 1 else x := x + 2
if n > 4 then x := x + 1 else x := x + 2
if n > 5 then x := x + 1 else x := x + 2
return x
theorem ifs_pure_triple : ⦃⌜True⌝⦄ ifs_pure n ⦃⇓ r => ⌜r > 0⌝⦄ := by
unfold ifs_pure
mvcgen +jp
/-
...
h✝⁵ : if n > 0 then x✝⁵ = 0 + 1 else x✝⁵ = 0 + 2
h✝⁴ : if n > 1 then x✝⁴ = x✝⁵ + 3 else x✝⁴ = x✝⁵ + 4
h✝³ : if n > 2 then x✝³ = x✝⁴ + 1 else x✝³ = x✝⁴ + 2
h✝² : if n > 3 then x✝² = x✝³ + 1 else x✝² = x✝³ + 2
h✝¹ : if n > 4 then x✝¹ = x✝² + 1 else x✝¹ = x✝² + 2
h✝ : if n > 5 then x✝ = x✝¹ + 1 else x✝ = x✝¹ + 2
⊢ x✝ > 0
-/
grind
```
This PR does what #9234 regrettably failed to do: actually reintroduce
the signatures of some `Subarray` functions that are now implemented via
slices (see #9017) in order to ensure backward compatibility and
consistency. With this PR, the old interface is restored. As an added
benefit, `Subarray.forIn` is no longer opaque.
This PR re-implements `IO.waitAny` using Lean instead of C++. This is to
reduce the size and
complexity of `task_manager` in order to ease future refactorings.
There is an import behavioral change of `IO.waitAny` in this PR.
Consider a situation where we have
two promises `p1`, `p2` and call `IO.waitAny [p1.result!, p2.result!]`
and `p1` resolves instantly.
Previously this would just return the result of `p1` and require nothing
else. With the new
implementation if `p2` is released before being resolved this can cause
a panic, even if
`IO.waitAny` has already finished. I argue that this is reasonable
behavior, given that an
invocation of `result!` promises that the promise will eventually be
resolved.
This PR moves the validation of cross-package `import all` to Lake and
the syntax validation of import keywords (`public`, `meta`, and `all`)
to the two import parsers.
It also fixes the error reporting of the fast import parser
(`Lean.parseImports`) and adds positions to its errors.
This PR addresses an outstanding feature in the module system to
automatically mark `let rec` and `where` helper declarations as private
unless they are defined in a public context such as under `@[expose]`.
This PR removes an error which implicitly assumes that the sort of type
dependency between erased types present in the test being added can not
occur. It would be difficult to refine the error using only the
information present in LCNF types, and it is of very little ongoing
value (I don't recall it ever finding an actual problem), so it makes
more sense to delete it.
Fixes#9692.
This PR changes the LCNF `elimDeadBranches` pass so that it considers
all non-`Nat` literal types to be `⊤`. It turns out that fixing this to
correctly handle all of these types with the current abstract value
representation is surprisingly nontrivial, and it's better to just land
the fix first.
This PR adds a version of `CommRing.Expr.toPoly` optimized for kernel
reduction. We use this function not only to implement `grind ring`, but
also to interface the ring module with `grind cutsat`.
This PR updates `release_repos.yml` to reflect that `import-graph` no
longer depends on `batteries`, and reorders the repositories to better
reflect dependencies.
This PR adds propagation rules for functions that take singleton types.
This feature is useful for discharging verification conditions produced
by `mvcgen`. For example:
```lean
example (h : (fun (_ : Unit) => x + 1) = (fun _ => 1 + y)) : x = y := by
grind
```
This removes the early call to `contradiction` from `simpH`, and
replaces it with a quick check if the pattern start with different
constructors.
We already call `simpH` quadratically often (unavoidable), so we want it
to be quick. Most common contradictions are found later on, so maybe we
don't want to the expensive `contradiction` tactic to be run early.
May help with #9598.
This PR adjusts the formatting type classes for `lake query` to no
longer require both a text and JSON form and instead work with any
combination of the two. The classes have also been renamed. In addition,
the query formatting of a text module header has been improved to only
produce valid headers.
This PR restricts Lake's production of thin archives to only the Windows
core build (i.e., `bootstrap = true`). The unbundled `ar` usually used
for core builds on macOS does not support `--thin`, so we avoid using it
unless necessary.
* Have asynchronous environment extensions specify whether they are
manipulate data for declarations from the "outside"/main branch (e.g.
attributes) or from the "inside"/async branch (e.g. data collected from
body elaboration) in order to avoid unnecessary waiting.
* Merge `findStateAsync?` into `getState` via a new, optional
`asyncDecl` parameter.
* Make `mayContainAsync` check an automatic part of `modifyState`.
This PR uses a more simple approach to proving the unfolding theorem for
a function defined by well-founded recursion. Instead of looping a bunch
of tactics, it uses simp in single-pass mode to (try to) exactly undo
the changes done in `WF.Fix`, using a dedicated theorem that pushes the
extra argument in for each matcher (or `casesOn`).
Improves performance for recursive functions with large `match`
statements, as in #9598.
This PR fixes a regression introduced by an optimization in the
`unfoldReducible` step used by the `grind` normalizer. It also ensures
that projection functions are not reduced, as they are folded in a later
step.
This PR adds build times to each build step of the build monitor (under
`-v` or in CI) and delays exiting on a `--no-build` until after the
build monitor finishes. Thus, a `--no-build` failure will now report
which targets blocked Lake by needing a rebuild.
This PR adds normalizers for nonstandard arithmetic instances. The types
`Nat` and `Int` have built-in support in `grind`, which uses the
standard instances for these types and assumes they are the ones in use.
However, users may define their own alternative instances that are
definitionally equal to the standard ones. This PR normalizes such
instances using simprocs. This situation actually occurs in Mathlib.
Example:
```lean
class Distrib (R : Type _) extends Mul R where
namespace Nat
instance instDistrib : Distrib Nat where
mul := (· * ·)
theorem odd_iff.extracted_1_4 {n : Nat} (m : Nat)
(hm : n =
@HMul.hMul _ _ _ (@instHMul Nat instDistrib.toMul)
2 m + 1) :
n % 2 = 1 := by
grind
end Nat
```
This PR adds support for `Fin.val` in `grind cutsat`. Examples:
```lean
example (a b : Fin 2) (n : Nat) : n = 1 → ↑(a + b) ≠ n → a ≠ 0 → b = 0 → False := by
grind
example (m n : Nat) (i : Fin (m + n)) (hi : m ≤ ↑i) : ↑i - m < n := by
grind
example {n : Nat} (m : Nat) (i : Fin n) ⦃j : Fin (n + m)⦄
(this : ↑i + m ≤ ↑j) : ↑j - m < n := by
grind
example {n : Nat} (i : Fin n) (j : Nat) (hj : j < ↑i) : j < n := by
grind
```
This PR ensures that `grind cutsat` processes `ToInt.toInt` applications
provided by the user. Example:
```lean
open Lean Grind
example (x : Fin 3) : ToInt.toInt x ≠ 0 → ToInt.toInt x ≠ 1 → ToInt.toInt x ≠ 2 → False := by
grind -ring
example (x y z : Fin 5) : ToInt.toInt (x + z) = ToInt.toInt y → z = 0 → x = y := by
grind -ring
```
This PR fixes support for `SMul.smul` in `grind ring`. `SMul.smul`
applications are now normalized. Example:
```lean
example (x : BitVec 2) : x - 2 • x + x = 0 := by
grind
```
This PR add constructors `.intCast k` and `.natCast k` to
`CommRing.Expr`. We need them because terms such as `Nat.cast (R := α)
1` and `(1 : α)` are not definitionally equal. This is pervaise in
Mathlib for the numerals `0` and `1`.
```lean
import Mathlib
example {α : Type} [AddMonoidWithOne α] : Nat.cast (R := α) 0 = (0 : α) := rfl -- not defeq
example {α : Type} [AddMonoidWithOne α] : Nat.cast (R := α) 1 = (1 : α) := rfl -- not defeq
example {α : Type} [AddMonoidWithOne α] : Nat.cast (R := α) 2 = (2 : α) := rfl -- defeq from here
-- Similarly for everything past `AddMonoidWithOne` in the Mathlib hierarchy, e.g. `Ring`.
```
This PR adjusts the import graph, primarily of `Lean`, such that the
worst case rebuild time of core (`lean` only) is below 3 minutes on the
speedcenter machine (not captured by benchmark yet).
This PR performs some micro optimizations on fuzzy matching for a `~20%`
instructions win.
The three key changes are:
- try to remove some unnecessary allocations of things such as tuples
- change `containsInOrderLower` to use the efficient `get'` and `next'`
primitives. I hope that we can replace these with iterators on strings
in the second half of this quarter
- Do the same thing as clangd and use `Int16` with the `minValue` being
used for "worst score" while this does have the potential to
over/underflow, if the user is working with a score in the 10000s
something weird is certainly going on already (the score usually seems
to be in the 2 digit area based on some).
As an additional bonus, once we finally have unboxed arrays we will get
some additional cache wins on the 16 bit arrays!
This PR introduces checks to make sure that the IO functions produce
errors when inputs contain NUL bytes (instead of ignoring everything
after the first NUL byte).
This PR continues #9644 , fixing the core build when using an older
system libuv.
This only affected users building Lean from scratch, since the lean
binaries we ship as part of toolchains statically link their own copy of
libuv 1.50+.
---------
Co-authored-by: Markus Himmel <markus@lean-fro.org>
This PR changes `lake setup-file` to use the server-provided header for
workspace modules.
This also reverts #9163 as the underlying issue is now fixed.
This PR modifies dot identifier notation so that `(.a : T)` resolves
`T.a` with respect to the root namespace, like for generalized field
notation. This lets the notation refer to private names, follow aliases,
and also use open namespaces. The LSP completions are improved to follow
how dot ident notation is resolved, but it doesn't yet take into account
aliases or open namespaces.
Closes#9629
This PR adds error explanations for two common errors caused by large
elimination from `Prop`. To support this functionality, "nested" named
errors thrown by sub-tactics are now able to display their error code
and explanation.
This PR fixes the core build when using an older system libuv.
This only affected users building Lean from scratch, since the `lean`
binaries we ship as part of toolchains statically link their own copy of
libuv 1.50+.
This PR introduces a `mutual_induct` variant of the generated
(co)induction proof principle for mutually defined (co)inductive
predicates. Unlike the standard (co)induction principle (which projects
conclusions separately for each predicate), `mutual_induct` produces a
conjunction of all conclusions.
## Example
Given the following mutual definition:
```lean4
mutual
def f : Prop := g
coinductive_fixpoint
def g : Prop := f
coinductive_fixpoint
end
```
Standard coinduction principles:
```lean4
f.coind : ∀ (pred_1 pred_2 : Prop), (pred_1 → pred_2) → (pred_2 → pred_1) → pred_1 → f
g.coind : ∀ (pred_1 pred_2 : Prop), (pred_1 → pred_2) → (pred_2 → pred_1) → pred_2 → g
```
New `mutual_induct`principle:
```lean4
f.mutual_induct: ∀ (pred_1 pred_2 : Prop), (pred_1 → pred_2) → (pred_2 → pred_1) → (pred_1 → f) ∧ (pred_2 → g)
```
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This PR adds support for generating lattice-theoretic (co)induction
proof principles for predicates defined via `mutual` blocks using
`inductive_fixpoint`/`coinductive_fixpoint` constructs.
### Key Changes
- The order on product lattices (used to define fixpoints of mutual
blocks) is unfolded.
- Hypotheses in generated principles are curried.
- Conclusions are projected to focus only on the predicate of interest
(rather than being a conjunction of conclusions for all functions
defined in the `mutual` block.
### Example
Given:
```lean4
mutual
def f : Prop :=
g
coinductive_fixpoint
def g : Prop :=
f
coinductive_fixpoint
end
```
The system now generates these coinduction principles:
```lean4
f.coinduct (pred_1 pred_2 : Prop) (hyp_1 : pred_1 → pred_2) (hyp_2 : pred_2 → pred_1) : pred_1 → f
```
and
```lean4
g.coinduct (pred_1 pred_2 : Prop) (hyp_1 : pred_1 → pred_2) (hyp_2 : pred_2 → pred_1) : pred_2 → g
```
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This PR adds the separate directions of
`List.pairwise_iff_forall_sublist` as named lemmas.
I want to explore how they could/should be used by `grind` in Mathlib.
This PR brings the Mac OSX build instructions up to date slightly. (They
currently refer to facts "...as of November 2014...")
- Remove specific OS version number from the title as it is out of date
with respect to filename.
- Nonetheless don't change filename for the sake of not breaking
incoming links.
- Update C++ language version to C++14, which I believe is what is
currently required, based on other platform documentation.
- Bump versions of C++ compilers that seem to be current. I expect the
exact values of these version numbers aren't crucial but maybe good for
the reader calibrating a vague sense of whether their compiler is in the
right ballpark.
- Add `lld` to the homebrew clang instructions, because homebrew changed
the way they package llvm tools, spinning the linker off into its own
package.
This PR updates the styling and wording of error messages produced in
inductive type declarations and anonymous constructor notation,
including hints for inferable constructor visibility updates.
This PR optimizes `Lean.Name.toString`, giving a 10% instruction
benefit.
Crucially this is a breaking change as the old `Lean.Name.toString`
method used to support a method for identifying tokens. This method is
now available as `Lean.Name.toStringWithToken` in order to allow for
specialization of the (highly common) `toString` code path which sets
this function to just return `false`.
This PR simplifies the docstring for `propext` significantly.
The old docstring explained general concepts of axioms that are now
covered in the reference manual, and had a large example that was out of
date and has been subsumed by reference manual content.
This PR adds `@[grind =]` to `Prod.lex_def`. Note that `omega` has
special handling for `Prod.Lex`, and this is needed for `grind`'s cutsat
module to achieve parity.
The `isUnderBinder` check is intended to avoid inlining repeated
computations into specializations, but this doesn’t apply to local
function decls whose bodies are already delayed.
This PR adds lemmas about `UIntX.toBitVec` and `UIntX.ofBitVec` and `^`.
These match the existing lemas for `*`.
After #7887 these can be made true by `rfl`.
This PR ensures `ite` and `dite` are to selected as E-matching patterns.
They are bad patterns because the then/else branches are only
internalized after `grind` decided whether the condition is
`True`/`False`.
The issue reported by #9572 has been fixed, but the fix exposed another
issue. The patterns for `List.Pairwise` produce an unbounded number of
E-matching instances.
```lean
example (l : List α) : l.Pairwise R := by
grind
```
This PR fixes an issue in `grind`'s disequality proof construction. The
issue occurs when an equality is merged with the `False` equivalence
class, but it is not the root of its congruence class, and its
congruence root has not yet been merged into the `False` equivalence
class yet.
closes#9562
This PR optimizes the proof terms generated by `grind ring`. For
example, before this PR, the kernel took 2.22 seconds (on a M4 Max) to
type-check the proof in the benchmark `grind_ring_5.lean`; it now takes
only 0.63 seconds.
This PR generalizes `Process.output` and `Process.run` with an optional
`String` argument that can be piped to `stdin`.
To date we have been using shims `Process.runCmdWithInput` in Batteries.
This PR fixes a bug introduced in #7830 where if the cursor is at the
indicated position
```lean
example (as bs : List Nat) : (as.append bs).length = as.length + bs.length := by
induction as with
| nil => -- cursor
| cons b bs ih =>
```
then the Infoview would show "no goals" rather than the `nil` goal. The
PR also fixes a separate bug where placing the cursor on the next line
after the `induction`/`cases` tactics like in
```lean
induction as with
| nil => sorry
| cons b bs ih => sorry
I -- < cursor
```
would report the original goal in the goal list. Furthermore, there are
numerous improvements to error recovery (including `allGoals`-type logic
for pre-tactics) and the visible tactic states when there are errors.
Adds `Tactic.throwOrLogErrorAt`/`Tactic.throwOrLogError` for throwing or
logging errors depending on the recovery state.
This PR restores the feature where in `induction`/`cases` for `Nat`, the
`zero` and `succ` labels are hoverable. This was added in #1660, but
broken in #3629 and #3655 when custom eliminators were added. In
general, if a custom eliminator `T.elim` for an inductive type `T` has
an alternative `foo`, and `T.foo` is a constant, then the `foo` label
will have `T.foo` hover information.
This PR consolidates common attribute-related error messages into
reusable functions and updates the wording and formatting of relevant
error messages.
This extends the specialization behavior of functions taking instance
implicits to ordinary implicit arguments that are of instance type. The
choice between the two is often made for subtle inference-related
reasons. It also affects visibility of these functions, because the
module system makes template-like decls visible to the compiler in other
modules.
This PR makes the second instance of the `inferVisibility` pass run
after the `saveMono` pass. As the comment above the first instance of
the pass indicates, this needs to be after `saveMono` in order to see
all decls with their updated bodies.
This PR upstreams some helper instances for `NameSet` from Batteries.
(These could be generalized to an arbitrary TreeSet, but I'll leave that
for someone else.)
This PR changes `Lean.Grind.NoNatZeroDivisors` so that it is
parametrised by a `NatModule` instance rather than just a `HMul`
instance. This is sufficiently general for our purposes, and is a
band-aid (~40% improvement) for the performance problems we've been
seeing coming from inference here. The problems observed in Mathlib may
not see much improvement, however.
This PR lets the equation compiler unfold abstracted proofs again if
they would otherwise hide recursive calls.
This fixes#8939.
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
This PR fixes Lake's handling of a module system `import all`.
Previously, Lake treated `import all` the same a non-module `import`,
importing all private data in the transitive import tree. Lake now
distinguishes the two, with `import all M` just importing the private
data of `M`. The direct private imports of `M` are followed, but they
are not promoted.
This also fixes some other Lake bugs with module system imports that
were discovered in the process.
In the early days of the new compiler, it was common to make tests that
manually compiled a definition with the new compiler. The arity
reduction pass in LCNF deliberately does not compute a fixed point to
find a minimal set of used parameters for performance reasons, but
running it a second time can lead to different decisions being made and
a decl arity mismatch. This has been an issue for multiple people during
development. Removing the tests fixes the problem.
Fixes#9186.
This PR uses `withAbstractAtoms` to prevent the kernel from accidentally
reducing the atoms in the arith normlizer while typechecking. This PR
also sets `implicitDefEqProofs := false` in the `grind` normalizer
This PR corrects the changes to `Lean.Grind.Field` made in #9500.
(The lack of examples of fields in the core repository is a problem! I
guess it is likely that for interval arithmetic we will at least need
`Rat` soon.)
(Almost) only typos in constant names and doc-strings were considered;
grammar was not considered. Also, along others,
`mkDefinitionValInferrringUnsafe` has been fixed :-)
This PR adds a benchmark for the persistent hashmap, in particular also
covering the non
linear insert case which is often hit in practical uses. Furthermore the
same test case is also
added to the treemap benchmark.
This PR makes `mframe`, `mspec` and `mvcgen` respect hygiene.
Inaccessible stateful hypotheses can now be named with a new tactic
`mrename_i` that works analogously to `rename_i`.
This PR surfaces kernel diagnostics even in `example`.
The problem was that the kernel checking happens asynchronously. We
cannot use `reportDiag` in `addDecl`, which spawns that task, due to the
module hierarchy. For non `example`-declaration, `reportDiag` is called
somewhere else later, but for `example`, the `withoutModifyingEnv` in
`elabMutualDef` hid the kernel diagnostics. (But only the kernel
diagnostics; they are in the `Environment`, while the others are in the
`State`).
I also observed that the `reportDiag` in `elabAsync` (but not in
`elabSync`) duplicated the reporting, so without `elab.Async true` you
get the message twice. To fix this, `reportDiag` now resets the
diagnostics. This should avoid reporting counts twice in general (at
least within a linear use of the state).
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
This PR removes vestigial syntax definitions in
`Lean.Elab.Tactic.Do.VCGen` that when imported undefine the `mvcgen`
tactic. Now it should be possible to import Mathlib and still use
`mvcgen`.
This PR adds a few more `*.by_wp` "adequacy theorems" that allows to
prove facts about programs in `ReaderM` and `ExceptM` using the `Std.Do`
framework.
This PR adds a `HPow \a Int \a` field to `Lean.Grind.Field`, and
sufficient axioms to connect it to the operations, so that in future we
can reason about exponents in `grind`. To avoid collisions, we also move
the `HPow \a Nat \a` field in `Semiring` from the extends clause to a
field. Finally, we add some failing tests about normalizing exponents.
This PR makes cdot function expansion take hygiene information into
account, fixing "parenthesis capturing" errors that can make erroneous
cdots trigger cdot expansion in conjunction with macros. For example,
given
```lean
macro "baz% " t:term : term => `(1 + ($t))
```
it used to be that `baz% ·` would expand to `1 + fun x => x`, but now
the parentheses in `($t)` do not capture the cdot. We also fix an
oversight where cdot function expansion ignored the fact that type
ascriptions and tuples were supposed to delimit expansion, and also now
the quotation prechecker ignores the identifier in `hygieneInfo`. (#9491
added the hygiene information to the parenthesis and cdot syntaxes.)
This fixes a bug discovered by [Google
DeepMind](https://storage.googleapis.com/deepmind-media/DeepMind.com/Blog/imo-2024-solutions/P1/index.html),
which made use of `useλy . x=>y.rec λS p=>?_`. The `use` tactic from
Mathlib wrapped the provided term in a type ascription, and so this was
equivalent to `use fun x => λy x x=>y.rec λS p=>?_`. (Note that cdot
function expansion is not able to take into account *where* the cdots
are located, and it is syntactically valid to insert an identifier into
the binder list like this. If we ever want to address this in the
future, we could have cdots expand into a special term that wraps an
identifier that evaluates to a local, but which would cause errors in
other contexts.)
Design note: we put the `hygieneInfo` on the open parenthesis rather
than at the end, since that way the hygiene information is available
even when there are parsing errors. This is important since we rely on
being able to elaborate partial syntax to get elab info (e.g. in `(a.`
to get completion info). Note that syntax matchers check that the
`hygieneInfo` is actually present, so such partial syntax would not be
matched.
This PR adds a feature where `structure` constructors can override the
inferred binder kinds of the type's parameters. In the following, the
`(p)` binder on `toLp` causes `p` to be an explicit parameter to
`WithLp.toLp`:
```lean
structure WithLp (p : Nat) (V : Type) where toLp (p) ::
ofLp : V
```
This reflects the syntax of the feature added in #7742 for overriding
binder kinds of structure projections. Similarly, only those parameters
in the header of the `structure` may be updated; it is an error to try
to update binder kinds of parameters included via `variable`.
Closes#9072.
Fixes a possible bug from stale caches when creating the type of the
constructor.
This PR resolves an issue where the `Meta.Context.configKey` field is
private but we still want to use the constructor of the structure for
setting other fields, which would be prevented by the module system
checks:
```lean
structure Context where
private config : Config := {}
private configKey : UInt64 := config.toKey
...
def ContextInfo.runMetaM (info : ContextInfo) (lctx : LocalContext) (x : MetaM α) : IO α := do
-- cannot call private constructor of `Meta.Context`!
(·.1) <$> info.runCoreM (x.run { lctx := lctx } { mctx := info.mctx })
```
Instead, the private field is extracted into an (existing) structure
that applies its default value:
```lean
/-- Configuration with key produced by `Config.toKey`. -/
structure ConfigWithKey where
private mk ::
config : Config := {}
key : UInt64 := config.toKey
structure Context where
keyedConfig : ConfigWithKey := default
```
Thus `Context`'s constructor remains public without exposing a way to
set `key` directly.
This PR fixes a kernel type mismatch that occurs when using `grind` on
goals containing non-standard `OfNat.ofNat` terms. For example, in issue
#9477, the `0` in the theorem `range_lower` has the form:
```lean
(@OfNat.ofNat
(Std.PRange.Bound (Std.PRange.RangeShape.lower (Std.PRange.RangeShape.mk Std.PRange.BoundShape.closed Std.PRange.BoundShape.open)) Nat)
(nat_lit 0)
(instOfNatNat (nat_lit 0)))
```
instead of the more standard form:
```lean
(@OfNat.ofNat
Nat
(nat_lit 0)
(instOfNatNat (nat_lit 0)))
```
Closes#9477
This PR improves the `evalInt?` function, which is used to evaluate
configuration parameters from the `ToInt` type class. This PR also adds
a new `evalNat?` function for handling the `IsCharP` type class, and
introduces a configuration option:
```
grind (exp := <num>)
```
This option controls the maximum exponent size considered during
expression evaluation. Previously, `evalInt?` used `whnf`, which could
run out of stack space when reducing terms such as `2^1024`.
closes#9427
This PR adds `binrel%` macros for `!=` and `≠` notation defined in
`Init.Core`. This allows the elaborator to insert coercions on both
sides of the relation, instead of committing to the type on the left
hand side.
I first discovered this bug while working on Brouwer's fixed point
theorem. See the discussion on Zulip at [#lean4 > Elaboration of
`≠` @
💬](https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/Elaboration.20of.20.60.E2.89.A0.60/near/526236907).
This PR replaces the proof of the simplification lemma `Nat.zero_mod`
with
`rfl` since it is, by design, a definitional equality. This solves an
issue
whereby the lemma could not be used by the simplifier when in 'dsimp'
mode.
Closes#9389
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This PR introduces tactic `mleave` that leaves the `SPred` proof mode by
eta expanding through its abstractions and applying some mild
simplifications. This is useful to apply automation such as `grind`
afterwards.
Relates to #9363.
This PR adds support in the `mintro` tactic for introducing `let`/`have`
binders in stateful targets, akin to `intro`. This is useful when
specifications introduce such let bindings.
Closes#9365.
This PR makes `PProdN.reduceProjs` also look for projection functions.
Previously, all redexes were created by the functions in `PProdN`, which
used primitive projections. But with `mkAdmProj` the projection
functions creep in via the types of the `admissible_pprod_fst` theorem.
So let's just reduce both of them.
Fixes#9462.
The `isRef` check being removed here used to be an optimization, because
this structure only tracked whether ref counting operations need to be
inserted at all. Now the structure also tracks whether the value needs
to be checked for being a scalar or not, which is something that can be
refined by a `cases` arm, since inductive types can have a mix of scalar
and non-scalar constructors.
This PR fixes an issue that caused some `deriving` handlers to fail when
the name of the type being declared matched that of a declaration in an
open namespace.
Closes#9366
This PR improves the 'Go to Definition' UX, specifically:
- Using 'Go to Definition' on a type class projection will now extract
the specific instances that were involved and provide them as locations
to jump to. For example, using 'Go to Definition' on the `toString` of
`toString 0` will yield results for `ToString.toString` and `ToString
Nat`.
- Using 'Go to Definition' on a macro that produces syntax with type
class projections will now also extract the specific instances that were
involved and provide them as locations to jump to. For example, using
'Go to Definition' on the `+` of `1 + 1` will yield results for
`HAdd.hAdd`, `HAdd α α α` and `Add Nat`.
- Using 'Go to Declaration' will now provide all the results of 'Go to
Definition' in addition to the elaborator and the parser that were
involved. For example, using 'Go to Declaration' on the `+` of `1 + 1`
will yield results for `HAdd.hAdd`, `HAdd α α α`, `Add Nat`,
``macro_rules | `($x + $y) => ...`` and `infixl:65 " + " => HAdd.hAdd`.
- Using 'Go to Type Definition' on a value with a type that contains
multiple constants will now provide 'Go to Definition' results for each
constant. For example, using 'Go to Type Definition' on `x` for `x :
Array Nat` will yield results for `Array` and `Nat`.
### Details
'Go to Definition' for type class projections was first implemented by
#1767, but there were still a couple of shortcomings with the
implementation. E.g. in order to jump to the instance in `toString 0`,
one had to add another space within the application and then use 'Go to
Definition' on that, or macros would block instances from being
displayed. Then, when the .ilean format was added, most 'Go to
Definition' requests were already handled using the .ileans in the
watchdog process, and so the file worker never received them to handle
them with the semantic information that it has available.
This PR resolves most of the issues with the previous implementation and
refactors the 'Go to Definition' control flow so that 'Go to Definition'
requests are always handled by the file worker, with the watchdog merely
using its .ilean position information to update the positions in the
response to a more up-to-date state. This is necessary because the file
worker obtains its position information from the .oleans, which need to
be rebuilt in order to be up-to-date, while the watchdog always receives
.ilean update notifications from each active file worker with the
current position information in the editor.
Finally, all of the 'Go to Definition' code is refactored to be easier
to maintain.
### Breaking changes
`InfoTree.hoverableInfoAt?` has been generalized to
`InfoTree.hoverableInfoAtM?` and now takes a general `filter` argument
instead of several boolean flags, as was the case before.
This PR removes uses of `Lean.RBMap` in Lean itself.
Furthermore some massaging of the import graph is done in order to avoid
having `Std.Data.TreeMap.AdditionalOperations` (which is quite
expensive) be the critical path for a large chunk of Lean. In particular
we can build `Lean.Meta.Simp` and `Lean.Meta.Grind` without it thanks to
these changes.
We did previously not conduct this change as `Std.TreeMap` was not
outperforming `Lean.RBMap` yet, however this has changed with the new
code generator.
This PR addresses the lean crash (stack overflow) with nested induction
and the generation of the `SizeOf` spec lemmas, reported at #9018.
It does not address the underlying issue that in these cases, the
generated SizeOf code does not match the the SizeOf function found by
instance search, and thus the generation fails.
This seem hard to fix: `mkSizeOfMinors` would have to recognize that
given, say, `List (Id Tree)`, the derived instance (assuming there was
one for `Tree`) is not the same as for `List Tree`.
The problem seems just about as hard as getting derived SizeOf right in
the presence of nested induction and non-canonical SizeOf instances.
This PR fixes the behavior of `String.prev`, aligning the runtime
implementation with the reference implementation. In particular, the
following statements hold now:
- `(s.prev p).byteIdx` is at least `p.byteIdx - 4` and at most
`p.byteIdx - 1`
- `s.prev 0 = 0`
- `s.prev` is monotone
Closes#9439
This PR adds the number of jobs run to the final message Lake produces
on a successfully run of `lake build`.
**Examples**
```
Build completed successfully (1 job).
Build completed successfully (6 jobs).
```
This PR adds the `libPrefixOnWindows` package and library configuration
option. When enabled, Lake will prefix static and shared libraries with
`lib` on Windows (i.e., the same way it does on Unix).
This PR changes the Lake local cache infrastructure to restore
executables and shared and static libraries from the cache. This means
they keep their expected names, which some use cases still rely on.
This PR adds a hint to the "invalid projection" message suggesting the
correct nested projection for expressions of the form `t.n` where `t` is
a tuple and `n > 2`.
This feature was originally proposed by @nomeata in #8986.
This PR improves the error messages produced by the `split` tactic,
including suggesting syntax fixes and related tactics with which it
might be confused.
Note that, to avoid clashing with the new error message styling
conventions used in these messages, this PR also updates the formatting
of the message produced by `throwTacticEx`.
Closes#6224
This PR changes `IRType.boxed` to map `erased` to `tobject` rather than
`object`, since `erased` has a representation of a boxed scalar 0 when
we are forced to represent it at runtime. This case does not occur at
all in the Lean codebase.
This PR updates the formatting of, and adds explanations for, "unknown
identifier" errors as well as "failed to infer type" errors for binders
and definitions.
It attempts to ameliorate some of the confusion encountered in #1592 by
modifying the wording of the "header is elaborated before body is
processed" note and adding further discussion and examples of this
behavior in the corresponding error explanation.
An earlier PR (#9017) replaced certain subarray functions such as
`Subarray.foldl` with generic slice functions `Slice.foldl`. For
backward compatibility reasons, This PR reintroduces `Subarray.foldl`
etc. as aliases for the `Slice` versions.
This PR adds Lake tests for builds involving the Lean module system and
fixes some bugs encountered in the process. In particular, it fixes the
parsing of private imports and how Lake handles the `import all` of a
private import.
This PR fixes some issues with the Lake tests on Windows and macOS. It
also avoids downloading Mathlib in the `init` test, which was currently
doing this after changes to the `math-lax` template in #8866.
To skip the Mathlib download in `init`, an undocumented `--offline`
option was added`. This option is currently meant for internal use only.
This PR increases the number of cases where `isArrowProposition` returns
a result other than `.undef`. This function is used to implement the
`isProof` predicate, which is invoked on every subterm visited by
`simp`.
This PR adds improves the "invalid named argument" error message in
function applications and match patterns by providing clickable hints
with valid argument names. In so doing, it also fixes an issue where
this error message would erroneously flag valid match-pattern argument
names.
This PR adds support for compilation of `casesOn` for subsingletons. We
rely on the elaborator's type checking to restrict this to inductives in
`Prop` that can actually eliminate into `Type n`. This does not yet
cover other recursors of these types (or of inductives not in `Prop` for
that matter).
This PR implements a simple optimization: dependent implications are no
longer treated as E-matching theorems in `grind`. In
`grind_bitvec2.lean`, this change saves around 3 seconds, as many
dependent implications are generated. Example:
```lean
∀ (h : i + 1 ≤ w), x.abs.getLsbD i = x.abs[i]
```
This PR adds a benchmark to our suite, specifically targeting the fact
that local hypotheses
are currently not indexed in simp and can thus cause significant
slowdowns compared to having them
as external declarations.
This PR splits up `Module.recBuildLean` into smaller functions and
optimizes the implementation of `Module.cacheOutputArtifacts` for the
new compiler. Now, all functions within `Lake.Build.Module` take Lean
<1s to compile.
This PR updates Lake to resolve the `.olean` files for transitive
imports for Lean through the `modules` field of `lean --setup`. This
enables means the Lean can now directly use the `.olean` files from the
Lake cache without needed to locate them at a specific hierarchical
path.
Resolving transitive imports still has a performance penalty, but it is
now much less.
This is mostly a refactoring that replaces other analyses with type
information, but due to the introduction of `tagged` it also has the
side effect of eliminating ref counting ops entirely for types that
always have a tagged scalar representation, e.g. `Unit`.
This PR fixes a bug at `mkCongrSimpCore?`. It fixes the issue reported
by @joehendrix at #9388.
The fix is just commit: afc4ba617f. The
rest of the PR is just cleaning up the file.
closes#9388
This PR fixes an unsafe trick where a sentinel for a hash table of Exprs
(keyed by pointer) is created by constructing a value whose runtime
representation can never be a valid Expr. The value chosen for this
purpose was Unit.unit, which violates the inference that Expr has no
scalar constructors. Instead, we change this to a freshly allocated Unit
× Unit value.
A micro-benchmark for plain, mostly first-order rewriting of simp:
This uses axiom to make it independent of specific optimization (e.g.
for `Nat`).
It generates a “list” of 128 `b`s followed by 128 `a` and uses
bubble-sort to to sort it and compares it against the expected output.
This PR changes the dependency cloning mechanism in lake so the log
message that lake is cloning a
dependency occurs before it is finished doing so (and instead before it
starts). This has been a
huge source of confusion for users that don't understand why lake seems
to be just stuck for no
reason when setting up a new project, the output now is:
```
λ lake +lean4 new math math
info: downloading mathlib `lean-toolchain` file
info: math: no previous manifest, creating one from scratch
info: leanprover-community/mathlib: cloning https://github.com/leanprover-community/mathlib4
<hang>
info: leanprover-community/mathlib: checking out revision 'cd11c28c6a0d514a41dd7be9a862a9c8815f8599'
```
This PR fixes a performance issue that occurs when generating equation
lemmas for functions that use match-expressions containing several
literals. This issue was exposed by #9322 and arises from a combination
of factors:
1. Literal values are compiled into a chain of dependent if-then-else
expressions.
2. Dependent if-then-else expressions are significantly more expensive
to simplify than regular ones.
3. The `split` tactic selects a target, splits it, and then invokes
`simp` on the resulting subgoals. Moreover, `simp` traverses the entire
goal bottom-up and does not stop after reaching the target.
This PR addresses the issue by introducing a custom simproc that avoids
recursively simplifying nested if-then-else expressions. It does **not**
alter the user-facing behavior of the `split` tactic because such a
change would be highly disruptive. Instead, the PR adds a new flag,
`backward.split` to control the behavior of the user-facing `split`
tactic. It is currently set to `true`, i.e., the old behavior is still
the default one. In a future PR, we should set this flag to `false` by
default and begin repairing all affected proofs.
closes#9322
This PR modifies the encoding from `Nat` to `Int` used in `grind
cutsat`. It is simpler, more extensible, and similar to the generic
`ToInt`. After update stage0, we will be able to delete the leftovers.
This PR correctly populates the `xType` field of the `IR.FnBody.case`
constructor. It turns out that there is no obvious consequence for this
being incorrect, because it is conservatively recomputed by the `Boxing`
pass.
This PR changes the implementation of `trace.Compiler.result` to use the
decls as they are provided rather than looking them up in the LCNF mono
environment extension, which was seemingly done to save the trouble of
re-normalizing fvar IDs before printing the decl. This means that the
`._closed` decls created by the `extractClosed` pass will now be
included in the output, which was definitely confusing before if you
didn't know what was happening.
This currently relies on the encoding pun of Nat.zero as the first
tagged constructor of Nat. Since Nat.succ is lowered to addition, it
makes sense to also lower Nat.zero to a zero literal. This might also
expose more optimization opportunities in the future.
This PR fixes IR constructor argument lowering to correctly handle an
irrelevant argument being passed for a relevant parameter in all cases.
This happened because constructor argument lowering (incompletely)
reimplemented general LCNF-to-IR argument lowering, and the fix is to
just adopt the generic helper functions. This is probably due to an
incomplete refactoring when the new compiler was still on a branch.
This PR uses the `mkCongrSimpForConst?` API in `simp` to reduce the
number of times the same congruence lemma is generated. Before this PR,
`grind` would spend `1.5`s creating congruence theorems during
normalization in the `grind_bitvec2.lean` benchmark. It now spends
`0.6`s. This PR should make an even bigger difference after we merge
#9300.
This PR removes the unnecessary requirement of `BEq α` for
`Array.any_push`, `Array.any_push'`, `Array.all_push`, `Array.all_push'`
as well as `Vector.any_push` and `Vector.all_push`.
This PR replaces the `reduceCtorEq` simproc used in `grind` by a much
more efficient one. The default one use in `simp` is just overhead
because the `grind` normalizer is already normalizing arithmetic.
In a separate PR, we will push performance improvements to the default
`reduceCtorEq`.
This PR fixes `toISO8601String` to produce a string that conforms to the
ISO 8601 format specification. The previous implementation separated the
minutes and seconds fragments with a `.` instead of a `:` and included
timezone offsets without the hour and minute fragments separated by a
`:`.
Closes#9235
This PR moves the implementation of `lean_add_extern`/`addExtern` from
C++ into Lean. I believe is the last C++ helper function from the
library/compiler directory being relied upon by the new compiler. I put
it into its own file and duplicated some code because this function
needs to execute in CoreM, whereas the other IR functions live in their
own monad stack. After the C++ compiler is removed, we can move the IR
functions into CoreM.
This PR optimizes support for `Decidable` instances in `grind`. Because
`Decidable` is a subsingleton, the canonicalizer no longer wastes time
normalizing such instances, a significant performance bottleneck in
benchmarks like `grind_bitvec2.lean`. In addition, the
congruence-closure module now handles `Decidable` instances, and can
solve examples such as:
```lean
example (p q : Prop) (h₁ : Decidable p) (h₂ : Decidable (p ∧ q)) : (p ↔ q) → h₁ ≍ h₂ := by
grind
```
This PR adds support for `.mdata` in LCNF mono types (and then drops it
at the IR type level instead). This better matches the behavior of
extern decls in the C++ code of the old compiler, which is still being
used to create extern decls at the moment and will soon be replaced.
This is covered by existing tests.
This PR fixes the bug that `collectAxioms` didn't collect axioms
referenced by other axioms. One of the results of this bug is that
axioms collected from a theorem proved by `native_decide` may not
include `Lean.trustCompiler`.
Closes#8840.
This PR demotes the builtin elaborators for `Std.Do.PostCond.total` and
`Std.Do.Triple` into macros, following the DefEq improvements of #9015.
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR makes `isDefEq` detect more stuck definitional equalities
involving smart unfoldings. Specifically, if `t =?= defn ?m` and `defn`
matches on its argument, then this equality is stuck on `?m`. Prior to
this change, we would not see this dependency and simply return `false`.
Fixes#8766.
Co-authored-by: Kyle Miller <kmill31415@gmail.com>
This PR improves the `congr` tactic so that it can handle function
applications with fewer arguments than the arity of the head function.
This also fixes a bug where `congr` could not make progress with
`Set`-valued functions in Mathlib, since `Set` was being unfolded and
making such functions have an apparently higher arity.
This addresses issue #2128 for the `congr` tactic, but not `simp` and
others.
This PR adds theorem `BitVec.clzAuxRec_eq_clzAuxRec_of_getLsbD_false` as
a more general statement than `BitVec.clzAuxRec_eq_clzAuxRec_of_le`,
replacing the latter in the bitblaster too.
This PR makes the logic and tactics of `Std.Do` universe polymorphic, at
the cost of a few definitional properties arising from the switch from
`Prop` to `ULift Prop` in the base case `SPred []`.
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR migrates usages of `Std.Range` to the new polymorphic ranges.
This PR unfortunately increases the transitive imports for
frequently-used parts of `Init` because the ranges now rely on iterators
in order to provide their functionality for types other than `Nat`.
However, iteration over ranges in compiled code is as efficient as
before in the examples I checked. This is because of a special
`IteratorLoop` implementation provided in the PR for this purpose.
There were two issues that were uncovered during migration:
* In `IndPredBelow.lean`, migrating the last remaining range causes
`compilerTest1.lean` to break. I have minimized the issue and came to
the conclusion it's a compiler bug. Therefore, I have not replaced said
old range usage yet (see #9186).
* In `BRecOn.lean`, we are publicly importing the ranges. Making this
import private should theoretically work, but there seems to be a
problem with the module system, causing the build to panic later in
`Init.Data.Grind.Poly` (see #9185).
* In `FuzzyMatching.lean`, inlining fails with the new ranges, which
would have led to significant slowdown. Therefore, I have not migrated
this file either.
This PR adds a benchmark for the rewriting engine of bv_decide, based on
a problem extracted from
SMT-LIB. Note that this problem has significant elaboration time itself
due to its sheer size though
the overall execution time is split approximately 50:50 between
elaboration and rewriting.
This PR improves the startup time for `grind ring` by generating the
required type classes on demand. This optimization is particularly
relevant for files that make hundreds of calls to `grind`, such as
`tests/lean/run/grind_bitvec2.lean`. For example, before this change,
`grind` spent 6.87 seconds synthesizing type classes, compared to 3.92
seconds after this PR.
We can probably remove `lcUnreachable` once we delete the old compiler,
but for now it makes more sense to move it earlier, since LCNF already
has `Code.unreachable`.
This PR changes the `toMono` pass to consider the type of an application
and erase all arguments corresponding to erased params. This enables a
lightweight form of relevance analysis by changing the mono type of a
decl. I would have liked to unify this with the behavior for
constructors, but my attempt to give constructors the same behavior in
#9222 (which was in preparation for this PR) had a minor performance
regression that is really incidental to the change. Still, I decided to
hold off on it for the time being. In the future, we can hopefully
extend this to constructors, extern decls, etc.
This PR removes code that has the false assumption that LCNF local vars
can occur in types. There are other comments in `ElimDead.lean`
asserting that this is not possible, so this must have been a change
early in the development of the new compiler.
This PR makes the LCNF `elimDeadBranches` pass handle unsafe decls a bit
more carefully. Now the result of an unsafe decl will only become ⊤ if
there is value flow from a recursive call.
These are used by the checker for `.ctor`, but I don't think that that
unboxed types will reuse `.ctor`, whose implementation details are
intimately connected to our runtime representation of objects.
This PR changes the `getLiteral` helper function of `elimDeadBranches`
to correctly handle inductives with constructors. This function is not
used as often as it could be, which makes this issue rare to hit outside
of targeted test cases.
This PR extends the `Eq` simproc used in `grind`. It covers more cases
now. It also adds 3 reducible declarations to the list of declarations
to unfold.
This PR implements `exists` normalization using a simproc instead of
rewriting rules in grind. This is the first part of the PR, after update
stage0, we must remove the normalization theorems.
This PR changes the compiler's specialization analysis to consider
higher-order params that are rebundled in a way that only changes their
`Prop` arguments to be fixed. This means that they get specialized with
a mere `@[specialize]`, rather than the compiler having to opt-in to
more aggressive parameter-specific specialization.
This PR implements `forall` normalization using a simproc instead of
rewriting rules in `grind`. This is the first part of the PR, after
update stage0, we must remove the normalization theorems.
This PR fixes stealing of `⇓` syntax by the new notation for total
postconditions by demoting it to non-builtin syntax and scoping it to
`Std.Do`.
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR tries to improve the E-matching pattern inference for `grind`.
That said, we still need better tools for annotating and maintaining
`grind` annotations in libraries.
closes#9125
This PR removes the `Subarray`-specific `toArray`, `foldlM` and `foldl`
methods and instead provides these operations on `Std.Slice`, which are
implemented with the `ToIterator` instance of the slice. Calling
`subarray.toArray` etc. still works, since `Subarray` is an abbreviation
for `Slice _`.
Because the benchmarks are not so clear, to be safe, I will merge this
only after the release. In contrast to the ranges, the iteration over
slices is not quite as efficient as the old `Subarray`-specific
implementation, which would require either more optimizations in the
iterator library (special `IteratorLoop` and `IteratorCollect`
implementations) or better unboxing support by the compiler.
This PR makes the `pullInstances` pass avoid pulling any instance
expressions containing erased propositions, because we don't correctly
represent the dependencies that remain after erasure.
This PR disables the use of the header produced by `lake setup-file` in
the server for now. It will be re-enabled once Lake takes into account
the header given by the server when processing workspace modules.
Without that, `setup-file` header can produce odd behavior when the file
on disk and in an editor disagree on whether the file participates in
the module system.
This PR fixes `undefined symbol: lean::mpz::divexact(lean::mpz const&,
lean::mpz const&)` when building without `LEAN_USE_GMP`
This fixes a regression in #8089
This PR makes `mvcgen` split ifs rather than applying specifications.
Doing so fixes a bug reported by Rish.
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR resolves a defeq diamond, which caused a problem in Mathlib:
```
import Mathlib
example (R : Type) [I : Ring R] :
@AddCommGroup.toGrindIntModule R (@Ring.toAddCommGroup R I) =
@Lean.Grind.Ring.instIntModule R (@Ring.toGrindRing R I) := rfl -- fails
```
This PR fixes two issues with Lake's process of creating static
archives.
Lake now always recreates static archives by first deleting any existing
one and then recreating it. `ar rcs` does not remove delete files, so
running it when the archive already exists can leave behind "ghost"
symbols of removed object files.
Second, Lake now use `T` rather than `--thin` to create thin archives.
While `--thin` is the recommended spelling, older versions of LLVM `ar`
do not support it. Thus, either choice produces tradeoffs. `T` is chosen
to make Lake consistent with the Lean core's own (Make) build scripts.
This PR enforces the non-inlining of _override impls in the base phase
of LCNF compilation. The current situation allows for constructor/cases
mismatches to be exposed to the simplifier, which triggers an assertion
failure. The reason this didn't show up sooner for Expr is that Expr has
a custom extern implementation of its computed field getter.
Fixes#9156.
This test was originally checked in for a panic in the pretty printer,
but at some point the output of every LCNF simp pass was added to
#guard_msgs output. Since this is printing LCNF built by the stage0
compiler, this causes a lot of unnecessary churn.
This PR changes the key Lake uses for the `,ir` artifact in the content
hash data structure to `r`, maintaining the convention of single
character key names.
This PR fixes the syntax of `grind` modifiers to use `patternIgnore` for
cases where both unicode and ascii variants are matched. This fixes an
issue where several variants of grind syntax weren't accepted (e.g.
`@[grind ← gen]`). Additionally, this reduces the chance that we get
another syntax matching bootstrap hell.
This PR wraps `simpLemma` and `grindLemma` in `ppGroup` to make sure
that the modifiers aren't printed separately from the term / identifier.
Example:
```
simp only [very_long_lemma_oh_no_can_you_please_stop_we're_getting_to_the_limit, ←
wait_this_is_rewritten_backwards_oh_uhh_where's_the_arrow_you_ask?_oh_wait_it's_up_there!]
==>
simp only [very_long_lemma_oh_no_can_you_please_stop_we're_getting_to_the_limit,
← wait_this_is_rewritten_backwards_and_wow_it's_very_clear_and_obvious]
```
This PR tightens the IR typing rules around applications of closures.
When re-reading some code, I realized that the code in `mkPartialApp`
has a clear typo—`.object` and `type` should be swapped. However, it
doesn't matter, because later IR passes smooth out the mismatch here. It
makes more sense to be strict up-front and require applications of
closures to always return an `.object`.
This PR removes a rather ugly hack in the module system, exposing the
bodies of theorems whose type mention `WellFounded`.
The original motivation was that reducing well-founded definitions (e.g.
in `by rfl`) requires reducing proofs, so they need to be available.
But reducing proofs is generally fraught with peril, and we have been
nudging our users away from using it for a while, e.g. in #5182. Since
the module system is opt-in and users will gradually migrate to it, it
may be reasonable to expect them to avoid reducing well-founded
recursion in the process
This way we don't need hacks like this (which, without evidence, I
believe would be incomplete anyways) and we get the nice guarantee that
within the module system, theorems bodies are always private.
This PR removes some unnecessary `Decidable*` instance arguments by
using lemmas in the `Classical` namespace instead of the `Decidable`
namespace.
This might lead to some additional dependency on classical axioms, but
large parts of the standard library are relying on them either way.
This PR ensures that the state is reverted when compilation using the
new compiler fails. This is especially important for noncomputable
sections where the compiler might generate half-compiled functions which
may then be erroneously used while compiling other functions.
This PR generalizes the `a^(m+n)` grind normalizer to any semirings.
Example:
```
variable [Field R]
example (M : R) (h₀ : M ≠ 0) {n : Nat} (hn : n > 0) : M ^ n / M = M ^ (n - 1) := by
cases n <;> grind
```
This PR adds support for representing more inductive as enums,
summarized up as extending support to those that fail to be enums
because of parameters or irrelevant fields. While this is nice to have,
it is actually motivated by correctness of a future desired
optimization. The existing type representation is unsound if we
implement `object`/`tobject` distinction between values guaranteed to be
an object pointer and those that may also be a tagged scalar. In
particular, types like the ones added in this PR's tests would have all
of their constructors encoded via tagged values, but under the natural
extension of the existing rules of type representation they would be
considered `object` rather than `tobject`.
This PR converts the `lowerEnumToScalarType?` cache to a cache of IR
types of named types. This is more sensible than just focusing on the
enum optimization, and due to uniform representation of polymorphism we
have to compile `Constant T1` and `Constant T2` to the same
representation.
Bumps
[dawidd6/action-download-artifact](https://github.com/dawidd6/action-download-artifact)
from 10 to 11.
<details>
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href="https://github.com/dawidd6/action-download-artifact/releases">dawidd6/action-download-artifact's
releases</a>.</em></p>
<blockquote>
<h2>v11</h2>
<p><strong>Full Changelog</strong>: <a
href="https://github.com/dawidd6/action-download-artifact/compare/v10...v11">https://github.com/dawidd6/action-download-artifact/compare/v10...v11</a></p>
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href="ac66b43f0e"><code>ac66b43</code></a>
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Update README.md</li>
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This PR changes ToIR to call `lowerEnumToScalarType?` with
`ConstructorVal.induct` rather than the name of the constructor itself.
This was an oversight in some refactoring of code in the new compiler
before landing it. It should not affect runtime of compiled code (due to
the extra tagging/untagging being optimized by LLVM), but it does make
IR for the interpreter slightly more efficient.
This PR fixes spacing in the `grind` attribute and tactic syntax.
Previously `@[grind]` was incorrectly pretty-printed as `@[grind ]`, and
`grind [...] on_failure ...` was pretty-printed `grind [...]on_failure
...`. Fixes that `on_failure` was reserved as keyword.
This PR moves the construction of the `Option.SomeLtNone.lt` (and `le`)
relation, in which `some` is less than `none`, to
`Init.Data.Option.Basic` and moves well-foundedness proofs for
`Option.lt` and `Option.SomeLtNone.lt` into `Init.Data.Option.Lemmas`.
This PR improves the “expected type mismatch” error message by omitting
the type's types when they are defeq, and putting them into separate
lines when not.
I found it rather tediuos to parse the error message when the expected
type is long, because I had to find the `:` in the middle of a large
expression somewhere. Also, when both are of sort `Prop` or `Type` it
doesn't add much value to print the sort (and it’s only one hover away
anyways).
This PR further improves release automation, automatically incorporating
material from `nightly-testing` and `bump/v4.X.0` branches in the bump
PRs to downstream repositories.
This PR adjusts the experimental module system to not import the IR of
non-`meta` declarations. It does this by replacing such IR with opaque
foreign declarations on export and adjusting the new compiler
accordingly.
This PR should not be merged before the new compiler.
Based on #8664.
This PR fixes a bug introduce by #9081 where the source file was dropped
from the module input trace and some entries were dropped from the
module job log.
This PR moves the constructor layout code from C++ to Lean. When
writing the new compiler, we just reused the existing C++ code,
even though it was a bit inconvenient, because we wanted to
ensure that constructor layout always matched the existing
compiler.
This fixes#2589 by handling struct field types just like any
other type being lowered, and thus applying the trivial structure
optimization in the process. Originally, I wanted to port the
code to Lean without any functional changes, but I found that
it took less code to just implement it "correctly" and get this
fix as a consequence than to emulate the bugs of the existing
C++ implementation.
This PR ensures that `mspec` uses the configured transparency setting
and makes `mvcgen` use default transparency when calling `mspec`.
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR further updates release automation. The per-repository update
scripts `script/release_steps.py` now actually performs the tests,
rather than outputting a script for the release manager to run line by
line. It's been tested on `v4.21.0` (i.e. the easy case of a stable
release), and we'll debug its behaviour on `v4.22.0-rc1` tonight.
This PR fixes some bugs with the local Lake artifact cache and cleans up
the surrounding API. It also adds the ability to opt-in to the cache on
packages without `enableArtifactCache` set using the
`LAKE_ARTIFACT_CACHE` environment variable.
Bug-wise, this fixes an issue where cached executable did not have right
permissions to run on Unix systems and a bug where cached artifacts
would not be invalidated on changes. Lake also now writes a trace file
to local build directory if there is none when fetching an artifact from
the cache. This trace has a new `synthetic` field set to `true` to
distinguish it from traces produced by full builds.
This PR removes the `irreducible` attribute from `letFun`, which is one
step toward removing special `letFun` support; part of #9086.
Removing the attribute seems to break some `module` tests in stage2.
This PR improves `pp.oneline`, where it now preserves tags when
truncating formatted syntax to a single line. Note that the `[...]`
continuation does not yet have any functionality to enable seeing the
untruncated syntax. Closes#3681.
This PR enables transforming nondependent `let`s into `have`s in a
number of contexts: the bodies of nonrecursive definitions, equation
lemmas, smart unfolding definitions, and types of theorems. A motivation
for this change is that when zeta reduction is disabled, `simp` can only
effectively rewrite `have` expressions (e.g. `split` uses `simp` with
zeta reduction disabled), and so we cache the nondependence calculations
by transforming `let`s to `have`s. The transformation can be disabled
using `set_option cleanup.letToHave false`.
Uses `Meta.letToHave`, introduced in #8954.
This PR adds a `warn.sorry` option (default true) that logs the
"declaration uses 'sorry'" warning when declarations contain `sorryAx`.
When false, the warning is not logged.
Closes#8611 (assuming that one would set `warn.sorry` as an extra flag
when building).
Other change: Uses `warn.sorry` when creating auxiliary declarations in
`structure` elaborator, to suppress irrelevant 'sorry' warnings.
We could include the sorries themselves in the message if they are
labeled, letting users "go to definition" to see where the sorries are
coming from.
In an earlier version, added additional information to the warning when
it is a synthetic sorry, since these can be caused by elaboration bugs
and they can also be caused by elaboration failures in previous
declarations. This idea needs some more work, so it's not included.
This PR fixes a bug with Lake where the job monitor would sit on a
top-level build (e.g., `mathlib/Mathlib:default`) instead of reporting
module build progress.
The issue was actually simpler than it initially appeared. The wrong
portion of the module build was being registered to job monitor. Moving
it to right place fixes it, no job priorities necessary.
This PR adds an unexpander for `OfSemiring.toQ`. This an auxiliary
function used by the `ring` module in `grind`, but we want to reduce the
clutter in the diagnostic information produced by `grind`. Example:
```
example [CommSemiring α] [AddRightCancel α] [IsCharP α 0] (x y : α)
: x^2*y = 1 → x*y^2 = y → x + y = 2 → False := by
grind
```
produces
```
[ring] Ring `Ring.OfSemiring.Q α` ▼
[basis] Basis ▼
[_] ↑x + ↑y + -2 = 0
[_] ↑y + -1 = 0
```
This PR uses the commutative ring module to normalize nonlinear
polynomials in `grind cutsat`. Examples:
```lean
example (a b : Nat) (h₁ : a + 1 ≠ a * b * a) (h₂ : a * a * b ≤ a + 1) : b * a^2 < a + 1 := by
grind
example (a b c : Int) (h₁ : a + 1 + c = b * a) (h₂ : c + 2*b*a = 0) : 6 * a * b - 2 * a ≤ 2 := by
grind
```
This PR implements support for the type class `LawfulEqCmp`. Examples:
```lean
example (a b c : Vector (List Nat) n)
: b = c → a.compareLex (List.compareLex compare) b = o → o = .eq → a = c := by
grind
example [Ord α] [Std.LawfulEqCmp (compare : α → α → Ordering)] (a b c : Array (Vector (List α) n))
: b = c → o = .eq → a.compareLex (Vector.compareLex (List.compareLex compare)) b = o → a = c := by
grind
```
This PR adjusts the experimental module system to make `private` the
default visibility modifier in `module`s, introducing `public` as a new
modifier instead. `public section` can be used to revert the default for
an entire section, though this is more intended to ease gradual adoption
of the new semantics such as in `Init` (and soon `Std`) where they
should be replaced by a future decl-by-decl re-review of visibilities.
This PR implements support for equations `<num> = 0` in rings and fields
of unknown characteristic. Examples:
```lean
example [Field α] (a : α) : (2 * a)⁻¹ = a⁻¹ / 2 := by grind
example [Field α] (a : α) : (2 : α) ≠ 0 → 1 / a + 1 / (2 * a) = 3 / (2 * a) := by grind
example [CommRing α] (a b : α) (h₁ : a + 2 = a) (h₂ : 2*b + a = 0) : a = 0 := by
grind
example [CommRing α] (a b : α) (h₁ : a + 6 = a) (h₂ : b + 9 = b) (h₂ : 3*b + a = 0) : a = 0 := by
grind
example [CommRing α] (a b : α) (h₁ : a + 6 = a) (h₂ : b + 9 = b) (h₂ : 3*b + a = 0) : a = 0 := by
grind
example [CommRing α] (a b : α) (h₁ : a + 2 = a) (h₂ : b = 0) : 4*a + b = 0 := by
grind
example [CommRing α] (a b c : α) (h₁ : a + 6 = a) (h₂ : c = c + 9) (h : b + 3*c = 0) : 27*a + b = 0 := by
grind
```
This PR proves that the default `toList`, `toListRev` and `toArray`
functions on slices can be described in terms of the slice iterator.
Relying on new lemmas for the `uLift` and `attachWith` iterator
combinators, a more concrete description of said functions is given for
`Subarray`.
This PR introduces a simple variable-reordering heuristic for `cutsat`.
It is needed by the `ToInt` adapter to support finite types such as
`UInt64`. The current encoding into `Int` produces large coefficients,
which can enlarge the search space when an unfavorable variable order is
used. Example:
```lean
example (a b c : UInt64) : a ≤ 2 → b ≤ 3 → c - a - b = 0 → c ≤ 5 := by
grind
```
This PR implements support for equalities and disequalities in `grind
cutsat`. We still have to improve the encoding. Examples:
```lean
example (a b c : Fin 11) : a ≤ 2 → b ≤ 3 → c = a + b → c ≤ 5 := by
grind
example (a : Fin 2) : a ≠ 0 → a ≠ 1 → False := by
grind
```
This PR enables the error explanation widget in named error messages.
Note that the displayed links won't work until the new manual version is
released (unless overriding `LEAN_MANUAL_ROOT` with a suitably recent
manual build).
This PR replaces all usages of `[:]` slice notation in `src` with the
new `[...]` notation in production code, tests and comments. The
underlying implementation of the `Subarray` functions stays the same.
Notation cheat sheet:
* `*...*` is the doubly-unbounded range.
* `*...a` or `*...<a` contains all elements that are less than `a`.
* `*...=a` contains all elements that are less than or equal to `a`.
* `a...*` contains all elements that are greater than or equal to `a`.
* `a...b` or `a...<b` contains all elements that are greater than or
equal to `a` and less than `b`.
* `a...=b` contains all elements that are greater than or equal to `a`
and less than or equal to `b`.
* `a<...*` contains all elements that are greater than `a`.
* `a<...b` or `a<...<b` contains all elements that are greater than `a`
and less than `b`.
* `a<...=b` contains all elements that are greater than `a` and less
than or equal to `b`.
Benchmarks have shown that importing the iterator-backed parts of the
polymorphic slice library in `Init` impacts build performance. This PR
avoids this problem by separating those parts of the library that do not
rely on iterators from those those that do. Whereever the new slice
notation is used, only the iterator-independent files are imported.
This PR implements support for strict inequalities in the `ToInt`
adapter used in `grind cutsat`. Example:
```lean
example (a b c : Fin 11) : c ≤ 9 → a ≤ b → b < c → a < c + 1 := by
grind
```
This PR fixes a type error in `mvcgen` and makes it turn fewer natural
goals into synthetic opaque ones, so that tactics such as `trivial` may
instantiate them more easily.
---------
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR makes `mspec` detect more viable assignments by `rfl` instead of
generating a VC.
---------
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
Co-authored-by: Rishikesh Vaishnav <rishhvaishnav@gmail.com>
This PR adds a Mathlib-like testing and feedback system for the
reference manual. Lean PRs will receive comments that reflect the status
of the language reference with respect to the PR.
This PR adds test cases for the VC generator and implements a few small
and tedious fixes to ensure they pass.
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR extends the list of acceptable characters to all the french ones
as well as some others,
by adding characters from the Latin-1-Supplement add Latin-Extended-A
unicode block.
This PR adds DNS functions to the standard library
---------
Co-authored-by: Henrik Böving <hargonix@gmail.com>
Co-authored-by: Markus Himmel <markus@himmel-villmar.de>
This PR adds a function called `lean_setup_libuv` that initializes
required LIBUV components. It needs to be outside of
`lean_initialize_runtime_module` because it requires `argv` and `argc`
to work correctly.
---------
Co-authored-by: Markus Himmel <markus@lean-fro.org>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
This PR fixes a couple of bootstrapping-related hiccups in the newly
added `Std.Do` module. More precisely,
* The `spec` attribute syntax was registered under the wrong name and
its implementation needed to use a different priority parser
* Elaborators and delaborators for `MGoal`, `Triple`, `PostCond` and
`PostCond.total` were broken and are now properly builtin
* `Std.Do` should not transitively import `Std.Tactic.Do.Syntax`
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR fixes a bug where semantic highlighting would only highlight
keywords that started with an alphanumeric character. Now, it uses
`Lean.isIdFirst`.
This PR provides an iterator combinator that lifts the emitted values
into a higher universe level via `ULift`. This combinator is then used
to make the subarray iterators universe-polymorphic. Previously, they
were only available for `Subarray α` if `α : Type`.
This PR implements support for (non strict) `ToInt` inequalities in
`grind cutsat`. `grind cutsat` can solve simple problems such as:
```lean
example (a b c : Fin 11) : a ≤ b → b ≤ c → a ≤ c := by
grind
example (a b c : Fin 11) : c ≤ 9 → a ≤ b → b ≤ c → a ≤ c + 1 := by
grind
example (a b c : UInt8) : a ≤ b → b ≤ c → a ≤ c := by
grind
example (a b c d : UInt32) : a ≤ b → b ≤ c → c ≤ d → a ≤ d := by
grind
```
Next step: strict inequalities, and equalities.
This PR introduces a local artifact cache for Lake. When enabled, Lake
will shared build artifacts (built files) across different instances of
the same package using an input- and content-addressed cache.
To enable support for the local cache, packages must set
`enableArtifactCache := true` in their package configuration. The reason
for this is twofold. This feature is new and experimental, so it should
be opt-in. Also, some packages may need to disable it as the cache
entails that artifacts are no longer necessarily available within the
build directory, which can break custom build scripts.
The cache location is determined by the system configuration. Lake's
first preference is to store it under the Lean toolchain in a
`lake/cache` directory. If Elan is not available, Lake will store it in
common system location (e.g., `$XDG_CACHE_HOME/lake`, or
`~/.cache/lake`). On an exotic system where neither of these exist, the
cache will be disabled. Users can override this location through the
`LAKE_CACHE_DIR` environment variable. If set to empty, caching will be
disabled.
The cache is both input and content-addressed. Mappings from input hash
to output content hash(es) are stored in a per-package JSON Lines file
(e.g., `<cache-dir>/inputs/<pkg-name>.jsonl`). Thus, mappings are shared
across different instances of a package, but not between packages. The
output content hashes are also now stored in trace files in a new
`outputs` field. The value of this field can be either a single hash or
an object of multiple content hashes for targets which produce multiple
artifacts (e.g., Lean module builds). Separately, artifacts are stored
in a single flat content-addressed cache (e.g.,
`<cache-dir>/artifacts/<hash>.art`. Artifacts are therefore shared
across all cache-enabled packages.
Module `*.olean` and and `*.ilean` artifacts are cached. However, each
package will still copy the files to their build directory, as Lean and
the server currently expect them to be at a specific path. This will be
changed for `*.olean` files when the performance issues with
pre-resolving modules in Lake for `lean --setup` are solved.
This PR adds the following features to `simp`:
- A routine for simplifying `have` telescopes in a way that avoids
quadratic complexity arising from locally nameless expression
representations, like what #6220 did for `letFun` telescopes.
Furthermore, simp converts `letFun`s into `have`s (nondependent lets),
and we remove the #6220 routine since we are moving away from `letFun`
encodings of nondependent lets.
- A `+letToHave` configuration option (enabled by default) that converts
lets into haves when possible, when `-zeta` is set. Previously Lean
would need to do a full typecheck of the bodies of `let`s, but the
`letToHave` procedure can skip checking some subexpressions, and it
modifies the `let`s in an entire expression at once rather than one at a
time.
- A `+zetaHave` configuration option, to turn off zeta reduction of
`have`s specifically. The motivation is that dependent `let`s can only
be dsimped by let, so zeta reducing just the dependent lets is a
reasonable way to make progress. The `+zetaHave` option is also added to
the meta configuration.
- When `simp` is zeta reducing, it now uses an algorithm that avoids
complexity quadratic in the depth of the let telescope.
- Additionally, the zeta reduction routines in `simp`, `whnf`, and
`isDefEq` now all are consistent with how they apply the `zeta`,
`zetaHave`, and `zetaUnused` configurations.
The `letToFun` option is addressing a TODO in `getSimpLetCase` ("handle
a block of nested let decls in a single pass if this becomes a
performance problem").
Performance should be compared to before #8804, which temporarily
disabled the #6220 optimizations for `letFun` telescopes.
Good kernel performance depends on carefully handling the `have`
encoding. Due to the way the kernel instantiates bvars (it does *not*
beta reduce when instantiating), we cannot use congruence theorems of
the form `(have x := v; f x) = (have x ;= v'; f' x)`, since the bodies
of the `have`s will not be syntactically equal, which triggers zeta
reduction in the kernel in `is_def_eq`. Instead, we work with `f v = f'
v'`, where `f` and `f'` are lambda expressions. There is still zeta
reduction, but only when converting between these two forms at the
outset of the generated proof.
This PR adds `BitVec.toFin_(sdiv, smod, srem)` and `BitVec.toNat_srem`.
The strategy for the `rhs` of the `toFin_*` lemmas is to consider what
the corresponding `toNat_*` theorems do and push the `toFin` closerto
the operands. For the `rhs` of `BitVec.toNat_srem` I used the same
strategy as `BitVec.toNat_smod`.
This PR closes#3791, making sure that the Syntax formatter inserts
whitespace before and after comments in the leading and trailing text of
Syntax to avoid having comments comment out any following syntax, and to
avoid comments' lexical syntax from being interpreted as being part of
another syntax. If the text contains newlines before or after any
comments, they are formatted as hard newlines rather than soft newlines.
For example, `--` comments will have a hard newline after them. Note:
metaprograms generating Syntax with comments should be sure to include
newlines at the ends of `--` comments.
This PR improves the error messages produced by invalid projections and
field notation. It also adds a hint to the "function expected" error
message noting the argument to which the term is being applied, which
can be helpful for debugging spurious "function expected" messages
actually caused by syntax errors.
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This PR introduces a Hoare logic for monadic programs in
`Std.Do.Triple`, and assorted tactics:
* `mspec` for applying Hoare triple specifications
* `mvcgen` to turn a Hoare triple proof obligation `⦃P⦄ prog ⦃Q⦄` into
pure verification conditoins (i.e., without any traces of Hoare triples
or weakest preconditions reminiscent of `prog`). The resulting
verification conditions in the stateful logic of `Std.Do.SPred` can be
discharged manually with the tactics coming with its custom proof mode
or with automation such as `simp` and `grind`.
This is pre-release of a planned feature and not yet intended for
production use. We are grateful for feedback of early adopters, though.
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR introduces polymorphic slices in their most basic form. They
come with a notation similar to the new range notation. `Subarray` is
now also a slice and can produce an iterator now. It is intended to
migrate more operations of `Subarray` to the `Slice` wrapper type to
make them available for slices of other types, too.
The PR also moves the `filterMap` combinators into `Init` because they
are used internally to implement iterators on array slices.
This PR adds the types `Std.ExtDTreeMap`, `Std.ExtTreeMap` and
`Std.ExtTreeSet` of extensional tree maps and sets. These are very
similar in construction to the existing extensional hash maps with one
exception: extensional tree maps and sets provide all functions from
regular tree maps and sets. This is possible because in contrast to hash
maps, tree maps are always ordered.
This PR adds a logic of stateful predicates SPred to Std.Do in order to
support reasoning about monadic programs. It comes with a dedicated
proof mode the tactics of which are accessible by importing
Std.Tactic.Do.
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR introduces ranges that are polymorphic, in contrast to the
existing `Std.Range` which only supports natural numbers.
Breakdown of core changes:
* `Lean.Parser.Basic`: Modified the number parser (`Lean.Parser.Basic`)
so that it will only consider a *single* dot to be part of a decimal
number. `1..` will no longer be parsed as `1.` followed by `.`, but as
`1` followed by `..`.
* The test `ellipsisProjIssue` ensures that `#check Nat.add ...succ`
produces a syntax error. After introducing the new range notation (see
below), it returns a different (less nice) error message. I updated the
test to reflect the new error message. (The error message will become
nicer as soon as a delaborator for the ranges is implemented. This is
out of scope for this PR.)
Breakdown of standard library changes:
Modified modules: `Init.Data.Range.Polymorphic` (added),
`Init.Data.Iterators`, `Std.Data.Iterators`
* Introduced the type `Std.PRange` that is parameterized over the type
in which the range operates and the shapes of the lower and upper bound.
* Introduced a new notation for ranges. Examples for this notation are:
`1...*`, `1...=3`, `1...<3`, `1<...=2`, `*...=3`.
* Defined lots of typeclasses for different capabilities of ranges,
depending on their shape and underlying type.
* Introduced `Iter(M).size`.
* Introduced the `Iter(M).stepSize n` combinator, which iterates over an
iterator with the given step size `n`. It will drop `n - 1` values
between every value it emits.
* Replaced `LawfulPureIterator` with a new and better typeclass
`LawfulDeterministicIterator`.
* Simplified some lemma statements in the iterator library such as
`IterM.toList_eq_match`, which unnecessarily matched over a `Subtype`,
hindering rewrites due to type dependencies.
Reasons for the concrete choice of notation:
* `lean4-cli` uses `...`-based notation for the `Cmd` notation and it
clashes with `...a` range notation.
* test `2461` fails when using two-dot-based notation because of the
existing `{ a.. }` notation.
This PR adds a generic `MonadLiftT Id m` instance. We do not implement a
`MonadLift Id m` instance because it would slow down instance resolution
and because it would create more non-canonical instances. This change
makes it possible to iterate over a pure iterator, such as `[1, 2,
3].iter`, in arbitrary monads.
This PR adds a new monadic interface for `Async` operations.
This is the design for the `Async` monad that I liked the most. The idea
was refined with the help of @tydeu. Before that, I had some
prerequisites in mind:
1. Good performance
2. Explicit `yield` points, so we could avoid using `bindTask` for every
lifted IO operation
3. A way to avoid creating an infinite chain of `Task`s during recursion
The 2 and 3 points are not covered in this PR, I wish I had a good
solution but right now only a few sketches of this.
### Explicit `yield` points
I thought this would be easy at first, but it actually turned out kinda
tricky. I ended up creating the `suspend` syntax, which is just a small
modification of the lift method (`<- ...`) syntax. It desugars to
`Suspend.suspend task fun _ => ...`. So something like:
```lean
do
IO.println "a"
IO.println "b"
let result := suspend (client.recv? 1024)
IO.println "c"
IO.println "d"
```
Would become:
```lean
Bind.bind (IO.println "a") fun _ =>
Bind.bind (IO.println "b") fun _ =>
Suspend.suspend (client.recv? 1024) fun message =>
Bind.bind (IO.println "c") fun _ =>
IO.println "d"
```
This makes things a bit more efficient. When using `bind`, we would try
to avoid creating a `Task` chain, and the `suspend` would be the only
place we use `Task.bind`. But there's a problem if we use `bind` with
something that needs `suspend`, it’ll block the whole task. Blocking is
the only way to prevent task accumulation when using plain `bind` inside
a structure like that:
```
inductive AsyncResult (ε σ α : Type u) where
| ok : α → σ → AsyncResult ε σ α
| error : ε → σ → AsyncResult ε σ α
| ofTask : Task (EStateM.Result ε σ α) → σ →AsyncResult ε σ α
```
Because we simply need to remove the `ofTask` and transform it into an
`ok`.
### Infinite chain of Tasks
If you create an infinite recursive function using `Task` (which is
super common in servers like HTTP ones), it can lead to a lot of memory
usage. Because those tasks get chained forever and won't be freed until
the function returns.
To get around that, I used CPS and instead of just calling `Task.bind`,
I’d spawn a new task and return an "empty" one like:
```lean
fun k => Task.bind (...) fun value => do k value; pure emptyTask
```
This works great with a CPS-style monad, but it generates a huge IR by
itself.
Just doing CPS alone was too much, though, because every lifted
operation created a new continuation and a `Task.bind`. So, I used it
with `suspend` and got a better performance, but the usage is not good
with `suspend`.
### The current monad
Right now, the monad I’m using is super simple. It doesn't solve the
earlier problems, but the API is clean, and the generated IR is small
enough. An example of how we should use it is:
```lean
-- A loop that repeatedly sends a message and waits for a reply.
partial def writeLoop (client : Socket.Client) (message : String) : Async (AsyncTask Unit) := async do
IO.println s!"sending: {message}"
await (← client.send (String.toUTF8 message))
if let some mes ← await (← client.recv? 1024) then
IO.println s!"received: {String.fromUTF8! mes}"
-- use parallel to avoid building up an infinite task chain
parallel (writeLoop client message)
else
IO.println "client disconnected from receiving"
-- Server’s main accept loop, keeps accepting and echoing for new clients.
partial def acceptLoop (server : Socket.Server) (promise : IO.Promise Unit) : Async (AsyncTask Unit) := async do
let client ← await (← server.accept)
await (← client.send (String.toUTF8 "tutturu "))
-- allow multiple clients to connect at the same time
parallel (writeLoop client "hi!!")
-- and keep accepting more clients, parallel again to avoid building up an infinite task chain
parallel (acceptLoop server promise)
-- A simple client that connects and sends a message.
def echoClient (addr : SocketAddress) (message : String) : Async (AsyncTask Unit) := async do
let socket ← Client.mk
await (← socket.connect addr)
parallel (writeLoop socket message)
-- TCP setup: bind, listen, serve, and run a sample client.
partial def mainTCP : Async Unit := do
let addr := SocketAddressV4.mk (.ofParts 127 0 0 1) 8080
let server ← Server.mk
server.bind addr
server.listen 128
-- promise exists since the server is (probably) never going to stop
let promise ← IO.Promise.new
let acceptAction ← acceptLoop server promise
await (← echoClient addr "hi!")
await acceptAction
await promise
-- Entry point
def main : IO Unit := mainTCP.wait
```
---------
Co-authored-by: Henrik Böving <hargonix@gmail.com>
Co-authored-by: Mac Malone <tydeu@hatpress.net>
This PR adjusts the `lean.redundantMatchAlt` error explanation to remove
the word "unprefixed," which the reference manual's style linter does
not recognize.
This PR refactors the juggling of universes in the linear
`noConfusionType` construction: Instead of using `PUnit.{…} → ` in the
to get the branches of `withCtorType` to the same universe level, we use
`PULift`.
This fixes https://github.com/leanprover/lean4/issues/8962, although
probably doesn’t solve all issues of that kind while level equality
checking is incomplete.
This PR updates the `solveMonoStep` function used in the `monotonicity`
tactic to check for definitional equality between the current goal and
the monotonicity proof obtained from a recursive call. This ensures
soundness by preventing incorrect applications when
`Lean.Order.PartialOrder` instances differ—an issue that can arise with
`mutual` blocks defined using the `partial_fixpoint` keyword, where
different `Lean.Order.CCPO` structures may be involved.
Closes https://github.com/leanprover/lean4/issues/8894.
This PR adds some missing `ToInt.X` typeclass instances for `grind`.
There are still several more to add (in particular, for `ToInt.Pow`),
but I am going to perform an intermediate refactor first.
This PR removes Lake's usage of `lean -R` and `moduleNameOfFileName` to
pass module names to Lean. For workspace names, it now relies on
directly passing the module name through `lean --setup`. For
non-workspace modules passed to `lake lean` or `lake setup-file`, it
uses a fixed module name of `_unknown`.
This means that `lake lean` and `lake setup-file` can be successfully
and consistently used on modules that do not lie under the working
directory or the workspace root.
This PR passes Lean options configured via CMake variables onto the Lake
build. For example, this will ensure CI' setting of `warningAsError` via
`LEAN_EXTRA_MAKE_OPTS` reaches Lake.
This PR both adds initial `@[grind]` annotations for `BitVec`, and uses
`grind` to remove many proofs from `BitVec/Lemmas`.
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
This PR adds `BitVec.(getElem, getLsbD, getMsbD)_(smod, sdiv, srem)`
theorems to complete the API for `sdiv`, `srem`, `smod`. Even though the
rhs is not particularly succint (it's hard to find a meaning for what it
means to have "the n-th bit of the result of a signed division/modulo
operation"), these lemmas prevent the need to `unfold` of operations.
---------
Co-authored-by: Kim Morrison <477956+kim-em@users.noreply.github.com>
This PR embeds a NatModule into its IntModule completion, which is
injective when we have AddLeftCancel, and monotone when the modules are
ordered. Also adds some (failing) grind test cases that can be verified
once `grind` uses this embedding.
This PR changes the CI setup to generate `lean-pr-testing-NNNN` branches
for Mathlib on the `leanprover-community/mathlib4-nightly-testing` fork,
rather than on the main repo.
This PR add instances showing that the Grothendieck (i.e. additive)
envelope of a semiring is an ordered ring if the original semiring is
ordered (and satisfies ExistsAddOfLE), and in this case the embedding is
monotone.
This PR improves the case splitting strategy used in `grind`, and
ensures `grind` also considers simple `match`-conditions for
case-splitting. Example:
```lean
example (x y : Nat)
: 0 < match x, y with
| 0, 0 => 1
| _, _ => x + y := by -- x or y must be greater than 0
grind
```
This PR adds configuration options to the `let`/`have` tactic syntaxes.
For example, `let (eq := h) x := v` adds `h : x = v` to the local
context. The configuration options are the same as those for the
`let`/`have` term syntaxes.
This PR changes `toLCNF` to stop caching translations of expressions
upon seeing an expression marked `never_extract`. This is more
coarse-grained than it needs to be, but it is difficult to do any
better, as the new compiler's `Expr` cache is based on structural
identity (rather than the pointer identity of the old compiler).
The newly added `tests/compiler/never_extract.lean` is also converted
into a `run` tests, because during development I found the order of the
output to `stderr` to be a bit finicky. The reason for making it a
`compiler` test in the first place is that closed term decls work
slightly differently between native code and the interpreter, and it
would be good to test both, but we already have separate tests for
`never_extract` and closed term extraction.
Fixes#8944.
This PR adds a procedure that efficiently transforms `let` expressions
into `have` expressions (`Meta.letToHave`). This is exposed as the
`let_to_have` tactic.
It uses the `withTrackingZetaDelta` technique: the expression is
typechecked, and any `let` variables that don't enter the zeta delta set
are nondependent. The procedure uses a number of heuristics to limit the
amount of typechecking performed. For example, it is ok to skip
subexpressions that do not contain fvars, mvars, or `let`s.
This PR implements support for normalization for commutative semirings
that do not implement `AddRightCancel`. Examples:
```lean
variable (R : Type u) [CommSemiring R]
example (a b c : R) : a * (b + c) = a * c + b * a := by grind
example (a b : R) : (a + b)^2 = a^2 + 2 * a * b + b^2 := by grind
example (a b : R) : (a + 2 * b)^2 = a^2 + 4 * a * b + 4 * b^2 := by grind
example (a b : R) : (a + 2 * b)^2 = 4 * b^2 + b * 4 * a + a^2 := by grind
```
This PR fixes the handling of the `never_extract` attribute in the
compiler's CSE pass. There is an interesting debate to be had about
exactly how hard the compiler should try to avoid duplicating anything
that transitively uses `never_extract`, but this is the simplest form
and roughly matches the check in the old compiler (although due to
different handling of local function decls in the two compilers, the
consequences might be slightly different).
This gets half of the way to #8944.
This PR adds support to the server for the new module setup process by
changing how `lake setup-file` is used.
In the new server setup, `lake setup-file` is invoked with the file name
of the edited module passed as a CLI argument and with the parsed header
passed to standard input in JSON form. Standard input is used to avoid
potentially exceeding the CLI length limits on Windows. Lake will build
the module's imports along with any other dependencies and then return
the module's workspace configuration via JSON (now in the form of
`ModuleSetup`). The server then post-processes this configuration a bit
and returns it back to the Lean language processor.
The server's header is currently only fully respected by Lake for
external modules (files that are not part of any workspace library). For
workspace modules, the saved module header is currently used to build
imports (as has been done since #7909). A follow-up Lake PR will align
both cases to follow the server's header.
Lean search paths (e.g., `LEAN_PATH`, `LEAN_SRC_PATH`) are no longer
negotiated between the server and Lake. These environment variables are
already configured during sever setup by `lake serve` and do not change
on a per-file basis. Lake can also pre-resolve the `.olean` files of
imports via the `importArts` field of `ModuleSetup`, limiting the
potential utility of communicating `LEAN_PATH`.
This PR skips attempting to compute a module name from the file name and
root directory (i.e., `lean -R`) if a name is already provided via `lean
--setup`.
This is accomplished by porting the rest of the frontend code in the
`try` block to Lean.
This PR adds explanations for a few errors concerning noncomputability,
redundant match alternatives, and invalid inductive declarations.
These adopt a lower-case error naming style, which is also applied to
existing error explanation tests.
This PR upgrades the `math` template for `lake init` and `lake new` to
configures the new project to meet rigorous Mathlib maintenance
standards. In comparison with the previous version (now available as
`lake new ... math-lax`), this automatically provides:
* Strict linting options matching Mathlib.
* GitHub workflow for automatic upgrades to newer Lean and Mathlib
releases.
* Automatic release tagging for toolchain upgrades.
* API documentation generated by
[doc-gen4](https://github.com/leanprover/doc-gen4) and hosted on
`github.io`.
* README with some GitHub-specific instructions.
The previous edition of the template is still available, renamed to
`math-lax`.
---------
Co-authored-by: Mac Malone <tydeu@hatpress.net>
This PR introduces antitonicity lemmas that support the elaboration of
mixed inductive-coinductive predicates defined using the
`least_fixpoint` / `greatest_fixpoint` constructs.
For instance, the following definition elaborates correctly because all
occurrences of the inductively defined predicate `tock `within the
coinductive definition of `tick` appear in negative positions. The dual
situation applies to the definition of `tock`:
```
mutual
def tick : Prop :=
tock → tick
greatest_fixpoint
def tock : Prop :=
tick → tock
least_fixpoint
end
```
This PR allows `simp` to recognize and warn about simp lemmas that are
likely looping in the current simp set. It does so automatically
whenever simplification fails with the dreaded “max recursion depth”
error fails, but it can be made to do it always with `set_option
linter.loopingSimpArgs true`. This check is not on by default because it
is somewhat costly, and can warn about simp calls that still happen to
work.
This closes#5111. In the end, this implemented much simpler logic than
described there (and tried in the abandoned #8688; see that PR
description for more background information), but it didn’t work as well
as I thought. The current logic is:
“Simplify the RHS of the simp theorem, complain if that fails”.
It is a reasonable policy for a Lean project to say that all simp
invocation should be so that this linter does not complain. Often it is
just a matter of explicitly disabling some simp theorems from the
default simp set, to make it clear and robust that in this call, we do
not want them to trigger. But given that often such simp call happen to
work, it’s too pedantic to impose it on everyone.
This PR adds the `+generalize` option to the `let` and `have` syntaxes.
For example, `have +generalize n := a + b; body` replaces all instances
of `a + b` in the expected type with `n` when elaborating `body`. This
can be likened to a term version of the `generalize` tactic. One can
combine this with `eq` in `have +generalize (eq := h) n := a + b; body`
as an analogue of `generalize h : n = a + b`.
This PR finishes post-stage0-cleanup after #8914 and #8929. Also:
- adds configuration options for `haveI` and `letI` terms.
- adds `letConfig` parser alias
This PR implements first-class support for nondependent let expressions
in the elaborator; recall that a let expression `let x : t := v; b` is
called *nondependent* if `fun x : t => b` typechecks, and the notation
for a nondependent let expression is `have x := v; b`. Previously we
encoded `have` using the `letFun` function, but now we make use of the
`nondep` flag in the `Expr.letE` constructor for the encoding. This has
been given full support throughout the metaprogramming interface and the
elaborator. Key changes to the metaprogramming interface:
- Local context `ldecl`s with `nondep := true` are generally treated as
`cdecl`s. This is because in the body of a `have` expression the
variable is opaque. Functions like `LocalDecl.isLet` by default return
`false` for nondependent `ldecl`s. In the rare case where it is needed,
they take an additional optional `allowNondep : Bool` flag (defaults to
`false`) if the variable is being processed in a context where the value
is relevant.
- Functions such as `mkLetFVars` by default generalize nondependent let
variables and create lambda expressions for them. The
`generalizeNondepLet` flag (default true) can be set to false if `have`
expressions should be produced instead. **Breaking change:** Uses of
`letLambdaTelescope`/`mkLetFVars` need to use `generalizeNondepLet :=
false`. See the next item.
- There are now some mapping functions to make telescoping operations
more convenient. See `mapLetTelescope` and `mapLambdaLetTelescope`.
There is also `mapLetDecl` as a counterpart to `withLetDecl` for
creating `let`/`have` expressions.
- Important note about the `generalizeNondepLet` flag: it should only be
used for variables in a local context that the metaprogram "owns". Since
nondependent let variables are treated as constants in most cases, the
`value` field might refer to variables that do not exist, if for example
those variables were cleared or reverted. Using `mapLetDecl` is always
fine.
- The simplifier will cache its let dependence calculations in the
nondep field of let expressions.
- The `intro` tactic still produces *dependent* local variables. Given
that the simplifier will transform lets into haves, it would be
surprising if that would prevent `intro` from creating a local variable
whose value cannot be used.
Note that nondependence of lets is not checked by the kernel. To
external checker authors: If the elaborator gets the nondep flag wrong,
we consider this to be an elaborator error. Feel free to typecheck `letE
n t v b true` as if it were `app (lam n t b default) v` and please
report issues.
This PR follows up from #8751, which made sure the nondep flag was
preserved in the C++ interface.
This PR is a followup to #8914, fixing an oversight where
`letIdDeclBinders` is was not updated with the new format. This relies
on some bootstrapping code to stay in place, but we do bootstrap cleanup
that is currently possible.
This PR adds `IO.FS.Stream.readToEnd` which parallels
`IO.FS.Handle.readToEnd` along with its upstream definitions (i.e.,
`readBinToEndInto` and `readBinToEnd`). It also removes an unnecessary
`partial` from `IO.FS.Handle.readBinToEnd`.
This function is useful for reading, for example, all of standard input.
This PR generalizes `IO.FS.lines` with `IO.FS.Handle.lines` and adds the
parallel `IO.FS.Stream.lines` for streams.
The stream version is useful for reading, for example, the lines of
standard input.
This PR adds a linter (`linter.unusedSimpArgs`) that complains when a
simp argument (`simp [foo]`) is unused. It should do the right thing if
the `simp` invocation is run multiple times, e.g. inside `all_goals`. It
does not trigger when the `simp` call is inside a macro. The linter
message contains a clickable hint to remove the simp argument.
I chose to display a separate warning for each unused argument. This
means that the user has to click multiple times to remove all of them
(and wait for re-elaboration in between). But this just means multiple
endorphine kicks, and the main benefit over a single warning that would
have to span the whole argument list is that already the squigglies tell
the users about unused arguments.
This closes#4483.
Making Init and Std clean wrt to this linter revealed close to 1000
unused simp args, a pleasant experience for anyone enjoying tidying
things: #8905
The `.impure` LCNF `Phase` is not currently used, but was intended for a
potential future where the current `IR` passes (which operate on a
highly impure representation) were rewritten to operate on LCNF instead.
For several reasons, I don't think this is very likely to happen, and
instead we are more likely to remove some of the unnecessary differences
between LCNF and IR while keeping them distinct.
This PR modifies `let` and `have` term syntaxes to be consistent with
each other. Adds configuration options; for example, `have` is
equivalent to `let +nondep`, for *nondependent* lets. Other options
include `+usedOnly` (for `let_tmp`), `+zeta` (for `letI`/`haveI`), and
`+postponeValue` (for `let_delayed)`. There is also `let (eq := h) x :=
v; b` for introducing `h : x = v` when elaborating `b`. The `eq` option
works for pattern matching as well, for example `let (eq := h) (x, y) :=
p; b`.
Future PRs will add these options to tactic syntax, once a stage0 update
has been done.
This PR implements support for (commutative) semirings in `grind`. It
uses the Grothendieck completion to construct a (commutative) ring
`Lean.Grind.Ring.OfSemiring.Q α` from a (commutative) semiring `α`. This
construction is mostly useful for semirings that implement
`AddRightCancel α`. Otherwise, the function `toQ` is not injective.
Examples:
```lean
example (x y : Nat) : x^2*y = 1 → x*y^2 = y → y*x = 1 := by
grind
example [CommSemiring α] [AddRightCancel α] (x y : α) : x^2*y = 1 → x*y^2 = y → y*x = 1 := by
grind
example (a b : Nat) : 3 * a * b = a * b * 3 := by grind
example (k z : Nat) : k * (z * 2 * (z * 2 + 1)) = z * (k * (2 * (z * 2 + 1))) := by grind
example [CommSemiring α] [AddRightCancel α] [IsCharP α 0] (x y : α)
: x^2*y = 1 → x*y^2 = y → x + y = 1 → False := by
grind
```
This PR makes `simp` consult its own cache more often, to avoid
replicating work.
Before, the simp cache was checked upon entry of `simpImpl` only, which
then calls `simpLoop`, which recursively iterates the `pre`-lemmas,
without checking the cache again.
Now, `simpLoop` itself checks the cache. This seems more principled,
given that `simpLoop` is actually putting entries into the cache for
each of its calls, so it’s more uniform if it checks the cache itself.
This avoids repeated rewrites. For example given
```
theorem ab : a = b := testSorry
theorem bc : b = c := testSorry
example (h : P c) : P b ∧ P a := by simp [ab, bc, h]
```
simp would rewrite `b ==> c` twice (once as part of `b ==> c` and then
again as part of `a ==> b ==> c`). And it’d be order dependent: With
```
example (h : P c) : P a ∧ P b := by simp [ab, bc, h]
```
the `a ==> b ==> c` chain would insert `b ==> c` into the cache, and
picked up by `simpImpl` when rewriting `P b`.
With this change, `b ==> c` is performed only once in both examples.
Instruction counts on stdlib and mathlib both show a mild improvement
across the board (0.5%), with individual modules improving by up to 4%
in stdlib and even more in mathlib.
(This does not check the cache before applying `post`, which explains
where there are still some repeated rewrites in the trace logs. But I’m
less sure about inserting a cache check here and so I am treading
carefully here. It’s also going to be at most one `post` application
that’s duplicated, because if `post` returns `.visit`, we go back to
`pre` and thus a cache check.)
This PR refactors the way simp arguments are elaborated: Instead of
changing the `SimpTheorems` structure as we go, this elaborates each
argument to a more declarative description of what it does, and then
apply those. This enables more interesting checks of simp arguments that
need to happen in the context of the eventually constructed simp context
(the checks in #8688), or after simp has run (unused argument linter
#8901).
The new data structure describing an elaborated simp argument isn’t the
most elegant, but follows from the code.
While I am at it, move handling of `[*]` into `elabSimpArgs`. Downstream
adaption branches exist (but may not be fully up to date because of the
permission changes).
While I am at it, I cleaned up `SimpTheorems.lean` file a bit (sorting
declarations, mild renaming) and added documentation.
This PR make sure that the local instance cache calculation applies more
reductions. In #2199 there was an issue where metavariables could
prevent local variables from being considered as local instances. We use
a slightly different approach that ensures that, for example, `let`s at
the ends of telescopes do not cause similar problems. These reductions
were already being calculated, so this does not require any additional
work to be done.
Metaprogramming interface addition: the various forall telescope
functions that do reduction now have a `whnfType` flag (default false).
If it's true, then the callback `k` is given the WHNF of the type. This
is a free operation, since the telescope function already computes it.
This PR refactors `Lean.Grind.NatModule/IntModule/Ring.IsOrdered`.
We ensure the the diamond from `Ring` to `NatModule` via either
`Semiring` or `IntModule` is defeq, which was not previously the case.
---------
Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
This PR corrects the pretty printing of `grind` modifiers. Previously
`@[grind →]` was being pretty printed as `@[grind→ ]` (Space on the
right of the symbol, rather than left.) This fixes the pretty printing
of attributes, and preserves the presence of spaces after the symbol in
the output of `grind?`.
---------
Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
This PR implements a `finally` section following a (potentially empty)
`where` block. `where ... finally` opens a tactic sequence block in
which the goals are the unassigned metavariables from the definition
body and its auxiliary definitions that arise from use of `let rec` and
`where`.
This can be useful for discharging multiple proof obligations in the
definition body by a single invocation of a tactic such as `all_goals`:
```lean
example (i j : Nat) (xs : Array Nat) (hi : i < xs.size) (hj: j < xs.size) :=
match i with
| 0 => x
| _ => xs[i]'?_ + xs[j]'?_
where x := 13
finally all_goals assumption
```
---------
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR adds a logic of stateful predicates `SPred` to `Std.Do` in order
to support reasoning about monadic programs. It comes with a dedicated
proof mode the tactics of which are accessible by importing
`Std.Tactic.Do`.
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR removes an old workaround around non-implemented C++11 features
in the thread finalization.
This `ifdef` dates back to approximately 2015 as can be seen
[here](https://github.com/leanprover/lean3/blame/master/src/util/thread.cpp#L177),
the comments mention that it was originally implemented because not all
compilers at the time were able to support the C++11 `thread_local`
keyword. 10 years later this is hopefully the case and we can remove
this workaround.
There is an additional motivation for doing this,
`lean::initialize_thread` contains the following allocation:
```cpp
g_thread_finalizers_mgr = new thread_finalizers_manager;
```
this is supposed to be freed at some point but:
```cpp
// TODO(gabriel): race condition with thread finalizers
void delete_thread_finalizer_manager() {
// delete g_thread_finalizers_mgr;
// g_thread_finalizers_mgr = nullptr;
}
```
so `g_thread_finalizers_mgr` leaks upon repeated invocation of
`lean::initialize_thread`.
Note that Windows has already been using this alternative implementation
for a while so the alternative implementation has (hopefully) not rotten
away in the meantime.
This PR changes the definition of `DHashMap` to a structure. This makes
it more consistent with the other map types, which are generally defined
as structures. It also ensures that the type `DHashMap α β` is already
in weak head normal form, making it easier for `grind` to successfully
generate patterns for `DHashMap` lemmas.
Although `HEq` was abbreviated as `≍` in #8503, many instances of the
form `HEq x y` still remain.
Therefore, I searched for occurrences of `HEq x y` using the regular
expression `(?<![A-Za-z/@]|``)HEq(?![A-Za-z.])` and replaced as many as
possible with the form `x ≍ y`.
This PR adds doc-strings to the `Lean.Grind` algebra typeclasses, as
these will appear in the reference manual explaining how to extend
`grind` algebra solvers to new types. Also removes some redundant
fields.
This PR adds `@[expose]` annotations to terms that appear in `grind`
proof certificates, so `grind` can be used in the module system. It's
possible/likely that I haven't identified all of them yet.
This PR provides a compact formula for the MSB of the sdiv. Most of the
work in the PR involves handling the corner cases of division
overflowing (e.g. `intMin / -1 = intMin`)
---------
Co-authored-by: Luisa Cicolini <48860705+luisacicolini@users.noreply.github.com>
Co-authored-by: Tobias Grosser <github@grosser.es>
This PR introduces a `ForIn'` instance and a `size` function for
iterators in a minimal fashion. The `ForIn'` instance is not marked as
an instance because it is unclear which `Membership` relation is
sufficiently useful. The `ForIn'` instance existing as a `def` and
inducing the `ForIn` instance, it becomes possible to provide more
specialized `ForIn'` instances, with nice `Membership` relations, for
various types of iterators. The `size` function has no lemmas yet.
This PR adds support for throwing named errors with associated error
explanations. In particular, it adds elaborators for the syntax defined
in #8649, which use the error-explanation infrastructure added in #8651.
This includes completions, hovers, and jump-to-definition for error
names.
Note that another stage0 rebuild will be required to define explanations
using `register_error_explanation`.
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
Co-authored-by: Marc Huisinga <mhuisi@protonmail.com>
This PR moves parts of the iterator library from `Std` to `Init`. The
reason is that the polymorphic range API must be in `Init` and it
depends on the iterators.
This PR reintroduces the basics of `lean --setup` integration into Lake
without the module computation which is still undergoing performance
debugging in #8787.
Partially reverts #8736 and partially reimplements #8447.
This PR makes the `clear_value` tactic preserve the order of variables
in the local context. This is done by adding
`Lean.MVarId.withRevertedFrom`, which reverts all local variables
starting from a given variable, rather than only the ones that depend on
it.
Note: an alternative implementation might convert the ldecl to a cdecl
and then reset the meta cache. This assumes that there are no other
caches that might still remember the value of the ldecl.
This PR adds `grind` annotations relating `Nat.fold/foldRev/any/all` and
`Fin.foldl/foldr/foldlM/foldrM` to the corresponding operations on
`List.finRange`.
This PR adds theorems `BitVec.(toNat, toInt,
toFin)_shiftLeftZeroExtend`, completing the API for
`BitVec.shiftLeftZeroExtend`.
---------
Co-authored-by: Tobias Grosser <github@grosser.es>
Co-authored-by: Henrik Böving <hargonix@gmail.com>
This PR allow structures to have non-bracketed binders, making it
consistent with `inductive`.
The change allows the following to be written instead of having to write
`S (n)`:
```lean
structure S n where
field : Fin n
```
This PR removes the auto-generated `binductionOn` and `ibelow`
implementations for inductive types in favor of the improved `brecOn`
implementation from #7639.
This PR defines the embedding of a `CommSemiring` into its `CommRing`
envelope, injective when the `CommSemiring` is cancellative. This will
be used by `grind` to prove results in `Nat`.
This test is essentially disabled on `master`, because it prints
nothing. With the new compiler enabled, it prints names of functions
throughout the Lean codebase satisfying certain conditions. Even just
maintaining this on the new compiler branch got old pretty quickly, so I
can't imagine we'd ever want to deal with this on `master`.
This PR avoids importing all of `BitVec.Lemmas` and `BitVec.BitBlast`
into `UInt.Lemmas`. (They are still imported into `SInt.Lemmas`; this
seems much harder to avoid.)
This PR renames `BitVec.getLsb'` to `BitVec.getLsb`, now that older
deprecated definition occupying that name has been removed. (Similarly
for `BitVec.getMsb'`.)
This PR improves IR generation for constructors of inductive types that
are represented by scalars. Surprisingly, this isn't required for
correctness, because the boxing pass will fix it up. The extra `unbox`
operation it inserts shouldn't matter when compiling to native code,
because it's trivial for a C compiler to optimize, but it does matter
for the interpreter.
This PR adds a cache for constructor info in toIR. This is called for
all constructors, projections, and cases alternatives, so it makes sense
to cache.
This PR adds constant folding for Char.ofNat in LCNF simp. This
implicitly relies on the representation of `Char` as `UInt32` rather
than making a separate `.char` literal type, which seems reasonable as
`Char` is erased by the trivial structure optimization in `toMono`.
This PR implements equality elimination in `grind linarith`. The current
implementation supports only `IntModule` and `IntModule` +
`NoNatZeroDivisors`
This PR filters out all declarations from `Lean.*`, `*.Tactic.*`, and
`*.Linter.*` from the results of `exact?` and `rw?`.
---------
Co-authored-by: damiano <adomani@gmail.com>
Co-authored-by: Markus Himmel <markus@lean-fro.org>
This PR introduces the basic theory of ordered modules over Nat (i.e.
without subtraction), for `grind`. We'll solve problems here by
embedding them in the `IntModule` envelope.
This PR fixes a bug in `floatLetIn` where if one decl (e.g. a join
point) is floated into a case arm and it uses another decl (e.g. another
join point) that does not have any other existing uses in that arm, then
the second decl does not get floated in despite this being perfectly
legal. This was causing artificial array linearity issues in
`Lean.Elab.Tactic.BVDecide.LRAT.trim.useAnalysis`.
This PR adds the following instance
```
instance [Field α] [LinearOrder α] [Ring.IsOrdered α] : IsCharP α 0
```
The goal is to ensure we do not perform unnecessary case-splits in our
test suite.
This PR ensures the `grind linarith` module is activated for any type
that implements only `IntModule`. That is, the type does not need to be
a preorder anymore.
This PR makes Lean code generation respect the module name provided
through `lean --setup`.
This is accomplished by porting to Lean the portion of `shell.cpp` that
spans running the frontend to exiting the process. This makes it easier
to load the module setup and control how its name is passed to the code
generation functions. This port attempts to minimize the changes made to
Lean. It marks the new Lean functions `private` and tries to preserve as
faithfully as possible the behavior of the original C++ code. Exposing
the new Lean interface publicly and/or further improving the code now
that is written in Lean is left for the future.
This PR adds a module `Lean.Util.CollectLooseBVars` with a function
`Expr.collectLooseBVars` that collects the set of loose bound variables
in an expression. That is, it computes the set of all `i` such that
`e.hasLooseBVar i` is true.
This PR modifies the `structure` elaborator to add local terminfo for
structure fields and explicit parent projections, enabling "go to
definition" when there are dependent fields.
Terminfo for inherited fields is still missing.
This PR adds `have` forms of simp lemmas that will be used in a future
`have` simplifier. This depends on #8751 and future elaboration changes,
since these are meant to elaborate using `Expr.letE (nondep := true) ..`
expressions; for now they are duplicates of the `letFun_*` lemmas.
This PR adds the `nondep` field of `Expr.letE` to the C++ data model.
Previously this field has been unused, and in followup PRs the
elaborator will use it to encode `have` expressions (non-dependent
`let`s). The kernel does not verify that `nondep` is correctly applied
during typechecking. The `letE` delaborator now prints `have`s when
`nondep` is true, though `have` still elaborates as `letFun` for now.
Breaking change: `Expr.updateLet!` is renamed to `Expr.updateLetE!`.
This PR also fixes a bug in `Expr.letFun?` and `Expr.letFunAppArgs?`
when the body is not a lambda. In any case, these functions will be
removed once the `Expr.letE (nondep := true)` encoding of `have`
expressions is complete.
This PR implements the Rabinowitsch transformation for `Field`
disequalities in `grind`. For example, this transformation is necessary
for solving:
```lean
example [Field α] (a : α) : a^2 = 0 → a = 0 := by
grind
```
This PR improves the support for fields in `grind`. New supported
examples:
```lean
example [Field α] [IsCharP α 0] (x : α) : x ≠ 0 → (4 / x)⁻¹ * ((3 * x^3) / x)^2 * ((1 / (2 * x))⁻¹)^3 = 18 * x^8 := by grind
example [Field α] (a : α) : 2 * a ≠ 0 → 1 / a + 1 / (2 * a) = 3 / (2 * a) := by grind
example [Field α] [IsCharP α 0] (a : α) : 1 / a + 1 / (2 * a) = 3 / (2 * a) := by grind
example [Field α] [IsCharP α 0] (a b : α) : 2*b - a = a + b → 1 / a + 1 / (2 * a) = 3 / b := by grind
example [Field α] [NoNatZeroDivisors α] (a : α) : 1 / a + 1 / (2 * a) = 3 / (2 * a) := by grind
example [Field α] {x y z w : α} : x / y = z / w → y ≠ 0 → w ≠ 0 → x * w = z * y := by grind
example [Field α] (a : α) : a = 0 → a ≠ 1 := by grind
example [Field α] (a : α) : a = 0 → a ≠ 1 - a := by grind
```
This PR implements basic `Field` support in the commutative ring module
in `grind`. It is just division by numerals for now. Examples:
```lean
open Lean Grind
example [Field α] [IsCharP α 0] (a b c : α) : a/3 = b → c = a/3 → a/2 + a/2 = b + 2*c := by
grind
example [Field α] (a b : α) : b = 0 → (a + a) / 0 = b := by
grind
example [Field α] [IsCharP α 3] (a b : α) : a/3 = b → b = 0 := by
grind
example [Field α] [IsCharP α 7] (a b c : α) : a/3 = b → c = a/3 → a/2 + a/2 = b + 2*c + 7 := by
grind
example [Field R] [IsCharP R 0] (x : R) (cos : R → R) :
(cos x ^ 2 + (2 * cos x ^ 2 - 1) ^ 2 + (4 * cos x ^ 3 - 3 * cos x) ^ 2 - 1) / 4 =
cos x * (cos x ^ 2 - 1 / 2) * (4 * cos x ^ 3 - 3 * cos x) := by
grind
```
This PR changes the generated `below` and `brecOn` implementations for
reflexive inductive types to support motives in `Sort u` rather than
`Type u`.
Closes#7638
This PR adds an option for disabling the cutsat procedure in `grind`.
The linarith module takes over linear integer/nat constraints. Example:
```lean
set_option trace.grind.cutsat.assert true in -- cutsat should **not** process the following constraints
example (x y z : Int) (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0) : ¬ 12*y - 4* z < 0 := by
grind -cutsat -- `linarith` module solves it
```
This PR implements support for the heterogeneous `(k : Nat) * (a : R)`
in ordered modules. Example:
```lean
variable (R : Type u) [IntModule R] [LinearOrder R] [IntModule.IsOrdered R]
example (x y z : R) (hx : x ≤ 3 * y) (h2 : y ≤ 2 * z) (h3 : x ≥ 6 * z) : x = 3 * y := by
grind
example (x y z : Int) (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0) (h3 : x * y < 5) : ¬ 12*y - 4* z < 0 := by
grind
```
This PR fixes a bug where the single-quote character `Char.ofNat 39`
would delaborate as `'''`, which causes a parse error if pasted back in
to the source code.
---------
Co-authored-by: Kyle Miller <kmill31415@gmail.com>
glibc adds `__attribute__((nothrow))` to its declarations, at least for
those related to malloc. glibc has yet to introduce `free_sized`, but
when it does it would cause compilation errors. This is due to the fact
that if a function declarations has `__attribute__((nothrow))` and it is
re-declared or implemented in C++ it must also have
`__attribute__((nothrow))` or `noexcept`, otherwise the compilation will
fail.
This is a follow up to https://github.com/leanprover/lean4/pull/6598.
Signed-off-by: Justin King <jcking@google.com>
This PR changes the LCNF pass pipeline so checks are no longer run by
default after every pass, only after `init`, `saveBase`, `toMono` and
`saveMono`. This is a compile time improvement, and the utility of these
checks is decreased a bit after the decision to no longer attempt to
preserve types throughout compilation. They have not been a significant
way to discover issues during development of the new compiler.
This PR implements model-based theory combination for grind linarith.
Example:
```lean
example [CommRing α] [LinearOrder α] [Ring.IsOrdered α] (f : α → α → α) (x y z : α)
: z ≤ x → x ≤ 1 → z = 1 → f x y = 2 → f 1 y = 2 := by
grind
```
This PR adds caching for the `hasTrivialStructure?` function for LCNF
types. This is one of the hottest small functions in the new compiler,
so adding a cache makes a lot of sense.
This PR fixes a bug in `simp` where it was not resetting the set of
zeta-delta reduced let definitions between `simp` calls. It also fixes a
bug where `simp` would report zeta-delta reduced let definitions that
weren't given as simp arguments (these extraneous let definitions appear
due to certain processes temporarily setting `zetaDelta := true`). This
PR also modifies the metaprogramming interface for the zeta-delta
tracking functions to be re-entrant and to prevent this kind of no-reset
bug from occurring again. Closes#6655.
Re-entrance of this metaprogramming interface is not needed to fix
#6655, but it is needed for some future PRs.
The `tests/lean/run/6655.lean` file has an example of a deficiency of
`simp?`, where `simp?` still over-reports unfolded let declarations.
This is likely due to `withInferTypeConfig` setting `zetaDelta := true`
from within `isDefEq`, but I did not verify this.
This PR supersedes #7539. The difference is that this PR has
`withResetZetaDeltaFVarIds` save and restore `zetaDeltaFVarIds`, but
that PR saves and then extends `zetaDeltaFVarIds` to persist unfolded
fvars. The behavior in this PR lets metaprograms control whether they
want to persist any of the unfolded fvars in this context themselves. In
practice, metaprograms that use `withResetZetaDeltaFVarIds` are creating
many temporary fvars and are doing dependence computations. These
temporary fvars shouldn't be persisted, and also dependence shouldn't be
inferred from the fact that a dependence calculation was done. (Concrete
example: the let-to-have transformation in an upcoming PR can be run
from within simp. Just because let-to-have unfolds an fvar while
calculating dependencies of lets doesn't mean that this fvar should be
included by `simp?`.)
This PR implements counterexamples for grind linarith. Example:
```lean
example [CommRing α] [LinearOrder α] [Ring.IsOrdered α] (a b c d : α)
: b ≥ 0 → c > b → d > b → a ≠ b + c → a > b + c → a < b + d → False := by
grind
```
produces the counterexample
```
a := 7/2
b := 1
c := 2
d := 3
```
```lean
example [IntModule α] [LinearOrder α] [IntModule.IsOrdered α] (a b c d : α)
: a ≤ b → a - c ≥ 0 + d → d ≤ 0 → b = c → a ≠ b → False := by
grind
```
generates the counterexample
```
a := 0
b := 1
c := 1
d := -1
```
This PR changes the `show t` tactic to match its documentation.
Previously it was a synonym for `change t`, but now it finds the first
goal that unifies with the term `t` and moves it to the front of the
goal list.
This PR changes the implementation of computed fields in the new
compiler, which should enable more optimizations (and remove a
questionable hack in `toLCNF` that was only suitable for bringup). We
convert `casesOn` to `cases` like we do for other inductive types, all
constructors get replaced by their real implementations late in the base
phase, and then the `cases` expression is rewritten to use the real
constructors in `toMono`.
In the future, it might be better to move to a model where the `cases`
expression gets rewritten earlier or the constructors get replaced
later, so that both are done at the same time.
This PR fixes an issue where the `extendJoinPointContext` pass can lift
join points containing projections to the top level, as siblings of
`cases` constructs matching on other projections of the same base value.
This prevents the `structProjCases` pass from projecting both at once,
extending the lifetime of the parent value and breaking linearity at
runtime.
This would theoretically be possible to fix in `structProjCases`, but it
would require some better infrastructure for handling join points. It's
also likely that the IR passes dealing with reference counting would
have similar bugs that pessimize the code. For this reason, the simplest
thing is to just perform the `structProjCases` pass earlier, which
prevents `extendJoinPointContext` from lifting these join points.
This PR adds grind annotations for `List/Array/Vector.ofFn` theorems and
additional `List.Impl` find operations.
The annotations are added to theorems that correspond to those already
annotated in the List implementation, ensuring consistency across all
three container types (List, Array, Vector) for ofFn operations and
related functionality.
Key theorems annotated include:
- Element access theorems (`getElem_ofFn`, `getElem?_ofFn`)
- Construction and conversion theorems (`ofFn_zero`, `toList_ofFn`,
`toArray_ofFn`)
- Membership theorems (`mem_ofFn`)
- Head/tail operations (`back_ofFn`)
- Monadic operations (`ofFnM_zero`, `toList_ofFnM`, `toArray_ofFnM`,
`idRun_ofFnM`)
- List.Impl find operations (`find?_singleton`, `find?_append`,
`findSome?_singleton`, `findSome?_append`)
This PR adds grind annotations for `Array/Vector.mapIdx` and `mapFinIdx`
theorems.
The annotations are added to theorems that correspond to those already
annotated in the List implementation, ensuring consistency across all
three container types (List, Array, Vector) for indexed mapping
operations.
Key theorems annotated include:
- Size and element access theorems (`size_mapIdx`, `getElem_mapIdx`,
`getElem?_mapIdx`)
- Construction theorems (`mapIdx_empty`, `mapIdx_push`, `mapIdx_append`)
- Membership and equality theorems (`mem_mapIdx`, `mapIdx_mapIdx`)
- Conversion theorems (`toList_mapIdx`, `mapIdx_toArray`, etc.)
- Reverse and composition operations
- Similar annotations for `mapFinIdx` variants
Thanks to `mmap`, startup time is not necessarily related to this
figure, but it can be used as a rough measure for that and how much data
the module depends on, i.e. the rebuild chance.
Also adds new cumulative benchmarks for this metric as well as the
number of imported constants and env ext entries.
This PR partially reverts #8024 which introduced a significant Lake
performance regression during builds. Once the cause is discovered and
fixed, a similar PR will be made to revert this.
This PR implements disequality splitting and non-chronological
backtracking for the `grind` linarith procedure.
```lean
example [IntModule α] [LinearOrder α] [IntModule.IsOrdered α] (a b c d : α)
: a ≤ b → a - c ≥ 0 + d → d ≤ 0 → d ≥ 0 → b = c → a ≠ b → False := by
grind
```
This PR changes LCNF's `FVarSubst` to use `Arg` rather than `Expr`. This
enforces the requirements on substitutions, which match the requirements
on `Arg`.
This PR adds the pre-stage0-update infrastructure for named error
messages. It adds macro syntax for registering and throwing named errors
(without elaborators), mechanisms for displaying error names in the
Infoview and at the command line, and the ability to link to error
explanations in the manual (once they are added).
This PR adds the pre-stage0-update infrastructure for error
explanations. It adds the environment-extension machinery for
registering and accessing explanations, and it provides a cursory parser
that validates that the high-level structure of error explanations
matches the prescribed format.
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
Replaces the previous `export/saveEntriesFn` split with a stricly more
general function such that `exportEntriesFn` could be deprecated at a
later point. Also gives the new function access to the `Environment`
while we're at it. Also gives `getModuleEntries` access to more olean
levels in preparation for `meta import`.
This PR adds documentation to builtin attributes like `@[refl]` or
`@[implemented_by]`.
Closes#8432
---------
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
Co-authored-by: David Thrane Christiansen <david@lean-fro.org>
This PR uses the fvar substitution mechanism to replace erased code.
This isn't entirely satisfactory, since LCNF's `.return` doesn't support
a general `Arg` (which has a `.erased` constructor), it only supports an
`FVarId`. This is in contrast to the IR `.ret`, which does support a
general `Arg`.
This PR makes any type application of an erased term to be erased. This
comes up a bit more than one would expect in the implementation of Lean
itself.
This PR optimizes let decls of an erased type to an erased value.
Specialization can create local functions that produce a Prop, and
there's no point in keeping them around.
This PR improves the release checklist and scripts:
* Check that the release's commit hash is not all-numeric starting with
0 (this can break SemVer, which [required us to release
v4.21.0-rc2](https://github.com/leanprover/lean4/releases/tag/v4.21.0-rc2)).
* Check that projects being bumped to a release tag do not reference
`nightly-testing` anymore.
* Clarify how to create subsequent release candidates if an `-rc1`
already exists.
* Fix typos in the release checklist documentation.
This PR handles constants with erased types in `toMonoType`. It is much
harder to write a test case for this than you would think, because most
references to such types get replaced with `lcErased` earlier.
This PR fixes an internalization bug in the interface between linarith
and ring modules in `grind`. The `CommRing` module may create new terms
during normalization.
This PR adds an equivalence relation to tree maps akin to the existing
one for hash maps. In order to get many congruence lemmas to eventually
use for defining functions on extensional tree maps, almost all of the
remaining tree map functions have also been given lemmas to relate them
to list functions, although these aren't currently used to prove lemmas
other than congruence lemmas.
This PR enables auto-implicits in the Lake math template. This resolves
an issue where new users sometimes set up a new project for math
formalization and then quickly realize that none of the code samples in
our official books and docs that use auto-implicits work in their
projects. With the introduction of [inlay hints for
auto-implicits](https://github.com/leanprover/lean4/pull/6768), we
consider the auto-implicit UX to be sufficiently usable that they can be
enabled by default in the math template.
Notably, this change does not affect Mathlib itself, which will proceed
to disable auto-implicits.
This change was previously discussed with and agreed to by the Mathlib
maintainer team.
This PR enhances the PR release workflow to create both short format and
SHA-suffixed release tags. Creates both pr-release-{PR_NUMBER} and
pr-release-{PR_NUMBER}-{SHORT_SHA} tags, generates separate releases for
both formats, adds separate GitHub status checks, and updates
Batteries/Mathlib testing branches to use SHA-suffixed tags for exact
commit traceability.
This removes the need for downstream repositories to deal with the
toolchain changing without the toolchain name changing.
This PR exports `LeanOption` in the `Lean` namespace from the `Lake`
namespace. `LeanOption` was moved from `Lean` to `Lake` in #8447, which
can cause unnecessary breakage without this.
This PR turns off the default warning when using `grind`, in preparation
for v4.22. I'll removing all the `set_option grind.warning false` in our
codebase in a second PR, after an update-stage0.
This PR implements support for inequalities in the `grind` linear
arithmetic procedure and simplifies its design. Some examples that can
already be solved:
```lean
open Lean.Grind
example [IntModule α] [Preorder α] [IntModule.IsOrdered α] (a b c d : α)
: a + d < c → b = a + (2:Int)*d → b - d > c → False := by
grind
example [CommRing α] [LinearOrder α] [Ring.IsOrdered α] (a b : α)
: a = 0 → b = 1 → a + b ≤ 2 := by
grind
example [CommRing α] [Preorder α] [Ring.IsOrdered α] (a b c d e : α) :
2*a + b ≥ 1 → b ≥ 0 → c ≥ 0 → d ≥ 0 → e ≥ 0
→ a ≥ 3*c → c ≥ 6*e → d - e*5 ≥ 0
→ a + b + 3*c + d + 2*e < 0 → False := by
grind
```
This PR makes `unsafeBaseIO` `noinline`. The new compiler is better at
optimizing `Result`-like types, which can cause the final operation in
an `unsafeBaseIO` block to be dropped, since `unsafeBaseIO` is
discarding the state.
This PR implements the main framework of the model search procedure for
the linarith component in grind. It currently handles only inequalities.
It can already solve simple goals such as
```lean
example [IntModule α] [Preorder α] [IntModule.IsOrdered α] (a b c : α)
: a < b → b < c → c < a → False := by
grind
example [IntModule α] [LinearOrder α] [IntModule.IsOrdered α] (a b c : α)
: a < b → b < c + d → a - d < c := by
grind
```
This PR implements the infrastructure for constructing proof terms in
the linarith procedure in `grind`. It also adds the `ToExpr` instances
for the reified objects.
This PR makes use of `lean --setup` in Lake builds of Lean modules and
adds Lake support for the new `.olean` artifacts produced by the module
system.
Lake now computes the entire transitive import graph of a module for
Lean, allowing it eagerly provide the artifacts managed by Lake to Lean
via the `modules` field of `lean --setup`.
`lake setup-file` no longer respects the imports passed to it and
instead just parses the file's header for imports. This is necessary
because import statements are now more complex than a simple module
name.
This PR adds an optimization to the LCNF simp pass where the
discriminant of a `cases` construct will only be mark used if it has a
non-default alternative.
This PR increases the precision of the new compiler's non computable
check, particularly around irrelevant uses of `noncomputable` defs in
applications.
There are no tests included because they don't pass with the old
compiler. They are on the new compiler's branch and they will be merged
when it is enabled.
This PR makes memoization of built-in facets toggleable through a
`memoize` option on the facet configuration. Built-in facets which are
essentially aliases (e.g., `default`, `o`) have had memoization
disabled.
This PR introduces an explicit `defeq` attribute to mark theorems that
can be used by `dsimp`. The benefit of an explicit attribute over the
prior logic of looking at the proof body is that we can reliably omit
theorem bodies across module boundaries. It also helps with intra-file
parallelism.
If a theorem is syntactically defined by `:= rfl`, then the attribute is
assumed and need not given explicitly. This is a purely syntactic check
and can be fooled, e.g. if in the current namespace, `rfl` is not
actually “the” `rfl` of `Eq`. In that case, some other syntax has be
used, such as `:= (rfl)`. This is also the way to go if a theorem can be
proved by `defeq`, but one does not actually want `dsimp` to use this
fact.
The `defeq` attribute will look at the *type* of the declaration, not
the body, to check if it really holds definitionally. Because of
different reduction settings, this can sometimes go wrong. Then one
should also write `:= (rfl)`, if one does not want this to be a defeq
theorem. (If one does then this is currently not possible, but it’s
probably a bad idea anyways).
The `set_option debug.tactic.simp.checkDefEqAttr true`, `dsimp` will
warn if could not apply a lemma due to a missing `defeq` attribute.
With `set_option backward.dsimp.useDefEqAttr.get false` one can revert
to the old behavior of inferring rfl-ness based on the theorem body.
Both options will go away eventually (too bad we can’t mark them as
deprecated right away, see #7969)
Meta programs that generate theorems (e.g. equational theorems) can use
`inferDefEqAttr` to set the attribute based on the theorem body of the
just created declaration.
This builds on #8501 to update Init to `@[expose]` a fair amount of
definitions that, if not exposed, would prevent some existing `:= rfl`
theorems from being `defeq` theorems. In the interest of starting
backwards compatible, I exposed these function. Hopefully many can be
un-exposed later again.
A mathlib adaption branch exists that includes both the meta programming
fixes and changes to the theorems (e.g. changing `:= by rfl` to `:=
rfl`).
With the module system there is now no special handling for `defeq`
theorem bodies, because we don’t look at the body anymore. The previous
hack is removed. The `defeq`-ness of the theorem needs to be checked in
the context of the theorem’s *type*; the error message contains a hint
if the defeq check fails because of the exported context.
This PR provides a special empty iterator type. Although its behavior
can be emulated with a list iterator (for example), having a special
type has the advantage of being easier to optimize for the compiler.
This PR replaces special, more optimized `IteratorLoop` instances, for
which no lawfulness proof has been made, with the verified default
implementation. The specialization of the loop/collect implementations
is low priority, but having lawfulness instances for all iterators is
important for verification.
This PR provides the means to reason about "equivalent" iterators.
Simply speaking, two iterators are equivalent if they behave the same as
long as consumers do not introspect their states.
This PR adds many helper theorems for the future `IntModule` linear
arithmetic procedure in `grind`.
It also adds helper theorems for normalizing input atoms and support for
disequality in the new linear arithmetic procedure in `grind`.
This PR improves the precision of the new compiler's `noncomputable`
check for projections. There is no test included because while this was
reduced from Mathlib, the old compiler does not correctly handle the
reduced test case. It's not entirely clear to me if the check is passing
with the old compiler for correct reasons. A test will be added to the
new compiler's branch.
This PR completes the `ToInt` family of typeclasses which `grind` will
use to embed types into the integers for `cutsat`. It contains instances
for the usual concrete data types (`Fin`, `UIntX`, `IntX`, `BitVec`),
and is extensible (e.g. for Mathlib's `PNat`).
This PR adds the `#print sig $ident` variant of the `#print` command,
which omits the body. This is useful for testing meta-code, in the
```
#guard_msgs (drop trace, all) in #print sig foo
```
idiom. The benefit over `#check` is that it shows the declaration kind,
reducibility attributes (and in the future more built-in attributes,
like `@[defeq]` in #8419). (One downside is that `#check` shows unused
function parameter names, e.g. in induction principles; this could
probably be refined.)
This PR adds a simp lemma that simplifies T-division where the numerator
is a `Nat` into an E-division:
```lean
@[simp] theorem ofNat_tdiv_eq_ediv {a : Nat} {b : Int} : (a : Int).tdiv b = a / b :=
tdiv_eq_ediv_of_nonneg (by simp)
```
---------
Co-authored-by: Tobias Grosser <tobias@grosser.es>
This PR adds trichotomy lemmas for unsigned and signed comparisons,
stating that only one of three cases may happen: either `x < y`, `x =
y`, or `x > y` (for both signed and unsigned comparsions). We use
explicit arguments so that users can write `rcases slt_trichotomy x y
with hlt | heq | hgt`.
This PR generalizes `Std.Sat.AIG. relabel(Nat)_unsat_iff` to allow the
AIG type to be empty. We generalize the proof, by showing that in the
case when `α` is empty, the environment doesn't matter, since all
environments `α → Bool` are isomorphic.
This showed up when reusing the AIG primitives for building a
k-induction based model checker to prove arbitrary width bitvector
identities.
This PR adds typeclasses for `grind` to embed types into `Int`, for
cutsat. This allows, for example, treating `Fin n`, or Mathlib's `ℕ+` in
a uniform and extensible way.
There is a primary typeclass that carries the `toInt` function, and a
description of the interval the type embeds in. There are then
individual typeclasses describing how arithmetic/order operations
interact with the embedding.
This PR makes the equational theorems of non-exposed defs private. If
the author of a module chose not to expose the body of their function,
then they likely don't want that implementation to leak through
equational theorems. Helps with #8419.
There is some amount of incidential complexity due to how `private`
works in lean, by mangling the name: lots of code paths that need now do
the right thing™ about private and non-private names, including the
whole reserved name machinery.
So this includes a number of refactorings:
* The logic for calculating an equational theorem name (or similar) is
now done by a single function, `mkEqLikeNameFor`, rather than all over
the place.
* Since the name of the equational theorem now depends on the current
context (in particular whether it’s a proper module, or a non-module
file), the forward map from declaration to equational theorem doesn’t
quite work anymore. This map is deleted; the list of equational theorems
are now always found by looking for declaration of the expected names
(`alreadyGenerated). If users define such theorems themselves (and make
it past the “do not allow reserved names to be declared”) they get to
keep both pieces.
* Because this map was deleted, mathlib’s `eqns` command can no longer
easily warn if equational lemmas have already been generated too early
(adaption branch exists). But in general I think lean could provide a
more principled way of supporting custom unfold lemmas, and ideally the
whole equational theorem machinery is just using that.
* The ReservedNamePredicate is used by `resolveExact`, so we need to
make sure that it returns the right name, including privateness. It is
not ok to just reserve both the private and non-private name but then
later in the ReservedNameAction produce just one of the two.
* We create `foo.def_eq` eagerly for well-founded recursion. This is
needed because we need feed in the proof of the rewriting done by
`wf_preprocess`. But if `foo.def_eq` is private in a module, then a
non-module importing it will still expect a non-private `foo.def_eq` to
exist. To patch that, we install a `copyPrivateUnfoldTheorem :
GetUnfoldEqnFn` that declares a theorem aliasing the private one. Seems
to work.
This PR removes the `NatCast (Fin n)` global instance (both the direct
instance, and the indirect one via `Lean.Grind.Semiring`), as that
instance causes causes `x < n` (for `x : Fin k`, `n : Nat`) to be
elaborated as `x < ↑n` rather than `↑x < n`, which is undesirable. Note
however that in Mathlib this happens anyway!
This PR adds a test case / use case example for `grind`, setting up the
very basics of `IndexMap`, modelled on Rust's
[`indexmap`](https://docs.rs/indexmap/latest/indexmap/). It is not
intended as a complete implementation: just enough to exercise `grind`.
(Thanks to @arthurpaulino for suggesting this as a test case.)
This PR fixes a bug in the equality-resolution procedure used by
`grind`.
The procedure now performs a topological sort so that every simplified
theorem declaration is emitted **before** any place where it is
referenced.
Previously, applying equality resolution to
```lean
h : ∀ x, p x a → ∀ y, p y b → x ≠ y
```
in the example
```lean
example
(p : Nat → Nat → Prop)
(a b c : Nat)
(h : ∀ x, p x a → ∀ y, p y b → x ≠ y)
(h₁ : p c a)
(h₂ : p c b) :
False := by
grind
```
caused `grind` to produce the incorrect term
```lean
p ?y a → ∀ y, p y b → False
```
The patch eliminates this error, and the following correct simplified
theorem is generated
```lean
∀ y, p y a → p y b → False
```
This PR fixes (1) an issue where private names are not unresolved when
they are pretty printed, (2) an issue where in `pp.universes` mode names
were allowed to shadow local names, (3) an issue where in `match`
patterns constants shadowing locals wouldn't use `_root_`, and (4) an
issue where tactics might have an incorrect "try this" when
`pp.fullNames` is set. Adds more delaboration tests for name
unresolution.
It also cleans up the `delabConst` delaborator so that it uses
`unresolveNameGlobalAvoidingLocals`, rather than doing any local context
analysis itself. The `inPattern` logic has been removed; it was a
heuristic added back in #575, but it now leads to incorrect results (and
in `match` patterns, local names shadow constants in name resolution).
This PR implements signature help support. When typing a function
application, editors with support for signature help will now display a
popup that designates the current (remaining) function type. This
removes the need to remember the function signature while typing the
function application, or having to constantly cycle between hovering
over the function identifier and typing the application. In VS Code, the
signature help can be triggered manually using `Ctrl+Shift+Space`.
### Other changes
- In order to support signature help for the partial syntax `f a <|` or
`f a $`, these notations now elaborate as `f a`, not `f a .missing`.
- The logic in `delabConstWithSignature` that delaborates parameters is
factored out into a function `delabForallParamsWithSignature` so that it
can be used for arbitrary `forall`s, not just constants.
- The `InfoTree` formatter is adjusted to produce output where it is
easier to identify the kind of `Info` in the `InfoTree`.
- A bug in `InfoTree.smallestInfo?` is fixed so that it doesn't panic
anymore when its predicate `p` does not ensure that both `pos?` and
`tailPos?` of the `Info` are present.
* Move constant registration with elab env from `Lean.addDecl` to
`Lean.Environment.addDeclCore` for compatibility
* Make module system behavior independent of `Elab.async` value
This PR makes `guard_msgs.diff=true` the default. The main usage of
`#guard_msgs` is for writing tests, and this makes staring at altered
test outputs considerably less tiring.
This PR adds support for server-sided `RpcRef` reuse and fixes a bug
where trace nodes in the InfoView would close while the file was still
being processed.
The core of the trace node issue is that the server always serves new
RPC references in every single response to the client, which means that
the client is forced to reset its UI state.
In a previous attempt at fixing this (#8056), the server would memorize
the RPC-encoded JSON of interactive diagnostics (which includes RPC
references) and serve it for as long as it could reuse the snapshot
containing the diagnostics, so that RPC references are reused. The
problem with this was that the client then had multiple finalizers
registered for the same RPC reference (one for every reused RPC
reference that was served), and once the first reference was
garbage-collected, all other reused references would point into the
void.
This PR takes a different approach to resolve the issue: The meaning of
`$/lean/rpc/release` is relaxed from "Free the object pointed to by this
RPC reference" to "Decrement the RPC reference count of the object
pointed to by this RPC reference", and the server now maintains a
reference count to track how often a given `RpcRef` was served. Only
when every single served instance of the `RpcRef` has been released, the
object is freed. Additionally, the reuse mechanism is generalized from
being only supported for interactive diagnostics, to being supported for
any object using `WithRpcRef`. In order to make use of reusable RPC
references, downstream users still need to memorize the `WithRpcRef`
instances accordingly.
Closes#8053.
### Breaking changes
Since `WithRpcRef` is now capable of tracking its identity to decide
which `WithRpcRef` usage constitutes a reuse, the constructor of
`WithRpcRef` has been made `private` to discourage downstream users from
creating `WithRpcRef` instances with manually-set `id`s. Instead,
`WithRpcRef.mk` (which lives in `BaseIO`) is now the preferred way to
create `WithRpcRef` instances.
This PR uses `grind` to shorten some proofs in the LRAT checker. The
intention is not particularly to improve the quality or maintainability
of these proofs (although hopefully this is a side effect), but just to
give `grind` a work out.
There are a number of remaining notes, either about places where `grind`
fails with an internal error (for which #8608 is hopefully
representative, and we can fix after that), or `omega` works but `grind`
doesn't (to be investigated later).
Only in some of the files have I thoroughly used grind. In many files
I've just replaced leaves or branches of proofs with `grind` where it
worked easily, without setting up the internal annotations in the LRAT
library required to optimize the use of `grind`. It's diminishing
returns to do this in a proof library that is not high priority, so I've
simply drawn a line.
This PR provides the iterator combinator `drop` that transforms any
iterator into one that drops the first `n` elements.
Additionally, the PR removes the specialized `IteratorLoop` instance on
`Take`. It currently does not have a `LawfulIteratorLoop` instance,
which needs to exist for the loop consumer lemmas to work. Having the
specialized instance is low priority.
This PR adds `@[grind]` to `getElem?_pos` and variants.
I'd initially thought these would result in too much case splitting, but
it seems to be only minor, and in use cases the payoff is good.
This PR adds support for the `compiler.extract_closed` option to the new
compiler, since this is used by the definition of `unsafeBaseIO`. We'll
revisit this once we switch to the new compiler and rethink its
relationship with IO.
This PR makes the lemma `BitVec.extractLsb'_append_eq_ite` more usable
by using the "simple case" more often, and uses this simplification to
make `BitVec.extractLsb'_append_eq_of_add_lt` stronger, renaming it to
`BitVec.extractLsb'_append_eq_of_add_le`.
This PR wraps the invocation of the new compiler in `withoutExporting`.
This is not necessary for the old compiler because it uses more direct
access to the kernel environment.
This PR removes incorrect optimizations for strictOr/strictAnd from the
old compiler, along with deleting an incorrect test. In order to do
these optimizations correctly, nontermination analysis is required.
Arguably, the correct way to express these optimizations is by exposing
the implementation of strictOr/strictAnd to a nontermination-aware phase
of the compiler, and then having them follow from more general
transformations.
This PR adjusts the grind annotation on
`Std.HashMap.map_fst_toList_eq_keys` and variants, so `grind` can reason
bidirectionally between `m.keys` and `m.toList`.
This PR avoids the likely unexpected behavior of `removeDirAll` to
delete through symlinks and adds the new function
`IO.FS.symlinkMetadata`.
---------
Co-authored-by: Rob23oba <152706811+Rob23oba@users.noreply.github.com>
This PR sets `ring := true` by default in `grind`. It also fixes a bug
in the reification procedure, and improves the term internalization in
the ring and cutsat modules.
This PR makes LCNF's simpAppApp? bail out on trivial aliases as
intended. It seems that there was a typo in the original logic, and this
PR also extends it to include aliases of global constants rather than
just local vars.
Just a typo. From my understanding (and the specification otherwise) the
resulting level is the maximum of `r` and `s` instead of the minimum.
No issue opened yet (thus the draft).
This PR clarifies the invalid field notation error when projected value
type is a metavariable.
Co-authored-by @sgraf812.
---------
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
This PR clarifies the invalid dotted identifier notation error when the
type is a sort.
Co-authored-by @sgraf812.
---------
Co-authored-by: Joseph Rotella <7482866+jrr6@users.noreply.github.com>
This PR improves the rendering of hints in error messages by
consistently indenting diffs and splitting large diffs less granularly;
it also improves the ergonomics of `Lean.MessageData.hint`. Note that
the changes to the signature of `Lean.MessageData.hint` are breaking.
This PR depends on #8457.
This PR changes the LCNF constant folding pass to not convert Nat
multiplication to a left shift by a power of 2. The fast path test for
this is sufficiently complex that it's simpler to just use the fast path
for multiplication.
This PR makes the LCNF specialization pass only treat type/instance
params as ground vars. The current policy was too liberal and would
result on computations being floated into specialized loops.
This PR simplifies the interface between the `grind` core and the cutsat
procedure. Before this PR, core would try to minimize the number of
numeric literals that have to be internalized in cutsat. This
optimization was buggy (see `grind_cutsat_zero.lean` test), and produced
counterintuitive counterexamples.
This PR increases maxHeartbeats in the isDefEqProjIssue test, because
when running under the new compiler the `run_meta` call includes the
allocations of the compiler itself. With the old compiler, many of the
corresponding allocations were internal to C++ code and would not
increase the heartbeat count.
This PR fixes an adversarial soundness attack described in #8554. The
attack exploits the fact that `assert!` no longer aborts execution, and
that users can redirect error messages.
Another PR will implement the same fix for `Expr.Data`.
This PR provides array iterators (`Array.iter(M)`,
`Array.iterFromIdx(M)`), infinite iterators produced by a step function
(`Iter.repeat`), and a `ForM` instance for finite iterators that is
implemented in terms of `ForIn`.
This PR fixes the hash function used to implement congruence closure in
`grind`. The hash of an `Expr` must not depend on whether the expression
has been internalized or not.
This PR provides the iterator combinators `takeWhile` (forwarding all
emitted values of another iterator until a predicate becomes false)
`dropWhile` (dropping values until some predicate on these values
becomes false, then forwarding all the others).
This PR provides the iterator combinator `filterMap` in a pure and
monadic version and specializations `map` and `filter`. This new
combinator allows to apply a function to the emitted values of a stream
while filtering out certain elements.
`map` should have an optimized `IteratorCollect` implementation but it
turns out that this is not possible without a major refactor of
`IteratorCollect`: `toArrayMapped` requires a proof that the iterator is
finite. If `it.mapM f` is `Finite` but `it` is not, then such a proof
does not exist. `IteratorCollect` needs to take a proof that the loop
will terminate for the given monadic function `f` instead. This will not
be done in this PR.
This PR provides the `take` iterator combinator that transforms any
iterator into an iterator that stops after a given number of steps. The
change contains the implementation and lemmas.
`take` has a special implementation of `IteratorLoop` that relies on a
potentially more efficient `forIn` implementation of the inner iterator.
The mysterious `@[specialize]` on a test has been removed because it is
not necessary anymore according to a manual inspection of the IR. Either
I erroneously concluded from experiments that it was necessary of
something has changed in the meantime that makes it unnecessary.
This PR upstreams the `LawfulMonadLift(T)` classes, lemmas and instances
from Batteries into Core because the iterator library needs them in
order to prove lemmas about the `mapM` operator, which relies on
`MonadLiftT`.
This PR fixes two inappropriate uses of `whnfD` in `grind`. They were
potential performance foot guns, and were producing unexpected errors
since `whnfD` is not consistently used (and it should not be) in all
modules.
This PR changes `lake lean` and `lake setup-file` to precompile the
imports of non-workspace files using the the import's whole library.
This ensures that additional link objects are linked and available
during elaboration.
Closes#8448.
This PR changes Lake to use relative path for the Lean messages produced
by a module build. This makes the message portable across different
machines, which is useful for Mathlib's cache.
This PR changes the LCNF specialize pass to allow ground variables to
depend on local fun decls (with no non-ground free variables). This
enables specialization of Monad instances that depend on local lambdas.
This PR fixes some places in Lake where `(sync := true)` was incorrectly
used on code that could block, and more generally improves `(sync :;=
true)` usage.
This PR fixes an issue when including a hard line break in a `Format`
that caused subsequent (ordinary) line breaks to be erroneously
flattened to spaces.
This issue is especially important for displaying notes and hints in
error messages, as these components could appear garbled due to improper
line-break rendering.
This PR fixes the heuristic Lake uses to determine whether a `lean_lib`
can be loaded via `lean --plugin` rather than `lean --load-dynlib`.
Previously, a mismatch between the single root's name and the library's
name would not be caught and cause loading to fail.
This is a subset of tests from #8518 that are fully minimized. I'll
merge this first.
---------
Co-authored-by: Wojciech Rozowski <wojciech@lean-fro.org>
This PR implements `match`-expressions in `grind` using `match`
congruence equations. The goal is to minimize the number of `cast`
operations that need to be inserted, and avoid `cast` over functions.
The new approach support `match`-expressions of the form `match h : ...
with ...`.
This PR moves the new compiler's noncomputable check into toMono,
matching the recent change in the old compiler. This is mildly more
complicated because we can't throw an error at the mere use of a
constant, we need to check for a later relevant use. This is still a bit
more conservative than it could theoretically be around join points and
local functions, but it's hard to imagine that mattering in practice
(and we can easily enable it if it does).
This PR modifies the pretty printer so that dot notation is used for
class parent projections. Previously, dot notation was never used for
classes.
We still need to modify dot notation to take the method resolution order
into account when collapsing parent projections.
This PR removes the `@[reducible]` annotation on `Array.size`. This is
probably best gone anyway in order to keep separation between the `List`
and `Array` APIs, but it also helps avoid uselessly instantiating
`Array` theorems when `grind` is working on `List` problems.
This PR adds a `value_of% ident` term that elaborates to the value of
the local or global constant `ident`. This is useful for creating
definition hypotheses:
```lean
let x := ... complicated expression ...
have hx : x = value_of% x := rfl
```
This PR adds the `@[expose]` attribute to many functions (and changes
some theorems to be by `:= (rfl)`) in preparation for the `@[defeq]`
attribute change in #8419.
This PR changes the behavior of `pp.showLetValues` to use a hoverable
`⋯` to hide let values. This is now false by default, and there is a new
option `pp.showLetValues.threshold` for allowing small expressions to be
shown anyway. For tactic metavariables, there is an additional option
`pp.showLetValues.tactic.threshold`, which by default is set to the
maximal value, since in tactic states local values are usually
significant.
This PR changes the new compiler to use the kernel environment to find
definitions, which causes compilation to be skipped when the decl had a
kernel error (e.g. due to an unresolved metavariable). This matches the
behavior of the old compiler.
This will need to be revisited in the future when we want to make
compilation more asynchronous.
This PR adds `simp` lemmas for `toInt_*` and `toNat_*` with arithmetic
operation given the hypothesis of no-overflow
(`toNat_add_of_not_uaddOverflow`, `toInt_add_of_not_saddOverflow`,
`toNat_sub_of_not_usubOverflow`, `toInt_sub_of_not_ssubOverflow`,
`toInt_neg_of_not_negOverflow`, `toNat_mul_of_not_umulOverflow`,
`toInt_mul_of_not_smulOverflow`). In particular, these are `simp` since
(1) the `rhs` is strictly simpler than the `lhs` and (2) this version is
also simpler than the standard operation when the hypothesis is
available.
co-authored by @tobiasgrosser
---------
Co-authored-by: Henrik Böving <hargonix@gmail.com>
This PR adds a feature to the `subst` tactic so that when `x : X := v`
is a local definition, `subst x` substitutes `v` for `x` in the goal and
removes `x`. Previously the tactic would throw an error.
This PR upstreams and extends the Mathlib `clear_value` tactic. Given a
local definition `x : T := v`, the tactic `clear_value x` replaces it
with a hypothesis `x : T`, or throws an error if the goal does not
depend on the value `v`. The syntax `clear_value x with h` creates a
hypothesis `h : x = v` before clearing the value of `x`. Furthermore,
`clear_value *` clears all values that can be cleared, or throws an
error if none can be cleared.
This PR switches the LCNF baseExt/monoExt environment extensions to use
a custom environment extension that uses a PersistentHashMap. The
optimizer relies upon the ability to update a decl multiple times, which
does not work with SimplePersistentEnvExtension.
This PR changes the CI check when the `awaiting-mathlib` label is
present. If `breaks-mathlib` is present, it shows a red cross, but if
neither `breaks-mathlib` nor `builds-mathlib` is present it shows a
yellow circle.
This PR adds `seal` commands at `grind_ite.lean` to workaround expensive
definitionally equality tests in the canonicalizer. The new module
system will automatically hide definitions such as `HashMap.insert` and
`TreeMap.insert` which are being unfolded by the canonicalizer in this
test.
This PR also adds a `profileItM` for tracking the time spent in the
`grind` canonicalizer.
The termination prover has gotten stronger since these definitions were
written, and now they can be proved terminating automatically. (One
definition had to be changed slightly because it wasn't actually
terminating before.)
This PR adds further `@[grind]` annotations for `Option`, as follow-up
to the recent additions to the `Option` API in #8379 and #8298.
**However**, I am concurrently investigating adding `attribute [grind
cases] Option`, which will result in many (most?) of the annotations for
`Option` being removed again. In any case, I'm going to merge this
first, as if that is viable I would like to test that most/all the
lemmas now marked with `@[grind]` are still provable by `grind`.
This PR adds a verification of `Array.qsort` properties, trying to use
`grind` and `fun_induction` where possible.
Currently this is in the `tests/` folder, but once `grind` is ready for
production use we will move it out into the library.
Note that the current `qsort` algorithm has quadratic behaviour on
constant lists, and needs to be adjusted. We'll only move the
verification out into the library once this has been fixed (and the
proofs adapted). These verification theorems may be commented out in the
meantime if it's urgent to fix `qsort`.
---------
Co-authored-by: Kyle Miller <kmill31415@gmail.com>
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This PR adds closed term extraction to the new compiler, closely
following the approach in the old compiler. In the future, we will
explore some ideas to improve upon this approach.
This PR implements non-chronological backtracking for the `grind`
tactic. This feature ensures that `grind` does not need to process
irrelevant branches after performing a case-split that is not relevant.
It is not just about performance, but also the size of the final proof
term. The new test demonstrates this feature in practice.
```lean
-- In the following test, the first 8 case-splits are irrelevant,
-- and non-choronological backtracking is used to avoid searching
-- (2^8 - 1) irrelevant branches
/--
trace:
[grind.split] p8 ∨ q8, generation: 0
[grind.split] p7 ∨ q7, generation: 0
[grind.split] p6 ∨ q6, generation: 0
[grind.split] p5 ∨ q5, generation: 0
[grind.split] p4 ∨ q4, generation: 0
[grind.split] p3 ∨ q3, generation: 0
[grind.split] p2 ∨ q2, generation: 0
[grind.split] p1 ∨ q1, generation: 0
[grind.split] ¬p ∨ ¬q, generation: 0
-/
#guard_msgs (trace) in
set_option trace.grind.split true in
theorem ex
: p ∨ q →
¬ p ∨ q →
p ∨ ¬ q →
¬ p ∨ ¬ q →
p1 ∨ q1 →
p2 ∨ q2 →
p3 ∨ q3 →
p4 ∨ q4 →
p5 ∨ q5 →
p6 ∨ q6 →
p7 ∨ q7 →
p8 ∨ q8 →
False := by
grind (splits := 10)
```
This PR fixes `split` in the presence of metavariables in the target.
The fix consists of replacing an internal use of `apply` for
instantiating match splitters by a new, simpler variant `applyN`. This
new `applyN` is not prone to #8436, which is the ultimate cause for
`split` failing on targets containing metavariables.
---------
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This PR adds a `@[simp]` lemma, and comments explaining that there is
intentionally no verification API for `Vector.take`, `Vector.drop`, or
`Vector.tail`, which should all be rewritten in terms of
`Vector.extract`.
This PR reworks the `simp` set around the `Id` monad, to not elide or
unfold `pure` and `Id.run`
In particular, it stops encoding the "defeq abuse" of `Id X = X` in the
statements of theorems, instead using `Id.run` and `pure` to pass back
and forth between these two spellings. Often when writing these with
`pure`, they generalize to other lawful monads; though such changes were
split off to other PRs.
This fixes the problem with the current simp set where `Id.run (pure x)`
is simplified to `Id.run x`, instead of the desirable `x`.
This is particularly bad because the` x` is sometimes inferred with type
`Id X` instead of `X`, which prevents other `simp` lemmas about `X` from
firing.
Making `Id` reducible instead is not an option, as then the `Monad`
instances would have nothing to key on.
---------
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
Co-authored-by: Kim Morrison <kim@tqft.net>
Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR introduces a `noConfusionType` construction that’s sub-quadratic
in size, and reduces faster.
The previous `noConfusion` construction with two nested `match`
statements is quadratic in size and reduction behavior. Using some
helper definitions, a linear size construction is possible.
With this, processing the RISC-V-AST definition from
https://github.com/opencompl/sail-riscv-lean takes 6s instead of 60s.
The previous construction is still used when processing the early
prelude, and can be enabled elsewhere using `set_option
backwards.linearNoConfusionType false`.
This PR changes namespace completion to use the same algorithm as
declaration identifier completion, which makes it use the short name
(last name component) for completions instead of the full name, avoiding
namespace duplications.
Closes#5654
This PR fixes a bug where the unknown identifier code actions wouldn't
work correctly for some unknown identifier error spans and adjusts
several unknown identifier spans to actually end on the identifier in
question.
The following additional adjustments are made:
- The fallback mechanism of the unknown identifier code actions is
removed, since it could produce severely incorrect suggestions for
unknown identifier errors on fields.
- A performance bug when using the code action to import all unknown
identifiers is fixed.
- A bug that occurs when the elaborator produces multiple overlapping
completion infos is fixed.
- A bug in the snapshot selection that could cause it to wait for
snapshots in snapshots with non-canonical syntax is fixed.
- Some invariants of the snapshot tree are documented.
- The snapshot tree formatting is adjusted to display the final info
tree again.
This PR provides simple lemmas about `toArray`, `toList` and `toListRev`
for the iterator library.
It also changes the definition of `Iter` and `IterM` so that they aren't
equal anymore and in particular not definitionally equal. While it was
very convenient to have them be definitionally equal when working with
dependent code, it was also confusing and annoying that one would
sometimes end up with something like `it.toList = IterM.toList it`,
where `it : Iter β`.
This PR adds `Lean.Grind.Ring.IsOrdered`, and cleans up the ring/module
grind API. These typeclasses are at present unused, but will support
future algorithmic improvements in `grind`.
This PR adds the attribute `[grind?]`. It is like `[grind]` but displays
inferred E-matching patterns. It is a more convinient than writing.
Thanks @kim-em for suggesting this feature.
```lean
set_option trace.grind.ematch.pattern true
```
This PR also improves some tests, and adds helper function
`ENode.isRoot`.
This PR introduces a very minimal version of the new iterator library.
It comes with list iterators and various consumers, namely `toArray`,
`toList`, `toListRev`, `ForIn`, `fold`, `foldM` and `drain`. All
consumers also come in a partial variant that can be used without any
proofs. This limited version of the iterator library generates decent
code, even with the old code generator.
This PR introduces `Lean.Grind.Field`, proves that a `IsCharP 0` field
satisfies `NoNatZeroDivisors`, and sets up some basic (currently
failing) tests for `grind`.
This PR adds the `List/Array/Vector.ofFnM`, the monadic analogues of
`ofFn`, along with basic theory.
At the same time we pave some potholes in nearby API.
---------
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
This PR adds variants of `HashMap.getElem?_filter` that assume
`LawfulBEq` and have a simpler right-hand-side. `simp` can already
achieve these, via rewriting with `getKey_eq` under the lambda. However
`grind` can not, and these lemmas help `grind` work with `HashMap`
goals. There are variants for all variants of `HashMap`,
`getElem?/getElem/getElem!/getD`, and for `filter` and `filterMap`.
This PR implements normalization rules that pull universal quantifiers
across disjunctions. This is a common normalization step performed by
first-order theorem provers.
This PR improves the error messages produced by invalid pattern-match
alternatives and improves parity in error placement between
pattern-matching tactics and elaborators.
Closes#7170
This PR improves the error messages displayed in `inductive`
declarations when type parameters are invalid or absent.
Closes#2195 by improving the relevant error message.
This PR adds missing `Option` lemmas.
Also:
- generalize `bindM` from `Monad` to `Pure`
- change the `simp` normal form of both `<|>` and `Option.orElse` to
`Option.or`
This PR unifies various ways of naming auxiliary declarations in a
conflict-free way and ensures the method is compatible with diverging
branches of elaboration such as parallelism or Aesop-like
backtracking+replaying search.
This PR ensures that using `mapError` to expand an error message uses
`addMessageContext` to include the current context, so that expressions
are rendered correctly. Also adds a `preprendError` variant with a more
convenient argument order for the common cases of
prepending-and-indenting.
This PR improves the functional cases principles, by making a more
educated guess which function parameters should be targets and which
should remain parameters (or be dropped). This simplifies the
principles, and increases the chance that `fun_cases` can unfold the
function call.
Fixes#8296 (at least for the common cases, I hope.)
This PR fixes a type error at `instantiateTheorem` function used in
`grind`. It was failing to instantiate theorems such as
```lean
theorem getElem_reverse {xs : Array α} {i : Nat} (hi : i < xs.reverse.size)
: (xs.reverse)[i] = xs[xs.size - 1 - i]'(by simp at hi; omega)
```
in examples such as
```lean
example (xs : Array Nat) (w : xs.reverse = xs) (j : Nat) (hj : 0 ≤ j) (hj' : j < xs.size / 2)
: xs[j] = xs[xs.size - 1 - j]
```
generating the issue
```lean
[issue] type error constructing proof for Array.getElem_reverse
when assigning metavariable ?hi with
‹j < xs.toList.length›
has type
j < xs.toList.length : Prop
but is expected to have type
j < xs.reverse.size : Prop
```
This PR adds a new `structProjCases` pass to the new compiler, analogous
to the `struct_cases_on` pass in the old compiler, which converts all
projections from structs into `cases` expressions. When lowered to IR,
this causes all of the projections from a single structure to be grouped
together, which is an invariant relied upon by the IR RC passes (at
least for linearity, if not general correctness).
This PR adds the `expose` attribute to `Ordering.then`. This is required
for building with the new compiler, but works fine with the old compiler
because it silently ignores the missing definition.
This PR fixes the transparency mode for ground patterns. This is
important for implicit instances. Here is a mwe for an issue detected
while testing `grind` in Mathlib.
```lean
example (a : Nat) : max a a = a := by
grind
instance : Max Nat where
max := Nat.max
example (a : Nat) : max a a = a := by
grind -- Should work
```
This PR adds basic support for eta-reduction to `grind`.
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
Co-authored-by: Kim Morrison <scott.morrison@gmail.com>
This PR fixes a bug in the `cases` tacic introduced in #3188 that arises
when cases (not induction) is used with a non-atomic expression in using
and the argument indexing gets confused.
This fixes#8360.
This PR tries harder to clean internals of the argument packing of n-ary
functions from the functional induction theorem, in particular the
unfolding variant
This PR adjusts the experimental module system to not export the bodies
of `def`s unless opted out by the new attribute `@[expose]` on the `def`
or on a surrounding `section`.
---------
Co-authored-by: Markus Himmel <markus@lean-fro.org>
This PR splits `Lean.Grind.CommRing` into 4 typeclasses, for semirings
and noncommutative rings. This does not yet change the behaviour of
`grind`, which expects to find all 4 typeclasses. Later we will make
some generalizations.
This PR adds a `register_linter_set` command for declaring linter sets.
The `getLinterValue` function now checks if the present linter is
contained in a set that has been enabled (using the `set_option` command
or on the command line).
The implementation stores linter set membership in an environment
extension. As a consequence, we need to pass more data to
`getLinterValue`: the argument of ype `Options` has been replaced with a
`LinterOptions`, which you can access by writing `getLinterOptions`
instead of `getOptions`. (The alternative I considered is to modify the
`Options` structure. The current approach seems a bit higher-level and
lower-impact.)
The logic for checking whether a linter should be enabled now goes in
four steps:
1. If the linter has been explicitly en/disabled, return that.
2. If `linter.all` has been explicitly set, return that.
3. If the linter is in any set that has been enabled, return true.
4. Return the default setting for the linter.
Reasoning:
* The linter's explicit setting should take precedence.
* We want to be able to disable all but the explicitly enabled linters
with `linter.all`, so it should take precedence over linter sets.
* We want to progressively enable more linters as they become available,
so the check over sets should be *any*.
* Falling back to the default value last, ensures compatibility with the
current way we define linters.
The public-facing API currently does not allow modifying sets: all
linters have to be added when the set is declared. This way, there is
one place where all the contents of the set are listed.
Linter sets can be declared to contain linters that have not been
declared (yet): this allows declaring linter sets low down in the import
hierarchy when not all the requested linters are defined yet.
---------
Co-authored-by: grunweg <rothgami@math.hu-berlin.de>
This PR stops `dsimp` from visiting proof terms, which should make
`simp` and `dsimp` more efficient.
In this attempt I have `dsimp` leave the proofs in place as-is, instead
of simplifying the proof type.
Closes#6960
This PR changes the types `AltCore`, `FunDeclCore` and `CasesCore` used
in the IRs of the new compiler into the mutual inductives `Alt`,
`FunDecl` and `Cases`.
This PR refines the new wording of the "application type mismatch" error
message to avoid ambiguity in references to the "final" argument in a
subexpression that may be followed by additional arguments.
It does so by replacing "final" with "last," rephrasing the message so
that this adjective modifies the argument itself rather than the word
"argument," and only displaying this wording when two arguments could be
confused (determined by expression equality).
These changes were motivated by a report that in cases where a function
application `f a b c` fails to elaborate because `b` is incorrectly
typed, the existing error message's reference to `b` being the "final"
argument in the application `f a b` may create confusion because it is
not the final argument in the full application expression.
This PR removes the old documentation overview site, as its content has
moved to the main Lean website infrastructure.
This should be merged when the new website section is deployed, after
installing appropriate redirects.
Developer documentation is remaining in Markdown form, but it will no
longer be part of the documentation hosted on the Lean website. Example
code stays here for CI, but it is now rendered via a Verso plugin.
This PR improves support for structure extensionality in `grind`. It now
uses eta expansion for structures instead of the extensionality theorems
generated by `[ext]`. Examples:
```lean
opaque f (a : Nat) : Nat × Bool
attribute [grind ext] Prod Subtype
example (a b : Nat) : (f a).1 = (f b).1 → (f a).2 = (f b).2 → f a = f b := by
grind
def g (a : Nat) : { x : Nat // x > 1 } :=
⟨a + 2, by grind⟩
example (a b : Nat) : (g a).1 = (g b).1 → g a = g b := by
grind
@[grind ext] structure S where
x : Nat
y : Int
example (x y : S) : x.1 = y.1 → x.2 = y.2 → x = y := by
grind
```
This PR adds the instances `Grind.CommRing (Fin n)` and `Grind.IsCharP
(Fin n) n`. New tests:
```lean
example (x y z : Fin 13) :
(x + y + z) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 * (x * y + y * z + z * x) := by
grind +ring
example (x y : Fin 17) : (x + y) ^ 3 = x ^ 3 + y ^ 3 + 3 * x * y * (x + y) := by
grind +ring
example (x y : Fin 19) : (x - y) * (x ^ 2 + x * y + y ^ 2) = x ^ 3 - y ^ 3 := by
grind +ring
```
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
This PR splits `Std.Classes.Ord` into `Std.Classes.Ord.Basic` (with few
imports) and `Std.Classes.Ord.SInt` and `Std.Classes.Ord.Vector`. These
changes avoid importing `Init.Data.BitVec.Lemmas` unnecessarily into
various basic files.
As the new import-only file `Std.Classes.Ord` imports all three of
these, end-users are not affected.
This PR adds lemmas about the length and use of `[]?` on results of
`List.intersperse`.
This was suggested by @TwoFX as discussed in
https://github.com/TwoFX/human-eval-lean/pull/164#discussion_r2074101914.
I am unsure about the correct naming of `intersperse_getElem?_even` and
`intersperse_getElem?_odd`.
This PR makes `fun_induction` and `fun_cases` (try to) unfold the
function application of interest in the goal. The old behavior can be
enabled with `set_option tactic.fun_induction.unfolding false`. For
`fun_cases` this does not work yet when the function’s result type
depends on one of the arguments, see issue #8296.
This PR improves the performance of the workspace symbol request.
In my testing on my machine, the time to respond to the workspace symbol
request containing just `c` in Mathlib has been reduced to ~1200ms from
~11000ms.
We also serve the nearest-matching 1000 symbols instead of just the
first 100 now and use the length of the symbol as a tie-breaker for when
the fuzzy matching score is equal.
Some further improvements might be gained in the future when #8087 is
fixed and we can switch back to `qsort`.
This PR makes the new compiler's specialization pass compute closures
the same way as the old compiler, in particular when it comes to
variables captured by lambdas.
This PR makes it possible for `bv_decide` to tackle situations for its
enum type preprocessing where the enums themselves are use in a
dependently type context (for example inside of a `GetElem` body) and
thus not trivially accessible to `simp` for rewriting. To do this we
drop`GetElem` on `BitVec` as well as `dite` as early as possible in the
pipeline.
This PR optimizes the `ToIR.lean` module, reducing the size of the
compiled C code by a bit over a factor of 3. This significantly improves
the compilation time, making `ToIR` relatively quick to compile.
Closes#8269
This PR lets `cases` fail gracefully when the motive has an complex
argument whose type is dependent type on the targets. While the
`induction` tactic can handle this well, `cases` does not. This change
at least gracefully degrades to not instantiating that motive parameter.
See issue #8296 for more details on this issue.
This PR shows that negating a bitvector created from a natural number
equals creating a bitvector from the the negative of that number (as an
integer).
```lean
theorem neg_ofNat_eq_ofInt_neg {w : Nat} (x : Nat) :
- BitVec.ofNat w x = BitVec.ofInt w (- x) := by
apply BitVec.eq_of_toInt_eq
simp [BitVec.toInt_neg, BitVec.toInt_ofNat]
```
---------
Co-authored-by: Luisa Cicolini <48860705+luisacicolini@users.noreply.github.com>
This PR improves the generation of `.induct_unfolding` by rewriting
`match` statements more reliably, using the new “congruence equations”
introduced in #8284. Fixes#8195.
This PR adds a new variant of equations for matchers, namely “congruence
equations” that generalize the normal matcher equations. They have
unrestricted left-hand-sides, extra equality assumptions relating the
discriminiants with the patterns and thus prove heterogenous equalities.
In that sense they combine congruence with rewriting. They can be used
to rewrite matcher applications where, due to dependencies, `simp` would
fail to rewrite the discriminants, and will be used when producing the
unfolding induction theorems.
This PR optimizes lean_nat_shiftr for scalar operands. The new compiler
converts Nat divisions into right shifts, so this now shows up as hot in
some profiles.
This PR improves the type-as-hole error message. Type-as-hole error for
theorem declarations should not admit the possibility of omitting the
type entirely.
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This PR changes `addPPExplicitToExposeDiff` to show universe differences
and to visit into projections, e.g.:
```
error: tactic 'rfl' failed, the left-hand side
(Test.mk (∀ (x : PUnit.{1}), True)).1
is not definitionally equal to the right-hand side
(Test.mk (∀ (x : PUnit.{2}), True)).1
```
for
```lean
inductive Test where
| mk (x : Prop)
example : (Test.mk (∀ _ : PUnit.{1}, True)).1 = (Test.mk (∀ _ : PUnit.{2}, True)).1 := by
rfl
```
This PR makes `#guard_msgs` to treat `trace` messages separate from
`info`, `warning` and `error`. It also introduce the ability to say
`#guard_msgs (pass info`, like `(drop info)` so far, and also adds
`(check info)` as the explicit form of `(info)`, for completeness.
Fixes#8266
This PR adjusts the error message when `apply` fails to unify. It is
clearer about distinguishing the term being applied and the goal, as
well as distinguishing the "conclusion" of the given term and the term
itself.
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This PR rewords the `application type mismatch` error message by more
specifically mentioning that the problem is with the final argument.
This is useful when the same argument is passed to the function multiple
times.
We decided against using a wording which specifically mentions the
"function expression", because users who are not used to currying might
not think of the `f a` in `f a b` as a function.
This PR adds additional infrastructure for error message formatting.
Specifically, it adds convenience formatters for hints and notes,
including the ability to attach code actions to hint messages using a
"Try This"-like widget, along with several convenience formatters for
message data.
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
This PR fixes unintended inlining of `ToJson`, `FromJson`, and `Repr`
instances, which was causing exponential compilation times in `deriving`
clauses for large structures.
This PR omits cases from functional induction/cases principles that are
implemented `by contradiction` (or, more generally, `False.elim`,
`absurd` or `noConfusion). Breaking change in the sense that there are
fewer goals to prove after using functional induction.
Fixes#8103.
This PR avoids an issue where, through other potential bugs, constants
that are tracked by `Kernel.Environment` but not `Environment` are not
persisted.
This PR changes the behaviour of `apply?` so that the `sorry` it uses to
close the goal is non-synthetic. (Recall that correct use of synthetic
sorries requires that the tactic also generates an error message, which
we don't want to do in this situation.) Either this PR or #8230 are
sufficient to defend against the problem reported in #8212.
This PR adds the `--setup` option to the `lean` CLI. It takes a path to
a JSON file containing information about a module's imports and
configuration, superseding that in the module's own file header. This
will be used by Lake to specify paths to module artifacts (e.g., oleans
and ileans) separate from the `LEAN_PATH` schema.
To facilitate JSON serialization of the header data structure, `NameMap`
JSON instances have been added to core, and `LeanOptions` now makes use
of them.
These lemmas were inconsistently marked as `@[simp]`, but they seem
generally useful, so this uniformly marks this lemmas as `@[simp]` for
all map variants.
This PR reduces the need for defeq in frequently used bv_decide rewrite
by turning them into simprocs that work on structural equality instead.
As the intended meaning of these rewrites is to simply work with
structural equality anyways this should not change the proving power of
`bv_decide`'s rewriter but just make it faster on certain very large
problems.
This PR takes the existing `getElem_map` statements for `HashMap`
variants (also `getElem?`, `getElem!`, and `getD` statements), adds a
prime to their name and an explanatory comment, and replaces the
unprimed statement with a simpler statement that is only true with
`LawfulBEq` present. The original statements which were simp lemmas are
now low priority simp lemmas, so the nicer statements should fire when
`LawfulBEq` is available.
This PR fixes an issue in the theory propagation used in `grind`. When
two equivalence classes are merged, the core may need to push additional
equalities or disequalities down to the satellite theory solvers (e.g.,
`cutsat`, `comm ring`, etc). Some solvers (e.g. `cutsat`) assume that
all of the core’s invariants hold before they receive those facts.
Propagating immediately therefore risks violating a solver’s
pre-conditions midway through the merge. To decouple the merge operation
from propagation and to keep the core solver-agnostic, this PR adds the
helper type `PendingTheoryPropagation`.
This PR improves the E-matching pattern inference procedure in `grind`.
Consider the following theorem:
```lean
@[grind →]
theorem eq_empty_of_append_eq_empty {xs ys : Array α} (h : xs ++ ys = #[]) : xs = #[] ∧ ys = #[] :=
append_eq_empty_iff.mp h
```
Before this PR, `grind` inferred the following pattern:
```lean
@HAppend.hAppend _ _ _ _ #2#1
```
Note that this pattern would match any `++` application, even if it had
nothing to do with arrays. With this PR, the inferred pattern becomes:
```lean
@HAppend.hAppend (Array #3) (Array _) (Array _) _ #2#1
```
With the new pattern, the theorem will not be considered by `grind` for
goals that do not involve `Array`s.
echo "... and Batteries has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
@@ -143,7 +183,6 @@ jobs:
echo "... but Batteries does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE="- ❗ Batteries CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Batteries CI should run now."
fi
else
echo "The most recently nightly tag on this branch has SHA: $NIGHTLY_SHA"
echo "... and the reference manual has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE=""
else
echo "... but the reference manual does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE="- ❗ Reference manual CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-manual\`, reference manual CI should run now."
fi
else
echo "The most recently nightly tag on this branch has SHA: $NIGHTLY_SHA"
MESSAGE="- ❗ Reference manual CI will not be attempted unless your PR branches off the \`nightly-with-manual\` branch. Try \`git rebase $MERGE_BASE_SHA --onto $NIGHTLY_WITH_MANUAL_SHA\`."
# The reference manual's `nightly-testing` branch or `nightly-testing-YYYY-MM-DD` tag may have moved since this branch was created, so merge their changes.
# (This should no longer be possible once `nightly-testing-YYYY-MM-DD` is a tag, but it is still safe to merge.)
# store all variables passed on the command line into CL_ARGS so we can pass them to the stage builds
# https://stackoverflow.com/a/48555098/161659
# MUST be done before call to 'project'
# Use standard release build (discarding LEAN_CXX_EXTRA_FLAGS etc.) for stage0 by default since it is assumed to be "good", but still pass through CMake platform arguments (compiler, toolchain file, ..).
# Use standard release build (discarding LEAN_EXTRA_CXX_FLAGS etc.) for stage0 by default since it is assumed to be "good", but still pass through CMake platform arguments (compiler, toolchain file, ..).
# Use `STAGE0_` prefix to pass variables to stage0 explicitly.
A declaration name is a hierarchical [identifier](lexical_structure.md#identifiers) that is interpreted relative to the current namespace as well as (during lookup) to the set of open namespaces.
```lean
namespaceA
opaqueB.c:Nat
#printB.c-- opaque A.B.c : Nat
endA
#printA.B.c-- opaque A.B.c : Nat
openA
#printB.c-- opaque A.B.c : Nat
```
Declaration names starting with an underscore are reserved for internal use. Names starting with the special atomic name ``_root_`` are interpreted as absolute names.
```lean
opaque a : Nat
namespace A
opaque a : Int
#print _root_.a -- opaque a : Nat
#print A.a -- opaque A.a : Int
end A
```
Contexts and Telescopes
=======================
When processing user input, Lean first parses text to a raw expression format. It then uses background information and type constants to disambiguate overloaded symbols and infer implicit arguments, resulting in a fully-formed expression. This process is known as *elaboration*.
As hinted in [Expression Syntax](expressions.md#expression_syntax),
expressions are parsed and elaborated with respect to an *environment*
and a *local context*. Roughly speaking, an environment represents the
state of Lean at the point where an expression is parsed, including
previously declared axioms, constants, definitions, and theorems. In a
given environment, a *local context* consists of a sequence ``(a₁ :
α₁) (a₂ : α₂) ... (aₙ : αₙ)`` where each ``aᵢ`` is a name denoting a
local constant and each ``αᵢ`` is an expression of type ``Sort u`` for
some ``u`` which can involve elements of the environment and the local
constants ``aⱼ`` for ``j < i``.
Intuitively, a local context is a list of variables that are held constant while an expression is being elaborated. Consider the following
```lean
def f (a b : Nat) : Nat → Nat := fun c => a + (b + c)
```
Here the expression ``fun c => a + (b + c)`` is elaborated in the context ``(a : Nat) (b : Nat)`` and the expression ``a + (b + c)`` is elaborated in the context ``(a : Nat) (b : Nat) (c : Nat)``. If you replace the expression ``a + (b + c)`` with an underscore, the error message from Lean will include the current *goal*:
```
a b c : Nat
⊢ Nat
```
Here ``a b c : Nat`` indicates the local context, and the second ``Nat`` indicates the expected type of the result.
A *context* is sometimes called a *telescope*, but the latter is used more generally to include a sequence of declarations occurring relative to a given context. For example, relative to the context ``(a₁ : α₁) (a₂ : α₂) ... (aₙ : αₙ)``, the types ``βᵢ`` in a telescope ``(b₁ : β₁) (b₂ : β₂) ... (bₙ : βₙ)`` can refer to ``a₁, ..., aₙ``. Thus a context can be viewed as a telescope relative to the empty context.
Telescopes are often used to describe a list of arguments, or parameters, to a declaration. In such cases, it is often notationally convenient to let ``(a : α)`` stand for a telescope rather than just a single argument. In general, the annotations described in [Implicit Arguments](expressions.md#implicit_arguments) can be used to mark arguments as implicit.
.. _basic_declarations:
Basic Declarations
==================
Lean provides ways of adding new objects to the environment. The following provide straightforward ways of declaring new objects:
* ``axiom c : α`` : declare a constant named ``c`` of type ``α``, it is postulating that `α` is not an empty type.
* ``def c : α := v`` : defines ``c`` to denote ``v``, which should have type ``α``.
* ``theorem c : p := v`` : similar to ``def``, but intended to be used when ``p`` is a proposition.
* ``opaque c : α (:= v)?`` : declares a opaque constant named ``c`` of type ``α``, the optional value `v` is must have type `α`
and can be viewed as a certificate that ``α`` is not an empty type. If the value is not provided, Lean tries to find one
using a procedure based on type class resolution. The value `v` is hidden from the type checker. You can assume that
Lean "forgets" `v` after type checking this kind of declaration.
It is sometimes useful to be able to simulate a definition or theorem without naming it or adding it to the environment.
* ``example : α := t`` : elaborates ``t`` and checks that it has sort ``α`` (often a proposition), without adding it to the environment.
In ``def``, the type (``α`` or ``p``, respectively) can be omitted when it can be inferred by Lean. Constants declared with ``theorem`` are marked as ``irreducible``.
Any of ``def``, ``theorem``, ``axiom``, or ``example`` can take a list of arguments (that is, a context) before the colon. If ``(a : α)`` is a context, the definition ``def foo (a : α) : β := t``
is interpreted as ``def foo : (a : α) → β := fun a : α => t``. Similarly, a theorem ``theorem foo (a : α) : p := t`` is interpreted as ``theorem foo : ∀ a : α, p := fun a : α => t``.
```lean
opaque c : Nat
opaque d : Nat
axiom cd_eq : c = d
def foo : Nat := 5
def bar := 6
def baz (x y : Nat) (s : List Nat) := [x, y] ++ s
theorem foo_eq_five : foo = 5 := rfl
theorem baz_theorem (x y : Nat) : baz x y [] = [x, y] := rfl
example (x y : Nat) : baz x y [] = [x, y] := rfl
```
Inductive Types
===============
Lean's axiomatic foundation allows users to declare arbitrary
inductive families, following the pattern described by [Dybjer]_. To
make the presentation more manageable, we first describe inductive
*types*, and then describe the generalization to inductive *families*
in the next section. The declaration of an inductive type has the
following form:
```
inductive Foo (a : α) where
| constructor₁ : (b : β₁) → Foo a
| constructor₂ : (b : β₂) → Foo a
...
| constructorₙ : (b : βₙ) → Foo a
```
Here ``(a : α)`` is a context and each ``(b : βᵢ)`` is a telescope in the context ``(a : α)`` together with ``Foo``, subject to the following constraints.
Suppose the telescope ``(b : βᵢ)`` is ``(b₁ : βᵢ₁) ... (bᵤ : βᵢᵤ)``. Each argument in the telescope is either *nonrecursive* or *recursive*.
- An argument ``(bⱼ : βᵢⱼ)`` is *nonrecursive* if ``βᵢⱼ`` does not refer to ``foo,`` the inductive type being defined. In that case, ``βᵢⱼ`` can be any type, so long as it does not refer to any nonrecursive arguments.
- An argument ``(bⱼ : βᵢⱼ)`` is *recursive* if it ``βᵢⱼ`` of the form ``Π (d : δ), foo`` where ``(d : δ)`` is a telescope which does not refer to ``foo`` or any nonrecursive arguments.
The inductive type ``foo`` represents a type that is freely generated by the constructors. Each constructor can take arbitrary data and facts as arguments (the nonrecursive arguments), as well as indexed sequences of elements of ``foo`` that have been previously constructed (the recursive arguments). In set theoretic models, such sets can be represented by well-founded trees labeled by the constructor data, or they can defined using other transfinite or impredicative means.
The declaration of the type ``foo`` as above results in the addition of the following constants to the environment:
- the *type former* ``foo : Π (a : α), Sort u``
- for each ``i``, the *constructor* ``foo.constructorᵢ : Π (a : α) (b : βᵢ), foo a``
- the *eliminator* ``foo.rec``, which takes arguments
+ ``(a : α)`` (the parameters)
+ ``{C : foo a → Type u}`` (the *motive* of the elimination)
+ for each ``i``, the *minor premise* corresponding to ``constructorᵢ``
+ ``(x : foo)`` (the *major premise*)
and returns an element of ``C x``. Here, The ith minor premise is a function which takes
+ ``(b : βᵢ)`` (the arguments to the constructor)
+ an argument of type ``Π (d : δ), C (bⱼ d)`` corresponding to each recursive argument ``(bⱼ : βᵢⱼ)``, where ``βᵢⱼ`` is of the form ``Π (d : δ), foo`` (the recursive values of the function being defined)
and returns an element of ``C (constructorᵢ a b)``, the intended value of the function at ``constructorᵢ a b``.
The eliminator represents a principle of recursion: to construct an element of ``C x`` where ``x : foo a``, it suffices to consider each of the cases where ``x`` is of the form ``constructorᵢ a b`` and to provide an auxiliary construction in each case. In the case where some of the arguments to ``constructorᵢ`` are recursive, we can assume that we have already constructed values of ``C y`` for each value ``y`` constructed at an earlier stage.
Under the propositions-as-type correspondence, when ``C x`` is an element of ``Prop``, the eliminator represents a principle of induction. In order to show ``∀ x, C x``, it suffices to show that ``C`` holds for each constructor, under the inductive hypothesis that it holds for all recursive inputs to the constructor.
The eliminator and constructors satisfy the following identities, in which all the arguments are shown explicitly. Suppose we set ``F := foo.rec a C f₁ ... fₙ``. Then for each constructor, we have the definitional reduction:
```
F (constructorᵢ a b) = fᵢ b ... (fun d : δᵢⱼ => F (bⱼ d)) ...
```
where the ellipses include one entry for each recursive argument.
Below are some common examples of inductive types, many of which are defined in the core library.
```lean
namespace Hide
universe u v
-- BEGIN
inductive Empty : Type
inductive Unit : Type
| unit : Unit
inductive Bool : Type
| false : Bool
| true : Bool
inductive Prod (α : Type u) (β : Type v) : Type (max u v)
inductive Subtype (α : Type u) (p : α → Prop) : Type u
| intro : ∀ x : α, p x → Subtype α p
inductive Nat : Type
| zero : Nat
| succ : Nat → Nat
inductive List (α : Type u)
| nil : List α
| cons : α → List α → List α
-- full binary tree with nodes and leaves labeled from α
inductive BinTree (α : Type u)
| leaf : α → BinTree α
| node : BinTree α → α → BinTree α → BinTree α
-- every internal node has subtrees indexed by Nat
inductive CBT (α : Type u)
| leaf : α → CBT α
| node : (Nat → CBT α) → CBT α
-- END
end Hide
```
Note that in the syntax of the inductive definition ``Foo``, the context ``(a : α)`` is left implicit. In other words, constructors and recursive arguments are written as though they have return type ``Foo`` rather than ``Foo a``.
Elements of the context ``(a : α)`` can be marked implicit as described in [Implicit Arguments](#implicit.md#implicit_arguments). These annotations bear only on the type former, ``Foo``. Lean uses a heuristic to determine which arguments to the constructors should be marked implicit, namely, an argument is marked implicit if it can be inferred from the type of a subsequent argument. If the annotation ``{}`` appears after the constructor, a argument is marked implicit if it can be inferred from the type of a subsequent argument *or the return type*. For example, it is useful to let ``nil`` denote the empty list of any type, since the type can usually be inferred in the context in which it appears. These heuristics are imperfect, and you may sometimes wish to define your own constructors in terms of the default ones. In that case, use the ``[match_pattern]`` [attribute](TODO: missing link) to ensure that these will be used appropriately by the [Equation Compiler](#the-equation-compiler).
There are restrictions on the universe ``u`` in the return type ``Sort u`` of the type former. There are also restrictions on the universe ``u`` in the return type ``Sort u`` of the motive of the eliminator. These will be discussed in the next section in the more general setting of inductive families.
Lean allows some additional syntactic conveniences. You can omit the return type of the type former, ``Sort u``, in which case Lean will infer the minimal possible nonzero value for ``u``. As with function definitions, you can list arguments to the constructors before the colon. In an enumerated type (that is, one where the constructors have no arguments), you can also leave out the return type of the constructors.
```lean
namespace Hide
universe u
-- BEGIN
inductive Weekday
| sunday | monday | tuesday | wednesday
| thursday | friday | saturday
inductive Nat
| zero
| succ (n : Nat) : Nat
inductive List (α : Type u)
| nil : List α
| cons (a : α) (l : List α) : List α
@[match_pattern]
def List.nil' (α : Type u) : List α := List.nil
def length {α : Type u} : List α → Nat
| (List.nil' _) => 0
| (List.cons a l) => 1 + length l
-- END
end Hide
```
The type former, constructors, and eliminator are all part of Lean's axiomatic foundation, which is to say, they are part of the trusted kernel. In addition to these axiomatically declared constants, Lean automatically defines some additional objects in terms of these, and adds them to the environment. These include the following:
- ``Foo.recOn`` : a variant of the eliminator, in which the major premise comes first
- ``Foo.casesOn`` : a restricted version of the eliminator which omits any recursive calls
- ``Foo.noConfusionType``, ``Foo.noConfusion`` : functions which witness the fact that the inductive type is freely generated, i.e. that the constructors are injective and that distinct constructors produce distinct objects
- ``Foo.below``, ``Foo.ibelow`` : functions used by the equation compiler to implement structural recursion
- ``instance : SizeOf Foo`` : a measure which can be used for well-founded recursion
Note that it is common to put definitions and theorems related to a datatype ``foo`` in a namespace of the same name. This makes it possible to use projection notation described in [Structures](struct.md#structures) and [Namespaces](namespaces.md#namespaces).
```lean
namespace Hide
universe u
-- BEGIN
inductive Nat
| zero
| succ (n : Nat) : Nat
#check Nat
#check @Nat.rec
#check Nat.zero
#check Nat.succ
#check @Nat.recOn
#check @Nat.casesOn
#check @Nat.noConfusionType
#check @Nat.noConfusion
#check @Nat.brecOn
#check Nat.below
#check Nat.ibelow
#check Nat._sizeOf_1
-- END
end Hide
```
.. _inductive_families:
Inductive Families
==================
In fact, Lean implements a slight generalization of the inductive types described in the previous section, namely, inductive *families*. The declaration of an inductive family in Lean has the following form:
```
inductive Foo (a : α) : Π (c : γ), Sort u
| constructor₁ : Π (b : β₁), Foo t₁
| constructor₂ : Π (b : β₂), Foo t₂
...
| constructorₙ : Π (b : βₙ), Foo tₙ
```
Here ``(a : α)`` is a context, ``(c : γ)`` is a telescope in context ``(a : α)``, each ``(b : βᵢ)`` is a telescope in the context ``(a : α)`` together with ``(Foo : Π (c : γ), Sort u)`` subject to the constraints below, and each ``tᵢ`` is a tuple of terms in the context ``(a : α) (b : βᵢ)`` having the types ``γ``. Instead of defining a single inductive type ``Foo a``, we are now defining a family of types ``Foo a c`` indexed by elements ``c : γ``. Each constructor, ``constructorᵢ``, places its result in the type ``Foo a tᵢ``, the member of the family with index ``tᵢ``.
The modifications to the scheme in the previous section are straightforward. Suppose the telescope ``(b : βᵢ)`` is ``(b₁ : βᵢ₁) ... (bᵤ : βᵢᵤ)``.
- As before, an argument ``(bⱼ : βᵢⱼ)`` is *nonrecursive* if ``βᵢⱼ`` does not refer to ``Foo,`` the inductive type being defined. In that case, ``βᵢⱼ`` can be any type, so long as it does not refer to any nonrecursive arguments.
- An argument ``(bⱼ : βᵢⱼ)`` is *recursive* if ``βᵢⱼ`` is of the form ``Π (d : δ), Foo s`` where ``(d : δ)`` is a telescope which does not refer to ``Foo`` or any nonrecursive arguments and ``s`` is a tuple of terms in context ``(a : α)`` and the previous nonrecursive ``bⱼ``'s with types ``γ``.
The declaration of the type ``Foo`` as above results in the addition of the following constants to the environment:
- the *type former* ``Foo : Π (a : α) (c : γ), Sort u``
- for each ``i``, the *constructor* ``Foo.constructorᵢ : Π (a : α) (b : βᵢ), Foo a tᵢ``
- the *eliminator* ``Foo.rec``, which takes arguments
+ ``(a : α)`` (the parameters)
+ ``{C : Π (c : γ), Foo a c → Type u}`` (the motive of the elimination)
+ for each ``i``, the minor premise corresponding to ``constructorᵢ``
+ ``(x : Foo a)`` (the major premise)
and returns an element of ``C x``. Here, The ith minor premise is a function which takes
+ ``(b : βᵢ)`` (the arguments to the constructor)
+ an argument of type ``Π (d : δ), C s (bⱼ d)`` corresponding to each recursive argument ``(bⱼ : βᵢⱼ)``, where ``βᵢⱼ`` is of the form ``Π (d : δ), Foo s``
and returns an element of ``C tᵢ (constructorᵢ a b)``.
Suppose we set ``F := Foo.rec a C f₁ ... fₙ``. Then for each constructor, we have the definitional reduction, as before:
```
F (constructorᵢ a b) = fᵢ b ... (fun d : δᵢⱼ => F (bⱼ d)) ...
```
where the ellipses include one entry for each recursive argument.
The following are examples of inductive families.
```lean
namespace Hide
universe u
-- BEGIN
inductive Vector (α : Type u) : Nat → Type u
| nil : Vector 0
| succ : Π n, Vector n → Vector (n + 1)
-- 'IsProd s n' means n is a product of elements of s
inductive IsProd (s : Set Nat) : Nat → Prop
| base : ∀ n ∈ s, IsProd n
| step : ∀ m n, IsProd m → IsProd n → IsProd (m * n)
inductive Eq {α : Sort u} (a : α) : α → Prop
| refl : Eq a
-- END
end Hide
```
We can now describe the constraints on the return type of the type former, ``Sort u``. We can always take ``u`` to be ``0``, in which case we are defining an inductive family of propositions. If ``u`` is nonzero, however, it must satisfy the following constraint: for each type ``βᵢⱼ : Sort v`` occurring in the constructors, we must have ``u ≥ v``. In the set-theoretic interpretation, this ensures that the universe in which the resulting type resides is large enough to contain the inductively generated family, given the number of distinctly-labeled constructors. The restriction does not hold for inductively defined propositions, since these contain no data.
Putting an inductive family in ``Prop``, however, does impose a restriction on the eliminator. Generally speaking, for an inductive family in ``Prop``, the motive in the eliminator is required to be in ``Prop``. But there is an exception to this rule: you are allowed to eliminate from an inductively defined ``Prop`` to an arbitrary ``Sort`` when there is only one constructor, and each argument to that constructor is either in ``Prop`` or an index. The intuition is that in this case the elimination does not make use of any information that is not already given by the mere fact that the type of argument is inhabited. This special case is known as *singleton elimination*.
.. _mutual_and_nested_inductive_definitions:
Mutual and Nested Inductive Definitions
=======================================
Lean supports two generalizations of the inductive families described above, namely, *mutual* and *nested* inductive definitions. These are *not* implemented natively in the kernel. Rather, the definitions are compiled down to the primitive inductive types and families.
The first generalization allows for multiple inductive types to be defined simultaneously.
```
mutual
inductive Foo (a : α) : Π (c : γ₁), Sort u
| constructor₁₁ : Π (b : β₁₁), Foo a t₁₁
| constructor₁₂ : Π (b : β₁₂), Foo a t₁₂
...
| constructor₁ₙ : Π (b : β₁ₙ), Foo a t₁ₙ
inductive Bar (a : α) : Π (c : γ₂), Sort u
| constructor₂₁ : Π (b : β₂₁), Bar a t₂₁
| constructor₂₂ : Π (b : β₂₂), Bar a t₂₂
...
| constructor₂ₘ : Π (b : β₂ₘ), Bar a t₂ₘ
end
```
Here the syntax is shown for defining two inductive families, ``Foo`` and ``Bar``, but any number is allowed. The restrictions are almost the same as for ordinary inductive families. For example, each ``(b : βᵢⱼ)`` is a telescope relative to the context ``(a : α)``. The difference is that the constructors can now have recursive arguments whose return types are any of the inductive families currently being defined, in this case ``Foo`` and ``Bar``. Note that all of the inductive definitions share the same parameters ``(a : α)``, though they may have different indices.
A mutual inductive definition is compiled down to an ordinary inductive definition using an extra finite-valued index to distinguish the components. The details of the internal construction are meant to be hidden from most users. Lean defines the expected type formers ``Foo`` and ``Bar`` and constructors ``constructorᵢⱼ`` from the internal inductive definition. There is no straightforward elimination principle, however. Instead, Lean defines an appropriate ``sizeOf`` measure, meant for use with well-founded recursion, with the property that the recursive arguments to a constructor are smaller than the constructed value.
The second generalization relaxes the restriction that in the recursive definition of ``Foo``, ``Foo`` can only occur strictly positively in the type of any of its recursive arguments. Specifically, in a nested inductive definition, ``Foo`` can appear as an argument to another inductive type constructor, so long as the corresponding parameter occurs strictly positively in the constructors for *that* inductive type. This process can be iterated, so that additional type constructors can be applied to those, and so on.
A nested inductive definition is compiled down to an ordinary inductive definition using a mutual inductive definition to define copies of all the nested types simultaneously. Lean then constructs isomorphisms between the mutually defined nested types and their independently defined counterparts. Once again, the internal details are not meant to be manipulated by users. Rather, the type former and constructors are made available and work as expected, while an appropriate ``sizeOf`` measure is generated for use with well-founded recursion.
```lean
universe u
-- BEGIN
mutual
inductive Even : Nat → Prop
| even_zero : Even 0
| even_succ : ∀ n, Odd n → Even (n + 1)
inductive Odd : Nat → Prop
| odd_succ : ∀ n, Even n → Odd (n + 1)
end
inductive Tree (α : Type u)
| mk : α → List (Tree α) → Tree α
inductive DoubleTree (α : Type u)
| mk : α → List (DoubleTree α) × List (DoubleTree α) → DoubleTree α
-- END
```
.. _the_equation_compiler:
The Equation Compiler
=====================
The equation compiler takes an equational description of a function or proof and tries to define an object meeting that specification. It expects input with the following syntax:
```
def foo (a : α) : Π (b : β), γ
| [patterns₁] => t₁
...
| [patternsₙ] => tₙ
```
Here ``(a : α)`` is a telescope, ``(b : β)`` is a telescope in the context ``(a : α)``, and ``γ`` is an expression in the context ``(a : α) (b : β)`` denoting a ``Type`` or a ``Prop``.
Each ``patternsᵢ`` is a sequence of patterns of the same length as ``(b : β)``. A pattern is either:
- a variable, denoting an arbitrary value of the relevant type,
- an underscore, denoting a *wildcard* or *anonymous variable*,
- an inaccessible term (see below), or
- a constructor for the inductive type of the corresponding argument, applied to a sequence of patterns.
In the last case, the pattern must be enclosed in parentheses.
Each term ``tᵢ`` is an expression in the context ``(a : α)`` together with the variables introduced on the left-hand side of the token ``=>``. The term ``tᵢ`` can also include recursive calls to ``foo``, as described below. The equation compiler does case splitting on the variables ``(b : β)`` as necessary to match the patterns, and defines ``foo`` so that it has the value ``tᵢ`` in each of the cases. In ideal circumstances (see below), the equations hold definitionally. Whether they hold definitionally or only propositionally, the equation compiler proves the relevant equations and assigns them internal names. They are accessible by the ``rewrite`` and ``simp`` tactics under the name ``foo`` (see [Rewrite](tactics.md#rewrite) and _[TODO: where is simplifier tactic documented?]_. If some of the patterns overlap, the equation compiler interprets the definition so that the first matching pattern applies in each case. Thus, if the last pattern is a variable, it covers all the remaining cases. If the patterns that are presented do not cover all possible cases, the equation compiler raises an error.
When identifiers are marked with the ``[match_pattern]`` attribute, the equation compiler unfolds them in the hopes of exposing a constructor. For example, this makes it possible to write ``n+1`` and ``0`` instead of ``Nat.succ n`` and ``Nat.zero`` in patterns.
For a nonrecursive definition involving case splits, the defining equations will hold definitionally. With inductive types like ``Char``, ``String``, and ``Fin n``, a case split would produce definitions with an inordinate number of cases. To avoid this, the equation compiler uses ``if ... then ... else`` instead of ``casesOn`` when defining the function. In this case, the defining equations hold definitionally as well.
```lean
open Nat
def sub2 : Nat → Nat
| zero => 0
| succ zero => 0
| succ (succ a) => a
def bar : Nat → List Nat → Bool → Nat
| 0, _, false => 0
| 0, b :: _, _ => b
| 0, [], true => 7
| a+1, [], false => a
| a+1, [], true => a + 1
| a+1, b :: _, _ => a + b
def baz : Char → Nat
| 'A' => 1
| 'B' => 2
| _ => 3
```
The case where patterns are matched against an argument whose type is an inductive family is known as *dependent pattern matching*. This is more complicated, because the type of the function being defined can impose constraints on the patterns that are matched. In this case, the equation compiler will detect inconsistent cases and rule them out.
```lean
universe u
inductive Vector (α : Type u) : Nat → Type u
| nil : Vector α 0
| cons : α → Vector α n → Vector α (n+1)
namespace Vector
def head : Vector α (n+1) → α
| cons h t => h
def tail : Vector α (n+1) → Vector α n
| cons h t => t
def map (f : α → β → γ) : Vector α n → Vector β n → Vector γ n
| nil, nil => nil
| cons a va, cons b vb => cons (f a b) (map f va vb)
end Vector
```
.. _recursive_functions:
Recursive functions
===================
Lean must ensure that a recursive function terminates, for which there are two strategies: _structural recursion_, in which all recursive calls are made on smaller parts of the input data, and _well-founded recursion_, in which recursive calls are justified by showing that arguments to recursive calls are smaller according to some other measure.
Structural recursion
--------------------
If the definition of a function contains recursive calls, Lean first tries to interpret the definition as a structural recursion. In order for that to succeed, the recursive arguments must be subterms of the corresponding arguments on the left-hand side.
The function is then defined using a *course of values* recursion, using automatically generated functions ``below`` and ``brec`` in the namespace corresponding to the inductive type of the recursive argument. In this case the defining equations hold definitionally, possibly with additional case splits.
If structural recursion fails, the equation compiler falls back on well-founded recursion. It tries to infer an instance of ``SizeOf`` for the type of each argument, and then tries to find a permutation of the arguments such that each recursive call is decreasing under the lexicographic order with respect to ``sizeOf`` measures. Lean uses information in the local context, so you can often provide the relevant proof manually using ``have`` in the body of the definition.
In the case of well-founded recursion, the equation used to declare the function holds only propositionally, but not definitionally, and can be accessed using ``unfold``, ``simp`` and ``rewrite`` with the function name (for example ``unfold foo`` or ``simp [foo]``, where ``foo`` is the function defined with well-founded recursion).
```lean
namespace Hide
open Nat
-- BEGIN
def div : Nat → Nat → Nat
| x, y =>
if h : 0 < y ∧ y ≤ x then
have : x - y < x :=
sub_lt (Nat.lt_of_lt_of_le h.left h.right) h.left
div (x - y) y + 1
else
0
example (x y : Nat) :
div x y = if 0 < y ∧ y ≤ x then div (x - y) y + 1 else 0 :=
by rw [div]; rfl
-- END
end Hide
```
If Lean cannot find a permutation of the arguments for which all recursive calls are decreasing, it will print a table that contains, for every recursive call, which arguments Lean could prove to be decreasing. For example, a function with three recursive calls and four parameters might cause the following message to be printed
```
example.lean:37:0-43:31: error: Could not find a decreasing measure.
The arguments relate at each recursive call as follows:
(<, ≤, =: relation proved, ? all proofs failed, _: no proof attempted)
x1 x2 x3 x4
1) 39:6-27 = = _ =
2) 40:6-25 = ? _ <
3) 41:6-25 < _ _ _
Please use `termination_by` to specify a decreasing measure.
```
This table should be read as follows:
* In the first recursive call, in line 39, arguments 1, 2 and 4 are equal to the function's parameters.
* The second recursive call, in line 40, has an equal first argument, a smaller fourth argument, and nothing could be inferred for the second argument.
* The third recursive call, in line 41, has a decreasing first argument.
* No other proofs were attempted, either because the parameter has a type without a non-trivial ``WellFounded`` instance (parameter 3), or because it is already clear that no decreasing measure can be found.
Lean will print the termination measure it found if ``set_option showInferredTerminationBy true`` is set.
If Lean does not find the termination measure, or if you want to be explicit, you can append a `termination_by` clause to the function definition, after the function's body, but before the `where` clause if present. It is of the form
```
termination_by e
```
where ``e`` is an expression that depends on the parameters of the function and should be decreasing at each recursive call. The type of `e` should be an instance of the class ``WellFoundedRelation``, which determines how to compare two values of that type.
If ``f`` has parameters “after the ``:``” (for example when defining functions via patterns using `|`), then these can be brought into scope using the syntax
```
termination_by a₁ … aₙ => e
```
By default, Lean uses the tactic ``decreasing_tactic`` when proving that an argument is decreasing; see its documentation for how to globally extend it. You can also choose to use a different tactic for a given function definition with the clause
```
decreasing_by <tac>
```
which should come after ``termination_by`, if present.
Note that recursive definitions can in general require nested recursions, that is, recursion on different arguments of ``foo`` in the template above. The equation compiler handles this by abstracting later arguments, and recursively defining higher-order functions to meet the specification.
Mutual recursion
----------------
The equation compiler also allows mutual recursive definitions, with a syntax similar to that of [Mutual and Nested Inductive Definitions](#mutual-and-nested-inductive-definitions). Mutual definitions are always compiled using well-founded recursion, and so once again the defining equations hold only propositionally.
```lean
mutual
def even : Nat → Bool
| 0 => true
| a+1 => odd a
def odd : Nat → Bool
| 0 => false
| a+1 => even a
end
example (a : Nat) : even (a + 1) = odd a :=
by simp [even]
example (a : Nat) : odd (a + 1) = even a :=
by simp [odd]
```
Well-founded recursion is especially useful with [Mutual and Nested Inductive Definitions](#mutual-and-nested-inductive-definitions), since it provides the canonical way of defining functions on these types.
```lean
mutual
inductive Even : Nat → Prop
| even_zero : Even 0
| even_succ : ∀ n, Odd n → Even (n + 1)
inductive Odd : Nat → Prop
| odd_succ : ∀ n, Even n → Odd (n + 1)
end
open Even Odd
theorem not_odd_zero : ¬ Odd 0 := fun x => nomatch x
mutual
theorem even_of_odd_succ : ∀ n, Odd (n + 1) → Even n
| _, odd_succ n h => h
theorem odd_of_even_succ : ∀ n, Even (n + 1) → Odd n
| _, even_succ n h => h
end
inductive Term
| const : String → Term
| app : String → List Term → Term
open Term
mutual
def num_consts : Term → Nat
| .const n => 1
| .app n ts => num_consts_lst ts
def num_consts_lst : List Term → Nat
| [] => 0
| t::ts => num_consts t + num_consts_lst ts
end
```
In a set of mutually recursive function, either all or no functions must have an explicit termination measure (``termination_by``). A change of the default termination tactic (``decreasing_by``) only affects the proofs about the recursive calls of that function, not the other functions in the group.
```
mutual
theorem even_of_odd_succ : ∀ n, Odd (n + 1) → Even n
| _, odd_succ n h => h
termination_by n h => h
decreasing_by decreasing_tactic
theorem odd_of_even_succ : ∀ n, Even (n + 1) → Odd n
| _, even_succ n h => h
termination_by n h => h
end
```
Another way to express mutual recursion is using local function definitions in ``where`` or ``let rec`` clauses: these can be mutually recursive with each other and their containing function:
```
theorem even_of_odd_succ : ∀ n, Odd (n + 1) → Even n
| _, odd_succ n h => h
termination_by n h => h
where
theorem odd_of_even_succ : ∀ n, Even (n + 1) → Odd n
| _, even_succ n h => h
termination_by n h => h
```
.. _match_expressions:
Match Expressions
=================
Lean supports a ``match ... with ...`` construct similar to ones found in most functional programming languages. The syntax is as follows:
```
match t₁, ..., tₙ with
| p₁₁, ..., p₁ₙ => s₁
...
| pₘ₁, ..., pₘₙ => sₘ
```
Here ``t₁, ..., tₙ`` are any terms in the context in which the expression appears, the expressions ``pᵢⱼ`` are patterns, and the terms ``sᵢ`` are expressions in the local context together with variables introduced by the patterns on the left-hand side. Each ``sᵢ`` should have the expected type of the entire ``match`` expression.
Any ``match`` expression is interpreted using the equation compiler, which generalizes ``t₁, ..., tₙ``, defines an internal function meeting the specification, and then applies it to ``t₁, ..., tₙ``. In contrast to the definitions in [The Equation Compiler](declarations.md#the-equation-compiler), the terms ``tᵢ`` are arbitrary terms rather than just variables, and the expression can occur anywhere within a Lean expression, not just at the top level of a definition. Note that the syntax here is somewhat different: both the terms ``tᵢ`` and the patterns ``pᵢⱼ`` are separated by commas.
```lean
def foo (n : Nat) (b c : Bool) :=
5 + match n - 5, b && c with
| 0, true => 0
| m+1, true => m + 7
| 0, false => 5
| m+1, false => m + 3
```
When a ``match`` has only one line, Lean provides alternative syntax with a destructuring ``let``, as well as a destructuring lambda abstraction. Thus the following definitions all have the same net effect.
```lean
def bar₁ : Nat × Nat → Nat
| (m, n) => m + n
def bar₂ (p : Nat × Nat) : Nat :=
match p with | (m, n) => m + n
def bar₃ : Nat × Nat → Nat :=
fun ⟨m, n⟩ => m + n
def bar₄ (p : Nat × Nat) : Nat :=
let ⟨m, n⟩ := p; m + n
```
Information about the term being matched can be preserved in each branch using the syntax `match h : t with`. For example, a user may want to match a term `ns ++ ms : List Nat`, while tracking the hypothesis `ns ++ ms = []` or `ns ++ ms= h :: t` in the respective match arm:
```lean
def foo (ns ms : List Nat) (h1 : ns ++ ms ≠ []) (k : Nat -> Char) : Char :=
match h2 : ns ++ ms with
-- in this arm, we have the hypothesis `h2 : ns ++ ms = []`
| [] => absurd h2 h1
-- in this arm, we have the hypothesis `h2 : ns ++ ms = h :: t`
| h :: t => k h
-- '7'
#eval foo [7, 8, 9] [] (by decide) Nat.digitChar
```
.. _structures_and_records:
Structures and Records
======================
The ``structure`` command in Lean is used to define an inductive data type with a single constructor and to define its projections at the same time. The syntax is as follows:
```
structure Foo (a : α) : Sort u extends Bar, Baz :=
constructor :: (field₁ : β₁) ... (fieldₙ : βₙ)
```
Here ``(a : α)`` is a telescope, that is, the parameters to the inductive definition. The name ``constructor`` followed by the double colon is optional; if it is not present, the name ``mk`` is used by default. The keyword ``extends`` followed by a list of previously defined structures is also optional; if it is present, an instance of each of these structures is included among the fields to ``Foo``, and the types ``βᵢ`` can refer to their fields as well. The output type, ``Sort u``, can be omitted, in which case Lean infers to smallest non-``Prop`` sort possible (unless all the fields are ``Prop``, in which case it infers ``Prop``).
Finally, ``(field₁ : β₁) ... (fieldₙ : βₙ)`` is a telescope relative to ``(a : α)`` and the fields in ``bar`` and ``baz``.
The declaration above is syntactic sugar for an inductive type declaration, and so results in the addition of the following constants to the environment:
- the eliminator ``Foo.rec`` for the inductive type with that constructor
In addition, Lean defines
- the projections : ``fieldᵢ : Π (a : α) (c : Foo) : βᵢ`` for each ``i``
where any other fields mentioned in ``βᵢ`` are replaced by the relevant projections from ``c``.
Given ``c : Foo``, Lean offers the following convenient syntax for the projection ``Foo.fieldᵢ c``:
- *anonymous projections* : ``c.fieldᵢ``
- *numbered projections* : ``c.i``
These can be used in any situation where Lean can infer that the type of ``c`` is of the form ``Foo a``. The convention for anonymous projections is extended to any function ``f`` defined in the namespace ``Foo``, as described in [Namespaces](namespaces.md).
Similarly, Lean offers the following convenient syntax for constructing elements of ``Foo``. They are equivalent to ``Foo.constructor b₁ b₂ f₁ f₁ ... fₙ``, where ``b₁ : Bar``, ``b₂ : Baz``, and each ``fᵢ : βᵢ`` :
The anonymous constructor can be used in any context where Lean can infer that the expression should have a type of the form ``Foo a``. The unicode brackets are entered as ``\<`` and ``\>`` respectively.
When using record notation, you can omit the annotation ``: Foo a`` when Lean can infer that the expression should have a type of the form ``Foo a``. You can replace either ``toBar`` or ``toBaz`` by assignments to *their* fields as well, essentially acting as though the fields of ``Bar`` and ``Baz`` are simply imported into ``Foo``. Finally, record notation also supports
- *record updates*: ``{ t with ... fieldᵢ := fᵢ ...}``
Here ``t`` is a term of type ``Foo a`` for some ``a``. The notation instructs Lean to take values from ``t`` for any field assignment that is omitted from the list.
Lean also allows you to specify a default value for any field in a structure by writing ``(fieldᵢ : βᵢ := t)``. Here ``t`` specifies the value to use when the field ``fieldᵢ`` is left unspecified in an instance of record notation.
```lean
universe u v
structure Vec (α : Type u) (n : Nat) :=
(l : List α) (h : l.length = n)
structure Foo (α : Type u) (β : Nat → Type v) : Type (max u v) :=
(a : α) (n : Nat) (b : β n)
structure Bar :=
(c : Nat := 8) (d : Nat)
structure Baz extends Foo Nat (Vec Nat), Bar :=
(v : Vec Nat n)
#check Foo
#check @Foo.mk
#check @Foo.rec
#check Foo.a
#check Foo.n
#check Foo.b
#check Baz
#check @Baz.mk
#check @Baz.rec
#check Baz.toFoo
#check Baz.toBar
#check Baz.v
def bzz := Vec.mk [1, 2, 3] rfl
#check Vec.l bzz
#check Vec.h bzz
#check bzz.l
#check bzz.h
#check bzz.1
#check bzz.2
example : Vec Nat 3 := Vec.mk [1, 2, 3] rfl
example : Vec Nat 3 := ⟨[1, 2, 3], rfl⟩
example : Vec Nat 3 := { l := [1, 2, 3], h := rfl : Vec Nat 3 }
example : Vec Nat 3 := { l := [1, 2, 3], h := rfl }
example : Foo Nat (Vec Nat) := ⟨1, 3, bzz⟩
example : Baz := ⟨⟨1, 3, bzz⟩, ⟨5, 7⟩, bzz⟩
example : Baz := { a := 1, n := 3, b := bzz, c := 5, d := 7, v := bzz}
def fzz : Foo Nat (Vec Nat) := {a := 1, n := 3, b := bzz}
example : Foo Nat (Vec Nat) := { fzz with a := 7 }
example : Baz := { fzz with c := 5, d := 7, v := bzz }
example : Bar := { c := 8, d := 9 }
example : Bar := { d := 9 } -- uses the default value for c
```
.. _type_classes:
Type Classes
============
(Classes and instances. Anonymous instances. Local instances.)
Since version 4, Lean is a partially bootstrapped program: most parts of the
Lean is a bootstrapped program: the
frontend and compiler are written in Lean itself and thus need to be built before
building Lean itself - which is needed to again build those parts. This cycle is
broken by using pre-built C files checked into the repository (which ultimately
@@ -73,6 +73,11 @@ update the archived C source code of the stage 0 compiler in `stage0/src`.
The github repository will automatically update stage0 on `master` once
`src/stdlib_flags.h` and `stage0/src/stdlib_flags.h` are out of sync.
NOTE: A full rebuild of stage 1 will only be triggered when the *committed* contents of `stage0/` are changed.
Thus if you change files in it manually instead of through `update-stage0-commit` (see below) or fetching updates from git, you either need to commit those changes first or run `make -C build/release clean-stdlib`.
The same is true for further stages except that a rebuild of them is retriggered on any committed change, not just to a specific directory.
Thus when debugging e.g. stage 2 failures, you can resume the build from these failures on but may want to explicitly call `clean-stdlib` to either observe changes from `.olean` files of modules that built successfully or to check that you did not break modules that built successfully at some prior point.
If you have write access to the lean4 repository, you can also manually
trigger that process, for example to be able to use new features in the compiler itself.
You can do that on <https://github.com/leanprover/lean4/actions/workflows/update-stage0.yml>
@@ -82,13 +87,13 @@ gh workflow run update-stage0.yml
```
Leaving stage0 updates to the CI automation is preferable, but should you need
to do it locally, you can use `make update-stage0-commit` in `build/release` to
update `stage0` from `stage1` or `make -C stageN update-stage0-commit` to
to do it locally, you can use `make -C build/release update-stage0-commit` to
update `stage0` from `stage1` or `make -C build/release/stageN update-stage0-commit` to
update from another stage. This command will automatically stage the updated files
and introduce a commit,so make sure to commit your work before that.
and introduce a commit,so make sure to commit your work before that.
If you rebased the branch (either onto a newer version of `master`, or fixing
up some commits prior to the stage0 update, recreate the stage0 update commits.
up some commits prior to the stage0 update), recreate the stage0 update commits.
The script `script/rebase-stage0.sh` can be used for that.
The CI should prevent PRs with changes to stage0 (besides `stdlib_flags.h`)
@@ -68,7 +68,7 @@ The memory order of the fields is derived from the types and order of the fields
* Fields of type `USize`
* Other scalar fields, in decreasing order by size
Within each group the fields are ordered in declaration order. **Warning**: Trivial wrapper types still count toward a field being treated as non-scalar for this purpose.
Within each group the fields are ordered in declaration order. Trivial wrapper types count as their underlying wrapped type for this purpose.
* To access fields of the first kind, use `lean_ctor_get(val, i)` to get the `i`th non-scalar field.
* To access `USize` fields, use `lean_ctor_get_usize(val, n+i)` to get the `i`th usize field and `n` is the total number of fields of the first kind.
@@ -80,32 +80,32 @@ structure S where
ptr_1 : Array Nat
usize_1 : USize
sc64_1 : UInt64
ptr_2 : { x : UInt64 // x > 0 } -- wrappers don't count as scalars
sc64_2 : Float -- `Float` is 64 bit
sc64_2 : { x : UInt64 // x > 0 } -- wrappers of scalars count as scalars
sc64_3 : Float -- `Float` is 64 bit
sc8_1 : Bool
sc16_1 : UInt16
sc8_2 : UInt8
sc64_3 : UInt64
sc64_4 : UInt64
usize_2 : USize
ptr_3 : Char -- trivial wrapper around `UInt32`
sc32_1 : UInt32
sc32_1 : Char -- trivial wrapper around `UInt32`
sc32_2 : UInt32
sc16_2 : UInt16
```
would get re-sorted into the following memory order:
@@ -131,14 +131,21 @@ Thus `[init]` functions are run iff their module is imported, regardless of whet
The initializer for module `A.B` is called `initialize_A_B` and will automatically initialize any imported modules.
Module initializers are idempotent (when run with the same `builtin` flag), but not thread-safe.
**Important for process-related functionality**: If your application needs to use process-related functions from libuv, such as `Std.Internal.IO.Process.getProcessTitle` and `Std.Internal.IO.Process.setProcessTitle`, you must call `lean_setup_args(argc, argv)` (which returns a potentially modified `argv` that must be used in place of the original) **before** calling `lean_initialize()` or `lean_initialize_runtime_module()`. This sets up process handling capabilities correctly, which is essential for certain system-level operations that Lean's runtime may depend on.
Together with initialization of the Lean runtime, you should execute code like the following exactly once before accessing any Lean declarations:
@@ -8,8 +8,8 @@ You should not edit the `stage0` directory except using the commands described i
## Development Setup
You can use any of the [supported editors](../setup.md) for editing the Lean source code.
If you set up `elan` as below, opening `src/` as a *workspace folder* should ensure that stage 0 (i.e. the stage that first compiles `src/`) will be used for files in that directory.
You can use any of the [supported editors](https://lean-lang.org/install/manual/) for editing the Lean source code.
Please see below for specific instructions for VS Code.
### Dev setup using elan
@@ -68,6 +68,10 @@ code lean.code-workspace
```
on the command line.
You can use the `Refresh File Dependencies` command as in other projects to rebuild modules from inside VS Code but be aware that this does not trigger any non-Lake build targets.
In particular, after updating `stage0/` (or fetching an update to it), you will want to invoke `make` directly to rebuild `stage0/bin/lean` as described in [building Lean](../make/index.md).
You should then run the `Restart Server` command to update all open files and the server watchdog process as well.
### `ccache`
Lean's build process uses [`ccache`](https://ccache.dev/) if it is
@@ -85,5 +89,29 @@ such that changing files in `Init` doesn't force a full rebuild of `Lean`.
You can test a Lean PR against Mathlib and Batteries by rebasing your PR
on to `nightly-with-mathlib` branch. (It is fine to force push after rebasing.)
CI will generate a branch of Mathlib and Batteries called `lean-pr-testing-NNNN`
that uses the toolchain for your PR, and will report back to the Lean PR with results from Mathlib CI.
on the `leanprover-community/mathlib4-nightly-testing` fork of Mathlib.
This branch uses the toolchain for your PR, and will report back to the Lean PR with results from Mathlib CI.
See https://leanprover-community.github.io/contribute/tags_and_branches.html for more details.
### Testing against the Lean Language Reference
You can test a Lean PR against the reference manual by rebasing your PR
on to `nightly-with-manual` branch. (It is fine to force push after rebasing.)
CI will generate a branch of the reference manual called `lean-pr-testing-NNNN`
in `leanprover/reference-manual`. This branch uses the toolchain for your PR,
and will report back to the Lean PR with results from Mathlib CI.
### Avoiding rebuilds for downstream projects
If you want to test changes to Lean on downstream projects and would like to avoid rebuilding modules you have already built/fetched using the project's configured Lean toolchain, you can often do so as long as your build of Lean is close enough to that Lean toolchain (compatible .olean format including structure of all relevant environment extensions).
To override the toolchain without rebuilding for a single command, for example `lake build` or `lake lean`, you can use the prefix
```
LEAN_GITHASH=$(lean --githash) lake +lean4 ...
```
Alternatively, use
```
export LEAN_GITHASH=$(lean --githash)
export ELAN_TOOLCHAIN=lean4
```
to persist these changes for the lifetime of the current shell, which will affect any processes spawned from it such as VS Code started via `code .`.
If you use a setup where you cannot directly start your editor from the command line, such as VS Code Remote, you might want to consider using [direnv](https://direnv.net/) together with an editor extension for it instead so that you can put the lines above into `.envrc`.
@@ -50,7 +50,7 @@ We'll use `v4.6.0` as the intended release version as a running example.
- Re-running `script/release_checklist.py` will then create the tag `v4.6.0` from `master`/`main` and push it (unless `toolchain-tag: false` in the `release_repos.yml` file)
-`script/release_checklist.py` will then merge the tag `v4.6.0` into the `stable` branch and push it (unless `stable-branch: false` in the `release_repos.yml` file).
- Special notes on repositories with exceptional requirements:
-`doc-gen4` has addition dependencies which we do not update at each toolchain release, although occasionally these break and need to be updated manually.
-`doc-gen4` has additional dependencies which we do not update at each toolchain release, although occasionally these break and need to be updated manually.
-`verso`:
- The `subverso` dependency is unusual in that it needs to be compatible with _every_ Lean release simultaneously.
Usually you don't need to do anything.
@@ -69,7 +69,7 @@ We'll use `v4.6.0` as the intended release version as a running example.
-`repl`:
There are two copies of `lean-toolchain`/`lakefile.lean`:
in the root, and in `test/Mathlib/`. Edit both, and run `lake update` in both directories.
- An awkward situtation that sometimes occurs (e.g. with Verso) is that the `master`/`main` branch has already been moved
- An awkward situation that sometimes occurs (e.g. with Verso) is that the `master`/`main` branch has already been moved
to a nightly toolchain that comes *after* the stable toolchain we are
targeting. In this case it is necessary to create a branch `releases/v4.6.0` from the last commit which was on
an earlier toolchain, move that branch to the stable toolchain, and create the toolchain tag from that branch.
@@ -94,6 +94,8 @@ We'll use `v4.6.0` as the intended release version as a running example.
This checklist walks you through creating the first release candidate for a version of Lean.
For subsequent release candidates, the process is essentially the same, but we start out with the `releases/v4.7.0` branch already created.
We'll use `v4.7.0-rc1` as the intended release version in this example.
- Decide which nightly release you want to turn into a release candidate.
@@ -112,7 +114,7 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
git fetch nightly tag nightly-2024-02-29
git checkout nightly-2024-02-29
git checkout -b releases/v4.7.0
git push --set-upstream origin releases/v4.18.0
git push --set-upstream origin releases/v4.7.0
```
- In `src/CMakeLists.txt`,
- verify that you see `set(LEAN_VERSION_MINOR 7)` (for whichever `7` is appropriate); this should already have been updated when the development cycle began.
@@ -144,6 +146,10 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
- Run `script/release_steps.py v4.7.0-rc1 <repo>` (e.g. replacing `<repo>` with `batteries`), which will walk you through the following steps:
- Create a new branch off `master`/`main` (as specified in the `branch` field), called `bump_to_v4.7.0-rc1`.
- Merge `origin/bump/v4.7.0` if relevant (i.e. `bump-branch: true` appears in `release_repos.yml`).
- Otherwise, you *may* need to merge `origin/nightly-testing`.
- Note that for `verso` and `reference-manual` development happens on `nightly-testing`, so
we will merge that branch into `bump_to_v4.7.0-rc1`, but it is essential in the GitHub interface that we do a rebase merge,
in order to preserve the history.
- Update the contents of `lean-toolchain` to `leanprover/lean4:v4.7.0-rc1`.
- In the `lakefile.toml` or `lakefile.lean`, if there are dependencies on `nightly-testing`, `bump/v4.7.0`, or specific version tags, update them to the new tag.
If they depend on `main` or `master`, don't change this; you've just updated the dependency, so `lake update` will take care of modifying the manifest.
@@ -151,7 +157,7 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
- Run `lake build && if lake check-test; then lake test; fi` to check things are working.
- Commit the changes as `chore: bump toolchain to v4.7.0-rc1` and push.
- Create a PR with title "chore: bump toolchain to v4.7.0-rc1".
- Merge the PR once CI completes.
- Merge the PR once CI completes. (Recall: for `verso` and `reference-manual` you will need to do a rebase merge.)
- Re-running `script/release_checklist.py` will then create the tag `v4.7.0-rc1` from `master`/`main` and push it (unless `toolchain-tag: false` in the `release_repos.yml` file)
- We do this for the same list of repositories as for stable releases, see above for notes about special cases.
As above, there are dependencies between these, and so the process above is iterative.
Every expression in Lean has a [Type](types.md). Every type is also an
expression of type `Sort u` for some universe level u. See [Type
Universes](types.md#type_universes).
Expression Syntax
=================
The set of expressions in Lean is defined inductively as follows:
* ``Sort u`` : the universe of types at universe level ``u``
* ``c`` : where ``c`` is an identifier denoting a declared constant or a defined object
* ``x`` : where ``x`` is a variable in the local context in which the expression is interpreted
*`m?` : where `m?` is a metavariable in the metavariable context in which the expression is interpreted,
you can view metavariable as a "hole" that still needs to be synthesized
* ``(x : α) → β`` : the type of functions taking an element ``x`` of ``α`` to an element of ``β``,
where ``β`` is an expression whose type is a ``Sort``
* ``s t`` : the result of applying ``s`` to ``t``, where ``s`` and ``t`` are expressions
* ``fun x : α => t`` or `λ x : α => t`: the function mapping any value ``x`` of type ``α`` to ``t``, where ``t`` is an expression
* ``let x := t; s`` : a local definition, denotes the value of ``s`` when ``x`` is replaced by ``t``
* `s.i` : a projection, denotes the value of the `i`-th field of `s`
* `lit` : a natural number or string literal
* `mdata k s` : the expression `s` decorated with metadata `k`, where is a key-value map
Every well formed term in Lean has a *type*, which itself is an expression of type ``Sort u`` for some ``u``. The fact that a term ``t`` has type ``α`` is written ``t : α``.
For an expression to be well formed, its components have to satisfy certain typing constraints. These, in turn, determine the type of the resulting term, as follows:
* ``Sort u : Sort (u + 1)``
* ``c : α``, where ``α`` is the type that ``c`` has been declared or defined to have
* ``x : α``, where ``α`` is the type that ``x`` has been assigned in the local context where it is interpreted
* ``?m : α``, where ``α`` is the type that ``?m`` has been declared in the metavariable context where it is interpreted
* ``(x : α) → β : Sort (imax u v)`` where ``α : Sort u``, and ``β : Sort v`` assuming ``x : α``
* ``s t : β[t/x]`` where ``s`` has type ``(x : α) → β`` and ``t`` has type ``α``
* ``(fun x : α => t) : (x : α) → β`` if ``t`` has type ``β`` whenever ``x`` has type ``α``
* ``(let x := t; s) : β[t/x]`` where ``t`` has type ``α`` and ``s`` has type ``β`` assuming ``x : α``
* `lit : Nat` if `lit` is a numeral
* `lit : String` if `lit` is a string literal
* `mdata k s : α` if `s : α`
* `s.i : α` if `s : β` and `β` is an inductive datatype with only one constructor, and `i`-th field has type `α`
``Prop`` abbreviates ``Sort 0``, ``Type`` abbreviates ``Sort 1``, and
``Type u`` abbreviates ``Sort (u + 1)`` when ``u`` is a universe
variable. We say "``α`` is a type" to express ``α : Type u`` for some
``u``, and we say "``p`` is a proposition" to express
``p : Prop``. Using the *propositions as types* correspondence, given
``p : Prop``, we refer to an expression ``t : p`` as a *proof* of ``p``. In
contrast, given ``α : Type u`` for some ``u`` and ``t : α``, we
sometimes refer to ``t`` as *data*.
When the expression ``β`` in ``(x : α) → β`` does not depend on ``x``,
it can be written ``α → β``. As usual, the variable ``x`` is bound in
``(x : α) → β``, ``fun x : α => t``, and ``let x := t; s``. The
expression ``∀ x : α, β`` is alternative syntax for ``(x : α) → β``,
and is intended to be used when ``β`` is a proposition. An underscore
can be used to generate an internal variable in a binder, as in
``fun _ : α => t``.
*Metavariables*, that is, temporary placeholders, are used in the
process of constructing terms. Terms that are added to the
environment contain neither metavariable nor variables, which is to
say, they are fully elaborated and make sense in the empty context.
Axioms can be declared using the ``axiom`` keyword.
Similarly, objects can be defined in various ways, such as using ``def`` and ``theorem`` keywords.
See [Chapter Declarations](./declarations.md) for more information.
Writing an expression ``(t : α)`` forces Lean to elaborate ``t`` so that it has type ``α`` or report an error if it fails.
directory of the core library. For more information, see also [Chapter libraries](./libraries.md).
```
/- numbers -/
def f1 (a b c : Nat) : Nat :=
a^2 + b^2 + c^2
def p1 (a b c d : Nat) : Prop :=
(a + b)^c ≤ d
def p2 (i j k : Int) : Prop :=
i % (j * k) = 0
/- booleans -/
def f2 (a b c : Bool) : Bool :=
a && (b || c)
/- pairs -/
#eval (1, 2)
def p : Nat × Bool := (1, false)
section
variable (a b c : Nat) (p : Nat × bool)
#check (1, 2)
#check p.1 * 2
#check p.2 && tt
#check ((1, 2, 3) : Nat × Nat × Nat)
end
/- lists -/
section
variable x y z : Nat
variable xs ys zs : list Nat
open list
#check (1 :: xs) ++ (y :: zs) ++ [1,2,3]
#check append (cons 1 xs) (cons y zs)
#check map (λ x, x^2) [1, 2, 3]
end
/- sets -/
section
variable s t u : set Nat
#check ({1, 2, 3} ∩ s) ∪ ({x | x < 7} ∩ t)
end
/- strings and characters -/
#check "hello world"
#check 'a'
/- assertions -/
#check ∀ a b c n : Nat,
a ≠ 0 ∧ b ≠ 0 ∧ c ≠ 0 ∧ n > 2 → a^n + b^n ≠ c^n
def unbounded (f : Nat → Nat) : Prop := ∀ M, ∃ n, f n ≥ M
```
.. _constructors_projections_and_matching:
Constructors, Projections, and Matching
=======================================
Lean's foundation, the *Calculus of Inductive Constructions*, supports the declaration of *inductive types*. Such types can have any number of *constructors*, and an associated *eliminator* (or *recursor*). Inductive types with one constructor, known as *structures*, have *projections*. The full syntax of inductive types is described in [Declarations](declarations.md), but here we describe some syntactic elements that facilitate their use in expressions.
When Lean can infer the type of an expression and it is an inductive type with one constructor, then one can write ``⟨a1, a2, ..., an⟩`` to apply the constructor without naming it. For example, ``⟨a, b⟩`` denotes ``prod.mk a b`` in a context where the expression can be inferred to be a pair, and ``⟨h₁, h₂⟩`` denotes ``and.intro h₁ h₂`` in a context when the expression can be inferred to be a conjunction. The notation will nest constructions automatically, so ``⟨a1, a2, a3⟩`` is interpreted as ``prod.mk a1 (prod.mk a2 a3)`` when the expression is expected to have a type of the form ``α1 ×α2 ×α3``. (The latter is interpreted as ``α1 × (α2 ×α3)``, since the product associates to the right.)
Similarly, one can use "dot notation" for projections: one can write ``p.fst`` and ``p.snd`` for ``prod.fst p`` and ``prod.snd p`` when Lean can infer that ``p`` is an element of a product, and ``h.left`` and ``h.right`` for ``and.left h`` and ``and.right h`` when ``h`` is a conjunction.
The anonymous projector notation can used more generally for any objects defined in a *namespace* (see [Other Commands](other_commands.md)). For example, if ``l`` has type ``list α`` then ``l.map f`` abbreviates ``list.map f l``, in which ``l`` has been placed at the first argument position where ``list.map`` expects a ``list``.
Finally, for data types with one constructor, one destruct an element by pattern matching using the ``let`` and ``assume`` constructs, as in the examples below. Internally, these are interpreted using the ``match`` construct, which is in turn compiled down for the eliminator for the inductive type, as described in [Declarations](declarations.md).
.. code-block:: lean
universes u v
variable {α : Type u} {β : Type v}
def p : Nat ×ℤ := ⟨1, 2⟩
#check p.fst
#check p.snd
def p' : Nat ×ℤ× bool := ⟨1, 2, tt⟩
#check p'.fst
#check p'.snd.fst
#check p'.snd.snd
def swap_pair (p : α× β) : β ×α :=
⟨p.snd, p.fst⟩
theorem swap_conj {a b : Prop} (h : a ∧ b) : b ∧ a :=
⟨h.right, h.left⟩
#check [1, 2, 3].append [2, 3, 4]
#check [1, 2, 3].map (λ x, x^2)
example (p q : Prop) : p ∧ q → q ∧ p :=
λ h, ⟨h.right, h.left⟩
def swap_pair' (p : α× β) : β ×α :=
let (x, y) := p in (y, x)
theorem swap_conj' {a b : Prop} (h : a ∧ b) : b ∧ a :=
let ⟨ha, hb⟩ := h in ⟨hb, ha⟩
def swap_pair'' : α× β → β ×α :=
λ ⟨x, y⟩, (y, x)
theorem swap_conj'' {a b : Prop} : a ∧ b → b ∧ a :=
assume ⟨ha, hb⟩, ⟨hb, ha⟩
Structured Proofs
=================
Syntactic sugar is provided for writing structured proof terms:
* ``have h : p := s; t`` is sugar for ``(fun h : p => t) s``
* ``suffices h : p from s; t`` is sugar for ``(λ h : p => s) t``
* ``suffices h : p by s; t`` is sugar for ``(suffixes h : p from by s; t)``
* ``show p from t`` is sugar for ``(have this : p := t; this)``
* ``show p by tac`` is sugar for ``(show p from by tac)``
Types can be omitted when they can be inferred by Lean. Lean also
allows ``have : p := t; s``, which gives the assumption the
name ``this`` in the local context. Similarly, Lean recognizes the
variant ``suffices p from s; t``, which use the name ``this`` for the new hypothesis.
The notation ``‹p›`` is notation for ``(by assumption : p)``, and can
therefore be used to apply hypotheses in the local context.
As noted in [Constructors, Projections and Matching](#constructors_projections_and_matching),
anonymous constructors and projections and match syntax can be used in proofs just as in expressions that denote data.
.. code-block:: lean
example (p q r : Prop) : p → (q ∧ r) → p ∧ q :=
assume h₁ : p,
assume h₂ : q ∧ r,
have h₃ : q, from and.left h₂,
show p ∧ q, from and.intro h₁ h₃
example (p q r : Prop) : p → (q ∧ r) → p ∧ q :=
assume : p,
assume : q ∧ r,
have q, from and.left this,
show p ∧ q, from and.intro ‹p› this
example (p q r : Prop) : p → (q ∧ r) → p ∧ q :=
assume h₁ : p,
assume h₂ : q ∧ r,
suffices h₃ : q, from and.intro h₁ h₃,
show q, from and.left h₂
Lean also supports a calculational environment, which is introduced with the keyword ``calc``. The syntax is as follows:
.. code-block:: text
calc
<expr>_0 'op_1' <expr>_1 ':' <proof>_1
'...' 'op_2' <expr>_2 ':' <proof>_2
...
'...' 'op_n' <expr>_n ':' <proof>_n
Each ``<proof>_i`` is a proof for ``<expr>_{i-1} op_i <expr>_i``.
Here is an example:
.. code-block:: lean
variable (a b c d e : Nat)
variable h1 : a = b
variable h2 : b = c + 1
variable h3 : c = d
variable h4 : e = 1 + d
theorem T : a = e :=
calc
a = b : h1
... = c + 1 : h2
... = d + 1 : congr_arg _ h3
... = 1 + d : add_comm d (1 : Nat)
... = e : eq.symm h4
The style of writing proofs is most effective when it is used in conjunction with the ``simp`` and ``rewrite`` tactics.
.. _computation:
Computation
===========
Two expressions that differ up to a renaming of their bound variables are said to be *α-equivalent*, and are treated as syntactically equivalent by Lean.
Every expression in Lean has a natural computational interpretation, unless it involves classical elements that block computation, as described in the next section. The system recognizes the following notions of *reduction*:
* *β-reduction* : An expression ``(λ x, t) s`` β-reduces to ``t[s/x]``, that is, the result of replacing ``x`` by ``s`` in ``t``.
* *ζ-reduction* : An expression ``let x := s in t`` ζ-reduces to ``t[s/x]``.
* *δ-reduction* : If ``c`` is a defined constant with definition ``t``, then ``c`` δ-reduces to ``t``.
* *ι-reduction* : When a function defined by recursion on an inductive type is applied to an element given by an explicit constructor, the result ι-reduces to the specified function value, as described in [Inductive Types](inductive.md).
The reduction relation is transitive, which is to say, is ``s`` reduces to ``s'`` and ``t`` reduces to ``t'``, then ``s t`` reduces to ``s' t'``, ``λ x, s`` reduces to ``λ x, s'``, and so on. If ``s`` and ``t`` reduce to a common term, they are said to be *definitionally equal*. Definitional equality is defined to be the smallest equivalence relation that satisfies all these properties and also includes α-equivalence and the following two relations:
* *η-equivalence* : An expression ``(λx, t x)`` is η-equivalent to ``t``, assuming ``x`` does not occur in ``t``.
* *proof irrelevance* : If ``p : Prop``, ``s : p``, and ``t : p``, then ``s`` and ``t`` are considered to be equivalent.
This last fact reflects the intuition that once we have proved a proposition ``p``, we only care that is has been proved; the proof does nothing more than witness the fact that ``p`` is true.
Definitional equality is a strong notion of equality of values. Lean's logical foundations sanction treating definitionally equal terms as being the same when checking that a term is well-typed and/or that it has a given type.
The reduction relation is believed to be strongly normalizing, which is to say, every sequence of reductions applied to a term will eventually terminate. The property guarantees that Lean's type-checking algorithm terminates, at least in principle. The consistency of Lean and its soundness with respect to set-theoretic semantics do not depend on either of these properties.
Lean provides two commands to compute with expressions:
* ``#reduce t`` : use the kernel type-checking procedures to carry out reductions on ``t`` until no more reductions are possible, and show the result
* ``#eval t`` : evaluate ``t`` using a fast bytecode evaluator, and show the result
Every computable definition in Lean is compiled to bytecode at definition time. Bytecode evaluation is more liberal than kernel evaluation: types and all propositional information are erased, and functions are evaluated using a stack-based virtual machine. As a result, ``#eval`` is more efficient than ``#reduce,`` and can be used to execute complex programs. In contrast, ``#reduce`` is designed to be small and reliable, and to produce type-correct terms at each step. Bytecode is never used in type checking, so as far as soundness and consistency are concerned, only kernel reduction is part of the trusted computing base.
.. code-block:: lean
#reduce (fun x => x + 3) 5
#eval (fun x => x + 3) 5
#reduce let x := 5; x + 3
#eval let x := 5; x + 3
def f x := x + 3
#reduce f 5
#eval f 5
#reduce @Nat.rec (λ n => Nat) (0 : Nat)
(λ n recval : Nat => recval + n + 1) (5 : Nat)
def g : Nat → Nat
| 0 => 0
| (n+1) => g n + n + 1
#reduce g 5
#eval g 5
#eval g 5000
example : (fun x => x + 3) 5 = 8 := rfl
example : (fun x => f x) = f := rfl
example (p : Prop) (h₁ h₂ : p) : h₁ = h₂ := rfl
Note: the combination of proof irrelevance and singleton ``Prop`` elimination in ι-reduction renders the ideal version of definitional equality, as described above, undecidable. Lean's procedure for checking definitional equality is only an approximation to the ideal. It is not transitive, as illustrated by the example below. Once again, this does not compromise the consistency or soundness of Lean; it only means that Lean is more conservative in the terms it recognizes as well typed, and this does not cause problems in practice. Singleton elimination will be discussed in greater detail in [Inductive Types](inductive.md).
.. code-block:: lean
def R (x y : unit) := false
def accrec := @acc.rec unit R (λ_, unit) (λ _ a ih, ()) ()
example (h) : accrec h = accrec (acc.intro _ (λ y, acc.inv h)) :=
rfl
example (h) : accrec (acc.intro _ (λ y, acc.inv h)) = () := rfl
example (h) : accrec h = () := sorry -- rfl fails
Axioms
======
Lean's foundational framework consists of:
- type universes and dependent function types, as described above
- inductive definitions, as described in [Inductive Types](inductive.md) and
``quot r`` represents the quotient of ``α`` by the smallest equivalence relation containing ``r``. ``quot.mk`` and ``quot.lift`` satisfy the following computation rule:
.. code-block:: text
quot.lift f h (quot.mk r a) = f a
- choice:
.. code-block:: lean
namespace hide
universe u
-- BEGIN
axiom choice {α : Sort u} : nonempty α → α
-- END
end hide
Here ``nonempty α`` is defined as follows:
.. code-block:: lean
namespace hide
universe u
-- BEGIN
class inductive nonempty (α : Sort u) : Prop
| intro : α → nonempty
-- END
end hide
It is equivalent to ``∃ x : α, true``.
The quotient construction implies function extensionality. The ``choice`` principle, in conjunction with the others, makes the axiomatic foundation classical; in particular, it implies the law of the excluded middle and propositional decidability. Functions that make use of ``choice`` to produce data are incompatible with a computational interpretation, and do not produce bytecode. They have to be declared ``noncomputable``.
For metaprogramming purposes, Lean also allows the definition of objects which stand outside the object language. These are denoted with the ``meta`` keyword, as described in [Metaprogramming](metaprogramming.md).
The goal of [this book](https://lean-lang.org/functional_programming_in_lean/) is to be an accessible introduction to using Lean 4 as a programming language.
It should be useful both to people who want to use Lean as a general-purpose programming language and to mathematicians who want to develop larger-scale proof automation but do not have a background in functional programming.
It does not assume any background with functional programming, though it's probably not a good first book on programming in general.
New content will be added once per month until it's done.
The last expression, for example, denotes the function that takes three types, ``α``, ``β``, and ``γ``, and two functions, ``g : β → γ`` and ``f : α → β``, and returns the composition of ``g`` and ``f``. (Making sense of the type of this function requires an understanding of dependent products, which we will explain below.) Within a lambda expression ``fun x : α => t``, the variable ``x`` is a "bound variable": it is really a placeholder, whose "scope" does not extend beyond ``t``.
For example, the variable ``b`` in the expression ``fun (b : β) (x : α) => b`` has nothing to do with the constant ``b`` declared earlier.
In fact, the expression denotes the same function as ``fun (u : β) (z : α), u``. Formally, the expressions that are the same up to a renaming of bound variables are called *alpha equivalent*, and are considered "the same." Lean recognizes this equivalence.
Notice that applying a term ``t : α → β`` to a term ``s : α`` yields an expression ``t s : β``.
Returning to the previous example and renaming bound variables for clarity, notice the types of the following expressions:
```lean
#check (fun x : Nat => x) 1 -- Nat
#check (fun x : Nat => true) 1 -- Bool
constant f : Nat → String
constant g : String → Bool
#check
(fun (α β γ : Type) (g : β → γ) (f : α → β) (x : α) => g (f x)) Nat String Bool g f 0
-- Bool
```
As expected, the expression ``(fun x : Nat => x) 1`` has type ``Nat``.
In fact, more should be true: applying the expression ``(fun x : Nat => x)`` to ``1`` should "return" the value ``1``. And, indeed, it does:
```lean
#reduce (fun x : Nat => x) 1 -- 1
#reduce (fun x : Nat => true) 1 -- true
constant f : Nat → String
constant g : String → Bool
#reduce
(fun (α β γ : Type) (g : β → γ) (f : α → β) (x : α) => g (f x)) Nat String Bool g f 0
-- g (f 0)
```
The command ``#reduce`` tells Lean to evaluate an expression by *reducing* it to its normal form,
which is to say, carrying out all the computational reductions that are sanctioned by its kernel.
The process of simplifying an expression ``(fun x => t) s`` to ``t[s/x]`` -- that is, ``t`` with ``s`` substituted for the variable ``x`` --
is known as *beta reduction*, and two terms that beta reduce to a common term are called *beta equivalent*.
But the ``#reduce`` command carries out other forms of reduction as well:
```lean
constant m : Nat
constant n : Nat
constant b : Bool
#reduce (m, n).1 -- m
#reduce (m, n).2 -- n
#reduce true && false -- false
#reduce false && b -- false
#reduce b && false -- Bool.rec false false b
#reduce n + 0 -- n
#reduce n + 2 -- Nat.succ (Nat.succ n)
#reduce 2 + 3 -- 5
```
We explain later how these terms are evaluated.
For now, we only wish to emphasize that this is an important feature of dependent type theory:
every term has a computational behavior, and supports a notion of reduction, or *normalization*.
In principle, two terms that reduce to the same value are called *definitionally equal*.
They are considered "the same" by Lean's type checker, and Lean does its best to recognize and support these identifications.
The `#reduce` command is mainly useful to understand why two terms are considered the same.
Lean is also a programming language. It has a compiler to native code and an interpreter.
You can use the command `#eval` to execute expressions, and it is the preferred way of testing your functions.
Note that `#eval` and `#reduce` are *not* equivalent. The command `#eval` first compiles Lean expressions
into an intermediate representation (IR) and then uses an interpreter to execute the generated IR.
Some builtin types (e.g., `Nat`, `String`, `Array`) have a more efficient representation in the IR.
The IR has support for using foreign functions that are opaque to Lean.
In contrast, the ``#reduce`` command relies on a reduction engine similar to the one used in Lean's trusted kernel,
the part of Lean that is responsible for checking and verifying the correctness of expressions and proofs.
It is less efficient than ``#eval``, and treats all foreign functions as opaque constants.
We later discuss other differences between the two commands.
We have rewritten most of the system, and took the opportunity to cleanup the syntax,
metaprogramming framework, and elaborator. In this section, we go over the most significant
changes.
## Lambda expressions
We do not use `,` anymore to separate the binders from the lambda expression body.
The Lean 3 syntax for lambda expressions was unconventional, and `,` has been overused in Lean 3.
For example, we believe a list of lambda expressions is quite confusing in Lean 3, since `,` is used
to separate the elements of a list, and in the lambda expression itself. We now use `=>` as the separator,
as an example, `fun x => x` is the identity function. One may still use the symbol `λ` as a shorthand for `fun`.
The lambda expression notation has many new features that are not supported in Lean 3.
## Pattern matching
In Lean 4, one can easily create new notation that abbreviates commonly used idioms. One of them is a
`fun` followed by a `match`. In the following examples, we define a few functions using `fun`+`match` notation.
```lean
#namespaceex1
defProd.str:Nat×Nat→String:=
fun(a,b)=>"("++toStringa++", "++toStringb++")"
structurePointwhere
x:Nat
y:Nat
z:Nat
defPoint.addX:Point→Point→Nat:=
fun{x:=a,..}{x:=b,..}=>a+b
defSum.str:OptionNat→String:=
fun
|somea=>"some "++toStringa
|none=>"none"
#endex1
```
## Implicit lambdas
In Lean 3 stdlib, we find many [instances](https://github.com/leanprover/lean/blob/master/library/init/category/reader.lean#L39) of the dreadful `@`+`_` idiom.
It is often used when the expected type is a function type with implicit arguments,
and we have a constant (`reader_t.pure` in the example) which also takes implicit arguments. In Lean 4, the elaborator automatically introduces lambdas
for consuming implicit arguments. We are still exploring this feature and analyzing its impact, but the experience so far has been very positive. As an example,
here is the example in the link above using Lean 4 implicit lambdas.
```lean
#variable(ρ:Type)(m:Type→Type)[Monadm]
instance:Monad(ReaderTρm)where
pure:=ReaderT.pure
bind:=ReaderT.bind
```
Users can disable the implicit lambda feature by using `@` or writing a lambda expression with `{}` or `[]` binder annotations.
Here are few examples
```lean
#namespaceex2
defid1:{α:Type}→α→α:=
funx=>x
deflistId:List({α:Type}→α→α):=
(funx=>x)::[]
-- In this example, implicit lambda introduction has been disabled because
-- we use `@` before `fun`
defid2:{α:Type}→α→α:=
@funα(x:α)=>id1x
defid3:{α:Type}→α→α:=
@funαx=>id1x
defid4:{α:Type}→α→α:=
funx=>id1x
-- In this example, implicit lambda introduction has been disabled
-- because we used the binder annotation `{...}`
defid5:{α:Type}→α→α:=
fun{α}x=>id1x
#endex2
```
## Sugar for simple functions
In Lean 3, we can create simple functions from infix operators by using parentheses. For example, `(+1)` is sugar for `fun x, x + 1`. In Lean 4, we generalize this notation using `·` as a placeholder. Here are a few examples:
```lean
#namespaceex3
#check(·+1)
-- fun a => a + 1
#check(2-·)
-- fun a => 2 - a
#eval[1,2,3,4,5].foldl(·*·)1
-- 120
deff(xyz:Nat):=
x+y+z
#check(f·1·)
-- fun a b => f a 1 b
#eval[(1,2),(3,4),(5,6)].map(·.1)
-- [1, 3, 5]
#endex3
```
As in Lean 3, the notation is activated using parentheses, and the lambda abstraction is created by collecting the nested `·`s.
The collection is interrupted by nested parentheses. In the following example, two different lambda expressions are created.
```lean
#check(Prod.mk·(·+1))
-- fun a => (a, fun b => b + 1)
```
## Function applications
In Lean 4, we have support for named arguments.
Named arguments enable you to specify an argument for a parameter by matching the argument with
its name rather than with its position in the parameter list.
If you don't remember the order of the parameters but know their names,
you can send the arguments in any order. You may also provide the value for an implicit parameter when
Lean failed to infer it. Named arguments also improve the readability of your code by identifying what
In the following examples, we illustrate the interaction between named and default arguments.
```lean
deff(x:Nat)(y:Nat:=1)(w:Nat:=2)(z:Nat):=
x+y+w-z
example(xz:Nat):f(z:=z)x=x+1+2-z:=rfl
example(xz:Nat):fx(z:=z)=x+1+2-z:=rfl
example(xy:Nat):fxy=funz=>x+y+2-z:=rfl
example:f=(funxz=>x+1+2-z):=rfl
example(x:Nat):fx=funz=>x+1+2-z:=rfl
example(y:Nat):f(y:=5)=funxz=>x+5+2-z:=rfl
defg{α}[Addα](a:α)(b?:Optionα:=none)(c:α):α:=
matchb?with
|none=>a+c
|someb=>a+b+c
variable{α}[Addα]
example:g=fun(ac:α)=>a+c:=rfl
example(x:α):g(c:=x)=fun(a:α)=>a+x:=rfl
example(x:α):g(b?:=somex)=fun(ac:α)=>a+x+c:=rfl
example(x:α):gx=fun(c:α)=>x+c:=rfl
example(xy:α):gxy=fun(c:α)=>x+y+c:=rfl
```
In Lean 4, we can use `..` to provide missing explicit arguments as `_`.
This feature combined with named arguments is useful for writing patterns. Here is an example:
```lean
inductiveTermwhere
|var(name:String)
|num(val:Nat)
|add(fn:Term)(arg:Term)
|lambda(name:String)(type:Term)(body:Term)
defgetBinderName:Term→OptionString
|Term.lambda(name:=n)..=>somen
|_=>none
defgetBinderType:Term→OptionTerm
|Term.lambda(type:=t)..=>somet
|_=>none
```
Ellipsis are also useful when explicit argument can be automatically inferred by Lean, and we want
to avoid a sequence of `_`s.
```lean
example(f:Nat→Nat)(abc:Nat):f(a+b+c)=f(a+(b+c)):=
congrArgf(Nat.add_assoc..)
```
In Lean 4, writing `f(x)` in place of `f x` is no longer allowed, you must use whitespace between the function and its arguments (e.g., `f (x)`).
## Dependent function types
Given `α : Type` and `β : α → Type`, `(x : α) → β x` denotes the type of functions `f` with the property that,
for each `a : α`, `f a` is an element of `β a`. In other words, the type of the value returned by `f` depends on its input.
We say `(x : α) → β x` is a dependent function type. In Lean 3, we write the dependent function type `(x : α) → β x` using
one of the following three equivalent notations:
`forall x : α, β x` or `∀ x : α, β x` or `Π x : α, β x`.
The first two were intended to be used for writing propositions, and the latter for writing code.
Although the notation `Π x : α, β x` has historical significance, we have removed it from Lean 4 because
it is awkward to use and often confuses new users. We can still write `forall x : α, β x` and `∀ x : α, β x`.
```lean
#checkforall(α:Type),α→α
#check∀(α:Type),α→α
#check∀α:Type,α→α
#check∀α,α→α
#check(α:Type)→α→α
#check{α:Type}→(a:Arrayα)→(i:Nat)→i<a.size→α
#check{α:Type}→[ToStringα]→α→String
#checkforall{α:Type}(a:Arrayα)(i:Nat),i<a.size→α
#check{αβ:Type}→α→β→α×β
```
## The `meta` keyword
In Lean 3, the keyword `meta` is used to mark definitions that can use primitives implemented in C/C++.
These metadefinitions can also call themselves recursively, relaxing the termination
restriction imposed by ordinary type theory. Metadefinitions may also use unsafe primitives such as
`eval_expr (α : Type u) [reflected α] : expr → tactic α`, or primitives that break referential transparency
`tactic.unsafe_run_io`.
The keyword `meta` has been currently removed from Lean 4. However, we may re-introduce it in the future,
but with a much more limited purpose: marking meta code that should not be included in the executables produced by Lean.
The keyword `constant` has been deleted in Lean 4, and `axiom` should be used instead. In Lean 4, the new command `opaque` is used to define an opaque definition. Here are two simple examples:
```lean
#namespacemeta1
opaquex:Nat:=1
-- The following example will not type check since `x` is opaque
-- example : x = 1 := rfl
-- We can evaluate `x`
#evalx
-- 1
-- When no value is provided, the elaborator tries to build one automatically for us
-- using the `Inhabited` type class
opaquey:Nat
#endmeta1
```
We can instruct Lean to use a foreign function as the implementation for any definition
using the attribute `@[extern "foreign_function"]`. It is the user's responsibility to ensure the
foreign implementation is correct.
However, a user mistake here will only impact the code generated by Lean, and
it will **not** compromise the logical soundness of the system.
That is, you cannot prove `False` using the `@[extern]` attribute.
We use `@[extern]` with definitions when we want to provide a reference implementation in Lean
that can be used for reasoning. When we write a definition such as
```lean
@[extern"lean_nat_add"]
defadd:Nat→Nat→Nat
|a,Nat.zero=>a
|a,Nat.succb=>Nat.succ(addab)
```
Lean assumes that the foreign function `lean_nat_add` implements the reference implementation above.
The `unsafe` keyword allows us to define functions using unsafe features such as general recursion,
and arbitrary type casting. Regular (safe) functions cannot directly use `unsafe` ones since it would
compromise the logical soundness of the system. As in regular programming languages, programs written
using unsafe features may crash at runtime. Here are a few unsafe examples:
```lean
unsafedefunsound:False:=
unsound
#check@unsafeCast
-- {α : Type _} → {β : Type _} → α → β
unsafedefnat2String(x:Nat):String:=
unsafeCastx
-- The following definition doesn't type check because it is not marked as `unsafe`
-- def nat2StringSafe (x : Nat) : String :=
-- unsafeCast x
```
The `unsafe` keyword is particularly useful when we want to take advantage of an implementation detail of the
Lean execution runtime. For example, we cannot prove in Lean that arrays have a maximum size, but
the runtime used to execute Lean programs guarantees that an array cannot have more than 2^64 (2^32) elements
in a 64-bit (32-bit) machine. We can take advantage of this fact to provide a more efficient implementation for
array functions. However, the efficient version would not be very useful if it can only be used in
unsafe code. Thus, Lean 4 provides the attribute `@[implemented_by functionName]`. The idea is to provide
an unsafe (and potentially more efficient) version of a safe definition or constant. The function `f`
at the attribute `@[implemented_by f]` is very similar to an extern/foreign function,
the key difference is that it is implemented in Lean itself. Again, the logical soundness of the system
cannot be compromised by using the attribute `implemented_by`, but if the implementation is incorrect your
program may crash at runtime. In the following example, we define `withPtrUnsafe a k h` which
executes `k` using the memory address where `a` is stored in memory. The argument `h` is proof
that `k` is a constant function. Then, we "seal" this unsafe implementation at `withPtr`. The proof `h`
ensures the reference implementation `k 0` is correct. For more information, see the article
"Sealing Pointer-Based Optimizations Behind Pure Functions".
General recursion is very useful in practice, and it would be impossible to implement Lean 4 without it.
The keyword `partial` implements a very simple and efficient approach for supporting general recursion.
Simplicity was key here because of the bootstrapping problem. That is, we had to implement Lean in Lean before
many of its features were implemented (e.g., the tactic framework or support for wellfounded recursion).
Another requirement for us was performance. Functions tagged with `partial` should be as efficient as the ones implemented in mainstream functional programming
languages such as OCaml. When the `partial` keyword is used, Lean generates an auxiliary `unsafe` definition that
uses general recursion, and then defines an opaque constant that is implemented by this auxiliary definition.
This is very simple, efficient, and is sufficient for users that want to use Lean as a regular programming language.
A `partial` definition cannot use unsafe features such as `unsafeCast` and `ptrAddrUnsafe`, and it can only be used to
implement types we already known to be inhabited. Finally, since we "seal" the auxiliary definition using an opaque
constant, we cannot reason about `partial` definitions.
We are aware that proof assistants such as Isabelle provide a framework for defining partial functions that does not
prevent users from proving properties about them. This kind of framework can be implemented in Lean 4. Actually,
it can be implemented by users since Lean 4 is an extensible system. The developers current have no plans to implement
this kind of support for Lean 4. However, we remark that users can implement it using a function that traverses
the auxiliary unsafe definition generated by Lean, and produces a safe one using an approach similar to the one used in Isabelle.
```lean
#namespacepartial1
partialdeff(x:Nat):IOUnit:=do
IO.printlnx
ifx<100then
f(x+1)
#evalf98
#endpartial1
```
## Library changes
These are changes to the library which may trip up Lean 3 users:
-`List` is no longer a monad.
## Style changes
Coding style changes have also been made:
- Term constants and variables are now `lowerCamelCase` rather than `snake_case`
- Type constants are now `UpperCamelCase`, eg `Nat`, `List`. Type variables are still lower case greek letters. Functors are still lower case latin `(m : Type → Type) [Monad m]`.
- When defining typeclasses, prefer not to use "has". Eg `ToString` or `Add` instead of `HasToString` or `HasAdd`.
- Prefer `return` to `pure` in monad expressions.
- Pipes `<|` are preferred to dollars `$` for function application.
- Declaration bodies should always be indented:
```lean
inductive Hello where
| foo
| bar
structure Point where
x : Nat
y : Nat
def Point.addX : Point → Point → Nat :=
fun { x := a, .. } { x := b, .. } => a + b
```
- In structures and typeclass definitions, prefer `where` to `:=` and don't surround fields with parentheses. (Shown in `Point` above)
String literals are enclosed by double quotes (``"``). They may contain line breaks, which are conserved in the string value. Backslash (`\`) is a special escape character which can be used to the following
special characters:
-`\\` represents an escaped backslash, so this escape causes one backslash to be included in the string.
-`\"` puts a double quote in the string.
-`\'` puts an apostrophe in the string.
-`\n` puts a new line character in the string.
-`\t` puts a tab character in the string.
-`\xHH` puts the character represented by the 2 digit hexadecimal into the string. For example
"this \x26 that" which become "this & that". Values above 0x80 will be interpreted according to the
These are instructions to set up a working development environment for those who wish to make changes to Lean itself. It is part of the [Development Guide](../dev/index.md).
We strongly suggest that new users instead follow the [Quickstart](../quickstart.md) to get started using Lean, since this sets up an environment that can automatically manage multiple Lean toolchain versions, which is necessary when working within the Lean ecosystem.
We strongly suggest that new users instead follow the [Installation Instructions](https://lean-lang.org/install/) to get started using Lean, since this sets up an environment that can automatically manage multiple Lean toolchain versions, which is necessary when working within the Lean ecosystem.
# Arithmetic as an embedded domain-specific language
Let's parse another classic grammar, the grammar of arithmetic expressions with
addition, multiplication, integers, and variables. In the process, we'll learn
how to:
- Convert identifiers such as `x` into strings within a macro.
- add the ability to "escape" the macro context from within the macro. This is useful to interpret identifiers with their _original_ meaning (predefined values)
instead of their new meaning within a macro (treat as a symbol).
Let's begin with the simplest thing possible. We'll define an AST, and use operators `+` and `*` to denote
building an arithmetic AST.
Here's the AST that we will be parsing:
```lean,ignore
{{#include metaprogramming-arith.lean:1:5}}
```
We declare a syntax category to describe the grammar that we will be parsing.
See that we control the precedence of `+` and `*` by writing `syntax:50` for addition and `syntax:60` for multiplication,
indicating that multiplication binds tighter than addition (higher the number, tighter the binding).
This allows us to declare _precedence_ when defining new syntax.
```lean,ignore
{{#include metaprogramming-arith.lean:7:13}}
```
Further, if we look at `syntax:60 arith:60 "+" arith:61 : arith`, the
precedence declarations at `arith:60 "+" arith:61` conveys that the left
argument must have precedence at least `60` or greater, and the right argument
must have precedence at least`61` or greater. Note that this forces left
associativity. To understand this, let's compare two hypothetical parses:
1. Launch VS Code and install the `Lean 4` extension by clicking on the 'Extensions' sidebar entry and searching for 'Lean 4'.
1. Open the Lean 4 setup guide by creating a new text file using 'File > New Text File' (`Ctrl+N` / `Cmd+N`), clicking on the ∀-symbol in the top right and selecting 'Documentation… > Docs: Show Setup Guide'.
1. Follow the Lean 4 setup guide. It will:
- walk you through learning resources for Lean,
- teach you how to set up Lean's dependencies on your platform,
- install Lean 4 for you at the click of a button,
The Lean language server provides semantic highlighting information to editors. In order to benefit from this in VSCode, you may need to activate the "Editor > Semantic Highlighting" option in the preferences (this is translates to `"editor.semanticHighlighting.enabled": true,`
in `settings.json`). The default option here is to let your color theme decides whether it activates semantic highlighting (the default themes Dark+ and Light+ do activate it for instance).
However this may be insufficient if your color theme does not distinguish enough syntax categories or distinguishes them very subtly. For instance the default Light+ theme uses color `#001080` for variables. This is awfully close to `#000000` that is used as the default text color. This makes it very easy to miss an accidental use of [auto bound implicit arguments](https://lean-lang.org/lean4/doc/autobound.html). For instance in
```lean
defmy_id(n:nat):=n
```
maybe `nat` is a typo and `Nat` was intended. If your color theme is good enough then you should see that `n` and `nat` have the same color since they are both marked as variables by semantic highlighting. If you rather write `(n : Nat)` then `n` keeps its variable color but `Nat` gets the default text color.
If you use such a bad theme, you can fix things by modifying the `Semantic Token Color Customizations` configuration. This cannot be done directly in the preferences dialog but you can click on "Edit in settings.json" to directly edit the settings file. Beware that you must save this file (in the same way you save any file opened in VSCode) before seeing any effect in other tabs or VSCode windows.
In the main config object, you can add something like
The colors in this example are not meant to be nice but to be easy to spot in your file when testing. Of course you need to replace `Default Light+` with the name of your theme, and you can customize several themes if you use several themes. VSCode will display small colored boxes next to the HTML color specifications. Hovering on top of a color specification opens a convenient color picker dialog.
In order to understand what `function`, `property` and `variable` mean in the above example, the easiest path is to open a Lean file and ask VSCode about its classification of various bits of your file. Open the command palette with Ctrl-shift-p (or ⌘-shift-p on a Mac) and search for "Inspect Editor Tokens and Scopes" (typing the word "tokens" should be enough to see it). You can then click on any word in your file and look if there is a "semantic token type" line in the displayed information.
Platforms built & tested by our CI, available as binary releases via elan (see below)
* x86-64 Linux with glibc 2.26+
* x86-64 macOS 10.15+
* aarch64 (Apple Silicon) macOS 10.15+
* x86-64 Windows 11 (any version), Windows 10 (version 1903 or higher), Windows Server 2022, Windows Server 2025
### Tier 2
Platforms cross-compiled but not tested by our CI, available as binary releases
Releases may be silently broken due to the lack of automated testing.
Issue reports and fixes are welcome.
* aarch64 Linux with glibc 2.27+
* x86 (32-bit) Linux
* Emscripten Web Assembly
<!--
### Tier 3
Platforms that are known to work from manual testing, but do not come with CI or official releases
-->
# Setting Up Lean
See also the [quickstart](./quickstart.md) instructions for a standard setup with VS Code as the editor.
Release builds for all supported platforms are available at <https://github.com/leanprover/lean4/releases>.
Instead of downloading these and setting up the paths manually, however, it is recommended to use the Lean version manager [`elan`](https://github.com/leanprover/elan) instead:
```sh
$ elan self update # in case you haven't updated elan in a while
Use `lake init foo` to initialize a Lean package `foo` in the current directory, and `lake build` to typecheck and build it as well as all its dependencies. Use `lake help` to learn about further commands.
The general directory structure of a package `foo` is
```sh
lakefile.lean # package configuration
lean-toolchain # specifies the lean version to use
Foo.lean # main file, import via `import Foo`
Foo/
A.lean # further files, import via e.g. `import Foo.A`
A/... # further nesting
.lake/ # `lake` build output directory
```
After running `lake build` you will see a binary named `./.lake/build/bin/foo` and when you run it you should see the output:
```
Hello, world!
```
## Editing
Lean implements the [Language Server Protocol](https://microsoft.github.io/language-server-protocol/) that can be used for interactive development in [Emacs](https://github.com/leanprover/lean4-mode), [VS Code](https://github.com/leanprover-community/vscode-lean4), and possibly other editors.
Changes must be saved to be visible in other files, which must then be invalidated using an editor command (see links above).
renderedStatement:="Std.DHashMap.Raw.Const.get.{u, v} {α : Type u} {β : Type v} [BEq α] [Hashable α]\n (m : Std.DHashMap.Raw α fun x => β) (a : α) (h : a ∈ m) : β",
description:="Operations that take as input an associative container and return a 'single' piece of information (e.g., `GetElem` or `isEmpty`, but not `toList`)."
- How to declare a syntax category for the Dyck grammar.
- How to specify parse trees of this grammar using `syntax`
- How to translate out of this grammar into Lean 4 terms using `macro_rules`.
The full program listing is given below:
```lean
{{#include syntax_example.lean}}
```
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