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3 Commits

Author SHA1 Message Date
Kim Morrison
06c955902c import all 2024-12-01 19:12:25 +11:00
Kim Morrison
c94934e2ae Merge remote-tracking branch 'origin/master' into array_perm 2024-12-01 19:10:53 +11:00
Kim Morrison
77ad0769fb feat: Array.swap_perm 2024-12-01 19:10:26 +11:00
676 changed files with 1713 additions and 4296 deletions

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@@ -14,7 +14,6 @@ jobs:
sparse-checkout: |
src/Lean
src/Std
src/lake/Lake
- name: Check Prelude
run: |
failed_files=""
@@ -22,7 +21,7 @@ jobs:
if ! grep -q "^prelude$" "$file"; then
failed_files="$failed_files$file\n"
fi
done < <(find src/Lean src/Std src/lake/Lake -name '*.lean' -print0)
done < <(find src/Lean src/Std -name '*.lean' -print0)
if [ -n "$failed_files" ]; then
echo -e "The following files should use 'prelude':\n$failed_files"
exit 1

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@@ -34,7 +34,7 @@ jobs:
- name: Download artifact from the previous workflow.
if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
id: download-artifact
uses: dawidd6/action-download-artifact@v7 # https://github.com/marketplace/actions/download-workflow-artifact
uses: dawidd6/action-download-artifact@v6 # https://github.com/marketplace/actions/download-workflow-artifact
with:
run_id: ${{ github.event.workflow_run.id }}
path: artifacts
@@ -111,7 +111,7 @@ jobs:
- name: 'Setup jq'
if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
uses: dcarbone/install-jq-action@v3.0.1
uses: dcarbone/install-jq-action@v2.1.0
# Check that the most recently nightly coincides with 'git merge-base HEAD master'
- name: Check merge-base and nightly-testing-YYYY-MM-DD

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@@ -8,299 +8,15 @@ This file contains work-in-progress notes for the upcoming release, as well as p
Please check the [releases](https://github.com/leanprover/lean4/releases) page for the current status
of each version.
v4.16.0
v4.15.0
----------
Development in progress.
v4.15.0
----------
Release candidate, release notes will be copied from the branch `releases/v4.15.0` once completed.
v4.14.0
----------
**Full Changelog**: https://github.com/leanprover/lean4/compare/v4.13.0...v4.14.0
### Language features, tactics, and metaprograms
* `structure` and `inductive` commands
* [#5517](https://github.com/leanprover/lean4/pull/5517) improves universe level inference for the resulting type of an `inductive` or `structure.` Recall that a `Prop`-valued inductive type is a syntactic subsingleton if it has at most one constructor and all the arguments to the constructor are in `Prop`. Such types have large elimination, so they could be defined in `Type` or `Prop` without any trouble. The way inference has changed is that if a type is a syntactic subsingleton with exactly one constructor, and the constructor has at least one parameter/field, then the `inductive`/`structure` command will prefer creating a `Prop` instead of a `Type`. The upshot is that the `: Prop` in `structure S : Prop` is often no longer needed. (With @arthur-adjedj).
* [#5842](https://github.com/leanprover/lean4/pull/5842) and [#5783](https://github.com/leanprover/lean4/pull/5783) implement a feature where the `structure` command can now define recursive inductive types:
```lean
structure Tree where
n : Nat
children : Fin n → Tree
def Tree.size : Tree → Nat
| {n, children} => Id.run do
let mut s := 0
for h : i in [0 : n] do
s := s + (children ⟨i, h.2⟩).size
pure s
```
* [#5814](https://github.com/leanprover/lean4/pull/5814) fixes a bug where Mathlib's `Type*` elaborator could lead to incorrect universe parameters with the `inductive` command.
* [#3152](https://github.com/leanprover/lean4/pull/3152) and [#5844](https://github.com/leanprover/lean4/pull/5844) fix bugs in default value processing for structure instance notation (with @arthur-adjedj).
* [#5399](https://github.com/leanprover/lean4/pull/5399) promotes instance synthesis order calculation failure from a soft error to a hard error.
* [#5542](https://github.com/leanprover/lean4/pull/5542) deprecates `:=` variants of `inductive` and `structure` (see breaking changes).
* **Application elaboration improvements**
* [#5671](https://github.com/leanprover/lean4/pull/5671) makes `@[elab_as_elim]` require at least one discriminant, since otherwise there is no advantage to this alternative elaborator.
* [#5528](https://github.com/leanprover/lean4/pull/5528) enables field notation in explicit mode. The syntax `@x.f` elaborates as `@S.f` with `x` supplied to the appropriate parameter.
* [#5692](https://github.com/leanprover/lean4/pull/5692) modifies the dot notation resolution algorithm so that it can apply `CoeFun` instances. For example, Mathlib has `Multiset.card : Multiset α →+ Nat`, and now with `m : Multiset α`, the notation `m.card` resolves to `⇑Multiset.card m`.
* [#5658](https://github.com/leanprover/lean4/pull/5658) fixes a bug where 'don't know how to synthesize implicit argument' errors might have the incorrect local context when the eta arguments feature is activated.
* [#5933](https://github.com/leanprover/lean4/pull/5933) fixes a bug where `..` ellipses in patterns made use of optparams and autoparams.
* [#5770](https://github.com/leanprover/lean4/pull/5770) makes dot notation for structures resolve using *all* ancestors. Adds a *resolution order* for generalized field notation. This is the order of namespaces visited during resolution when trying to resolve names. The algorithm to compute a resolution order is the commonly used C3 linearization (used for example by Python), which when successful ensures that immediate parents' namespaces are considered before more distant ancestors' namespaces. By default we use a relaxed version of the algorithm that tolerates inconsistencies, but using `set_option structure.strictResolutionOrder true` makes inconsistent parent orderings into warnings.
* **Recursion and induction principles**
* [#5619](https://github.com/leanprover/lean4/pull/5619) fixes functional induction principle generation to avoid over-eta-expanding in the preprocessing step.
* [#5766](https://github.com/leanprover/lean4/pull/5766) fixes structural nested recursion so that it is not confused when a nested type appears first.
* [#5803](https://github.com/leanprover/lean4/pull/5803) fixes a bug in functional induction principle generation when there are `let` bindings.
* [#5904](https://github.com/leanprover/lean4/pull/5904) improves functional induction principle generation to unfold aux definitions more carefully.
* [#5850](https://github.com/leanprover/lean4/pull/5850) refactors code for `Predefinition.Structural`.
* **Error messages**
* [#5276](https://github.com/leanprover/lean4/pull/5276) fixes a bug in "type mismatch" errors that would structurally assign metavariables during the algorithm to expose differences.
* [#5919](https://github.com/leanprover/lean4/pull/5919) makes "type mismatch" errors add type ascriptions to expose differences for numeric literals.
* [#5922](https://github.com/leanprover/lean4/pull/5922) makes "type mismatch" errors expose differences in the bodies of functions and pi types.
* [#5888](https://github.com/leanprover/lean4/pull/5888) improves the error message for invalid induction alternative names in `match` expressions (@josojo).
* [#5719](https://github.com/leanprover/lean4/pull/5719) improves `calc` error messages.
* [#5627](https://github.com/leanprover/lean4/pull/5627) and [#5663](https://github.com/leanprover/lean4/pull/5663) improve the **`#eval` command** and introduce some new features.
* Now results can be pretty printed if there is a `ToExpr` instance, which means **hoverable output**. If `ToExpr` fails, it then tries looking for a `Repr` or `ToString` instance like before. Setting `set_option eval.pp false` disables making use of `ToExpr` instances.
* There is now **auto-derivation** of `Repr` instances, enabled with the `pp.derive.repr` option (default to **true**). For example:
```lean
inductive Baz
| a | b
#eval Baz.a
-- Baz.a
```
It simply does `deriving instance Repr for Baz` when there's no way to represent `Baz`.
* The option `eval.type` controls whether or not to include the type in the output. For now the default is false.
* Now expressions such as `#eval do return 2`, where monad is unknown, work. It tries unifying the monad with `CommandElabM`, `TermElabM`, or `IO`.
* The classes `Lean.Eval` and `Lean.MetaEval` have been removed. These each used to be responsible for adapting monads and printing results. Now the `MonadEval` class is responsible for adapting monads for evaluation (it is similar to `MonadLift`, but instances are allowed to use default data when initializing state), and representing results is handled through a separate process.
* Error messages about failed instance synthesis are now more precise. Once it detects that a `MonadEval` class applies, then the error message will be specific about missing `ToExpr`/`Repr`/`ToString` instances.
* Fixes bugs where evaluating `MetaM` and `CoreM` wouldn't collect log messages.
* Fixes a bug where `let rec` could not be used in `#eval`.
* `partial` definitions
* [#5780](https://github.com/leanprover/lean4/pull/5780) improves the error message when `partial` fails to prove a type is inhabited. Add delta deriving.
* [#5821](https://github.com/leanprover/lean4/pull/5821) gives `partial` inhabitation the ability to create local `Inhabited` instances from parameters.
* **New tactic configuration syntax.** The configuration syntax for all core tactics has been given an upgrade. Rather than `simp (config := { contextual := true, maxSteps := 22})`, one can now write `simp +contextual (maxSteps := 22)`. Tactic authors can migrate by switching from `(config)?` to `optConfig` in tactic syntaxes and potentially deleting `mkOptionalNode` in elaborators. [#5883](https://github.com/leanprover/lean4/pull/5883), [#5898](https://github.com/leanprover/lean4/pull/5898), [#5928](https://github.com/leanprover/lean4/pull/5928), and [#5932](https://github.com/leanprover/lean4/pull/5932). (Tactic authors, see breaking changes.)
* `simp` tactic
* [#5632](https://github.com/leanprover/lean4/pull/5632) fixes the simpproc for `Fin` literals to reduce more consistently.
* [#5648](https://github.com/leanprover/lean4/pull/5648) fixes a bug in `simpa ... using t` where metavariables in `t` were not properly accounted for, and also improves the type mismatch error.
* [#5838](https://github.com/leanprover/lean4/pull/5838) fixes the docstring of `simp!` to actually talk about `simp!`.
* [#5870](https://github.com/leanprover/lean4/pull/5870) adds support for `attribute [simp ←]` (note the reverse direction). This adds the reverse of a theorem as a global simp theorem.
* `decide` tactic
* [#5665](https://github.com/leanprover/lean4/pull/5665) adds `decide!` tactic for using kernel reduction (warning: this is renamed to `decide +kernel` in a future release).
* `bv_decide` tactic
* [#5714](https://github.com/leanprover/lean4/pull/5714) adds inequality regression tests (@alexkeizer).
* [#5608](https://github.com/leanprover/lean4/pull/5608) adds `bv_toNat` tag for `toNat_ofInt` (@bollu).
* [#5618](https://github.com/leanprover/lean4/pull/5618) adds support for `at` in `ac_nf` and uses it in `bv_normalize` (@tobiasgrosser).
* [#5628](https://github.com/leanprover/lean4/pull/5628) adds udiv support.
* [#5635](https://github.com/leanprover/lean4/pull/5635) adds auxiliary bitblasters for negation and subtraction.
* [#5637](https://github.com/leanprover/lean4/pull/5637) adds more `getLsbD` bitblaster theory.
* [#5652](https://github.com/leanprover/lean4/pull/5652) adds umod support.
* [#5653](https://github.com/leanprover/lean4/pull/5653) adds performance benchmark for modulo.
* [#5655](https://github.com/leanprover/lean4/pull/5655) reduces error on `bv_check` to warning.
* [#5670](https://github.com/leanprover/lean4/pull/5670) adds `~~~(-x)` support.
* [#5673](https://github.com/leanprover/lean4/pull/5673) disables `ac_nf` by default.
* [#5675](https://github.com/leanprover/lean4/pull/5675) fixes context tracking in `bv_decide` counter example.
* [#5676](https://github.com/leanprover/lean4/pull/5676) adds an error when the LRAT proof is invalid.
* [#5781](https://github.com/leanprover/lean4/pull/5781) introduces uninterpreted symbols everywhere.
* [#5823](https://github.com/leanprover/lean4/pull/5823) adds `BitVec.sdiv` support.
* [#5852](https://github.com/leanprover/lean4/pull/5852) adds `BitVec.ofBool` support.
* [#5855](https://github.com/leanprover/lean4/pull/5855) adds `if` support.
* [#5869](https://github.com/leanprover/lean4/pull/5869) adds support for all the SMTLIB BitVec divison/remainder operations.
* [#5886](https://github.com/leanprover/lean4/pull/5886) adds embedded constraint substitution.
* [#5918](https://github.com/leanprover/lean4/pull/5918) fixes loose mvars bug in `bv_normalize`.
* Documentation:
* [#5636](https://github.com/leanprover/lean4/pull/5636) adds remarks about multiplication.
* `conv` mode
* [#5861](https://github.com/leanprover/lean4/pull/5861) improves the `congr` conv tactic to handle "over-applied" functions.
* [#5894](https://github.com/leanprover/lean4/pull/5894) improves the `arg` conv tactic so that it can access more arguments and so that it can handle "over-applied" functions (it generates a specialized congruence lemma for the specific argument in question). Makes `arg 1` and `arg 2` apply to pi types in more situations. Adds negative indexing, for example `arg -2` is equivalent to the `lhs` tactic. Makes the `enter [...]` tactic show intermediate states like `rw`.
* **Other tactics**
* [#4846](https://github.com/leanprover/lean4/pull/4846) fixes a bug where `generalize ... at *` would apply to implementation details (@ymherklotz).
* [#5730](https://github.com/leanprover/lean4/pull/5730) upstreams the `classical` tactic combinator.
* [#5815](https://github.com/leanprover/lean4/pull/5815) improves the error message when trying to unfold a local hypothesis that is not a local definition.
* [#5862](https://github.com/leanprover/lean4/pull/5862) and [#5863](https://github.com/leanprover/lean4/pull/5863) change how `apply` and `simp` elaborate, making them not disable error recovery. This improves hovers and completions when the term has elaboration errors.
* `deriving` clauses
* [#5899](https://github.com/leanprover/lean4/pull/5899) adds declaration ranges for delta-derived instances.
* [#5265](https://github.com/leanprover/lean4/pull/5265) removes unused syntax in `deriving` clauses for providing arguments to deriving handlers (see breaking changes).
* [#5065](https://github.com/leanprover/lean4/pull/5065) upstreams and updates `#where`, a command that reports the current scope information.
* **Linters**
* [#5338](https://github.com/leanprover/lean4/pull/5338) makes the unused variables linter ignore variables defined in tactics by default now, avoiding performance bottlenecks.
* [#5644](https://github.com/leanprover/lean4/pull/5644) ensures that linters in general do not run on `#guard_msgs` itself.
* **Metaprogramming interface**
* [#5720](https://github.com/leanprover/lean4/pull/5720) adds `pushGoal`/`pushGoals` and `popGoal` for manipulating the goal state. These are an alternative to `replaceMainGoal` and `getMainGoal`, and with them you don't need to worry about making sure nothing clears assigned metavariables from the goal list between assigning the main goal and using `replaceMainGoal`. Modifies `closeMainGoalUsing`, which is like a `TacticM` version of `liftMetaTactic`. Now the callback is run in a context where the main goal is removed from the goal list, and the callback is free to modify the goal list. Furthermore, the `checkUnassigned` argument has been replaced with `checkNewUnassigned`, which checks whether the value assigned to the goal has any *new* metavariables, relative to the start of execution of the callback. Modifies `withCollectingNewGoalsFrom` to take the `parentTag` argument explicitly rather than indirectly via `getMainTag`. Modifies `elabTermWithHoles` to optionally take `parentTag?`.
* [#5563](https://github.com/leanprover/lean4/pull/5563) fixes `getFunInfo` and `inferType` to use `withAtLeastTransparency` rather than `withTransparency`.
* [#5679](https://github.com/leanprover/lean4/pull/5679) fixes `RecursorVal.getInduct` to return the name of major arguments type. This makes "structure eta" work for nested inductives.
* [#5681](https://github.com/leanprover/lean4/pull/5681) removes unused `mkRecursorInfoForKernelRec`.
* [#5686](https://github.com/leanprover/lean4/pull/5686) makes discrimination trees index the domains of foralls, for better performance of the simplify and type class search.
* [#5760](https://github.com/leanprover/lean4/pull/5760) adds `Lean.Expr.name?` recognizer for `Name` expressions.
* [#5800](https://github.com/leanprover/lean4/pull/5800) modifies `liftCommandElabM` to preserve more state, fixing an issue where using it would drop messages.
* [#5857](https://github.com/leanprover/lean4/pull/5857) makes it possible to use dot notation in `m!` strings, for example `m!"{.ofConstName n}"`.
* [#5841](https://github.com/leanprover/lean4/pull/5841) and [#5853](https://github.com/leanprover/lean4/pull/5853) record the complete list of `structure` parents in the `StructureInfo` environment extension.
* **Other fixes or improvements**
* [#5566](https://github.com/leanprover/lean4/pull/5566) fixes a bug introduced in [#4781](https://github.com/leanprover/lean4/pull/4781) where heartbeat exceptions were no longer being handled properly. Now such exceptions are tagged with `runtime.maxHeartbeats` (@eric-wieser).
* [#5708](https://github.com/leanprover/lean4/pull/5708) modifies the proof objects produced by the proof-by-reflection tactics `ac_nf0` and `simp_arith` so that the kernel is less prone to reducing expensive atoms.
* [#5768](https://github.com/leanprover/lean4/pull/5768) adds a `#version` command that prints Lean's version information.
* [#5822](https://github.com/leanprover/lean4/pull/5822) fixes elaborator algorithms to match kernel algorithms for primitive projections (`Expr.proj`).
* [#5811](https://github.com/leanprover/lean4/pull/5811) improves the docstring for the `rwa` tactic.
### Language server, widgets, and IDE extensions
* [#5224](https://github.com/leanprover/lean4/pull/5224) fixes `WorkspaceClientCapabilities` to make `applyEdit` optional, in accordance with the LSP specification (@pzread).
* [#5340](https://github.com/leanprover/lean4/pull/5340) fixes a server deadlock when shutting down the language server and a desync between client and language server after a file worker crash.
* [#5560](https://github.com/leanprover/lean4/pull/5560) makes `initialize` and `builtin_initialize` participate in the call hierarchy and other requests.
* [#5650](https://github.com/leanprover/lean4/pull/5650) makes references in attributes participate in the call hierarchy and other requests.
* [#5666](https://github.com/leanprover/lean4/pull/5666) add auto-completion in tactic blocks without having to type the first character of the tactic, and adds tactic completion docs to tactic auto-completion items.
* [#5677](https://github.com/leanprover/lean4/pull/5677) fixes several cases where goal states were not displayed in certain text cursor positions.
* [#5707](https://github.com/leanprover/lean4/pull/5707) indicates deprecations in auto-completion items.
* [#5736](https://github.com/leanprover/lean4/pull/5736), [#5752](https://github.com/leanprover/lean4/pull/5752), [#5763](https://github.com/leanprover/lean4/pull/5763), [#5802](https://github.com/leanprover/lean4/pull/5802), and [#5805](https://github.com/leanprover/lean4/pull/5805) fix various performance issues in the language server.
* [#5801](https://github.com/leanprover/lean4/pull/5801) distinguishes theorem auto-completions from non-theorem auto-completions.
### Pretty printing
* [#5640](https://github.com/leanprover/lean4/pull/5640) fixes a bug where goal states in messages might print newlines as spaces.
* [#5643](https://github.com/leanprover/lean4/pull/5643) adds option `pp.mvars.delayed` (default false), which when false causes delayed assignment metavariables to pretty print with what they are assigned to. Now `fun x : Nat => ?a` pretty prints as `fun x : Nat => ?a` rather than `fun x ↦ ?m.7 x`.
* [#5711](https://github.com/leanprover/lean4/pull/5711) adds options `pp.mvars.anonymous` and `pp.mvars.levels`, which when false respectively cause expression metavariables and level metavariables to pretty print as `?_`.
* [#5710](https://github.com/leanprover/lean4/pull/5710) adjusts the `` elaboration warning to mention `pp.maxSteps`.
* [#5759](https://github.com/leanprover/lean4/pull/5759) fixes the app unexpander for `sorryAx`.
* [#5827](https://github.com/leanprover/lean4/pull/5827) improves accuracy of binder names in the signature pretty printer (like in output of `#check`). Also fixes the issue where consecutive hygienic names pretty print without a space separating them, so we now have `(x✝ y✝ : Nat)` rather than `(x✝y✝ : Nat)`.
* [#5830](https://github.com/leanprover/lean4/pull/5830) makes sure all the core delaborators respond to `pp.explicit` when appropriate.
* [#5639](https://github.com/leanprover/lean4/pull/5639) makes sure name literals use escaping when pretty printing.
* [#5854](https://github.com/leanprover/lean4/pull/5854) adds delaborators for `<|>`, `<*>`, `>>`, `<*`, and `*>`.
### Library
* `Array`
* [#5687](https://github.com/leanprover/lean4/pull/5687) deprecates `Array.data`.
* [#5705](https://github.com/leanprover/lean4/pull/5705) uses a better default value for `Array.swapAt!`.
* [#5748](https://github.com/leanprover/lean4/pull/5748) moves `Array.mapIdx` lemmas to a new file.
* [#5749](https://github.com/leanprover/lean4/pull/5749) simplifies signature of `Array.mapIdx`.
* [#5758](https://github.com/leanprover/lean4/pull/5758) upstreams `Array.reduceOption`.
* [#5786](https://github.com/leanprover/lean4/pull/5786) adds simp lemmas for `Array.isEqv` and `BEq`.
* [#5796](https://github.com/leanprover/lean4/pull/5796) renames `Array.shrink` to `Array.take`, and relates it to `List.take`.
* [#5798](https://github.com/leanprover/lean4/pull/5798) upstreams `List.modify`, adds lemmas, relates to `Array.modify`.
* [#5799](https://github.com/leanprover/lean4/pull/5799) relates `Array.forIn` and `List.forIn`.
* [#5833](https://github.com/leanprover/lean4/pull/5833) adds `Array.forIn'`, and relates to `List`.
* [#5848](https://github.com/leanprover/lean4/pull/5848) fixes deprecations in `Init.Data.Array.Basic` to not recommend the deprecated constant.
* [#5895](https://github.com/leanprover/lean4/pull/5895) adds `LawfulBEq (Array α) ↔ LawfulBEq α`.
* [#5896](https://github.com/leanprover/lean4/pull/5896) moves `@[simp]` from `back_eq_back?` to `back_push`.
* [#5897](https://github.com/leanprover/lean4/pull/5897) renames `Array.back` to `back!`.
* `List`
* [#5605](https://github.com/leanprover/lean4/pull/5605) removes `List.redLength`.
* [#5696](https://github.com/leanprover/lean4/pull/5696) upstreams `List.mapIdx` and adds lemmas.
* [#5697](https://github.com/leanprover/lean4/pull/5697) upstreams `List.foldxM_map`.
* [#5701](https://github.com/leanprover/lean4/pull/5701) renames `List.join` to `List.flatten`.
* [#5703](https://github.com/leanprover/lean4/pull/5703) upstreams `List.sum`.
* [#5706](https://github.com/leanprover/lean4/pull/5706) marks `prefix_append_right_inj` as a simp lemma.
* [#5716](https://github.com/leanprover/lean4/pull/5716) fixes `List.drop_drop` addition order.
* [#5731](https://github.com/leanprover/lean4/pull/5731) renames `List.bind` and `Array.concatMap` to `flatMap`.
* [#5732](https://github.com/leanprover/lean4/pull/5732) renames `List.pure` to `List.singleton`.
* [#5742](https://github.com/leanprover/lean4/pull/5742) upstreams `ne_of_mem_of_not_mem`.
* [#5743](https://github.com/leanprover/lean4/pull/5743) upstreams `ne_of_apply_ne`.
* [#5816](https://github.com/leanprover/lean4/pull/5816) adds more `List.modify` lemmas.
* [#5879](https://github.com/leanprover/lean4/pull/5879) renames `List.groupBy` to `splitBy`.
* [#5913](https://github.com/leanprover/lean4/pull/5913) relates `for` loops over `List` with `foldlM`.
* `Nat`
* [#5694](https://github.com/leanprover/lean4/pull/5694) removes `instBEqNat`, which is redundant with `instBEqOfDecidableEq` but not defeq.
* [#5746](https://github.com/leanprover/lean4/pull/5746) deprecates `Nat.sum`.
* [#5785](https://github.com/leanprover/lean4/pull/5785) adds `Nat.forall_lt_succ` and variants.
* Fixed width integers
* [#5323](https://github.com/leanprover/lean4/pull/5323) redefine unsigned fixed width integers in terms of `BitVec`.
* [#5735](https://github.com/leanprover/lean4/pull/5735) adds `UIntX.[val_ofNat, toBitVec_ofNat]`.
* [#5790](https://github.com/leanprover/lean4/pull/5790) defines `Int8`.
* [#5901](https://github.com/leanprover/lean4/pull/5901) removes native code for `UInt8.modn`.
* `BitVec`
* [#5604](https://github.com/leanprover/lean4/pull/5604) completes `BitVec.[getMsbD|getLsbD|msb]` for shifts (@luisacicolini).
* [#5609](https://github.com/leanprover/lean4/pull/5609) adds lemmas for division when denominator is zero (@bollu).
* [#5620](https://github.com/leanprover/lean4/pull/5620) documents Bitblasting (@bollu)
* [#5623](https://github.com/leanprover/lean4/pull/5623) moves `BitVec.udiv/umod/sdiv/smod` after `add/sub/mul/lt` (@tobiasgrosser).
* [#5645](https://github.com/leanprover/lean4/pull/5645) defines `udiv` normal form to be `/`, resp. `umod` and `%` (@bollu).
* [#5646](https://github.com/leanprover/lean4/pull/5646) adds lemmas about arithmetic inequalities (@bollu).
* [#5680](https://github.com/leanprover/lean4/pull/5680) expands relationship with `toFin` (@tobiasgrosser).
* [#5691](https://github.com/leanprover/lean4/pull/5691) adds `BitVec.(getMSbD, msb)_(add, sub)` and `BitVec.getLsbD_sub` (@luisacicolini).
* [#5712](https://github.com/leanprover/lean4/pull/5712) adds `BitVec.[udiv|umod]_[zero|one|self]` (@tobiasgrosser).
* [#5718](https://github.com/leanprover/lean4/pull/5718) adds `BitVec.sdiv_[zero|one|self]` (@tobiasgrosser).
* [#5721](https://github.com/leanprover/lean4/pull/5721) adds `BitVec.(msb, getMsbD, getLsbD)_(neg, abs)` (@luisacicolini).
* [#5772](https://github.com/leanprover/lean4/pull/5772) adds `BitVec.toInt_sub`, simplifies `BitVec.toInt_neg` (@tobiasgrosser).
* [#5778](https://github.com/leanprover/lean4/pull/5778) prove that `intMin` the smallest signed bitvector (@alexkeizer).
* [#5851](https://github.com/leanprover/lean4/pull/5851) adds `(msb, getMsbD)_twoPow` (@luisacicolini).
* [#5858](https://github.com/leanprover/lean4/pull/5858) adds `BitVec.[zero_ushiftRight|zero_sshiftRight|zero_mul]` and cleans up BVDecide (@tobiasgrosser).
* [#5865](https://github.com/leanprover/lean4/pull/5865) adds `BitVec.(msb, getMsbD)_concat` (@luisacicolini).
* [#5881](https://github.com/leanprover/lean4/pull/5881) adds `Hashable (BitVec n)`
* `String`/`Char`
* [#5728](https://github.com/leanprover/lean4/pull/5728) upstreams `String.dropPrefix?`.
* [#5745](https://github.com/leanprover/lean4/pull/5745) changes `String.dropPrefix?` signature.
* [#5747](https://github.com/leanprover/lean4/pull/5747) adds `Hashable Char` instance
* `HashMap`
* [#5880](https://github.com/leanprover/lean4/pull/5880) adds interim implementation of `HashMap.modify`/`alter`
* **Other**
* [#5704](https://github.com/leanprover/lean4/pull/5704) removes `@[simp]` from `Option.isSome_eq_isSome`.
* [#5739](https://github.com/leanprover/lean4/pull/5739) upstreams material on `Prod`.
* [#5740](https://github.com/leanprover/lean4/pull/5740) moves `Antisymm` to `Std.Antisymm`.
* [#5741](https://github.com/leanprover/lean4/pull/5741) upstreams basic material on `Sum`.
* [#5756](https://github.com/leanprover/lean4/pull/5756) adds `Nat.log2_two_pow` (@spinylobster).
* [#5892](https://github.com/leanprover/lean4/pull/5892) removes duplicated `ForIn` instances.
* [#5900](https://github.com/leanprover/lean4/pull/5900) removes `@[simp]` from `Sum.forall` and `Sum.exists`.
* [#5812](https://github.com/leanprover/lean4/pull/5812) removes redundant `Decidable` assumptions (@FR-vdash-bot).
### Compiler, runtime, and FFI
* [#5685](https://github.com/leanprover/lean4/pull/5685) fixes help message flags, removes the `-f` flag and adds the `-g` flag (@James-Oswald).
* [#5930](https://github.com/leanprover/lean4/pull/5930) adds `--short-version` (`-V`) option to display short version (@juhp).
* [#5144](https://github.com/leanprover/lean4/pull/5144) switches all 64-bit platforms over to consistently using GMP for bignum arithmetic.
* [#5753](https://github.com/leanprover/lean4/pull/5753) raises the minimum supported Windows version to Windows 10 1903 (released May 2019).
### Lake
* [#5715](https://github.com/leanprover/lean4/pull/5715) changes `lake new math` to use `autoImplicit false` (@eric-wieser).
* [#5688](https://github.com/leanprover/lean4/pull/5688) makes `Lake` not create core aliases in the `Lake` namespace.
* [#5924](https://github.com/leanprover/lean4/pull/5924) adds a `text` option for `buildFile*` utilities.
* [#5789](https://github.com/leanprover/lean4/pull/5789) makes `lake init` not `git init` when inside git work tree (@haoxins).
* [#5684](https://github.com/leanprover/lean4/pull/5684) has Lake update a package's `lean-toolchain` file on `lake update` if it finds the package's direct dependencies use a newer compatible toolchain. To skip this step, use the `--keep-toolchain` CLI option. (See breaking changes.)
* [#6218](https://github.com/leanprover/lean4/pull/6218) makes Lake no longer automatically fetch GitHub cloud releases if the package build directory is already present (mirroring the behavior of the Reservoir cache). This prevents the cache from clobbering existing prebuilt artifacts. Users can still manually fetch the cache and clobber the build directory by running `lake build <pkg>:release`.
* [#6231](https://github.com/leanprover/lean4/pull/6231) improves the errors Lake produces when it fails to fetch a dependency from Reservoir. If the package is not indexed, it will produce a suggestion about how to require it from GitHub.
### Documentation
* [#5617](https://github.com/leanprover/lean4/pull/5617) fixes MSYS2 build instructions.
* [#5725](https://github.com/leanprover/lean4/pull/5725) points out that `OfScientific` is called with raw literals (@eric-wieser).
* [#5794](https://github.com/leanprover/lean4/pull/5794) adds a stub for application ellipsis notation (@eric-wieser).
### Breaking changes
* The syntax for providing arguments to deriving handlers has been removed, which was not used by any major Lean projects in the ecosystem. As a result, the `applyDerivingHandlers` now takes one fewer argument, `registerDerivingHandlerWithArgs` is now simply `registerDerivingHandler`, `DerivingHandler` no longer includes the unused parameter, and `DerivingHandlerNoArgs` has been deprecated. To migrate code, delete the unused `none` argument and use `registerDerivingHandler` and `DerivingHandler`. ([#5265](https://github.com/leanprover/lean4/pull/5265))
* The minimum supported Windows version has been raised to Windows 10 1903, released May 2019. ([#5753](https://github.com/leanprover/lean4/pull/5753))
* The `--lean` CLI option for `lake` was removed. Use the `LEAN` environment variable instead. ([#5684](https://github.com/leanprover/lean4/pull/5684))
* The `inductive ... :=`, `structure ... :=`, and `class ... :=` syntaxes have been deprecated in favor of the `... where` variants. The old syntax produces a warning, controlled by the `linter.deprecated` option. ([#5542](https://github.com/leanprover/lean4/pull/5542))
* The generated tactic configuration elaborators now land in `TacticM` to make use of the current recovery state. Commands that wish to elaborate configurations should now use `declare_command_config_elab` instead of `declare_config_elab` to get an elaborator landing in `CommandElabM`. Syntaxes should migrate to `optConfig` instead of `(config)?`, but the elaborators are reverse compatible. ([#5883](https://github.com/leanprover/lean4/pull/5883))
Release candidate, release notes will be copied from the branch `releases/v4.14.0` once completed.
v4.13.0
----------
@@ -372,7 +88,7 @@ v4.13.0
* [#4768](https://github.com/leanprover/lean4/pull/4768) fixes a parse error when `..` appears with a `.` on the next line
* Metaprogramming
* [#3090](https://github.com/leanprover/lean4/pull/3090) handles level parameters in `Meta.evalExpr` (@eric-wieser)
* [#3090](https://github.com/leanprover/lean4/pull/3090) handles level parameters in `Meta.evalExpr` (@eric-wieser)
* [#5401](https://github.com/leanprover/lean4/pull/5401) instance for `Inhabited (TacticM α)` (@alexkeizer)
* [#5412](https://github.com/leanprover/lean4/pull/5412) expose Kernel.check for debugging purposes
* [#5556](https://github.com/leanprover/lean4/pull/5556) improves the "invalid projection" type inference error in `inferType`.

1
debug.log Normal file
View File

@@ -0,0 +1 @@
[0829/202002.254:ERROR:crashpad_client_win.cc(868)] not connected

View File

@@ -1,4 +1,4 @@
#!/usr/bin/env bash
source ../../tests/common.sh
exec_check_raw lean -Dlinter.all=false "$f"
exec_check lean -Dlinter.all=false "$f"

View File

@@ -128,16 +128,16 @@ Numeric literals can be specified in various bases.
```
numeral : numeral10 | numeral2 | numeral8 | numeral16
numeral10 : [0-9]+ ("_"+ [0-9]+)*
numeral2 : "0" [bB] ("_"* [0-1]+)+
numeral8 : "0" [oO] ("_"* [0-7]+)+
numeral16 : "0" [xX] ("_"* hex_char+)+
numeral10 : [0-9]+
numeral2 : "0" [bB] [0-1]+
numeral8 : "0" [oO] [0-7]+
numeral16 : "0" [xX] hex_char+
```
Floating point literals are also possible with optional exponent:
```
float : numeral10 "." numeral10? [eE[+-]numeral10]
float : [0-9]+ "." [0-9]+ [[eE[+-][0-9]+]
```
For example:
@@ -147,7 +147,6 @@ constant w : Int := 55
constant x : Nat := 26085
constant y : Nat := 0x65E5
constant z : Float := 2.548123e-05
constant b : Bool := 0b_11_01_10_00
```
Note: that negative numbers are created by applying the "-" negation prefix operator to the number, for example:

View File

@@ -139,7 +139,7 @@ You might be wondering, how does the context actually move through the `ReaderM`
add an input argument to a function by modifying its return type? There is a special command in
Lean that will show you the reduced types:
-/
#reduce (types := true) ReaderM Environment String -- Environment → String
#reduce ReaderM Environment String -- Environment → String
/-!
And you can see here that this type is actually a function! It's a function that takes an
`Environment` as input and returns a `String`.
@@ -196,4 +196,4 @@ entirely.
Now it's time to move on to [StateM Monad](states.lean.md) which is like a `ReaderM` that is
also updatable.
-/
-/

View File

@@ -1,12 +0,0 @@
#! /bin/env bash
# Open a Mathlib4 PR for benchmarking a given Lean 4 PR
set -euo pipefail
[ $# -eq 1 ] || (echo "usage: $0 <lean4 PR #>"; exit 1)
LEAN_PR=$1
PR_RESPONSE=$(gh api repos/leanprover-community/mathlib4/pulls -X POST -f head=lean-pr-testing-$LEAN_PR -f base=nightly-testing -f title="leanprover/lean4#$LEAN_PR benchmarking" -f draft=true -f body="ignore me")
PR_NUMBER=$(echo "$PR_RESPONSE" | jq '.number')
echo "opened https://github.com/leanprover-community/mathlib4/pull/$PR_NUMBER"
gh api repos/leanprover-community/mathlib4/issues/$PR_NUMBER/comments -X POST -f body="!bench" > /dev/null

View File

@@ -10,7 +10,7 @@ endif()
include(ExternalProject)
project(LEAN CXX C)
set(LEAN_VERSION_MAJOR 4)
set(LEAN_VERSION_MINOR 16)
set(LEAN_VERSION_MINOR 15)
set(LEAN_VERSION_PATCH 0)
set(LEAN_VERSION_IS_RELEASE 0) # This number is 1 in the release revision, and 0 otherwise.
set(LEAN_SPECIAL_VERSION_DESC "" CACHE STRING "Additional version description like 'nightly-2018-03-11'")
@@ -122,7 +122,7 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
# From https://emscripten.org/docs/compiling/WebAssembly.html#backends:
# > The simple and safe thing is to pass all -s flags at both compile and link time.
set(EMSCRIPTEN_SETTINGS "-s ALLOW_MEMORY_GROWTH=1 -fwasm-exceptions -pthread -flto")
string(APPEND LEANC_EXTRA_CC_FLAGS " -pthread")
string(APPEND LEANC_EXTRA_FLAGS " -pthread")
string(APPEND LEAN_EXTRA_CXX_FLAGS " -D LEAN_EMSCRIPTEN ${EMSCRIPTEN_SETTINGS}")
string(APPEND LEAN_EXTRA_LINKER_FLAGS " ${EMSCRIPTEN_SETTINGS}")
endif()
@@ -157,11 +157,11 @@ if ((${MULTI_THREAD} MATCHES "ON") AND (${CMAKE_SYSTEM_NAME} MATCHES "Darwin"))
endif ()
# We want explicit stack probes in huge Lean stack frames for robust stack overflow detection
string(APPEND LEANC_EXTRA_CC_FLAGS " -fstack-clash-protection")
string(APPEND LEANC_EXTRA_FLAGS " -fstack-clash-protection")
# This makes signed integer overflow guaranteed to match 2's complement.
string(APPEND CMAKE_CXX_FLAGS " -fwrapv")
string(APPEND LEANC_EXTRA_CC_FLAGS " -fwrapv")
string(APPEND LEANC_EXTRA_FLAGS " -fwrapv")
if(NOT MULTI_THREAD)
message(STATUS "Disabled multi-thread support, it will not be safe to run multiple threads in parallel")
@@ -451,7 +451,7 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Linux")
string(APPEND TOOLCHAIN_SHARED_LINKER_FLAGS " -Wl,-Bsymbolic")
endif()
string(APPEND CMAKE_CXX_FLAGS " -fPIC -ftls-model=initial-exec")
string(APPEND LEANC_EXTRA_CC_FLAGS " -fPIC")
string(APPEND LEANC_EXTRA_FLAGS " -fPIC")
string(APPEND TOOLCHAIN_SHARED_LINKER_FLAGS " -Wl,-rpath=\\$$ORIGIN/..:\\$$ORIGIN")
string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -Wl,--no-whole-archive")
string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath=\\\$ORIGIN/../lib:\\\$ORIGIN/../lib/lean")
@@ -464,7 +464,7 @@ elseif(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath,@executable_path/../lib -Wl,-rpath,@executable_path/../lib/lean")
elseif(${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
string(APPEND CMAKE_CXX_FLAGS " -fPIC")
string(APPEND LEANC_EXTRA_CC_FLAGS " -fPIC")
string(APPEND LEANC_EXTRA_FLAGS " -fPIC")
elseif(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libLake_shared.dll.a -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -Wl,--no-whole-archive")
endif()
@@ -479,7 +479,7 @@ if(NOT(${CMAKE_SYSTEM_NAME} MATCHES "Windows") AND NOT(${CMAKE_SYSTEM_NAME} MATC
string(APPEND CMAKE_EXE_LINKER_FLAGS " -rdynamic")
# hide all other symbols
string(APPEND CMAKE_CXX_FLAGS " -fvisibility=hidden -fvisibility-inlines-hidden")
string(APPEND LEANC_EXTRA_CC_FLAGS " -fvisibility=hidden")
string(APPEND LEANC_EXTRA_FLAGS " -fvisibility=hidden")
endif()
# On Windows, add bcrypt for random number generation
@@ -544,10 +544,9 @@ include_directories(${CMAKE_BINARY_DIR}/include) # config.h etc., "public" head
string(TOUPPER "${CMAKE_BUILD_TYPE}" uppercase_CMAKE_BUILD_TYPE)
string(APPEND LEANC_OPTS " ${CMAKE_CXX_FLAGS_${uppercase_CMAKE_BUILD_TYPE}}")
# Do embed flag for finding system headers and libraries in dev builds
# Do embed flag for finding system libraries in dev builds
if(CMAKE_OSX_SYSROOT AND NOT LEAN_STANDALONE)
string(APPEND LEANC_EXTRA_CC_FLAGS " ${CMAKE_CXX_SYSROOT_FLAG}${CMAKE_OSX_SYSROOT}")
string(APPEND LEAN_EXTRA_LINKER_FLAGS " ${CMAKE_CXX_SYSROOT_FLAG}${CMAKE_OSX_SYSROOT}")
string(APPEND LEANC_EXTRA_FLAGS " ${CMAKE_CXX_SYSROOT_FLAG}${CMAKE_OSX_SYSROOT}")
endif()
add_subdirectory(initialize)

View File

@@ -21,7 +21,6 @@ import Init.Data.Fin
import Init.Data.UInt
import Init.Data.SInt
import Init.Data.Float
import Init.Data.Float32
import Init.Data.Option
import Init.Data.Ord
import Init.Data.Random

View File

@@ -21,4 +21,3 @@ import Init.Data.Array.Set
import Init.Data.Array.Monadic
import Init.Data.Array.FinRange
import Init.Data.Array.Perm
import Init.Data.Array.Find

View File

@@ -251,7 +251,7 @@ theorem getElem?_attach {xs : Array α} {i : Nat} :
theorem getElem_attachWith {xs : Array α} {P : α Prop} {H : a xs, P a}
{i : Nat} (h : i < (xs.attachWith P H).size) :
(xs.attachWith P H)[i] = xs[i]'(by simpa using h), H _ (getElem_mem (by simpa using h)) :=
getElem_pmap _ _ h
getElem_pmap ..
@[simp]
theorem getElem_attach {xs : Array α} {i : Nat} (h : i < xs.attach.size) :

View File

@@ -11,7 +11,7 @@ import Init.Data.UInt.BasicAux
import Init.Data.Repr
import Init.Data.ToString.Basic
import Init.GetElem
import Init.Data.List.ToArrayImpl
import Init.Data.List.ToArray
import Init.Data.Array.Set
universe u v w
@@ -85,8 +85,6 @@ theorem ext' {as bs : Array α} (h : as.toList = bs.toList) : as = bs := by
@[simp] theorem getElem_toList {a : Array α} {i : Nat} (h : i < a.size) : a.toList[i] = a[i] := rfl
@[simp] theorem getElem?_toList {a : Array α} {i : Nat} : a.toList[i]? = a[i]? := rfl
/-- `a ∈ as` is a predicate which asserts that `a` is in the array `as`. -/
-- NB: This is defined as a structure rather than a plain def so that a lemma
-- like `sizeOf_lt_of_mem` will not apply with no actual arrays around.
@@ -99,9 +97,6 @@ instance : Membership α (Array α) where
theorem mem_def {a : α} {as : Array α} : a as a as.toList :=
fun | .mk h => h, Array.Mem.mk
@[simp] theorem mem_toArray {a : α} {l : List α} : a l.toArray a l := by
simp [mem_def]
@[simp] theorem getElem_mem {l : Array α} {i : Nat} (h : i < l.size) : l[i] l := by
rw [Array.mem_def, getElem_toList]
apply List.getElem_mem
@@ -247,7 +242,7 @@ def singleton (v : α) : Array α :=
mkArray 1 v
def back! [Inhabited α] (a : Array α) : α :=
a[a.size - 1]!
a.get! (a.size - 1)
@[deprecated back! (since := "2024-10-31")] abbrev back := @back!
@@ -479,10 +474,6 @@ def findSomeM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f
| _ => pure
return none
/--
Note that the universe level is contrained to `Type` here,
to avoid having to have the predicate live in `p : α → m (ULift Bool)`.
-/
@[inline]
def findM? {α : Type} {m : Type Type} [Monad m] (p : α m Bool) (as : Array α) : m (Option α) := do
for a in as do
@@ -594,12 +585,8 @@ def zipWithIndex (arr : Array α) : Array (α × Nat) :=
arr.mapIdx fun i a => (a, i)
@[inline]
def find? {α : Type u} (p : α Bool) (as : Array α) : Option α :=
Id.run do
for a in as do
if p a then
return a
return none
def find? {α : Type} (p : α Bool) (as : Array α) : Option α :=
Id.run <| as.findM? p
@[inline]
def findSome? {α : Type u} {β : Type v} (f : α Option β) (as : Array α) : Option β :=
@@ -663,7 +650,7 @@ def all (as : Array α) (p : α → Bool) (start := 0) (stop := as.size) : Bool
Id.run <| as.allM p start stop
def contains [BEq α] (as : Array α) (a : α) : Bool :=
as.any (a == ·)
as.any (· == a)
def elem [BEq α] (a : α) (as : Array α) : Bool :=
as.contains a

View File

@@ -81,7 +81,7 @@ theorem getElem_zero_flatten.proof {L : Array (Array α)} (h : 0 < L.flatten.siz
(L.findSome? fun l => l[0]?).isSome := by
cases L using array_array_induction
simp only [List.findSome?_toArray, List.findSome?_map, Function.comp_def, List.getElem?_toArray,
List.findSome?_isSome_iff, isSome_getElem?]
List.findSome?_isSome_iff, List.isSome_getElem?]
simp only [flatten_toArray_map_toArray, size_toArray, List.length_flatten,
Nat.sum_pos_iff_exists_pos, List.mem_map] at h
obtain _, xs, m, rfl, h := h

File diff suppressed because it is too large Load Diff

View File

@@ -12,7 +12,7 @@ namespace Array
theorem exists_of_uset (self : Array α) (i d h) :
l₁ l₂, self.toList = l₁ ++ self[i] :: l₂ List.length l₁ = i.toNat
(self.uset i d h).toList = l₁ ++ d :: l₂ := by
simpa only [ugetElem_eq_getElem, getElem_toList, uset, toList_set] using
simpa only [ugetElem_eq_getElem, getElem_eq_getElem_toList, uset, toList_set] using
List.exists_of_set _
end Array

View File

@@ -40,9 +40,6 @@ theorem BEq.symm [BEq α] [PartialEquivBEq α] {a b : α} : a == b → b == a :=
theorem BEq.comm [BEq α] [PartialEquivBEq α] {a b : α} : (a == b) = (b == a) :=
Bool.eq_iff_iff.2 BEq.symm, BEq.symm
theorem bne_comm [BEq α] [PartialEquivBEq α] {a b : α} : (a != b) = (b != a) := by
rw [bne, BEq.comm, bne]
theorem BEq.symm_false [BEq α] [PartialEquivBEq α] {a b : α} : (a == b) = false (b == a) = false :=
BEq.comm (α := α) id

View File

@@ -351,17 +351,17 @@ end relations
section cast
/-- `cast eq x` embeds `x` into an equal `BitVec` type. -/
@[inline] protected def cast (eq : n = m) (x : BitVec n) : BitVec m := .ofNatLt x.toNat (eq x.isLt)
@[inline] def cast (eq : n = m) (x : BitVec n) : BitVec m := .ofNatLt x.toNat (eq x.isLt)
@[simp] theorem cast_ofNat {n m : Nat} (h : n = m) (x : Nat) :
(BitVec.ofNat n x).cast h = BitVec.ofNat m x := by
cast h (BitVec.ofNat n x) = BitVec.ofNat m x := by
subst h; rfl
@[simp] theorem cast_cast {n m k : Nat} (h₁ : n = m) (h₂ : m = k) (x : BitVec n) :
(x.cast h).cast h = x.cast (h₁ h₂) :=
cast h (cast h x) = cast (h₁ h₂) x :=
rfl
@[simp] theorem cast_eq {n : Nat} (h : n = n) (x : BitVec n) : x.cast h = x := rfl
@[simp] theorem cast_eq {n : Nat} (h : n = n) (x : BitVec n) : cast h x = x := rfl
/--
Extraction of bits `start` to `start + len - 1` from a bit vector of size `n` to yield a

View File

@@ -462,7 +462,7 @@ theorem msb_neg {w : Nat} {x : BitVec w} :
case true =>
apply hmin
apply eq_of_getMsbD_eq
intro i hi
rintro i, hi
simp only [getMsbD_intMin, w_pos, decide_true, Bool.true_and]
cases i
case zero => exact hmsb
@@ -470,7 +470,7 @@ theorem msb_neg {w : Nat} {x : BitVec w} :
case false =>
apply hzero
apply eq_of_getMsbD_eq
intro i hi
rintro i, hi
simp only [getMsbD_zero]
cases i
case zero => exact hmsb
@@ -573,11 +573,11 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow (x : BitVec w) (i
setWidth w (x.setWidth (i + 1)) =
setWidth w (x.setWidth i) + (x &&& twoPow w i) := by
rw [add_eq_or_of_and_eq_zero]
· ext k h
simp only [getLsbD_setWidth, h, decide_true, Bool.true_and, getLsbD_or, getLsbD_and]
· ext k
simp only [getLsbD_setWidth, Fin.is_lt, decide_true, Bool.true_and, getLsbD_or, getLsbD_and]
by_cases hik : i = k
· subst hik
simp [h]
simp
· simp only [getLsbD_twoPow, hik, decide_false, Bool.and_false, Bool.or_false]
by_cases hik' : k < (i + 1)
· have hik'' : k < i := by omega

View File

@@ -173,21 +173,21 @@ theorem getMsbD_eq_getMsb?_getD (x : BitVec w) (i : Nat) :
-- We choose `eq_of_getLsbD_eq` as the `@[ext]` theorem for `BitVec`
-- somewhat arbitrarily over `eq_of_getMsbD_eq`.
@[ext] theorem eq_of_getLsbD_eq {x y : BitVec w}
(pred : i, i < w x.getLsbD i = y.getLsbD i) : x = y := by
(pred : (i : Fin w), x.getLsbD i.val = y.getLsbD i.val) : x = y := by
apply eq_of_toNat_eq
apply Nat.eq_of_testBit_eq
intro i
if i_lt : i < w then
exact pred i i_lt
exact pred i, i_lt
else
have p : i w := Nat.le_of_not_gt i_lt
simp [testBit_toNat, getLsbD_ge _ _ p]
theorem eq_of_getMsbD_eq {x y : BitVec w}
(pred : i, i < w x.getMsbD i = y.getMsbD i) : x = y := by
(pred : (i : Fin w), x.getMsbD i.val = y.getMsbD i.val) : x = y := by
simp only [getMsbD] at pred
apply eq_of_getLsbD_eq
intro i i_lt
intro i, i_lt
if w_zero : w = 0 then
simp [w_zero]
else
@@ -199,7 +199,7 @@ theorem eq_of_getMsbD_eq {x y : BitVec w}
simp only [Nat.sub_sub]
apply Nat.sub_lt w_pos
simp [Nat.succ_add]
have q := pred (w - 1 - i) q_lt
have q := pred w - 1 - i, q_lt
simpa [q_lt, Nat.sub_sub_self, r] using q
-- This cannot be a `@[simp]` lemma, as it would be tried at every term.
@@ -410,21 +410,21 @@ theorem toNat_ge_of_msb_true {x : BitVec n} (p : BitVec.msb x = true) : x.toNat
/-! ### cast -/
@[simp, bv_toNat] theorem toNat_cast (h : w = v) (x : BitVec w) : (x.cast h).toNat = x.toNat := rfl
@[simp, bv_toNat] theorem toNat_cast (h : w = v) (x : BitVec w) : (cast h x).toNat = x.toNat := rfl
@[simp] theorem toFin_cast (h : w = v) (x : BitVec w) :
(x.cast h).toFin = x.toFin.cast (by rw [h]) :=
(cast h x).toFin = x.toFin.cast (by rw [h]) :=
rfl
@[simp] theorem getLsbD_cast (h : w = v) (x : BitVec w) : (x.cast h).getLsbD i = x.getLsbD i := by
@[simp] theorem getLsbD_cast (h : w = v) (x : BitVec w) : (cast h x).getLsbD i = x.getLsbD i := by
subst h; simp
@[simp] theorem getMsbD_cast (h : w = v) (x : BitVec w) : (x.cast h).getMsbD i = x.getMsbD i := by
@[simp] theorem getMsbD_cast (h : w = v) (x : BitVec w) : (cast h x).getMsbD i = x.getMsbD i := by
subst h; simp
@[simp] theorem getElem_cast (h : w = v) (x : BitVec w) (p : i < v) : (x.cast h)[i] = x[i] := by
@[simp] theorem getElem_cast (h : w = v) (x : BitVec w) (p : i < v) : (cast h x)[i] = x[i] := by
subst h; simp
@[simp] theorem msb_cast (h : w = v) (x : BitVec w) : (x.cast h).msb = x.msb := by
@[simp] theorem msb_cast (h : w = v) (x : BitVec w) : (cast h x).msb = x.msb := by
simp [BitVec.msb]
/-! ### toInt/ofInt -/
@@ -498,9 +498,6 @@ theorem toInt_ofNat {n : Nat} (x : Nat) :
@[simp] theorem ofInt_ofNat (w n : Nat) :
BitVec.ofInt w (no_index (OfNat.ofNat n)) = BitVec.ofNat w (OfNat.ofNat n) := rfl
@[simp] theorem ofInt_toInt {x : BitVec w} : BitVec.ofInt w x.toInt = x := by
by_cases h : 2 * x.toNat < 2^w <;> ext <;> simp [getLsbD, h, BitVec.toInt]
theorem toInt_neg_iff {w : Nat} {x : BitVec w} :
BitVec.toInt x < 0 2 ^ w 2 * x.toNat := by
simp [toInt_eq_toNat_cond]; omega
@@ -572,10 +569,6 @@ theorem zeroExtend_eq_setWidth {v : Nat} {x : BitVec w} :
(x.setWidth v).toInt = Int.bmod x.toNat (2^v) := by
simp [toInt_eq_toNat_bmod, toNat_setWidth, Int.emod_bmod]
@[simp] theorem toFin_setWidth {x : BitVec w} :
(x.setWidth v).toFin = Fin.ofNat' (2^v) x.toNat := by
ext; simp
theorem setWidth'_eq {x : BitVec w} (h : w v) : x.setWidth' h = x.setWidth v := by
apply eq_of_toNat_eq
rw [toNat_setWidth, toNat_setWidth']
@@ -652,20 +645,6 @@ theorem getElem?_setWidth (m : Nat) (x : BitVec n) (i : Nat) :
getLsbD (setWidth m x) i = (decide (i < m) && getLsbD x i) := by
simp [getLsbD, toNat_setWidth, Nat.testBit_mod_two_pow]
theorem getMsbD_setWidth {m : Nat} {x : BitVec n} {i : Nat} :
getMsbD (setWidth m x) i = (decide (m - n i) && getMsbD x (i + n - m)) := by
unfold setWidth
by_cases h : n m <;> simp only [h]
· by_cases h' : m - n i
<;> simp [h', show i - (m - n) = i + n - m by omega]
· simp only [show m - n = 0 by omega, getMsbD, getLsbD_setWidth]
by_cases h' : i < m
· simp [show m - 1 - i < m by omega, show i + n - m < n by omega,
show n - 1 - (i + n - m) = m - 1 - i by omega]
omega
· simp [h']
omega
@[simp] theorem getMsbD_setWidth_add {x : BitVec w} (h : k i) :
(x.setWidth (w + k)).getMsbD i = x.getMsbD (i - k) := by
by_cases h : w = 0
@@ -679,7 +658,7 @@ theorem getMsbD_setWidth {m : Nat} {x : BitVec n} {i : Nat} :
<;> omega
@[simp] theorem cast_setWidth (h : v = v') (x : BitVec w) :
(x.setWidth v).cast h = x.setWidth v' := by
cast h (setWidth v x) = setWidth v' x := by
subst h
ext
simp
@@ -692,7 +671,7 @@ theorem getMsbD_setWidth {m : Nat} {x : BitVec n} {i : Nat} :
revert p
cases getLsbD x i <;> simp; omega
@[simp] theorem setWidth_cast {x : BitVec w} {h : w = v} : (x.cast h).setWidth k = x.setWidth k := by
@[simp] theorem setWidth_cast {h : w = v} : (cast h x).setWidth k = x.setWidth k := by
apply eq_of_getLsbD_eq
simp
@@ -710,15 +689,14 @@ theorem msb_setWidth'' (x : BitVec w) : (x.setWidth (k + 1)).msb = x.getLsbD k :
/-- zero extending a bitvector to width 1 equals the boolean of the lsb. -/
theorem setWidth_one_eq_ofBool_getLsb_zero (x : BitVec w) :
x.setWidth 1 = BitVec.ofBool (x.getLsbD 0) := by
ext i h
simp at h
simp [getLsbD_setWidth, h]
ext i
simp [getLsbD_setWidth, Fin.fin_one_eq_zero i]
/-- Zero extending `1#v` to `1#w` equals `1#w` when `v > 0`. -/
theorem setWidth_ofNat_one_eq_ofNat_one_of_lt {v w : Nat} (hv : 0 < v) :
(BitVec.ofNat v 1).setWidth w = BitVec.ofNat w 1 := by
ext i h
simp only [getLsbD_setWidth, h, decide_true, getLsbD_ofNat, Bool.true_and,
ext i, hilt
simp only [getLsbD_setWidth, hilt, decide_true, getLsbD_ofNat, Bool.true_and,
Bool.and_iff_right_iff_imp, decide_eq_true_eq]
intros hi₁
have hv := Nat.testBit_one_eq_true_iff_self_eq_zero.mp hi₁
@@ -745,7 +723,8 @@ protected theorem extractLsb_ofFin {n} (x : Fin (2^n)) (hi lo : Nat) :
@[simp]
protected theorem extractLsb_ofNat (x n : Nat) (hi lo : Nat) :
extractLsb hi lo (BitVec.ofNat n x) = .ofNat (hi - lo + 1) ((x % 2^n) >>> lo) := by
ext i
apply eq_of_getLsbD_eq
intro i, _lt
simp [BitVec.ofNat]
@[simp] theorem extractLsb'_toNat (s m : Nat) (x : BitVec n) :
@@ -832,8 +811,8 @@ theorem extractLsb'_eq_extractLsb {w : Nat} (x : BitVec w) (start len : Nat) (h
@[simp] theorem setWidth_or {x y : BitVec w} :
(x ||| y).setWidth k = x.setWidth k ||| y.setWidth k := by
ext i h
simp [h]
ext
simp
theorem or_assoc (x y z : BitVec w) :
x ||| y ||| z = x ||| (y ||| z) := by
@@ -866,12 +845,12 @@ instance : Std.LawfulCommIdentity (α := BitVec n) (· ||| · ) (0#n) where
simp
@[simp] theorem or_allOnes {x : BitVec w} : x ||| allOnes w = allOnes w := by
ext i h
simp [h]
ext i
simp
@[simp] theorem allOnes_or {x : BitVec w} : allOnes w ||| x = allOnes w := by
ext i h
simp [h]
ext i
simp
/-! ### and -/
@@ -905,8 +884,8 @@ instance : Std.LawfulCommIdentity (α := BitVec n) (· ||| · ) (0#n) where
@[simp] theorem setWidth_and {x y : BitVec w} :
(x &&& y).setWidth k = x.setWidth k &&& y.setWidth k := by
ext i h
simp [h]
ext
simp
theorem and_assoc (x y z : BitVec w) :
x &&& y &&& z = x &&& (y &&& z) := by
@@ -936,15 +915,15 @@ instance : Std.IdempotentOp (α := BitVec n) (· &&& · ) where
simp
@[simp] theorem and_allOnes {x : BitVec w} : x &&& allOnes w = x := by
ext i h
simp [h]
ext i
simp
instance : Std.LawfulCommIdentity (α := BitVec n) (· &&& · ) (allOnes n) where
right_id _ := BitVec.and_allOnes
@[simp] theorem allOnes_and {x : BitVec w} : allOnes w &&& x = x := by
ext i h
simp [h]
ext i
simp
/-! ### xor -/
@@ -981,8 +960,8 @@ instance : Std.LawfulCommIdentity (α := BitVec n) (· &&& · ) (allOnes n) wher
@[simp] theorem setWidth_xor {x y : BitVec w} :
(x ^^^ y).setWidth k = x.setWidth k ^^^ y.setWidth k := by
ext i h
simp [h]
ext
simp
theorem xor_assoc (x y z : BitVec w) :
x ^^^ y ^^^ z = x ^^^ (y ^^^ z) := by
@@ -1075,9 +1054,9 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
rw [Nat.testBit_two_pow_sub_succ x.isLt]
simp [h]
@[simp] theorem setWidth_not {x : BitVec w} (_ : k w) :
@[simp] theorem setWidth_not {x : BitVec w} (h : k w) :
(~~~x).setWidth k = ~~~(x.setWidth k) := by
ext i h
ext
simp [h]
omega
@@ -1090,17 +1069,17 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
simp
@[simp] theorem xor_allOnes {x : BitVec w} : x ^^^ allOnes w = ~~~ x := by
ext i h
simp [h]
ext i
simp
@[simp] theorem allOnes_xor {x : BitVec w} : allOnes w ^^^ x = ~~~ x := by
ext i h
simp [h]
ext i
simp
@[simp]
theorem not_not {b : BitVec w} : ~~~(~~~b) = b := by
ext i h
simp [h]
ext i
simp
theorem not_eq_comm {x y : BitVec w} : ~~~ x = y x = ~~~ y := by
constructor
@@ -1123,19 +1102,19 @@ theorem not_eq_comm {x y : BitVec w} : ~~~ x = y ↔ x = ~~~ y := by
/-! ### cast -/
@[simp] theorem not_cast {x : BitVec w} (h : w = w') : ~~~(x.cast h) = (~~~x).cast h := by
@[simp] theorem not_cast {x : BitVec w} (h : w = w') : ~~~(cast h x) = cast h (~~~x) := by
ext
simp_all [lt_of_getLsbD]
@[simp] theorem and_cast {x y : BitVec w} (h : w = w') : x.cast h &&& y.cast h = (x &&& y).cast h := by
@[simp] theorem and_cast {x y : BitVec w} (h : w = w') : cast h x &&& cast h y = cast h (x &&& y) := by
ext
simp_all [lt_of_getLsbD]
@[simp] theorem or_cast {x y : BitVec w} (h : w = w') : x.cast h ||| y.cast h = (x ||| y).cast h := by
@[simp] theorem or_cast {x y : BitVec w} (h : w = w') : cast h x ||| cast h y = cast h (x ||| y) := by
ext
simp_all [lt_of_getLsbD]
@[simp] theorem xor_cast {x y : BitVec w} (h : w = w') : x.cast h ^^^ y.cast h = (x ^^^ y).cast h := by
@[simp] theorem xor_cast {x y : BitVec w} (h : w = w') : cast h x ^^^ cast h y = cast h (x ^^^ y) := by
ext
simp_all [lt_of_getLsbD]
@@ -1175,21 +1154,24 @@ theorem zero_shiftLeft (n : Nat) : 0#w <<< n = 0#w := by
theorem shiftLeft_xor_distrib (x y : BitVec w) (n : Nat) :
(x ^^^ y) <<< n = (x <<< n) ^^^ (y <<< n) := by
ext i h
simp only [getLsbD_shiftLeft, h, decide_true, Bool.true_and, getLsbD_xor]
by_cases h' : i < n <;> simp [h']
ext i
simp only [getLsbD_shiftLeft, Fin.is_lt, decide_true, Bool.true_and, getLsbD_xor]
by_cases h : i < n
<;> simp [h]
theorem shiftLeft_and_distrib (x y : BitVec w) (n : Nat) :
(x &&& y) <<< n = (x <<< n) &&& (y <<< n) := by
ext i h
simp only [getLsbD_shiftLeft, h, decide_true, Bool.true_and, getLsbD_and]
by_cases h' : i < n <;> simp [h']
ext i
simp only [getLsbD_shiftLeft, Fin.is_lt, decide_true, Bool.true_and, getLsbD_and]
by_cases h : i < n
<;> simp [h]
theorem shiftLeft_or_distrib (x y : BitVec w) (n : Nat) :
(x ||| y) <<< n = (x <<< n) ||| (y <<< n) := by
ext i h
simp only [getLsbD_shiftLeft, h, decide_true, Bool.true_and, getLsbD_or]
by_cases h' : i < n <;> simp [h']
ext i
simp only [getLsbD_shiftLeft, Fin.is_lt, decide_true, Bool.true_and, getLsbD_or]
by_cases h : i < n
<;> simp [h]
@[simp] theorem getMsbD_shiftLeft (x : BitVec w) (i) :
(x <<< i).getMsbD k = x.getMsbD (k + i) := by
@@ -1334,61 +1316,6 @@ theorem toNat_ushiftRight_lt (x : BitVec w) (n : Nat) (hn : n ≤ w) :
· apply hn
· apply Nat.pow_pos (by decide)
/-- Shifting right by `n`, which is larger than the bitwidth `w` produces `0. -/
theorem ushiftRight_eq_zero {x : BitVec w} {n : Nat} (hn : w n) :
x >>> n = 0#w := by
simp only [toNat_eq, toNat_ushiftRight, toNat_ofNat, Nat.zero_mod]
have : 2^w 2^n := Nat.pow_le_pow_of_le Nat.one_lt_two hn
rw [Nat.shiftRight_eq_div_pow, Nat.div_eq_of_lt (by omega)]
/--
Unsigned shift right by at least one bit makes the interpretations of the bitvector as an `Int` or `Nat` agree,
because it makes the value of the bitvector less than or equal to `2^(w-1)`.
-/
theorem toInt_ushiftRight_of_lt {x : BitVec w} {n : Nat} (hn : 0 < n) :
(x >>> n).toInt = x.toNat >>> n := by
rw [toInt_eq_toNat_cond]
simp only [toNat_ushiftRight, ite_eq_left_iff, Nat.not_lt]
intros h
by_cases hn : n w
· have h1 := Nat.mul_lt_mul_of_pos_left (toNat_ushiftRight_lt x n hn) Nat.two_pos
simp only [toNat_ushiftRight, Nat.zero_lt_succ, Nat.mul_lt_mul_left] at h1
have : 2 ^ (w - n).succ 2^ w := Nat.pow_le_pow_of_le (by decide) (by omega)
have := show 2 * x.toNat >>> n < 2 ^ w by
omega
omega
· have : x.toNat >>> n = 0 := by
apply Nat.shiftRight_eq_zero
have : 2^w 2^n := Nat.pow_le_pow_of_le (by decide) (by omega)
omega
simp [this] at h
omega
/--
Unsigned shift right by at least one bit makes the interpretations of the bitvector as an `Int` or `Nat` agree,
because it makes the value of the bitvector less than or equal to `2^(w-1)`.
In the case when `n = 0`, then the shift right value equals the integer interpretation.
-/
@[simp]
theorem toInt_ushiftRight {x : BitVec w} {n : Nat} :
(x >>> n).toInt = if n = 0 then x.toInt else x.toNat >>> n := by
by_cases hn : n = 0
· simp [hn]
· rw [toInt_ushiftRight_of_lt (by omega), toInt_eq_toNat_cond]
simp [hn]
@[simp]
theorem toFin_uShiftRight {x : BitVec w} {n : Nat} :
(x >>> n).toFin = x.toFin / (Fin.ofNat' (2^w) (2^n)) := by
apply Fin.eq_of_val_eq
by_cases hn : n < w
· simp [Nat.shiftRight_eq_div_pow, Nat.mod_eq_of_lt (Nat.pow_lt_pow_of_lt Nat.one_lt_two hn)]
· simp only [Nat.not_lt] at hn
rw [ushiftRight_eq_zero (by omega)]
simp [Nat.dvd_iff_mod_eq_zero.mp (Nat.pow_dvd_pow 2 hn)]
@[simp]
theorem getMsbD_ushiftRight {x : BitVec w} {i n : Nat} :
(x >>> n).getMsbD i = (decide (i < w) && (!decide (i < n) && x.getMsbD (i - n))) := by
@@ -1528,12 +1455,12 @@ theorem msb_sshiftRight {n : Nat} {x : BitVec w} :
simp [show n = 0 by omega]
@[simp] theorem sshiftRight_zero {x : BitVec w} : x.sshiftRight 0 = x := by
ext i h
simp [getLsbD_sshiftRight, h]
ext i
simp [getLsbD_sshiftRight]
@[simp] theorem zero_sshiftRight {n : Nat} : (0#w).sshiftRight n = 0#w := by
ext i h
simp [getLsbD_sshiftRight, h]
ext i
simp [getLsbD_sshiftRight]
theorem sshiftRight_add {x : BitVec w} {m n : Nat} :
x.sshiftRight (m + n) = (x.sshiftRight m).sshiftRight n := by
@@ -1634,7 +1561,7 @@ private theorem Int.negSucc_emod (m : Nat) (n : Int) :
-(m + 1) % n = Int.subNatNat (Int.natAbs n) ((m % Int.natAbs n) + 1) := rfl
/-- The sign extension is the same as zero extending when `msb = false`. -/
theorem signExtend_eq_setWidth_of_msb_false {x : BitVec w} {v : Nat} (hmsb : x.msb = false) :
theorem signExtend_eq_not_setWidth_not_of_msb_false {x : BitVec w} {v : Nat} (hmsb : x.msb = false) :
x.signExtend v = x.setWidth v := by
ext i
by_cases hv : i < v
@@ -1670,36 +1597,21 @@ theorem signExtend_eq_not_setWidth_not_of_msb_true {x : BitVec w} {v : Nat} (hms
theorem getLsbD_signExtend (x : BitVec w) {v i : Nat} :
(x.signExtend v).getLsbD i = (decide (i < v) && if i < w then x.getLsbD i else x.msb) := by
rcases hmsb : x.msb with rfl | rfl
· rw [signExtend_eq_setWidth_of_msb_false hmsb]
· rw [signExtend_eq_not_setWidth_not_of_msb_false hmsb]
by_cases (i < v) <;> by_cases (i < w) <;> simp_all <;> omega
· rw [signExtend_eq_not_setWidth_not_of_msb_true hmsb]
by_cases (i < v) <;> by_cases (i < w) <;> simp_all <;> omega
theorem getMsbD_signExtend {x : BitVec w} {v i : Nat} :
(x.signExtend v).getMsbD i =
(decide (i < v) && if v - w i then x.getMsbD (i + w - v) else x.msb) := by
rcases hmsb : x.msb with rfl | rfl
· simp only [signExtend_eq_setWidth_of_msb_false hmsb, getMsbD_setWidth]
by_cases h : v - w i <;> simp [h, getMsbD] <;> omega
· simp only [signExtend_eq_not_setWidth_not_of_msb_true hmsb, getMsbD_not, getMsbD_setWidth]
by_cases h : i < v <;> by_cases h' : v - w i <;> simp [h, h'] <;> omega
theorem getElem_signExtend {x : BitVec w} {v i : Nat} (h : i < v) :
(x.signExtend v)[i] = if i < w then x.getLsbD i else x.msb := by
rw [getLsbD_eq_getElem, getLsbD_signExtend]
simp [h]
theorem msb_signExtend {x : BitVec w} :
(x.signExtend v).msb = (decide (0 < v) && if w v then x.getMsbD (w - v) else x.msb) := by
by_cases h : w v
· simp [h, BitVec.msb, getMsbD_signExtend, show v - w = 0 by omega]
· simp [h, BitVec.msb, getMsbD_signExtend, show ¬ (v - w = 0) by omega]
/-- Sign extending to a width smaller than the starting width is a truncation. -/
theorem signExtend_eq_setWidth_of_lt (x : BitVec w) {v : Nat} (hv : v w):
x.signExtend v = x.setWidth v := by
ext i h
simp only [getLsbD_signExtend, h, decide_true, Bool.true_and, getLsbD_setWidth,
ext i
simp only [getLsbD_signExtend, Fin.is_lt, decide_true, Bool.true_and, getLsbD_setWidth,
ite_eq_left_iff, Nat.not_lt]
omega
@@ -1793,34 +1705,35 @@ theorem append_def (x : BitVec v) (y : BitVec w) :
rfl
theorem getLsbD_append {x : BitVec n} {y : BitVec m} :
getLsbD (x ++ y) i = if i < m then getLsbD y i else getLsbD x (i - m) := by
getLsbD (x ++ y) i = bif i < m then getLsbD y i else getLsbD x (i - m) := by
simp only [append_def, getLsbD_or, getLsbD_shiftLeftZeroExtend, getLsbD_setWidth']
by_cases h : i < m
· simp [h]
· simp_all [h]
theorem getElem_append {x : BitVec n} {y : BitVec m} (h : i < n + m) :
(x ++ y)[i] = if i < m then getLsbD y i else getLsbD x (i - m) := by
(x ++ y)[i] = bif i < m then getLsbD y i else getLsbD x (i - m) := by
simp only [append_def, getElem_or, getElem_shiftLeftZeroExtend, getElem_setWidth']
by_cases h' : i < m
· simp [h']
· simp_all [h']
@[simp] theorem getMsbD_append {x : BitVec n} {y : BitVec m} :
getMsbD (x ++ y) i = if n i then getMsbD y (i - n) else getMsbD x i := by
getMsbD (x ++ y) i = bif n i then getMsbD y (i - n) else getMsbD x i := by
simp only [append_def]
by_cases h : n i
· simp [h]
· simp [h]
theorem msb_append {x : BitVec w} {y : BitVec v} :
(x ++ y).msb = if w = 0 then y.msb else x.msb := by
(x ++ y).msb = bif (w == 0) then (y.msb) else (x.msb) := by
rw [ append_eq, append]
simp only [msb_or, msb_shiftLeftZeroExtend, msb_setWidth']
by_cases h : w = 0
· subst h
simp [BitVec.msb, getMsbD]
· have q : 0 < w + v := by omega
· rw [cond_eq_if]
have q : 0 < w + v := by omega
have t : y.getLsbD (w + v - 1) = false := getLsbD_ge _ _ (by omega)
simp [h, q, t, BitVec.msb, getMsbD]
@@ -1829,17 +1742,17 @@ theorem msb_append {x : BitVec w} {y : BitVec v} :
rw [getLsbD_append] -- Why does this not work with `simp [getLsbD_append]`?
simp
@[simp] theorem zero_width_append (x : BitVec 0) (y : BitVec v) : x ++ y = y.cast (by omega) := by
@[simp] theorem zero_width_append (x : BitVec 0) (y : BitVec v) : x ++ y = cast (by omega) y := by
ext
rw [getLsbD_append]
simpa using lt_of_getLsbD
@[simp] theorem zero_append_zero : 0#v ++ 0#w = 0#(v + w) := by
ext
simp only [getLsbD_append, getLsbD_zero, ite_self]
simp only [getLsbD_append, getLsbD_zero, Bool.cond_self]
@[simp] theorem cast_append_right (h : w + v = w + v') (x : BitVec w) (y : BitVec v) :
(x ++ y).cast h = x ++ y.cast (by omega) := by
cast h (x ++ y) = x ++ cast (by omega) y := by
ext
simp only [getLsbD_cast, getLsbD_append, cond_eq_if, decide_eq_true_eq]
split <;> split
@@ -1850,25 +1763,27 @@ theorem msb_append {x : BitVec w} {y : BitVec v} :
omega
@[simp] theorem cast_append_left (h : w + v = w' + v) (x : BitVec w) (y : BitVec v) :
(x ++ y).cast h = x.cast (by omega) ++ y := by
cast h (x ++ y) = cast (by omega) x ++ y := by
ext
simp [getLsbD_append]
theorem setWidth_append {x : BitVec w} {y : BitVec v} :
(x ++ y).setWidth k = if h : k v then y.setWidth k else (x.setWidth (k - v) ++ y).cast (by omega) := by
ext i h
simp only [getLsbD_setWidth, h, getLsbD_append]
split <;> rename_i h₁ <;> split <;> rename_i h₂
· simp [h]
· simp [getLsbD_append, h₁]
· omega
· simp [getLsbD_append, h₁]
omega
apply eq_of_getLsbD_eq
intro i
simp only [getLsbD_setWidth, Fin.is_lt, decide_true, getLsbD_append, Bool.true_and]
split
· have t : i < v := by omega
simp [t]
· by_cases t : i < v
· simp [t, getLsbD_append]
· have t' : i - v < k - v := by omega
simp [t, t', getLsbD_append]
@[simp] theorem setWidth_append_of_eq {x : BitVec v} {y : BitVec w} (h : w' = w) : setWidth (v' + w') (x ++ y) = setWidth v' x ++ setWidth w' y := by
subst h
ext i h
simp only [getLsbD_setWidth, h, decide_true, getLsbD_append, cond_eq_if,
ext i
simp only [getLsbD_setWidth, Fin.is_lt, decide_true, getLsbD_append, cond_eq_if,
decide_eq_true_eq, Bool.true_and, setWidth_eq]
split
· simp_all
@@ -1918,12 +1833,12 @@ theorem shiftLeft_ushiftRight {x : BitVec w} {n : Nat}:
case succ n ih =>
rw [BitVec.shiftLeft_add, Nat.add_comm, BitVec.shiftRight_add, ih,
Nat.add_comm, BitVec.shiftLeft_add, BitVec.shiftLeft_and_distrib]
ext i h
ext i
by_cases hw : w = 0
· simp [hw]
· by_cases hi₂ : i = 0
· by_cases hi₂ : i.val = 0
· simp [hi₂]
· simp [Nat.lt_one_iff, hi₂, h, show 1 + (i - 1) = i by omega]
· simp [Nat.lt_one_iff, hi₂, show 1 + (i.val - 1) = i by omega]
@[simp]
theorem msb_shiftLeft {x : BitVec w} {n : Nat} :
@@ -2008,12 +1923,13 @@ theorem getElem_cons {b : Bool} {n} {x : BitVec n} {i : Nat} (h : i < n + 1) :
theorem setWidth_succ (x : BitVec w) :
setWidth (i+1) x = cons (getLsbD x i) (setWidth i x) := by
ext j h
simp only [getLsbD_setWidth, getLsbD_cons, h, decide_true, Bool.true_and]
if j_eq : j = i then
apply eq_of_getLsbD_eq
intro j
simp only [getLsbD_setWidth, getLsbD_cons, j.isLt, decide_true, Bool.true_and]
if j_eq : j.val = i then
simp [j_eq]
else
have j_lt : j < i := Nat.lt_of_le_of_ne (Nat.le_of_succ_le_succ h) j_eq
have j_lt : j.val < i := Nat.lt_of_le_of_ne (Nat.le_of_succ_le_succ j.isLt) j_eq
simp [j_eq, j_lt]
@[simp] theorem cons_msb_setWidth (x : BitVec (w+1)) : (cons x.msb (x.setWidth w)) = x := by
@@ -2086,64 +2002,20 @@ theorem getElem_concat (x : BitVec w) (b : Bool) (i : Nat) (h : i < w + 1) :
(concat x b)[i + 1] = x[i] := by
simp [getElem_concat, h, getLsbD_eq_getElem]
@[simp]
theorem getMsbD_concat {i w : Nat} {b : Bool} {x : BitVec w} :
(x.concat b).getMsbD i = if i < w then x.getMsbD i else decide (i = w) && b := by
simp only [getMsbD_eq_getLsbD, Nat.add_sub_cancel, getLsbD_concat]
by_cases h₀ : i = w
· simp [h₀]
· by_cases h₁ : i < w
· simp [h₀, h₁, show ¬ w - i = 0 by omega, show i < w + 1 by omega, Nat.sub_sub, Nat.add_comm]
· simp only [show w - i = 0 by omega, reduceIte, h₁, h₀, decide_false, Bool.false_and,
Bool.and_eq_false_imp, decide_eq_true_eq]
intro
omega
@[simp]
theorem msb_concat {w : Nat} {b : Bool} {x : BitVec w} :
(x.concat b).msb = if 0 < w then x.msb else b := by
simp only [BitVec.msb, getMsbD_eq_getLsbD, Nat.zero_lt_succ, decide_true, Nat.add_one_sub_one,
Nat.sub_zero, Bool.true_and]
by_cases h₀ : 0 < w
· simp only [Nat.lt_add_one, getLsbD_eq_getElem, getElem_concat, h₀, reduceIte, decide_true,
Bool.true_and, ite_eq_right_iff]
intro
omega
· simp [h₀, show w = 0 by omega]
@[simp] theorem toInt_concat (x : BitVec w) (b : Bool) :
(concat x b).toInt = if w = 0 then -b.toInt else x.toInt * 2 + b.toInt := by
simp only [BitVec.toInt, toNat_concat]
cases w
· cases b <;> simp [eq_nil x]
· cases b <;> simp <;> omega
@[simp] theorem toFin_concat (x : BitVec w) (b : Bool) :
(concat x b).toFin = Fin.mk (x.toNat * 2 + b.toNat) (by
have := Bool.toNat_lt b
simp [ Nat.two_pow_pred_add_two_pow_pred, Bool.toNat_lt b]
omega
) := by
simp [ Fin.val_inj]
@[simp] theorem not_concat (x : BitVec w) (b : Bool) : ~~~(concat x b) = concat (~~~x) !b := by
ext (_ | i) h <;> simp [getLsbD_concat]
ext i; cases i using Fin.succRecOn <;> simp [*, Nat.succ_lt_succ]
@[simp] theorem concat_or_concat (x y : BitVec w) (a b : Bool) :
(concat x a) ||| (concat y b) = concat (x ||| y) (a || b) := by
ext (_ | i) h <;> simp [getLsbD_concat]
ext i; cases i using Fin.succRecOn <;> simp
@[simp] theorem concat_and_concat (x y : BitVec w) (a b : Bool) :
(concat x a) &&& (concat y b) = concat (x &&& y) (a && b) := by
ext (_ | i) h <;> simp [getLsbD_concat]
ext i; cases i using Fin.succRecOn <;> simp
@[simp] theorem concat_xor_concat (x y : BitVec w) (a b : Bool) :
(concat x a) ^^^ (concat y b) = concat (x ^^^ y) (a ^^ b) := by
ext (_ | i) h <;> simp [getLsbD_concat]
@[simp] theorem zero_concat_false : concat 0#w false = 0#(w + 1) := by
ext
simp [getLsbD_concat]
ext i; cases i using Fin.succRecOn <;> simp
/-! ### shiftConcat -/
@@ -2160,8 +2032,8 @@ theorem getLsbD_shiftConcat_eq_decide (x : BitVec w) (b : Bool) (i : Nat) :
theorem shiftRight_sub_one_eq_shiftConcat (n : BitVec w) (hwn : 0 < wn) :
n >>> (wn - 1) = (n >>> wn).shiftConcat (n.getLsbD (wn - 1)) := by
ext i h
simp only [getLsbD_ushiftRight, getLsbD_shiftConcat, h, decide_true, Bool.true_and]
ext i
simp only [getLsbD_ushiftRight, getLsbD_shiftConcat, Fin.is_lt, decide_true, Bool.true_and]
split
· simp [*]
· congr 1; omega
@@ -2190,6 +2062,35 @@ theorem toNat_shiftConcat_lt_of_lt {x : BitVec w} {b : Bool} {k : Nat}
have := Bool.toNat_lt b
omega
@[simp] theorem zero_concat_false : concat 0#w false = 0#(w + 1) := by
ext
simp [getLsbD_concat]
@[simp]
theorem getMsbD_concat {i w : Nat} {b : Bool} {x : BitVec w} :
(x.concat b).getMsbD i = if i < w then x.getMsbD i else decide (i = w) && b := by
simp only [getMsbD_eq_getLsbD, Nat.add_sub_cancel, getLsbD_concat]
by_cases h₀ : i = w
· simp [h₀]
· by_cases h₁ : i < w
· simp [h₀, h₁, show ¬ w - i = 0 by omega, show i < w + 1 by omega, Nat.sub_sub, Nat.add_comm]
· simp only [show w - i = 0 by omega, reduceIte, h₁, h₀, decide_false, Bool.false_and,
Bool.and_eq_false_imp, decide_eq_true_eq]
intro
omega
@[simp]
theorem msb_concat {w : Nat} {b : Bool} {x : BitVec w} :
(x.concat b).msb = if 0 < w then x.msb else b := by
simp only [BitVec.msb, getMsbD_eq_getLsbD, Nat.zero_lt_succ, decide_true, Nat.add_one_sub_one,
Nat.sub_zero, Bool.true_and]
by_cases h₀ : 0 < w
· simp only [Nat.lt_add_one, getLsbD_eq_getElem, getElem_concat, h₀, reduceIte, decide_true,
Bool.true_and, ite_eq_right_iff]
intro
omega
· simp [h₀, show w = 0 by omega]
/-! ### add -/
theorem add_def {n} (x y : BitVec n) : x + y = .ofNat n (x.toNat + y.toNat) := rfl
@@ -3172,8 +3073,8 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_of_getLsbD_false
{x : BitVec w} {i : Nat} (hx : x.getLsbD i = false) :
setWidth w (x.setWidth (i + 1)) =
setWidth w (x.setWidth i) := by
ext k h
simp only [getLsbD_setWidth, h, decide_true, Bool.true_and, getLsbD_or, getLsbD_and]
ext k
simp only [getLsbD_setWidth, Fin.is_lt, decide_true, Bool.true_and, getLsbD_or, getLsbD_and]
by_cases hik : i = k
· subst hik
simp [hx]
@@ -3188,17 +3089,20 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_or_twoPow_of_getLsbD_true
{x : BitVec w} {i : Nat} (hx : x.getLsbD i = true) :
setWidth w (x.setWidth (i + 1)) =
setWidth w (x.setWidth i) ||| (twoPow w i) := by
ext k h
simp only [getLsbD_setWidth, h, decide_true, Bool.true_and, getLsbD_or, getLsbD_and]
ext k
simp only [getLsbD_setWidth, Fin.is_lt, decide_true, Bool.true_and, getLsbD_or, getLsbD_and]
by_cases hik : i = k
· subst hik
simp [hx, h]
simp [hx]
· by_cases hik' : k < i + 1 <;> simp [hik, hik'] <;> omega
/-- Bitwise and of `(x : BitVec w)` with `1#w` equals zero extending `x.lsb` to `w`. -/
theorem and_one_eq_setWidth_ofBool_getLsbD {x : BitVec w} :
(x &&& 1#w) = setWidth w (ofBool (x.getLsbD 0)) := by
ext (_ | i) h <;> simp [Bool.and_comm]
ext i
simp only [getLsbD_and, getLsbD_one, getLsbD_setWidth, Fin.is_lt, decide_true, getLsbD_ofBool,
Bool.true_and]
by_cases h : ((i : Nat) = 0) <;> simp [h] <;> omega
@[simp]
theorem replicate_zero_eq {x : BitVec w} : x.replicate 0 = 0#0 := by
@@ -3222,7 +3126,7 @@ theorem getLsbD_replicate {n w : Nat} (x : BitVec w) :
· simp only [hi, decide_true, Bool.true_and]
by_cases hi' : i < w * n
· simp [hi', ih]
· simp [hi', decide_false]
· simp only [hi', decide_false, cond_false]
rw [Nat.sub_mul_eq_mod_of_lt_of_le] <;> omega
· rw [Nat.mul_succ] at hi
simp only [show ¬i < w * n by omega, decide_false, cond_false, hi, Bool.false_and]
@@ -3528,7 +3432,7 @@ theorem forall_zero_iff {P : BitVec 0 → Prop} :
· intro h
apply h
· intro h v
obtain (rfl : v = 0#0) := (by ext i )
obtain (rfl : v = 0#0) := (by ext i, h; simp at h)
apply h
theorem forall_cons_iff {P : BitVec (n + 1) Prop} :
@@ -3544,7 +3448,7 @@ theorem forall_cons_iff {P : BitVec (n + 1) → Prop} :
instance instDecidableForallBitVecZero (P : BitVec 0 Prop) :
[Decidable (P 0#0)], Decidable ( v, P v)
| .isTrue h => .isTrue fun v => by
obtain (rfl : v = 0#0) := (by ext i )
obtain (rfl : v = 0#0) := (by ext i, h; cases h)
exact h
| .isFalse h => .isFalse (fun w => h (w _))
@@ -3589,9 +3493,6 @@ instance instDecidableExistsBitVec :
set_option linter.missingDocs false
@[deprecated signExtend_eq_setWidth_of_msb_false (since := "2024-12-08")]
abbrev signExtend_eq_not_setWidth_not_of_msb_false := @signExtend_eq_setWidth_of_msb_false
@[deprecated truncate_eq_setWidth (since := "2024-09-18")]
abbrev truncate_eq_zeroExtend := @truncate_eq_setWidth
@@ -3694,8 +3595,8 @@ abbrev truncate_xor := @setWidth_xor
@[deprecated setWidth_not (since := "2024-09-18")]
abbrev truncate_not := @setWidth_not
@[deprecated signExtend_eq_setWidth_of_msb_false (since := "2024-09-18")]
abbrev signExtend_eq_not_zeroExtend_not_of_msb_false := @signExtend_eq_setWidth_of_msb_false
@[deprecated signExtend_eq_not_setWidth_not_of_msb_false (since := "2024-09-18")]
abbrev signExtend_eq_not_zeroExtend_not_of_msb_false := @signExtend_eq_not_setWidth_not_of_msb_false
@[deprecated signExtend_eq_not_setWidth_not_of_msb_true (since := "2024-09-18")]
abbrev signExtend_eq_not_zeroExtend_not_of_msb_true := @signExtend_eq_not_setWidth_not_of_msb_true

View File

@@ -384,15 +384,6 @@ theorem toNat_lt (b : Bool) : b.toNat < 2 :=
@[simp] theorem toNat_eq_one {b : Bool} : b.toNat = 1 b = true := by
cases b <;> simp
/-! ## toInt -/
/-- convert a `Bool` to an `Int`, `false -> 0`, `true -> 1` -/
def toInt (b : Bool) : Int := cond b 1 0
@[simp] theorem toInt_false : false.toInt = 0 := rfl
@[simp] theorem toInt_true : true.toInt = 1 := rfl
/-! ### ite -/
@[simp] theorem if_true_left (p : Prop) [h : Decidable p] (f : Bool) :

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@@ -8,8 +8,6 @@ import Init.Data.Queue
import Init.System.Promise
import Init.System.Mutex
set_option linter.deprecated false
namespace IO
/--
@@ -17,7 +15,6 @@ Internal state of an `Channel`.
We maintain the invariant that at all times either `consumers` or `values` is empty.
-/
@[deprecated "Use Std.Channel.State from Std.Sync.Channel instead" (since := "2024-12-02")]
structure Channel.State (α : Type) where
values : Std.Queue α :=
consumers : Std.Queue (Promise (Option α)) :=
@@ -30,14 +27,12 @@ FIFO channel with unbounded buffer, where `recv?` returns a `Task`.
A channel can be closed. Once it is closed, all `send`s are ignored, and
`recv?` returns `none` once the queue is empty.
-/
@[deprecated "Use Std.Channel from Std.Sync.Channel instead" (since := "2024-12-02")]
def Channel (α : Type) : Type := Mutex (Channel.State α)
instance : Nonempty (Channel α) :=
inferInstanceAs (Nonempty (Mutex _))
/-- Creates a new `Channel`. -/
@[deprecated "Use Std.Channel.new from Std.Sync.Channel instead" (since := "2024-12-02")]
def Channel.new : BaseIO (Channel α) :=
Mutex.new {}
@@ -46,7 +41,6 @@ Sends a message on an `Channel`.
This function does not block.
-/
@[deprecated "Use Std.Channel.send from Std.Sync.Channel instead" (since := "2024-12-02")]
def Channel.send (ch : Channel α) (v : α) : BaseIO Unit :=
ch.atomically do
let st get
@@ -60,7 +54,6 @@ def Channel.send (ch : Channel α) (v : α) : BaseIO Unit :=
/--
Closes an `Channel`.
-/
@[deprecated "Use Std.Channel.close from Std.Sync.Channel instead" (since := "2024-12-02")]
def Channel.close (ch : Channel α) : BaseIO Unit :=
ch.atomically do
let st get
@@ -74,7 +67,6 @@ Every message is only received once.
Returns `none` if the channel is closed and the queue is empty.
-/
@[deprecated "Use Std.Channel.recv? from Std.Sync.Channel instead" (since := "2024-12-02")]
def Channel.recv? (ch : Channel α) : BaseIO (Task (Option α)) :=
ch.atomically do
let st get
@@ -93,7 +85,6 @@ def Channel.recv? (ch : Channel α) : BaseIO (Task (Option α)) :=
Note that if this function is called twice, each `forAsync` only gets half the messages.
-/
@[deprecated "Use Std.Channel.forAsync from Std.Sync.Channel instead" (since := "2024-12-02")]
partial def Channel.forAsync (f : α BaseIO Unit) (ch : Channel α)
(prio : Task.Priority := .default) : BaseIO (Task Unit) := do
BaseIO.bindTask (prio := prio) ( ch.recv?) fun
@@ -105,13 +96,11 @@ Receives all currently queued messages from the channel.
Those messages are dequeued and will not be returned by `recv?`.
-/
@[deprecated "Use Std.Channel.recvAllCurrent from Std.Sync.Channel instead" (since := "2024-12-02")]
def Channel.recvAllCurrent (ch : Channel α) : BaseIO (Array α) :=
ch.atomically do
modifyGet fun st => (st.values.toArray, { st with values := })
/-- Type tag for synchronous (blocking) operations on a `Channel`. -/
@[deprecated "Use Std.Channel.Sync from Std.Sync.Channel instead" (since := "2024-12-02")]
def Channel.Sync := Channel
/--
@@ -121,7 +110,6 @@ For example, `ch.sync.recv?` blocks until the next message,
and `for msg in ch.sync do ...` iterates synchronously over the channel.
These functions should only be used in dedicated threads.
-/
@[deprecated "Use Std.Channel.sync from Std.Sync.Channel instead" (since := "2024-12-02")]
def Channel.sync (ch : Channel α) : Channel.Sync α := ch
/--
@@ -130,11 +118,9 @@ Synchronously receives a message from the channel.
Every message is only received once.
Returns `none` if the channel is closed and the queue is empty.
-/
@[deprecated "Use Std.Channel.Sync.recv? from Std.Sync.Channel instead" (since := "2024-12-02")]
def Channel.Sync.recv? (ch : Channel.Sync α) : BaseIO (Option α) := do
IO.wait ( Channel.recv? ch)
@[deprecated "Use Std.Channel.Sync.forIn from Std.Sync.Channel instead" (since := "2024-12-02")]
private partial def Channel.Sync.forIn [Monad m] [MonadLiftT BaseIO m]
(ch : Channel.Sync α) (f : α β m (ForInStep β)) : β m β := fun b => do
match ch.recv? with

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@@ -176,7 +176,7 @@ protected theorem pos (i : Fin n) : 0 < n :=
@[inline] def castLE (h : n m) (i : Fin n) : Fin m := i, Nat.lt_of_lt_of_le i.2 h
/-- `cast eq i` embeds `i` into an equal `Fin` type. -/
@[inline] protected def cast (eq : n = m) (i : Fin n) : Fin m := i, eq i.2
@[inline] def cast (eq : n = m) (i : Fin n) : Fin m := i, eq i.2
/-- `castAdd m i` embeds `i : Fin n` in `Fin (n+m)`. See also `Fin.natAdd` and `Fin.addNat`. -/
@[inline] def castAdd (m) : Fin n Fin (n + m) :=

View File

@@ -13,14 +13,14 @@ namespace Fin
/-- Folds over `Fin n` from the left: `foldl 3 f x = f (f (f x 0) 1) 2`. -/
@[inline] def foldl (n) (f : α Fin n α) (init : α) : α := loop init 0 where
/-- Inner loop for `Fin.foldl`. `Fin.foldl.loop n f x i = f (f (f x i) ...) (n-1)` -/
@[semireducible, specialize] loop (x : α) (i : Nat) : α :=
@[semireducible] loop (x : α) (i : Nat) : α :=
if h : i < n then loop (f x i, h) (i+1) else x
termination_by n - i
/-- Folds over `Fin n` from the right: `foldr 3 f x = f 0 (f 1 (f 2 x))`. -/
@[inline] def foldr (n) (f : Fin n α α) (init : α) : α := loop n (Nat.le_refl n) init where
/-- Inner loop for `Fin.foldr`. `Fin.foldr.loop n f i x = f 0 (f ... (f (i-1) x))` -/
@[specialize] loop : (i : _) i n α α
loop : (i : _) i n α α
| 0, _, x => x
| i+1, h, x => loop i (Nat.le_of_lt h) (f i, h x)
termination_by structural i => i
@@ -47,7 +47,7 @@ Fin.foldlM n f x₀ = do
pure xₙ
```
-/
@[semireducible, specialize] loop (x : α) (i : Nat) : m α := do
loop (x : α) (i : Nat) : m α := do
if h : i < n then f x i, h >>= (loop · (i+1)) else pure x
termination_by n - i
decreasing_by decreasing_trivial_pre_omega
@@ -76,7 +76,7 @@ Fin.foldrM n f xₙ = do
pure x₀
```
-/
@[semireducible, specialize] loop : {i // i n} α m α
loop : {i // i n} α m α
| 0, _, x => pure x
| i+1, h, x => f i, h x >>= loop i, Nat.le_of_lt h
@@ -125,7 +125,7 @@ theorem foldrM_loop [Monad m] [LawfulMonad m] (f : Fin (n+1) → α → m α) (x
| zero =>
rw [foldrM_loop_zero, foldrM_loop_succ, pure_bind]
conv => rhs; rw [bind_pure (f 0 x)]
congr; funext
congr; funext; exact foldrM_loop_zero ..
| succ i ih =>
rw [foldrM_loop_succ, foldrM_loop_succ, bind_assoc]
congr; funext; exact ih ..

View File

@@ -370,25 +370,25 @@ theorem succ_succ_ne_one (a : Fin n) : Fin.succ (Fin.succ a) ≠ 1 :=
Fin.castLE mn Fin.castLE km = Fin.castLE (Nat.le_trans km mn) :=
funext (castLE_castLE km mn)
@[simp] theorem coe_cast (h : n = m) (i : Fin n) : (i.cast h : Nat) = i := rfl
@[simp] theorem coe_cast (h : n = m) (i : Fin n) : (cast h i : Nat) = i := rfl
@[simp] theorem cast_last {n' : Nat} {h : n + 1 = n' + 1} : (last n).cast h = last n' :=
@[simp] theorem cast_last {n' : Nat} {h : n + 1 = n' + 1} : cast h (last n) = last n' :=
Fin.ext (by rw [coe_cast, val_last, val_last, Nat.succ.inj h])
@[simp] theorem cast_mk (h : n = m) (i : Nat) (hn : i < n) : Fin.cast h i, hn = i, h hn := rfl
@[simp] theorem cast_mk (h : n = m) (i : Nat) (hn : i < n) : cast h i, hn = i, h hn := rfl
@[simp] theorem cast_refl (n : Nat) (h : n = n) : Fin.cast h = id := by
@[simp] theorem cast_refl (n : Nat) (h : n = n) : cast h = id := by
ext
simp
@[simp] theorem cast_trans {k : Nat} (h : n = m) (h' : m = k) {i : Fin n} :
(i.cast h).cast h' = i.cast (Eq.trans h h') := rfl
cast h' (cast h i) = cast (Eq.trans h h') i := rfl
theorem castLE_of_eq {m n : Nat} (h : m = n) {h' : m n} : castLE h' = Fin.cast h := rfl
@[simp] theorem coe_castAdd (m : Nat) (i : Fin n) : (castAdd m i : Nat) = i := rfl
@[simp] theorem castAdd_zero : (castAdd 0 : Fin n Fin (n + 0)) = Fin.cast rfl := rfl
@[simp] theorem castAdd_zero : (castAdd 0 : Fin n Fin (n + 0)) = cast rfl := rfl
theorem castAdd_lt {m : Nat} (n : Nat) (i : Fin m) : (castAdd n i : Nat) < m := by simp
@@ -406,37 +406,37 @@ theorem castAdd_cast {n n' : Nat} (m : Nat) (i : Fin n') (h : n' = n) :
castAdd m (Fin.cast h i) = Fin.cast (congrArg (. + m) h) (castAdd m i) := Fin.ext rfl
theorem cast_castAdd_left {n n' m : Nat} (i : Fin n') (h : n' + m = n + m) :
(i.castAdd m).cast h = (i.cast (Nat.add_right_cancel h)).castAdd m := rfl
cast h (castAdd m i) = castAdd m (cast (Nat.add_right_cancel h) i) := rfl
@[simp] theorem cast_castAdd_right {n m m' : Nat} (i : Fin n) (h : n + m' = n + m) :
(i.castAdd m').cast h = i.castAdd m := rfl
cast h (castAdd m' i) = castAdd m i := rfl
theorem castAdd_castAdd {m n p : Nat} (i : Fin m) :
(i.castAdd n).castAdd p = (i.castAdd (n + p)).cast (Nat.add_assoc ..).symm := rfl
castAdd p (castAdd n i) = cast (Nat.add_assoc ..).symm (castAdd (n + p) i) := rfl
/-- The cast of the successor is the successor of the cast. See `Fin.succ_cast_eq` for rewriting in
the reverse direction. -/
@[simp] theorem cast_succ_eq {n' : Nat} (i : Fin n) (h : n.succ = n'.succ) :
i.succ.cast h = (i.cast (Nat.succ.inj h)).succ := rfl
cast h i.succ = (cast (Nat.succ.inj h) i).succ := rfl
theorem succ_cast_eq {n' : Nat} (i : Fin n) (h : n = n') :
(i.cast h).succ = i.succ.cast (by rw [h]) := rfl
(cast h i).succ = cast (by rw [h]) i.succ := rfl
@[simp] theorem coe_castSucc (i : Fin n) : (i.castSucc : Nat) = i := rfl
@[simp] theorem coe_castSucc (i : Fin n) : (Fin.castSucc i : Nat) = i := rfl
@[simp] theorem castSucc_mk (n i : Nat) (h : i < n) : castSucc i, h = i, Nat.lt.step h := rfl
@[simp] theorem cast_castSucc {n' : Nat} {h : n + 1 = n' + 1} {i : Fin n} :
i.castSucc.cast h = (i.cast (Nat.succ.inj h)).castSucc := rfl
cast h (castSucc i) = castSucc (cast (Nat.succ.inj h) i) := rfl
theorem castSucc_lt_succ (i : Fin n) : i.castSucc < i.succ :=
theorem castSucc_lt_succ (i : Fin n) : Fin.castSucc i < i.succ :=
lt_def.2 <| by simp only [coe_castSucc, val_succ, Nat.lt_succ_self]
theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i j.castSucc i < j.succ := by
theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i Fin.castSucc j i < j.succ := by
simpa only [lt_def, le_def] using Nat.add_one_le_add_one_iff.symm
theorem castSucc_lt_iff_succ_le {n : Nat} {i : Fin n} {j : Fin (n + 1)} :
i.castSucc < j i.succ j := .rfl
Fin.castSucc i < j i.succ j := .rfl
@[simp] theorem succ_last (n : Nat) : (last n).succ = last n.succ := rfl
@@ -444,48 +444,48 @@ theorem castSucc_lt_iff_succ_le {n : Nat} {i : Fin n} {j : Fin (n + 1)} :
i.succ = last (n + 1) i = last n := by rw [ succ_last, succ_inj]
@[simp] theorem castSucc_castLT (i : Fin (n + 1)) (h : (i : Nat) < n) :
(castLT i h).castSucc = i := rfl
castSucc (castLT i h) = i := rfl
@[simp] theorem castLT_castSucc {n : Nat} (a : Fin n) (h : (a : Nat) < n) :
castLT a.castSucc h = a := rfl
castLT (castSucc a) h = a := rfl
@[simp] theorem castSucc_lt_castSucc_iff {a b : Fin n} :
a.castSucc < b.castSucc a < b := .rfl
Fin.castSucc a < Fin.castSucc b a < b := .rfl
theorem castSucc_inj {a b : Fin n} : a.castSucc = b.castSucc a = b := by simp [Fin.ext_iff]
theorem castSucc_inj {a b : Fin n} : castSucc a = castSucc b a = b := by simp [Fin.ext_iff]
theorem castSucc_lt_last (a : Fin n) : a.castSucc < last n := a.is_lt
theorem castSucc_lt_last (a : Fin n) : castSucc a < last n := a.is_lt
@[simp] theorem castSucc_zero : castSucc (0 : Fin (n + 1)) = 0 := rfl
@[simp] theorem castSucc_one {n : Nat} : castSucc (1 : Fin (n + 2)) = 1 := rfl
/-- `castSucc i` is positive when `i` is positive -/
theorem castSucc_pos {i : Fin (n + 1)} (h : 0 < i) : 0 < i.castSucc := by
theorem castSucc_pos {i : Fin (n + 1)} (h : 0 < i) : 0 < castSucc i := by
simpa [lt_def] using h
@[simp] theorem castSucc_eq_zero_iff {a : Fin (n + 1)} : a.castSucc = 0 a = 0 := by simp [Fin.ext_iff]
@[simp] theorem castSucc_eq_zero_iff {a : Fin (n + 1)} : castSucc a = 0 a = 0 := by simp [Fin.ext_iff]
theorem castSucc_ne_zero_iff {a : Fin (n + 1)} : a.castSucc 0 a 0 :=
theorem castSucc_ne_zero_iff {a : Fin (n + 1)} : castSucc a 0 a 0 :=
not_congr <| castSucc_eq_zero_iff
theorem castSucc_fin_succ (n : Nat) (j : Fin n) :
j.succ.castSucc = (j.castSucc).succ := by simp [Fin.ext_iff]
castSucc (Fin.succ j) = Fin.succ (castSucc j) := by simp [Fin.ext_iff]
@[simp]
theorem coeSucc_eq_succ {a : Fin n} : a.castSucc + 1 = a.succ := by
theorem coeSucc_eq_succ {a : Fin n} : castSucc a + 1 = a.succ := by
cases n
· exact a.elim0
· simp [Fin.ext_iff, add_def, Nat.mod_eq_of_lt (Nat.succ_lt_succ a.is_lt)]
theorem lt_succ {a : Fin n} : a.castSucc < a.succ := by
theorem lt_succ {a : Fin n} : castSucc a < a.succ := by
rw [castSucc, lt_def, coe_castAdd, val_succ]; exact Nat.lt_succ_self a.val
theorem exists_castSucc_eq {n : Nat} {i : Fin (n + 1)} : ( j, castSucc j = i) i last n :=
fun j, hj => hj Fin.ne_of_lt j.castSucc_lt_last,
fun hi => i.castLT <| Fin.val_lt_last hi, rfl
theorem succ_castSucc {n : Nat} (i : Fin n) : i.castSucc.succ = i.succ.castSucc := rfl
theorem succ_castSucc {n : Nat} (i : Fin n) : i.castSucc.succ = castSucc i.succ := rfl
@[simp] theorem coe_addNat (m : Nat) (i : Fin n) : (addNat i m : Nat) = i + m := rfl
@@ -502,17 +502,17 @@ theorem le_coe_addNat (m : Nat) (i : Fin n) : m ≤ addNat i m :=
addNat i, hi n = i + n, Nat.add_lt_add_right hi n := rfl
@[simp] theorem cast_addNat_zero {n n' : Nat} (i : Fin n) (h : n + 0 = n') :
(addNat i 0).cast h = i.cast ((Nat.add_zero _).symm.trans h) := rfl
cast h (addNat i 0) = cast ((Nat.add_zero _).symm.trans h) i := rfl
/-- For rewriting in the reverse direction, see `Fin.cast_addNat_left`. -/
theorem addNat_cast {n n' m : Nat} (i : Fin n') (h : n' = n) :
addNat (i.cast h) m = (addNat i m).cast (congrArg (. + m) h) := rfl
addNat (cast h i) m = cast (congrArg (. + m) h) (addNat i m) := rfl
theorem cast_addNat_left {n n' m : Nat} (i : Fin n') (h : n' + m = n + m) :
(addNat i m).cast h = addNat (i.cast (Nat.add_right_cancel h)) m := rfl
cast h (addNat i m) = addNat (cast (Nat.add_right_cancel h) i) m := rfl
@[simp] theorem cast_addNat_right {n m m' : Nat} (i : Fin n) (h : n + m' = n + m) :
(addNat i m').cast h = addNat i m :=
cast h (addNat i m') = addNat i m :=
Fin.ext <| (congrArg ((· + ·) (i : Nat)) (Nat.add_left_cancel h) : _)
@[simp] theorem coe_natAdd (n : Nat) {m : Nat} (i : Fin m) : (natAdd n i : Nat) = n + i := rfl
@@ -522,46 +522,46 @@ theorem cast_addNat_left {n n' m : Nat} (i : Fin n') (h : n' + m = n + m) :
theorem le_coe_natAdd (m : Nat) (i : Fin n) : m natAdd m i := Nat.le_add_right ..
@[simp] theorem natAdd_zero {n : Nat} : natAdd 0 = Fin.cast (Nat.zero_add n).symm := by ext; simp
@[simp] theorem natAdd_zero {n : Nat} : natAdd 0 = cast (Nat.zero_add n).symm := by ext; simp
/-- For rewriting in the reverse direction, see `Fin.cast_natAdd_right`. -/
theorem natAdd_cast {n n' : Nat} (m : Nat) (i : Fin n') (h : n' = n) :
natAdd m (i.cast h) = (natAdd m i).cast (congrArg _ h) := rfl
natAdd m (cast h i) = cast (congrArg _ h) (natAdd m i) := rfl
theorem cast_natAdd_right {n n' m : Nat} (i : Fin n') (h : m + n' = m + n) :
(natAdd m i).cast h = natAdd m (i.cast (Nat.add_left_cancel h)) := rfl
cast h (natAdd m i) = natAdd m (cast (Nat.add_left_cancel h) i) := rfl
@[simp] theorem cast_natAdd_left {n m m' : Nat} (i : Fin n) (h : m' + n = m + n) :
(natAdd m' i).cast h = natAdd m i :=
cast h (natAdd m' i) = natAdd m i :=
Fin.ext <| (congrArg (· + (i : Nat)) (Nat.add_right_cancel h) : _)
theorem castAdd_natAdd (p m : Nat) {n : Nat} (i : Fin n) :
castAdd p (natAdd m i) = (natAdd m (castAdd p i)).cast (Nat.add_assoc ..).symm := rfl
castAdd p (natAdd m i) = cast (Nat.add_assoc ..).symm (natAdd m (castAdd p i)) := rfl
theorem natAdd_castAdd (p m : Nat) {n : Nat} (i : Fin n) :
natAdd m (castAdd p i) = (castAdd p (natAdd m i)).cast (Nat.add_assoc ..) := rfl
natAdd m (castAdd p i) = cast (Nat.add_assoc ..) (castAdd p (natAdd m i)) := rfl
theorem natAdd_natAdd (m n : Nat) {p : Nat} (i : Fin p) :
natAdd m (natAdd n i) = (natAdd (m + n) i).cast (Nat.add_assoc ..) :=
natAdd m (natAdd n i) = cast (Nat.add_assoc ..) (natAdd (m + n) i) :=
Fin.ext <| (Nat.add_assoc ..).symm
@[simp]
theorem cast_natAdd_zero {n n' : Nat} (i : Fin n) (h : 0 + n = n') :
(natAdd 0 i).cast h = i.cast ((Nat.zero_add _).symm.trans h) :=
cast h (natAdd 0 i) = cast ((Nat.zero_add _).symm.trans h) i :=
Fin.ext <| Nat.zero_add _
@[simp]
theorem cast_natAdd (n : Nat) {m : Nat} (i : Fin m) :
(natAdd n i).cast (Nat.add_comm ..) = addNat i n := Fin.ext <| Nat.add_comm ..
cast (Nat.add_comm ..) (natAdd n i) = addNat i n := Fin.ext <| Nat.add_comm ..
@[simp]
theorem cast_addNat {n : Nat} (m : Nat) (i : Fin n) :
(addNat i m).cast (Nat.add_comm ..) = natAdd m i := Fin.ext <| Nat.add_comm ..
cast (Nat.add_comm ..) (addNat i m) = natAdd m i := Fin.ext <| Nat.add_comm ..
@[simp] theorem natAdd_last {m n : Nat} : natAdd n (last m) = last (n + m) := rfl
@[simp] theorem addNat_last (n : Nat) :
addNat (last n) m = (last (n + m)).cast (by omega) := by
addNat (last n) m = cast (by omega) (last (n + m)) := by
ext
simp
@@ -657,7 +657,7 @@ theorem pred_add_one (i : Fin (n + 2)) (h : (i : Nat) < n + 1) :
subNat m (addNat i m) h = i := Fin.ext <| Nat.add_sub_cancel i m
@[simp] theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n i) :
natAdd n (subNat n (i.cast (Nat.add_comm ..)) h) = i := by simp [ cast_addNat]
natAdd n (subNat n (cast (Nat.add_comm ..) i) h) = i := by simp [ cast_addNat]
/-! ### recursion and induction principles -/

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@@ -1,180 +0,0 @@
/-
Copyright (c) 2023 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Core
import Init.Data.Int.Basic
import Init.Data.ToString.Basic
import Init.Data.Float
/-
#exit -- TODO: Remove after update stage0
-- Just show FloatSpec is inhabited.
opaque float32Spec : FloatSpec := {
float := Unit,
val := (),
lt := fun _ _ => True,
le := fun _ _ => True,
decLt := fun _ _ => inferInstanceAs (Decidable True),
decLe := fun _ _ => inferInstanceAs (Decidable True)
}
/-- Native floating point type, corresponding to the IEEE 754 *binary32* format
(`float` in C or `f32` in Rust). -/
structure Float32 where
val : float32Spec.float
instance : Nonempty Float32 := ⟨{ val := float32Spec.val }⟩
@[extern "lean_float32_add"] opaque Float32.add : Float32 → Float32 → Float32
@[extern "lean_float32_sub"] opaque Float32.sub : Float32 → Float32 → Float32
@[extern "lean_float32_mul"] opaque Float32.mul : Float32 → Float32 → Float32
@[extern "lean_float32_div"] opaque Float32.div : Float32 → Float32 → Float32
@[extern "lean_float32_negate"] opaque Float32.neg : Float32 → Float32
set_option bootstrap.genMatcherCode false
def Float32.lt : Float32 → Float32 → Prop := fun a b =>
match a, b with
| ⟨a⟩, ⟨b⟩ => float32Spec.lt a b
def Float32.le : Float32 → Float32 → Prop := fun a b =>
float32Spec.le a.val b.val
/--
Raw transmutation from `UInt32`.
Float32s and UInts have the same endianness on all supported platforms.
IEEE 754 very precisely specifies the bit layout of floats.
-/
@[extern "lean_float32_of_bits"] opaque Float32.ofBits : UInt32 → Float32
/--
Raw transmutation to `UInt32`.
Float32s and UInts have the same endianness on all supported platforms.
IEEE 754 very precisely specifies the bit layout of floats.
Note that this function is distinct from `Float32.toUInt32`, which attempts
to preserve the numeric value, and not the bitwise value.
-/
@[extern "lean_float32_to_bits"] opaque Float32.toBits : Float32 → UInt32
instance : Add Float32 := ⟨Float32.add⟩
instance : Sub Float32 := ⟨Float32.sub⟩
instance : Mul Float32 := ⟨Float32.mul⟩
instance : Div Float32 := ⟨Float32.div⟩
instance : Neg Float32 := ⟨Float32.neg⟩
instance : LT Float32 := ⟨Float32.lt⟩
instance : LE Float32 := ⟨Float32.le⟩
/-- Note: this is not reflexive since `NaN != NaN`.-/
@[extern "lean_float32_beq"] opaque Float32.beq (a b : Float32) : Bool
instance : BEq Float32 := ⟨Float32.beq⟩
@[extern "lean_float32_decLt"] opaque Float32.decLt (a b : Float32) : Decidable (a < b) :=
match a, b with
| ⟨a⟩, ⟨b⟩ => float32Spec.decLt a b
@[extern "lean_float32_decLe"] opaque Float32.decLe (a b : Float32) : Decidable (a ≤ b) :=
match a, b with
| ⟨a⟩, ⟨b⟩ => float32Spec.decLe a b
instance float32DecLt (a b : Float32) : Decidable (a < b) := Float32.decLt a b
instance float32DecLe (a b : Float32) : Decidable (a ≤ b) := Float32.decLe a b
@[extern "lean_float32_to_string"] opaque Float32.toString : Float32 → String
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
If negative or NaN, returns `0`.
If larger than the maximum value for `UInt8` (including Inf), returns the maximum value of `UInt8`
(i.e. `UInt8.size - 1`).
-/
@[extern "lean_float32_to_uint8"] opaque Float32.toUInt8 : Float32 → UInt8
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
If negative or NaN, returns `0`.
If larger than the maximum value for `UInt16` (including Inf), returns the maximum value of `UInt16`
(i.e. `UInt16.size - 1`).
-/
@[extern "lean_float32_to_uint16"] opaque Float32.toUInt16 : Float32 → UInt16
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
If negative or NaN, returns `0`.
If larger than the maximum value for `UInt32` (including Inf), returns the maximum value of `UInt32`
(i.e. `UInt32.size - 1`).
-/
@[extern "lean_float32_to_uint32"] opaque Float32.toUInt32 : Float32 → UInt32
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
If negative or NaN, returns `0`.
If larger than the maximum value for `UInt64` (including Inf), returns the maximum value of `UInt64`
(i.e. `UInt64.size - 1`).
-/
@[extern "lean_float32_to_uint64"] opaque Float32.toUInt64 : Float32 → UInt64
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
If negative or NaN, returns `0`.
If larger than the maximum value for `USize` (including Inf), returns the maximum value of `USize`
(i.e. `USize.size - 1`). This value is platform dependent).
-/
@[extern "lean_float32_to_usize"] opaque Float32.toUSize : Float32 → USize
@[extern "lean_float32_isnan"] opaque Float32.isNaN : Float32 → Bool
@[extern "lean_float32_isfinite"] opaque Float32.isFinite : Float32 → Bool
@[extern "lean_float32_isinf"] opaque Float32.isInf : Float32 → Bool
/-- Splits the given float `x` into a significand/exponent pair `(s, i)`
such that `x = s * 2^i` where `s ∈ (-1;-0.5] [0.5; 1)`.
Returns an undefined value if `x` is not finite.
-/
@[extern "lean_float32_frexp"] opaque Float32.frExp : Float32 → Float32 × Int
instance : ToString Float32 where
toString := Float32.toString
@[extern "lean_uint64_to_float"] opaque UInt64.toFloat32 (n : UInt64) : Float32
instance : Inhabited Float32 where
default := UInt64.toFloat32 0
instance : Repr Float32 where
reprPrec n prec := if n < UInt64.toFloat32 0 then Repr.addAppParen (toString n) prec else toString n
instance : ReprAtom Float32 := ⟨⟩
@[extern "sinf"] opaque Float32.sin : Float32 → Float32
@[extern "cosf"] opaque Float32.cos : Float32 → Float32
@[extern "tanf"] opaque Float32.tan : Float32 → Float32
@[extern "asinf"] opaque Float32.asin : Float32 → Float32
@[extern "acosf"] opaque Float32.acos : Float32 → Float32
@[extern "atanf"] opaque Float32.atan : Float32 → Float32
@[extern "atan2f"] opaque Float32.atan2 : Float32 → Float32 → Float32
@[extern "sinhf"] opaque Float32.sinh : Float32 → Float32
@[extern "coshf"] opaque Float32.cosh : Float32 → Float32
@[extern "tanhf"] opaque Float32.tanh : Float32 → Float32
@[extern "asinhf"] opaque Float32.asinh : Float32 → Float32
@[extern "acoshf"] opaque Float32.acosh : Float32 → Float32
@[extern "atanhf"] opaque Float32.atanh : Float32 → Float32
@[extern "expf"] opaque Float32.exp : Float32 → Float32
@[extern "exp2f"] opaque Float32.exp2 : Float32 → Float32
@[extern "logf"] opaque Float32.log : Float32 → Float32
@[extern "log2f"] opaque Float32.log2 : Float32 → Float32
@[extern "log10f"] opaque Float32.log10 : Float32 → Float32
@[extern "powf"] opaque Float32.pow : Float32 → Float32 → Float32
@[extern "sqrtf"] opaque Float32.sqrt : Float32 → Float32
@[extern "cbrtf"] opaque Float32.cbrt : Float32 → Float32
@[extern "ceilf"] opaque Float32.ceil : Float32 → Float32
@[extern "floorf"] opaque Float32.floor : Float32 → Float32
@[extern "roundf"] opaque Float32.round : Float32 → Float32
@[extern "fabsf"] opaque Float32.abs : Float32 → Float32
instance : HomogeneousPow Float32 := ⟨Float32.pow⟩
instance : Min Float32 := minOfLe
instance : Max Float32 := maxOfLe
/--
Efficiently computes `x * 2^i`.
-/
@[extern "lean_float32_scaleb"]
opaque Float32.scaleB (x : Float32) (i : @& Int) : Float32
-/

View File

@@ -34,8 +34,4 @@ theorem shiftRight_eq_div_pow (m : Int) (n : Nat) :
theorem zero_shiftRight (n : Nat) : (0 : Int) >>> n = 0 := by
simp [Int.shiftRight_eq_div_pow]
@[simp]
theorem shiftRight_zero (n : Int) : n >>> 0 = n := by
simp [Int.shiftRight_eq_div_pow]
end Int

View File

@@ -29,8 +29,6 @@ At that time, we did not rename `div` and `mod` to `tdiv` and `tmod` (along with
In September 2024, we decided to do this rename (with deprecations in place),
and later we intend to rename `ediv` and `emod` to `div` and `mod`, as nearly all users will only
ever need to use these functions and their associated lemmas.
In December 2024, we removed `tdiv` and `tmod`, but have not yet renamed `ediv` and `emod`.
-/
/-! ### T-rounding division -/
@@ -73,6 +71,8 @@ def tdiv : (@& Int) → (@& Int) → Int
| -[m +1], ofNat n => -ofNat (succ m / n)
| -[m +1], -[n +1] => ofNat (succ m / succ n)
@[deprecated tdiv (since := "2024-09-11")] abbrev div := tdiv
/-- Integer modulo. This function uses the
[*"T-rounding"*][t-rounding] (**T**runcation-rounding) convention
to pair with `Int.tdiv`, meaning that `tmod a b + b * (tdiv a b) = a`
@@ -107,6 +107,8 @@ def tmod : (@& Int) → (@& Int) → Int
| -[m +1], ofNat n => -ofNat (succ m % n)
| -[m +1], -[n +1] => -ofNat (succ m % succ n)
@[deprecated tmod (since := "2024-09-11")] abbrev mod := tmod
/-! ### F-rounding division
This pair satisfies `fdiv x y = floor (x / y)`.
-/
@@ -249,6 +251,8 @@ instance : Mod Int where
theorem ofNat_tdiv (m n : Nat) : (m / n) = tdiv m n := rfl
@[deprecated ofNat_tdiv (since := "2024-09-11")] abbrev ofNat_div := ofNat_tdiv
theorem ofNat_fdiv : m n : Nat, (m / n) = fdiv m n
| 0, _ => by simp [fdiv]
| succ _, _ => rfl

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@@ -125,7 +125,7 @@ theorem eq_one_of_mul_eq_one_right {a b : Int} (H : 0 ≤ a) (H' : a * b = 1) :
eq_one_of_dvd_one H b, H'.symm
theorem eq_one_of_mul_eq_one_left {a b : Int} (H : 0 b) (H' : a * b = 1) : b = 1 :=
eq_one_of_mul_eq_one_right (b := a) H <| by rw [Int.mul_comm, H']
eq_one_of_mul_eq_one_right H <| by rw [Int.mul_comm, H']
/-! ### *div zero -/
@@ -1315,3 +1315,65 @@ theorem bmod_natAbs_plus_one (x : Int) (w : 1 < x.natAbs) : bmod x (x.natAbs + 1
all_goals decide
· exact ofNat_nonneg x
· exact succ_ofNat_pos (x + 1)
/-! ### Deprecations -/
@[deprecated Int.zero_tdiv (since := "2024-09-11")] protected abbrev zero_div := @Int.zero_tdiv
@[deprecated Int.tdiv_zero (since := "2024-09-11")] protected abbrev div_zero := @Int.tdiv_zero
@[deprecated tdiv_eq_ediv (since := "2024-09-11")] abbrev div_eq_ediv := @tdiv_eq_ediv
@[deprecated fdiv_eq_tdiv (since := "2024-09-11")] abbrev fdiv_eq_div := @fdiv_eq_tdiv
@[deprecated zero_tmod (since := "2024-09-11")] abbrev zero_mod := @zero_tmod
@[deprecated tmod_zero (since := "2024-09-11")] abbrev mod_zero := @tmod_zero
@[deprecated tmod_add_tdiv (since := "2024-09-11")] abbrev mod_add_div := @tmod_add_tdiv
@[deprecated tdiv_add_tmod (since := "2024-09-11")] abbrev div_add_mod := @tdiv_add_tmod
@[deprecated tmod_add_tdiv' (since := "2024-09-11")] abbrev mod_add_div' := @tmod_add_tdiv'
@[deprecated tdiv_add_tmod' (since := "2024-09-11")] abbrev div_add_mod' := @tdiv_add_tmod'
@[deprecated tmod_def (since := "2024-09-11")] abbrev mod_def := @tmod_def
@[deprecated tmod_eq_emod (since := "2024-09-11")] abbrev mod_eq_emod := @tmod_eq_emod
@[deprecated fmod_eq_tmod (since := "2024-09-11")] abbrev fmod_eq_mod := @fmod_eq_tmod
@[deprecated Int.tdiv_one (since := "2024-09-11")] protected abbrev div_one := @Int.tdiv_one
@[deprecated Int.tdiv_neg (since := "2024-09-11")] protected abbrev div_neg := @Int.tdiv_neg
@[deprecated Int.neg_tdiv (since := "2024-09-11")] protected abbrev neg_div := @Int.neg_tdiv
@[deprecated Int.neg_tdiv_neg (since := "2024-09-11")] protected abbrev neg_div_neg := @Int.neg_tdiv_neg
@[deprecated Int.tdiv_nonneg (since := "2024-09-11")] protected abbrev div_nonneg := @Int.tdiv_nonneg
@[deprecated Int.tdiv_nonpos (since := "2024-09-11")] protected abbrev div_nonpos := @Int.tdiv_nonpos
@[deprecated Int.tdiv_eq_zero_of_lt (since := "2024-09-11")] abbrev div_eq_zero_of_lt := @Int.tdiv_eq_zero_of_lt
@[deprecated Int.mul_tdiv_cancel (since := "2024-09-11")] protected abbrev mul_div_cancel := @Int.mul_tdiv_cancel
@[deprecated Int.mul_tdiv_cancel_left (since := "2024-09-11")] protected abbrev mul_div_cancel_left := @Int.mul_tdiv_cancel_left
@[deprecated Int.tdiv_self (since := "2024-09-11")] protected abbrev div_self := @Int.tdiv_self
@[deprecated Int.mul_tdiv_cancel_of_tmod_eq_zero (since := "2024-09-11")] abbrev mul_div_cancel_of_mod_eq_zero := @Int.mul_tdiv_cancel_of_tmod_eq_zero
@[deprecated Int.tdiv_mul_cancel_of_tmod_eq_zero (since := "2024-09-11")] abbrev div_mul_cancel_of_mod_eq_zero := @Int.tdiv_mul_cancel_of_tmod_eq_zero
@[deprecated Int.dvd_of_tmod_eq_zero (since := "2024-09-11")] abbrev dvd_of_mod_eq_zero := @Int.dvd_of_tmod_eq_zero
@[deprecated Int.mul_tdiv_assoc (since := "2024-09-11")] protected abbrev mul_div_assoc := @Int.mul_tdiv_assoc
@[deprecated Int.mul_tdiv_assoc' (since := "2024-09-11")] protected abbrev mul_div_assoc' := @Int.mul_tdiv_assoc'
@[deprecated Int.tdiv_dvd_tdiv (since := "2024-09-11")] abbrev div_dvd_div := @Int.tdiv_dvd_tdiv
@[deprecated Int.natAbs_tdiv (since := "2024-09-11")] abbrev natAbs_div := @Int.natAbs_tdiv
@[deprecated Int.tdiv_eq_of_eq_mul_right (since := "2024-09-11")] protected abbrev div_eq_of_eq_mul_right := @Int.tdiv_eq_of_eq_mul_right
@[deprecated Int.eq_tdiv_of_mul_eq_right (since := "2024-09-11")] protected abbrev eq_div_of_mul_eq_right := @Int.eq_tdiv_of_mul_eq_right
@[deprecated Int.ofNat_tmod (since := "2024-09-11")] abbrev ofNat_mod := @Int.ofNat_tmod
@[deprecated Int.tmod_one (since := "2024-09-11")] abbrev mod_one := @Int.tmod_one
@[deprecated Int.tmod_eq_of_lt (since := "2024-09-11")] abbrev mod_eq_of_lt := @Int.tmod_eq_of_lt
@[deprecated Int.tmod_lt_of_pos (since := "2024-09-11")] abbrev mod_lt_of_pos := @Int.tmod_lt_of_pos
@[deprecated Int.tmod_nonneg (since := "2024-09-11")] abbrev mod_nonneg := @Int.tmod_nonneg
@[deprecated Int.tmod_neg (since := "2024-09-11")] abbrev mod_neg := @Int.tmod_neg
@[deprecated Int.mul_tmod_left (since := "2024-09-11")] abbrev mul_mod_left := @Int.mul_tmod_left
@[deprecated Int.mul_tmod_right (since := "2024-09-11")] abbrev mul_mod_right := @Int.mul_tmod_right
@[deprecated Int.tmod_eq_zero_of_dvd (since := "2024-09-11")] abbrev mod_eq_zero_of_dvd := @Int.tmod_eq_zero_of_dvd
@[deprecated Int.dvd_iff_tmod_eq_zero (since := "2024-09-11")] abbrev dvd_iff_mod_eq_zero := @Int.dvd_iff_tmod_eq_zero
@[deprecated Int.neg_mul_tmod_right (since := "2024-09-11")] abbrev neg_mul_mod_right := @Int.neg_mul_tmod_right
@[deprecated Int.neg_mul_tmod_left (since := "2024-09-11")] abbrev neg_mul_mod_left := @Int.neg_mul_tmod_left
@[deprecated Int.tdiv_mul_cancel (since := "2024-09-11")] protected abbrev div_mul_cancel := @Int.tdiv_mul_cancel
@[deprecated Int.mul_tdiv_cancel' (since := "2024-09-11")] protected abbrev mul_div_cancel' := @Int.mul_tdiv_cancel'
@[deprecated Int.eq_mul_of_tdiv_eq_right (since := "2024-09-11")] protected abbrev eq_mul_of_div_eq_right := @Int.eq_mul_of_tdiv_eq_right
@[deprecated Int.tmod_self (since := "2024-09-11")] abbrev mod_self := @Int.tmod_self
@[deprecated Int.neg_tmod_self (since := "2024-09-11")] abbrev neg_mod_self := @Int.neg_tmod_self
@[deprecated Int.lt_tdiv_add_one_mul_self (since := "2024-09-11")] abbrev lt_div_add_one_mul_self := @Int.lt_tdiv_add_one_mul_self
@[deprecated Int.tdiv_eq_iff_eq_mul_right (since := "2024-09-11")] protected abbrev div_eq_iff_eq_mul_right := @Int.tdiv_eq_iff_eq_mul_right
@[deprecated Int.tdiv_eq_iff_eq_mul_left (since := "2024-09-11")] protected abbrev div_eq_iff_eq_mul_left := @Int.tdiv_eq_iff_eq_mul_left
@[deprecated Int.eq_mul_of_tdiv_eq_left (since := "2024-09-11")] protected abbrev eq_mul_of_div_eq_left := @Int.eq_mul_of_tdiv_eq_left
@[deprecated Int.tdiv_eq_of_eq_mul_left (since := "2024-09-11")] protected abbrev div_eq_of_eq_mul_left := @Int.tdiv_eq_of_eq_mul_left
@[deprecated Int.eq_zero_of_tdiv_eq_zero (since := "2024-09-11")] protected abbrev eq_zero_of_div_eq_zero := @Int.eq_zero_of_tdiv_eq_zero
@[deprecated Int.tdiv_left_inj (since := "2024-09-11")] protected abbrev div_left_inj := @Int.tdiv_left_inj
@[deprecated Int.tdiv_sign (since := "2024-09-11")] abbrev div_sign := @Int.tdiv_sign
@[deprecated Int.sign_eq_tdiv_abs (since := "2024-09-11")] protected abbrev sign_eq_div_abs := @Int.sign_eq_tdiv_abs
@[deprecated Int.tdiv_eq_ediv_of_dvd (since := "2024-09-11")] abbrev div_eq_ediv_of_dvd := @Int.tdiv_eq_ediv_of_dvd

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@@ -24,7 +24,6 @@ import Init.Data.List.Zip
import Init.Data.List.Perm
import Init.Data.List.Sort
import Init.Data.List.ToArray
import Init.Data.List.ToArrayImpl
import Init.Data.List.MapIdx
import Init.Data.List.OfFn
import Init.Data.List.FinRange

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@@ -666,14 +666,10 @@ def isEmpty : List α → Bool
/-! ### elem -/
/--
`O(|l|)`.
`l.contains a` or `elem a l` is true if there is an element in `l` equal (according to `==`) to `a`.
`O(|l|)`. `elem a l` or `l.contains a` is true if there is an element in `l` equal to `a`.
* `[1, 4, 2, 3, 3, 7].contains 3 = true`
* `[1, 4, 2, 3, 3, 7].contains 5 = false`
The preferred simp normal form is `l.contains a`, and when `LawfulBEq α` is available,
`l.contains a = true ↔ a ∈ l` and `l.contains a = false ↔ a ∉ l`.
* `elem 3 [1, 4, 2, 3, 3, 7] = true`
* `elem 5 [1, 4, 2, 3, 3, 7] = false`
-/
def elem [BEq α] (a : α) : List α Bool
| [] => false

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@@ -155,8 +155,7 @@ def mapMono (as : List α) (f : αα) : List α :=
/-! ## Additional lemmas required for bootstrapping `Array`. -/
theorem getElem_append_left {as bs : List α} (h : i < as.length) {h' : i < (as ++ bs).length} :
(as ++ bs)[i] = as[i] := by
theorem getElem_append_left {as bs : List α} (h : i < as.length) {h'} : (as ++ bs)[i] = as[i] := by
induction as generalizing i with
| nil => trivial
| cons a as ih =>

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@@ -162,10 +162,6 @@ theorem countP_filterMap (p : β → Bool) (f : α → Option β) (l : List α)
@[deprecated countP_flatten (since := "2024-10-14")] abbrev countP_join := @countP_flatten
theorem countP_flatMap (p : β Bool) (l : List α) (f : α List β) :
countP p (l.flatMap f) = sum (map (countP p f) l) := by
rw [List.flatMap, countP_flatten, map_map]
@[simp] theorem countP_reverse (l : List α) : countP p l.reverse = countP p l := by
simp [countP_eq_length_filter, filter_reverse]
@@ -330,9 +326,6 @@ theorem count_filterMap {α} [BEq β] (b : β) (f : α → Option β) (l : List
· simp
· simp
theorem count_flatMap {α} [BEq β] (l : List α) (f : α List β) (x : β) :
count x (l.flatMap f) = sum (map (count x f) l) := countP_flatMap _ _ _
theorem count_erase (a b : α) :
l : List α, count a (l.erase b) = count a l - if b == a then 1 else 0
| [] => by simp

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@@ -220,6 +220,15 @@ We simplify `l[n]!` to `(l[n]?).getD default`.
/-! ### getElem? and getElem -/
@[simp] theorem getElem?_eq_getElem {l : List α} {n} (h : n < l.length) : l[n]? = some l[n] := by
simp only [getElem?_def, h, reduceDIte]
theorem getElem?_eq_some_iff {l : List α} : l[n]? = some a h : n < l.length, l[n] = a := by
simp only [ get?_eq_getElem?, get?_eq_some_iff, get_eq_getElem]
theorem some_eq_getElem?_iff {l : List α} : some a = l[n]? h : n < l.length, l[n] = a := by
rw [eq_comm, getElem?_eq_some_iff]
@[simp] theorem getElem?_eq_none_iff : l[n]? = none length l n := by
simp only [ get?_eq_getElem?, get?_eq_none_iff]
@@ -228,20 +237,11 @@ We simplify `l[n]!` to `(l[n]?).getD default`.
theorem getElem?_eq_none (h : length l n) : l[n]? = none := getElem?_eq_none_iff.mpr h
@[simp] theorem getElem?_eq_getElem {l : List α} {n} (h : n < l.length) : l[n]? = some l[n] :=
getElem?_pos ..
theorem getElem?_eq_some_iff {l : List α} : l[n]? = some a h : n < l.length, l[n] = a := by
simp only [ get?_eq_getElem?, get?_eq_some_iff, get_eq_getElem]
theorem some_eq_getElem?_iff {l : List α} : some a = l[n]? h : n < l.length, l[n] = a := by
rw [eq_comm, getElem?_eq_some_iff]
@[simp] theorem some_getElem_eq_getElem?_iff (xs : List α) (i : Nat) (h : i < xs.length) :
@[simp] theorem some_getElem_eq_getElem?_iff {α} (xs : List α) (i : Nat) (h : i < xs.length) :
(some xs[i] = xs[i]?) True := by
simp [h]
@[simp] theorem getElem?_eq_some_getElem_iff (xs : List α) (i : Nat) (h : i < xs.length) :
@[simp] theorem getElem?_eq_some_getElem_iff {α} (xs : List α) (i : Nat) (h : i < xs.length) :
(xs[i]? = some xs[i]) True := by
simp [h]
@@ -255,11 +255,6 @@ theorem getElem_eq_getElem?_get (l : List α) (i : Nat) (h : i < l.length) :
@[simp] theorem getElem?_nil {n : Nat} : ([] : List α)[n]? = none := rfl
theorem getElem_cons {l : List α} (w : i < (a :: l).length) :
(a :: l)[i] =
if h : i = 0 then a else l[i-1]'(match i, h with | i+1, _ => succ_lt_succ_iff.mp w) := by
cases i <;> simp
theorem getElem?_cons_zero {l : List α} : (a::l)[0]? = some a := by simp
@[simp] theorem getElem?_cons_succ {l : List α} : (a::l)[n+1]? = l[n]? := by
@@ -269,13 +264,6 @@ theorem getElem?_cons_zero {l : List α} : (a::l)[0]? = some a := by simp
theorem getElem?_cons : (a :: l)[i]? = if i = 0 then some a else l[i-1]? := by
cases i <;> simp
@[simp] theorem getElem_singleton (a : α) (h : i < 1) : [a][i] = a :=
match i, h with
| 0, _ => rfl
theorem getElem?_singleton (a : α) (i : Nat) : [a][i]? = if i = 0 then some a else none := by
simp [getElem?_cons]
/--
If one has `l[i]` in an expression and `h : l = l'`,
`rw [h]` will give a "motive it not type correct" error, as it cannot rewrite the
@@ -285,6 +273,10 @@ such a rewrite, with `rw [getElem_of_eq h]`.
theorem getElem_of_eq {l l' : List α} (h : l = l') {i : Nat} (w : i < l.length) :
l[i] = l'[i]'(h w) := by cases h; rfl
@[simp] theorem getElem_singleton (a : α) (h : i < 1) : [a][i] = a :=
match i, h with
| 0, _ => rfl
theorem getElem_zero {l : List α} (h : 0 < l.length) : l[0] = l.head (length_pos.mp h) :=
match l, h with
| _ :: _, _ => rfl
@@ -308,6 +300,12 @@ theorem ext_getElem {l₁ l₂ : List α} (hl : length l₁ = length l₂)
theorem getElem?_concat_length (l : List α) (a : α) : (l ++ [a])[l.length]? = some a := by
simp
theorem isSome_getElem? {l : List α} {n : Nat} : l[n]?.isSome n < l.length := by
simp
theorem isNone_getElem? {l : List α} {n : Nat} : l[n]?.isNone l.length n := by
simp
/-! ### mem -/
@[simp] theorem not_mem_nil (a : α) : ¬ a [] := nofun
@@ -418,9 +416,8 @@ theorem getElem_of_mem : ∀ {a} {l : List α}, a ∈ l → ∃ (n : Nat) (h : n
| _, _ :: _, .head .. => 0, Nat.succ_pos _, rfl
| _, _ :: _, .tail _ m => let n, h, e := getElem_of_mem m; n+1, Nat.succ_lt_succ h, e
theorem getElem?_of_mem {a} {l : List α} (h : a l) : n : Nat, l[n]? = some a := by
let n, _, e := getElem_of_mem h
exact n, e getElem?_eq_getElem _
theorem getElem?_of_mem {a} {l : List α} (h : a l) : n : Nat, l[n]? = some a :=
let n, _, e := getElem_of_mem h; n, e getElem?_eq_getElem _
theorem mem_of_getElem? {l : List α} {n : Nat} {a : α} (e : l[n]? = some a) : a l :=
let _, e := getElem?_eq_some_iff.1 e; e getElem_mem ..
@@ -451,10 +448,6 @@ theorem forall_getElem {l : List α} {p : α → Prop} :
simp only [getElem_cons_succ]
exact getElem_mem (lt_of_succ_lt_succ h)
@[simp] theorem elem_eq_contains [BEq α] {a : α} {l : List α} :
elem a l = l.contains a := by
simp [contains]
@[simp] theorem decide_mem_cons [BEq α] [LawfulBEq α] {l : List α} :
decide (y a :: l) = (y == a || decide (y l)) := by
cases h : y == a <;> simp_all
@@ -462,27 +455,16 @@ theorem forall_getElem {l : List α} {p : α → Prop} :
theorem elem_iff [BEq α] [LawfulBEq α] {a : α} {as : List α} :
elem a as = true a as := mem_of_elem_eq_true, elem_eq_true_of_mem
theorem contains_iff [BEq α] [LawfulBEq α] {a : α} {as : List α} :
as.contains a = true a as := mem_of_elem_eq_true, elem_eq_true_of_mem
theorem elem_eq_mem [BEq α] [LawfulBEq α] (a : α) (as : List α) :
@[simp] theorem elem_eq_mem [BEq α] [LawfulBEq α] (a : α) (as : List α) :
elem a as = decide (a as) := by rw [Bool.eq_iff_iff, elem_iff, decide_eq_true_iff]
@[simp] theorem contains_eq_mem [BEq α] [LawfulBEq α] (a : α) (as : List α) :
as.contains a = decide (a as) := by rw [Bool.eq_iff_iff, elem_iff, decide_eq_true_iff]
@[simp] theorem contains_cons [BEq α] {a : α} {b : α} {l : List α} :
(a :: l).contains b = (b == a || l.contains b) := by
simp only [contains, elem_cons]
split <;> simp_all
/-! ### `isEmpty` -/
theorem isEmpty_iff {l : List α} : l.isEmpty l = [] := by
cases l <;> simp
theorem isEmpty_eq_false_iff_exists_mem {xs : List α} :
xs.isEmpty = false x, x xs := by
(List.isEmpty xs = false) x, x xs := by
cases xs <;> simp
theorem isEmpty_iff_length_eq_zero {l : List α} : l.isEmpty l.length = 0 := by
@@ -520,21 +502,17 @@ theorem decide_forall_mem {l : List α} {p : α → Prop} [DecidablePred p] :
@[simp] theorem all_eq_false {l : List α} : l.all p = false x, x l ¬p x := by
simp [all_eq]
theorem any_beq [BEq α] {l : List α} {a : α} : (l.any fun x => a == x) = l.contains a := by
induction l <;> simp_all [contains_cons]
theorem any_beq [BEq α] [LawfulBEq α] {l : List α} : (l.any fun x => a == x) a l := by
simp
/-- Variant of `any_beq` with `==` reversed. -/
theorem any_beq' [BEq α] [PartialEquivBEq α] {l : List α} :
(l.any fun x => x == a) = l.contains a := by
simp only [BEq.comm, any_beq]
theorem any_beq' [BEq α] [LawfulBEq α] {l : List α} : (l.any fun x => x == a) a l := by
simp
theorem all_bne [BEq α] {l : List α} : (l.all fun x => a != x) = !l.contains a := by
induction l <;> simp_all [bne]
theorem all_bne [BEq α] [LawfulBEq α] {l : List α} : (l.all fun x => a != x) a l := by
induction l <;> simp_all
/-- Variant of `all_bne` with `!=` reversed. -/
theorem all_bne' [BEq α] [PartialEquivBEq α] {l : List α} :
(l.all fun x => x != a) = !l.contains a := by
simp only [bne_comm, all_bne]
theorem all_bne' [BEq α] [LawfulBEq α] {l : List α} : (l.all fun x => x != a) a l := by
induction l <;> simp_all [eq_comm (a := a)]
/-! ### set -/
@@ -971,7 +949,7 @@ theorem getLast_eq_getElem : ∀ (l : List α) (h : l ≠ []),
| _ :: _ :: _, _ => by
simp [getLast, get, Nat.succ_sub_succ, getLast_eq_getElem]
theorem getElem_length_sub_one_eq_getLast (l : List α) (h : l.length - 1 < l.length) :
theorem getElem_length_sub_one_eq_getLast (l : List α) (h) :
l[l.length - 1] = getLast l (by cases l; simp at h; simp) := by
rw [ getLast_eq_getElem]
@@ -1099,8 +1077,7 @@ theorem head_eq_getElem (l : List α) (h : l ≠ []) : head l h = l[0]'(length_p
| nil => simp at h
| cons _ _ => simp
theorem getElem_zero_eq_head (l : List α) (h : 0 < l.length) :
l[0] = head l (by simpa [length_pos] using h) := by
theorem getElem_zero_eq_head (l : List α) (h) : l[0] = head l (by simpa [length_pos] using h) := by
cases l with
| nil => simp at h
| cons _ _ => simp
@@ -1692,7 +1669,7 @@ theorem filterMap_eq_cons_iff {l} {b} {bs} :
@[simp] theorem cons_append_fun (a : α) (as : List α) :
(fun bs => ((a :: as) ++ bs)) = fun bs => a :: (as ++ bs) := rfl
theorem getElem_append {l₁ l₂ : List α} (n : Nat) (h : n < (l₁ ++ l₂).length) :
theorem getElem_append {l₁ l₂ : List α} (n : Nat) (h) :
(l₁ ++ l₂)[n] = if h' : n < l₁.length then l₁[n] else l₂[n - l₁.length]'(by simp at h h'; exact Nat.sub_lt_left_of_lt_add h' h) := by
split <;> rename_i h'
· rw [getElem_append_left h']
@@ -2234,11 +2211,6 @@ theorem flatMap_def (l : List α) (f : α → List β) : l.flatMap f = flatten (
@[simp] theorem flatMap_id (l : List (List α)) : List.flatMap l id = l.flatten := by simp [flatMap_def]
@[simp]
theorem length_flatMap (l : List α) (f : α List β) :
length (l.flatMap f) = sum (map (length f) l) := by
rw [List.flatMap, length_flatten, map_map]
@[simp] theorem mem_flatMap {f : α List β} {b} {l : List α} : b l.flatMap f a, a l b f a := by
simp [flatMap_def, mem_flatten]
exact fun _, a, h₁, rfl, h₂ => a, h₁, h₂, fun a, h₁, h₂ => _, a, h₁, rfl, h₂
@@ -2847,6 +2819,11 @@ theorem leftpad_suffix (n : Nat) (a : α) (l : List α) : l <:+ (leftpad n a l)
theorem elem_cons_self [BEq α] [LawfulBEq α] {a : α} : (a::as).elem a = true := by simp
@[simp] theorem contains_cons [BEq α] :
(a :: as : List α).contains x = (x == a || as.contains x) := by
simp only [contains, elem]
split <;> simp_all
theorem contains_eq_any_beq [BEq α] (l : List α) (a : α) : l.contains a = l.any (a == ·) := by
induction l with simp | cons b l => cases b == a <;> simp [*]
@@ -2890,7 +2867,7 @@ are often used for theorems about `Array.pop`.
@[simp] theorem getElem_dropLast : (xs : List α) (i : Nat) (h : i < xs.dropLast.length),
xs.dropLast[i] = xs[i]'(Nat.lt_of_lt_of_le h (length_dropLast .. Nat.pred_le _))
| _::_::_, 0, _ => rfl
| _::_::_, i+1, h => getElem_dropLast _ i (Nat.add_one_lt_add_one_iff.mp h)
| _::_::_, i+1, _ => getElem_dropLast _ i _
@[deprecated getElem_dropLast (since := "2024-06-12")]
theorem get_dropLast (xs : List α) (i : Fin xs.dropLast.length) :
@@ -3545,12 +3522,7 @@ theorem getElem?_eq (l : List α) (i : Nat) :
getElem?_def _ _
@[deprecated getElem?_eq_none (since := "2024-11-29")] abbrev getElem?_len_le := @getElem?_eq_none
@[deprecated _root_.isSome_getElem? (since := "2024-12-09")]
theorem isSome_getElem? {l : List α} {n : Nat} : l[n]?.isSome n < l.length := by
simp
@[deprecated _root_.isNone_getElem? (since := "2024-12-09")]
theorem isNone_getElem? {l : List α} {n : Nat} : l[n]?.isNone l.length n := by
simp
end List

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@@ -237,15 +237,15 @@ theorem getElem?_mapIdx_go : ∀ {l : List α} {arr : Array β} {i : Nat},
if h : i < arr.size then some arr[i] else Option.map (f i) l[i - arr.size]?
| [], arr, i => by
simp only [mapIdx.go, Array.toListImpl_eq, getElem?_def, Array.length_toList,
Array.getElem_toList, length_nil, Nat.not_lt_zero, reduceDIte, Option.map_none']
Array.getElem_eq_getElem_toList, length_nil, Nat.not_lt_zero, reduceDIte, Option.map_none']
| a :: l, arr, i => by
rw [mapIdx.go, getElem?_mapIdx_go]
simp only [Array.size_push]
split <;> split
· simp only [Option.some.injEq]
rw [ Array.getElem_toList]
rw [Array.getElem_eq_getElem_toList]
simp only [Array.push_toList]
rw [getElem_append_left, Array.getElem_toList]
rw [getElem_append_left, Array.getElem_eq_getElem_toList]
· have : i = arr.size := by omega
simp_all
· omega

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@@ -841,7 +841,7 @@ theorem isPrefix_iff : l₁ <+: l₂ ↔ ∀ i (h : i < l₁.length), l₂[i]? =
theorem isPrefix_iff_getElem {l₁ l₂ : List α} :
l₁ <+: l₂ (h : l₁.length l₂.length), x (hx : x < l₁.length),
l₁[x] = l₂[x]'(Nat.lt_of_lt_of_le hx h) where
mp h := h.length_le, fun _ h' h.getElem h'
mp h := h.length_le, fun _ _ h.getElem _
mpr h := by
obtain hl, h := h
induction l₂ generalizing l₁ with

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@@ -65,13 +65,13 @@ theorem lt_length_of_take_ne_self {l : List α} {n} (h : l.take n ≠ l) : n < l
theorem getElem_cons_drop : (l : List α) (i : Nat) (h : i < l.length),
l[i] :: drop (i + 1) l = drop i l
| _::_, 0, _ => rfl
| _::_, i+1, h => getElem_cons_drop _ i (Nat.add_one_lt_add_one_iff.mp h)
| _::_, i+1, _ => getElem_cons_drop _ i _
@[deprecated getElem_cons_drop (since := "2024-06-12")]
theorem get_cons_drop (l : List α) (i) : get l i :: drop (i + 1) l = drop i l := by
simp
theorem drop_eq_getElem_cons {n} {l : List α} (h : n < l.length) : drop n l = l[n] :: drop (n + 1) l :=
theorem drop_eq_getElem_cons {n} {l : List α} (h) : drop n l = l[n] :: drop (n + 1) l :=
(getElem_cons_drop _ n h).symm
@[deprecated drop_eq_getElem_cons (since := "2024-06-12")]

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@@ -1,366 +1,23 @@
/-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Copyright (c) 2024 Lean FRO. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Authors: Henrik Böving
-/
prelude
import Init.Data.List.Impl
import Init.Data.List.Nat.Erase
import Init.Data.List.Monadic
import Init.Data.List.Basic
/-! ### Lemmas about `List.toArray`.
We prefer to pull `List.toArray` outwards past `Array` operations.
/--
Auxiliary definition for `List.toArray`.
`List.toArrayAux as r = r ++ as.toArray`
-/
namespace List
@[inline_if_reduce]
def List.toArrayAux : List α Array α Array α
| nil, r => r
| cons a as, r => toArrayAux as (r.push a)
open Array
theorem toArray_inj {a b : List α} (h : a.toArray = b.toArray) : a = b := by
cases a with
| nil => simpa using h
| cons a as =>
cases b with
| nil => simp at h
| cons b bs => simpa using h
@[simp] theorem size_toArrayAux {a : List α} {b : Array α} :
(a.toArrayAux b).size = b.size + a.length := by
simp [size]
@[simp] theorem push_toArray (l : List α) (a : α) : l.toArray.push a = (l ++ [a]).toArray := by
apply ext'
simp
/-- Unapplied variant of `push_toArray`, useful for monadic reasoning. -/
@[simp] theorem push_toArray_fun (l : List α) : l.toArray.push = fun a => (l ++ [a]).toArray := by
funext a
simp
@[simp] theorem isEmpty_toArray (l : List α) : l.toArray.isEmpty = l.isEmpty := by
cases l <;> simp
@[simp] theorem toArray_singleton (a : α) : (List.singleton a).toArray = singleton a := rfl
@[simp] theorem back!_toArray [Inhabited α] (l : List α) : l.toArray.back! = l.getLast! := by
simp only [back!, size_toArray, Array.get!_eq_getElem!, getElem!_toArray, getLast!_eq_getElem!]
@[simp] theorem back?_toArray (l : List α) : l.toArray.back? = l.getLast? := by
simp [back?, List.getLast?_eq_getElem?]
@[simp] theorem set_toArray (l : List α) (i : Nat) (a : α) (h : i < l.length) :
(l.toArray.set i a) = (l.set i a).toArray := rfl
@[simp] theorem forIn'_loop_toArray [Monad m] (l : List α) (f : (a : α) a l.toArray β m (ForInStep β)) (i : Nat)
(h : i l.length) (b : β) :
Array.forIn'.loop l.toArray f i h b =
forIn' (l.drop (l.length - i)) b (fun a m b => f a (by simpa using mem_of_mem_drop m) b) := by
induction i generalizing l b with
| zero =>
simp [Array.forIn'.loop]
| succ i ih =>
simp only [Array.forIn'.loop, size_toArray, getElem_toArray, ih]
have t : drop (l.length - (i + 1)) l = l[l.length - i - 1] :: drop (l.length - i) l := by
simp only [Nat.sub_add_eq]
rw [List.drop_sub_one (by omega), List.getElem?_eq_getElem (by omega)]
simp only [Option.toList_some, singleton_append]
simp [t]
have t : l.length - 1 - i = l.length - i - 1 := by omega
simp only [t]
congr
@[simp] theorem forIn'_toArray [Monad m] (l : List α) (b : β) (f : (a : α) a l.toArray β m (ForInStep β)) :
forIn' l.toArray b f = forIn' l b (fun a m b => f a (mem_toArray.mpr m) b) := by
change Array.forIn' _ _ _ = List.forIn' _ _ _
rw [Array.forIn', forIn'_loop_toArray]
simp
@[simp] theorem forIn_toArray [Monad m] (l : List α) (b : β) (f : α β m (ForInStep β)) :
forIn l.toArray b f = forIn l b f := by
simpa using forIn'_toArray l b fun a m b => f a b
theorem foldrM_toArray [Monad m] (f : α β m β) (init : β) (l : List α) :
l.toArray.foldrM f init = l.foldrM f init := by
rw [foldrM_eq_reverse_foldlM_toList]
simp
theorem foldlM_toArray [Monad m] (f : β α m β) (init : β) (l : List α) :
l.toArray.foldlM f init = l.foldlM f init := by
rw [foldlM_toList]
theorem foldr_toArray (f : α β β) (init : β) (l : List α) :
l.toArray.foldr f init = l.foldr f init := by
rw [foldr_toList]
theorem foldl_toArray (f : β α β) (init : β) (l : List α) :
l.toArray.foldl f init = l.foldl f init := by
rw [foldl_toList]
/-- Variant of `foldrM_toArray` with a side condition for the `start` argument. -/
@[simp] theorem foldrM_toArray' [Monad m] (f : α β m β) (init : β) (l : List α)
(h : start = l.toArray.size) :
l.toArray.foldrM f init start 0 = l.foldrM f init := by
subst h
rw [foldrM_eq_reverse_foldlM_toList]
simp
/-- Variant of `foldlM_toArray` with a side condition for the `stop` argument. -/
@[simp] theorem foldlM_toArray' [Monad m] (f : β α m β) (init : β) (l : List α)
(h : stop = l.toArray.size) :
l.toArray.foldlM f init 0 stop = l.foldlM f init := by
subst h
rw [foldlM_toList]
/-- Variant of `foldr_toArray` with a side condition for the `start` argument. -/
@[simp] theorem foldr_toArray' (f : α β β) (init : β) (l : List α)
(h : start = l.toArray.size) :
l.toArray.foldr f init start 0 = l.foldr f init := by
subst h
rw [foldr_toList]
/-- Variant of `foldl_toArray` with a side condition for the `stop` argument. -/
@[simp] theorem foldl_toArray' (f : β α β) (init : β) (l : List α)
(h : stop = l.toArray.size) :
l.toArray.foldl f init 0 stop = l.foldl f init := by
subst h
rw [foldl_toList]
@[simp] theorem append_toArray (l₁ l₂ : List α) :
l₁.toArray ++ l₂.toArray = (l₁ ++ l₂).toArray := by
apply ext'
simp
@[simp] theorem push_append_toArray {as : Array α} {a : α} {bs : List α} : as.push a ++ bs.toArray = as ++ (a ::bs).toArray := by
cases as
simp
@[simp] theorem foldl_push {l : List α} {as : Array α} : l.foldl Array.push as = as ++ l.toArray := by
induction l generalizing as <;> simp [*]
@[simp] theorem foldr_push {l : List α} {as : Array α} : l.foldr (fun a b => push b a) as = as ++ l.reverse.toArray := by
rw [foldr_eq_foldl_reverse, foldl_push]
@[simp] theorem findSomeM?_toArray [Monad m] [LawfulMonad m] (f : α m (Option β)) (l : List α) :
l.toArray.findSomeM? f = l.findSomeM? f := by
rw [Array.findSomeM?]
simp only [bind_pure_comp, map_pure, forIn_toArray]
induction l with
| nil => simp
| cons a l ih =>
simp only [forIn_cons, LawfulMonad.bind_assoc, findSomeM?]
congr
ext1 (_|_) <;> simp [ih]
theorem findSomeRevM?_find_toArray [Monad m] [LawfulMonad m] (f : α m (Option β)) (l : List α)
(i : Nat) (h) :
findSomeRevM?.find f l.toArray i h = (l.take i).reverse.findSomeM? f := by
induction i generalizing l with
| zero => simp [Array.findSomeRevM?.find.eq_def]
| succ i ih =>
rw [size_toArray] at h
rw [Array.findSomeRevM?.find, take_succ, getElem?_eq_getElem (by omega)]
simp only [ih, reverse_append]
congr
ext1 (_|_) <;> simp
-- This is not marked as `@[simp]` as later we simplify all occurrences of `findSomeRevM?`.
theorem findSomeRevM?_toArray [Monad m] [LawfulMonad m] (f : α m (Option β)) (l : List α) :
l.toArray.findSomeRevM? f = l.reverse.findSomeM? f := by
simp [Array.findSomeRevM?, findSomeRevM?_find_toArray]
-- This is not marked as `@[simp]` as later we simplify all occurrences of `findRevM?`.
theorem findRevM?_toArray [Monad m] [LawfulMonad m] (f : α m Bool) (l : List α) :
l.toArray.findRevM? f = l.reverse.findM? f := by
rw [Array.findRevM?, findSomeRevM?_toArray, findM?_eq_findSomeM?]
@[simp] theorem findM?_toArray [Monad m] [LawfulMonad m] (f : α m Bool) (l : List α) :
l.toArray.findM? f = l.findM? f := by
rw [Array.findM?]
simp only [bind_pure_comp, map_pure, forIn_toArray]
induction l with
| nil => simp
| cons a l ih =>
simp only [forIn_cons, LawfulMonad.bind_assoc, findM?]
congr
ext1 (_|_) <;> simp [ih]
@[simp] theorem findSome?_toArray (f : α Option β) (l : List α) :
l.toArray.findSome? f = l.findSome? f := by
rw [Array.findSome?, findSomeM?_id, findSomeM?_toArray, Id.run]
@[simp] theorem find?_toArray (f : α Bool) (l : List α) :
l.toArray.find? f = l.find? f := by
rw [Array.find?]
simp only [Id.run, Id, Id.pure_eq, Id.bind_eq, forIn_toArray]
induction l with
| nil => simp
| cons a l ih =>
simp only [forIn_cons, Id.pure_eq, Id.bind_eq, find?]
by_cases f a <;> simp_all
theorem isPrefixOfAux_toArray_succ [BEq α] (l₁ l₂ : List α) (hle : l₁.length l₂.length) (i : Nat) :
Array.isPrefixOfAux l₁.toArray l₂.toArray hle (i + 1) =
Array.isPrefixOfAux l₁.tail.toArray l₂.tail.toArray (by simp; omega) i := by
rw [Array.isPrefixOfAux]
conv => rhs; rw [Array.isPrefixOfAux]
simp only [size_toArray, getElem_toArray, Bool.if_false_right, length_tail, getElem_tail]
split <;> rename_i h₁ <;> split <;> rename_i h₂
· rw [isPrefixOfAux_toArray_succ]
· omega
· omega
· rfl
theorem isPrefixOfAux_toArray_succ' [BEq α] (l₁ l₂ : List α) (hle : l₁.length l₂.length) (i : Nat) :
Array.isPrefixOfAux l₁.toArray l₂.toArray hle (i + 1) =
Array.isPrefixOfAux (l₁.drop (i+1)).toArray (l₂.drop (i+1)).toArray (by simp; omega) 0 := by
induction i generalizing l₁ l₂ with
| zero => simp [isPrefixOfAux_toArray_succ]
| succ i ih =>
rw [isPrefixOfAux_toArray_succ, ih]
simp
theorem isPrefixOfAux_toArray_zero [BEq α] (l₁ l₂ : List α) (hle : l₁.length l₂.length) :
Array.isPrefixOfAux l₁.toArray l₂.toArray hle 0 =
l₁.isPrefixOf l₂ := by
rw [Array.isPrefixOfAux]
match l₁, l₂ with
| [], _ => rw [dif_neg] <;> simp
| _::_, [] => simp at hle
| a::l₁, b::l₂ =>
simp [isPrefixOf_cons₂, isPrefixOfAux_toArray_succ', isPrefixOfAux_toArray_zero]
@[simp] theorem isPrefixOf_toArray [BEq α] (l₁ l₂ : List α) :
l₁.toArray.isPrefixOf l₂.toArray = l₁.isPrefixOf l₂ := by
rw [Array.isPrefixOf]
split <;> rename_i h
· simp [isPrefixOfAux_toArray_zero]
· simp only [Bool.false_eq]
induction l₁ generalizing l₂ with
| nil => simp at h
| cons a l₁ ih =>
cases l₂ with
| nil => simp
| cons b l₂ =>
simp only [isPrefixOf_cons₂, Bool.and_eq_false_imp]
intro w
rw [ih]
simp_all
theorem zipWithAux_toArray_succ (as : List α) (bs : List β) (f : α β γ) (i : Nat) (cs : Array γ) :
zipWithAux as.toArray bs.toArray f (i + 1) cs = zipWithAux as.tail.toArray bs.tail.toArray f i cs := by
rw [zipWithAux]
conv => rhs; rw [zipWithAux]
simp only [size_toArray, getElem_toArray, length_tail, getElem_tail]
split <;> rename_i h₁
· split <;> rename_i h₂
· rw [dif_pos (by omega), dif_pos (by omega), zipWithAux_toArray_succ]
· rw [dif_pos (by omega)]
rw [dif_neg (by omega)]
· rw [dif_neg (by omega)]
theorem zipWithAux_toArray_succ' (as : List α) (bs : List β) (f : α β γ) (i : Nat) (cs : Array γ) :
zipWithAux as.toArray bs.toArray f (i + 1) cs = zipWithAux (as.drop (i+1)).toArray (bs.drop (i+1)).toArray f 0 cs := by
induction i generalizing as bs cs with
| zero => simp [zipWithAux_toArray_succ]
| succ i ih =>
rw [zipWithAux_toArray_succ, ih]
simp
theorem zipWithAux_toArray_zero (f : α β γ) (as : List α) (bs : List β) (cs : Array γ) :
zipWithAux as.toArray bs.toArray f 0 cs = cs ++ (List.zipWith f as bs).toArray := by
rw [Array.zipWithAux]
match as, bs with
| [], _ => simp
| _, [] => simp
| a :: as, b :: bs =>
simp [zipWith_cons_cons, zipWithAux_toArray_succ', zipWithAux_toArray_zero, push_append_toArray]
@[simp] theorem zipWith_toArray (as : List α) (bs : List β) (f : α β γ) :
Array.zipWith as.toArray bs.toArray f = (List.zipWith f as bs).toArray := by
rw [Array.zipWith]
simp [zipWithAux_toArray_zero]
@[simp] theorem zip_toArray (as : List α) (bs : List β) :
Array.zip as.toArray bs.toArray = (List.zip as bs).toArray := by
simp [Array.zip, zipWith_toArray, zip]
theorem zipWithAll_go_toArray (as : List α) (bs : List β) (f : Option α Option β γ) (i : Nat) (cs : Array γ) :
zipWithAll.go f as.toArray bs.toArray i cs = cs ++ (List.zipWithAll f (as.drop i) (bs.drop i)).toArray := by
unfold zipWithAll.go
split <;> rename_i h
· rw [zipWithAll_go_toArray]
simp at h
simp only [getElem?_toArray, push_append_toArray]
if ha : i < as.length then
if hb : i < bs.length then
rw [List.drop_eq_getElem_cons ha, List.drop_eq_getElem_cons hb]
simp only [ha, hb, getElem?_eq_getElem, zipWithAll_cons_cons]
else
simp only [Nat.not_lt] at hb
rw [List.drop_eq_getElem_cons ha]
rw [(drop_eq_nil_iff (l := bs)).mpr (by omega), (drop_eq_nil_iff (l := bs)).mpr (by omega)]
simp only [zipWithAll_nil, map_drop, map_cons]
rw [getElem?_eq_getElem ha]
rw [getElem?_eq_none hb]
else
if hb : i < bs.length then
simp only [Nat.not_lt] at ha
rw [List.drop_eq_getElem_cons hb]
rw [(drop_eq_nil_iff (l := as)).mpr (by omega), (drop_eq_nil_iff (l := as)).mpr (by omega)]
simp only [nil_zipWithAll, map_drop, map_cons]
rw [getElem?_eq_getElem hb]
rw [getElem?_eq_none ha]
else
omega
· simp only [size_toArray, Nat.not_lt] at h
rw [drop_eq_nil_of_le (by omega), drop_eq_nil_of_le (by omega)]
simp
termination_by max as.length bs.length - i
decreasing_by simp_wf; decreasing_trivial_pre_omega
@[simp] theorem zipWithAll_toArray (f : Option α Option β γ) (as : List α) (bs : List β) :
Array.zipWithAll as.toArray bs.toArray f = (List.zipWithAll f as bs).toArray := by
simp [Array.zipWithAll, zipWithAll_go_toArray]
@[simp] theorem toArray_appendList (l₁ l₂ : List α) :
l₁.toArray ++ l₂ = (l₁ ++ l₂).toArray := by
apply ext'
simp
@[simp] theorem pop_toArray (l : List α) : l.toArray.pop = l.dropLast.toArray := by
apply ext'
simp
theorem takeWhile_go_succ (p : α Bool) (a : α) (l : List α) (i : Nat) :
takeWhile.go p (a :: l).toArray (i+1) r = takeWhile.go p l.toArray i r := by
rw [takeWhile.go, takeWhile.go]
simp only [size_toArray, length_cons, Nat.add_lt_add_iff_right, Array.get_eq_getElem,
getElem_toArray, getElem_cons_succ]
split
rw [takeWhile_go_succ]
rfl
theorem takeWhile_go_toArray (p : α Bool) (l : List α) (i : Nat) :
Array.takeWhile.go p l.toArray i r = r ++ (takeWhile p (l.drop i)).toArray := by
induction l generalizing i r with
| nil => simp [takeWhile.go]
| cons a l ih =>
rw [takeWhile.go]
cases i with
| zero =>
simp [takeWhile_go_succ, ih, takeWhile_cons]
split <;> simp
| succ i =>
simp only [size_toArray, length_cons, Nat.add_lt_add_iff_right, Array.get_eq_getElem,
getElem_toArray, getElem_cons_succ, drop_succ_cons]
split <;> rename_i h₁
· rw [takeWhile_go_succ, ih]
rw [ getElem_cons_drop_succ_eq_drop h₁, takeWhile_cons]
split <;> simp_all
· simp_all [drop_eq_nil_of_le]
@[simp] theorem takeWhile_toArray (p : α Bool) (l : List α) :
l.toArray.takeWhile p = (l.takeWhile p).toArray := by
simp [Array.takeWhile, takeWhile_go_toArray]
end List
/-- Convert a `List α` into an `Array α`. This is O(n) in the length of the list. -/
-- This function is exported to C, where it is called by `Array.mk`
-- (the constructor) to implement this functionality.
@[inline, match_pattern, pp_nodot, export lean_list_to_array]
def List.toArrayImpl (as : List α) : Array α :=
as.toArrayAux (Array.mkEmpty as.length)

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@@ -1,23 +0,0 @@
/-
Copyright (c) 2024 Lean FRO. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henrik Böving
-/
prelude
import Init.Data.List.Basic
/--
Auxiliary definition for `List.toArray`.
`List.toArrayAux as r = r ++ as.toArray`
-/
@[inline_if_reduce]
def List.toArrayAux : List α Array α Array α
| nil, r => r
| cons a as, r => toArrayAux as (r.push a)
/-- Convert a `List α` into an `Array α`. This is O(n) in the length of the list. -/
-- This function is exported to C, where it is called by `Array.mk`
-- (the constructor) to implement this functionality.
@[inline, match_pattern, pp_nodot, export lean_list_to_array]
def List.toArrayImpl (as : List α) : Array α :=
as.toArrayAux (Array.mkEmpty as.length)

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@@ -71,9 +71,6 @@ theorem shiftRight_eq_div_pow (m : Nat) : ∀ n, m >>> n = m / 2 ^ n
rw [shiftRight_add, shiftRight_eq_div_pow m k]
simp [Nat.div_div_eq_div_mul, Nat.pow_succ, shiftRight_succ]
theorem shiftRight_eq_zero (m n : Nat) (hn : m < 2^n) : m >>> n = 0 := by
simp [Nat.shiftRight_eq_div_pow, Nat.div_eq_of_lt hn]
/-!
### testBit
We define an operation for testing individual bits in the binary representation

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@@ -39,9 +39,9 @@ protected theorem dvd_add_iff_right {k m n : Nat} (h : k m) : k n ↔ k
protected theorem dvd_add_iff_left {k m n : Nat} (h : k n) : k m k m + n := by
rw [Nat.add_comm]; exact Nat.dvd_add_iff_right h
theorem dvd_mod_iff {k m n : Nat} (h: k n) : k m % n k m := by
have := Nat.dvd_add_iff_left (m := m % n) <| Nat.dvd_trans h <| Nat.dvd_mul_right n (m / n)
rwa [mod_add_div] at this
theorem dvd_mod_iff {k m n : Nat} (h: k n) : k m % n k m :=
have := Nat.dvd_add_iff_left <| Nat.dvd_trans h <| Nat.dvd_mul_right n (m / n)
by rwa [mod_add_div] at this
theorem le_of_dvd {m n : Nat} (h : 0 < n) : m n m n
| k, e => by

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@@ -1046,25 +1046,6 @@ instance decidableExistsLE [DecidablePred p] : DecidablePred fun n => ∃ m : Na
fun n => decidable_of_iff ( m, m < n + 1 p m)
(exists_congr fun _ => and_congr_left' Nat.lt_succ_iff)
/-- Dependent version of `decidableExistsLT`. -/
instance decidableExistsLT' {p : (m : Nat) m < k Prop} [I : m h, Decidable (p m h)] :
Decidable ( m : Nat, h : m < k, p m h) :=
match k, p, I with
| 0, _, _ => isFalse (by simp)
| (k + 1), p, I => @decidable_of_iff _ (( m, h : m < k, p m (by omega)) p k (by omega))
by rintro (m, h, w | w); exact m, by omega, w; exact k, by omega, w,
fun m, h, w => if h' : m < k then .inl m, h', w else
by obtain rfl := (by omega : m = k); exact .inr w
(@instDecidableOr _ _
(decidableExistsLT' (p := fun m h => p m (by omega)) (I := fun m h => I m (by omega)))
inferInstance)
/-- Dependent version of `decidableExistsLE`. -/
instance decidableExistsLE' {p : (m : Nat) m k Prop} [I : m h, Decidable (p m h)] :
Decidable ( m : Nat, h : m k, p m h) :=
decidable_of_iff ( m, h : m < k + 1, p m (by omega)) (exists_congr fun _ =>
fun h, w => le_of_lt_succ h, w, fun h, w => lt_add_one_of_le h, w)
/-! ### Results about `List.sum` specialized to `Nat` -/
protected theorem sum_pos_iff_exists_pos {l : List Nat} : 0 < l.sum x l, 0 < x := by

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@@ -10,4 +10,3 @@ import Init.Data.Option.Instances
import Init.Data.Option.Lemmas
import Init.Data.Option.Attach
import Init.Data.Option.List
import Init.Data.Option.Monadic

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@@ -119,14 +119,10 @@ theorem attachWith_map_subtype_val {p : α → Prop} (o : Option α) (H : ∀ a
· simp at h
· simp [get_some]
theorem toList_attach (o : Option α) :
@[simp] theorem toList_attach (o : Option α) :
o.attach.toList = o.toList.attach.map fun x, h => x, by simpa using h := by
cases o <;> simp
@[simp] theorem attach_toList (o : Option α) :
o.toList.attach = (o.attach.map fun a, h => a, by simpa using h).toList := by
cases o <;> simp
theorem attach_map {o : Option α} (f : α β) :
(o.map f).attach = o.attach.map (fun x, h => f x, mem_map_of_mem f h) := by
cases o <;> simp

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@@ -70,13 +70,6 @@ satisfy `p`, using the proof to apply `f`.
| none, _ => none
| some a, H => f a (H a rfl)
/-- Partial elimination. If `o : Option α` and `f : (a : α) → a ∈ o → β`, then `o.pelim b f` is
the same as `o.elim b f` but `f` is passed the proof that `a ∈ o`. -/
@[inline] def pelim (o : Option α) (b : β) (f : (a : α) a o β) : β :=
match o with
| none => b
| some a => f a rfl
/-- Map a monadic function which returns `Unit` over an `Option`. -/
@[inline] protected def forM [Pure m] : Option α (α m PUnit) m PUnit
| none , _ => pure

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@@ -629,12 +629,4 @@ theorem pbind_eq_some_iff {o : Option α} {f : (a : α) → a ∈ o → Option
· rintro h, rfl
rfl
/-! ### pelim -/
@[simp] theorem pelim_none : pelim none b f = b := rfl
@[simp] theorem pelim_some : pelim (some a) b f = f a rfl := rfl
@[simp] theorem pelim_eq_elim : pelim o b (fun a _ => f a) = o.elim b f := by
cases o <;> simp
end Option

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@@ -15,25 +15,17 @@ namespace Option
forIn' none b f = pure b := by
rfl
@[simp] theorem forIn'_some [Monad m] [LawfulMonad m] (a : α) (b : β) (f : (a' : α) a' some a β m (ForInStep β)) :
forIn' (some a) b f = bind (f a rfl b) (fun r => pure (ForInStep.value r)) := by
simp only [forIn', bind_pure_comp]
rw [map_eq_pure_bind]
congr
funext x
split <;> rfl
@[simp] theorem forIn'_some [Monad m] (a : α) (b : β) (f : (a' : α) a' some a β m (ForInStep β)) :
forIn' (some a) b f = bind (f a rfl b) (fun | .done r | .yield r => pure r) := by
rfl
@[simp] theorem forIn_none [Monad m] (b : β) (f : α β m (ForInStep β)) :
forIn none b f = pure b := by
rfl
@[simp] theorem forIn_some [Monad m] [LawfulMonad m] (a : α) (b : β) (f : α β m (ForInStep β)) :
forIn (some a) b f = bind (f a b) (fun r => pure (ForInStep.value r)) := by
simp only [forIn, forIn', bind_pure_comp]
rw [map_eq_pure_bind]
congr
funext x
split <;> rfl
@[simp] theorem forIn_some [Monad m] (a : α) (b : β) (f : α β m (ForInStep β)) :
forIn (some a) b f = bind (f a b) (fun | .done r | .yield r => pure r) := by
rfl
@[simp] theorem forIn'_toList [Monad m] (o : Option α) (b : β) (f : (a : α) a o.toList β m (ForInStep β)) :
forIn' o.toList b f = forIn' o b fun a m b => f a (by simpa using m) b := by
@@ -43,20 +35,4 @@ namespace Option
forIn o.toList b f = forIn o b f := by
cases o <;> rfl
@[simp] theorem foldlM_toList [Monad m] [LawfulMonad m] (o : Option β) (a : α) (f : α β m α) :
o.toList.foldlM f a = o.elim (pure a) (fun b => f a b) := by
cases o <;> simp
@[simp] theorem foldrM_toList [Monad m] [LawfulMonad m] (o : Option β) (a : α) (f : β α m α) :
o.toList.foldrM f a = o.elim (pure a) (fun b => f b a) := by
cases o <;> simp
@[simp] theorem foldl_toList (o : Option β) (a : α) (f : α β α) :
o.toList.foldl f a = o.elim a (fun b => f a b) := by
cases o <;> simp
@[simp] theorem foldr_toList (o : Option β) (a : α) (f : β α α) :
o.toList.foldr f a = o.elim a (fun b => f b a) := by
cases o <;> simp
end Option

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@@ -1,75 +0,0 @@
/-
Copyright (c) 2024 Lean FRO. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
prelude
import Init.Data.Option.Attach
import Init.Control.Lawful.Basic
namespace Option
@[congr] theorem forIn'_congr [Monad m] [LawfulMonad m]{as bs : Option α} (w : as = bs)
{b b' : β} (hb : b = b')
{f : (a' : α) a' as β m (ForInStep β)}
{g : (a' : α) a' bs β m (ForInStep β)}
(h : a m b, f a (by simpa [w] using m) b = g a m b) :
forIn' as b f = forIn' bs b' g := by
cases as <;> cases bs
· simp [hb]
· simp at w
· simp at w
· simp only [some.injEq] at w
subst w
simp [hb, h]
theorem forIn'_eq_pelim [Monad m] [LawfulMonad m]
(o : Option α) (f : (a : α) a o β m (ForInStep β)) (b : β) :
forIn' o b f =
o.pelim (pure b) (fun a h => ForInStep.value <$> f a h b) := by
cases o <;> simp
@[simp] theorem forIn'_yield_eq_pelim [Monad m] [LawfulMonad m] (o : Option α)
(f : (a : α) a o β m γ) (g : (a : α) a o β γ β) (b : β) :
forIn' o b (fun a m b => (fun c => .yield (g a m b c)) <$> f a m b) =
o.pelim (pure b) (fun a h => g a h b <$> f a h b) := by
cases o <;> simp
theorem forIn'_pure_yield_eq_pelim [Monad m] [LawfulMonad m]
(o : Option α) (f : (a : α) a o β β) (b : β) :
forIn' o b (fun a m b => pure (.yield (f a m b))) =
pure (f := m) (o.pelim b (fun a h => f a h b)) := by
cases o <;> simp
@[simp] theorem forIn'_id_yield_eq_pelim
(o : Option α) (f : (a : α) a o β β) (b : β) :
forIn' (m := Id) o b (fun a m b => .yield (f a m b)) =
o.pelim b (fun a h => f a h b) := by
cases o <;> simp
theorem forIn_eq_elim [Monad m] [LawfulMonad m]
(o : Option α) (f : (a : α) β m (ForInStep β)) (b : β) :
forIn o b f =
o.elim (pure b) (fun a => ForInStep.value <$> f a b) := by
cases o <;> simp
@[simp] theorem forIn_yield_eq_elim [Monad m] [LawfulMonad m] (o : Option α)
(f : (a : α) β m γ) (g : (a : α) β γ β) (b : β) :
forIn o b (fun a b => (fun c => .yield (g a b c)) <$> f a b) =
o.elim (pure b) (fun a => g a b <$> f a b) := by
cases o <;> simp
theorem forIn_pure_yield_eq_elim [Monad m] [LawfulMonad m]
(o : Option α) (f : (a : α) β β) (b : β) :
forIn o b (fun a b => pure (.yield (f a b))) =
pure (f := m) (o.elim b (fun a => f a b)) := by
cases o <;> simp
@[simp] theorem forIn_id_yield_eq_elim
(o : Option α) (f : (a : α) β β) (b : β) :
forIn (m := Id) o b (fun a b => .yield (f a b)) =
o.elim b (fun a => f a b) := by
cases o <;> simp
end Option

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@@ -1,39 +1,25 @@
/-
Copyright (c) 2024 Lean FRO, LLC. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Mac Malone
Authors: Markus Himmel
-/
prelude
import Init.Data.UInt.Lemmas
import Init.Data.UInt.Basic
import Init.Data.Fin.Bitwise
import Init.Data.BitVec.Lemmas
set_option hygiene false in
macro "declare_bitwise_uint_theorems" typeName:ident bits:term:arg : command =>
macro "declare_bitwise_uint_theorems" typeName:ident : command =>
`(
namespace $typeName
@[simp] protected theorem toBitVec_and (a b : $typeName) : (a &&& b).toBitVec = a.toBitVec &&& b.toBitVec := rfl
@[simp] protected theorem toBitVec_or (a b : $typeName) : (a ||| b).toBitVec = a.toBitVec ||| b.toBitVec := rfl
@[simp] protected theorem toBitVec_xor (a b : $typeName) : (a ^^^ b).toBitVec = a.toBitVec ^^^ b.toBitVec := rfl
@[simp] protected theorem toBitVec_shiftLeft (a b : $typeName) : (a <<< b).toBitVec = a.toBitVec <<< (b.toBitVec % $bits) := rfl
@[simp] protected theorem toBitVec_shiftRight (a b : $typeName) : (a >>> b).toBitVec = a.toBitVec >>> (b.toBitVec % $bits) := rfl
@[simp] protected theorem toNat_and (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := by simp [toNat]
@[simp] protected theorem toNat_or (a b : $typeName) : (a ||| b).toNat = a.toNat ||| b.toNat := by simp [toNat]
@[simp] protected theorem toNat_xor (a b : $typeName) : (a ^^^ b).toNat = a.toNat ^^^ b.toNat := by simp [toNat]
@[simp] protected theorem toNat_shiftLeft (a b : $typeName) : (a <<< b).toNat = a.toNat <<< (b.toNat % $bits) % 2 ^ $bits := by simp [toNat]
@[simp] protected theorem toNat_shiftRight (a b : $typeName) : (a >>> b).toNat = a.toNat >>> (b.toNat % $bits) := by simp [toNat]
open $typeName (toNat_and) in
@[deprecated toNat_and (since := "2024-11-28")]
protected theorem and_toNat (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := BitVec.toNat_and ..
@[simp] protected theorem and_toNat (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := BitVec.toNat_and ..
end $typeName
)
declare_bitwise_uint_theorems UInt8 8
declare_bitwise_uint_theorems UInt16 16
declare_bitwise_uint_theorems UInt32 32
declare_bitwise_uint_theorems UInt64 64
declare_bitwise_uint_theorems USize System.Platform.numBits
declare_bitwise_uint_theorems UInt8
declare_bitwise_uint_theorems UInt16
declare_bitwise_uint_theorems UInt32
declare_bitwise_uint_theorems UInt64
declare_bitwise_uint_theorems USize

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@@ -11,15 +11,6 @@ import Init.Data.Vector.Basic
Lemmas about `Vector α n`
-/
namespace Array
theorem toVector_inj {a b : Array α} (h₁ : a.size = b.size) (h₂ : a.toVector.cast h₁ = b.toVector) : a = b := by
ext i ih₁ ih₂
· exact h₁
· simpa using congrArg (fun a => a[i]) h₂
end Array
namespace Vector
@[simp] theorem getElem_mk {data : Array α} {size : data.size = n} {i : Nat} (h : i < n) :
@@ -124,9 +115,6 @@ theorem toArray_mk (a : Array α) (h : a.size = n) : (Vector.mk a h).toArray = a
(Vector.mk a h).eraseIdx! i = Vector.mk (a.eraseIdx i) (by simp [h, hi]) := by
simp [Vector.eraseIdx!, hi]
@[simp] theorem cast_mk (a : Array α) (h : a.size = n) (h' : n = m) :
(Vector.mk a h).cast h' = Vector.mk a (by simp [h, h']) := rfl
@[simp] theorem extract_mk (a : Array α) (h : a.size = n) (start stop) :
(Vector.mk a h).extract start stop = Vector.mk (a.extract start stop) (by simp [h]) := rfl
@@ -197,9 +185,6 @@ theorem toArray_mk (a : Array α) (h : a.size = n) : (Vector.mk a h).toArray = a
(a.eraseIdx! i).toArray = a.toArray.eraseIdx! i := by
cases a; simp_all [Array.eraseIdx!]
@[simp] theorem toArray_cast (a : Vector α n) (h : n = m) :
(a.cast h).toArray = a.toArray := rfl
@[simp] theorem toArray_extract (a : Vector α n) (start stop) :
(a.extract start stop).toArray = a.toArray.extract start stop := rfl
@@ -254,137 +239,6 @@ theorem length_toList {α n} (xs : Vector α n) : xs.toList.length = n := by sim
theorem getElem_toList {α n} (xs : Vector α n) (i : Nat) (h : i < xs.toList.length) :
xs.toList[i] = xs[i]'(by simpa using h) := by simp
theorem toList_inj {a b : Vector α n} (h : a.toList = b.toList) : a = b := by
rcases a with a, ha
rcases b with b, hb
simpa using h
/-! ### set -/
theorem getElem_set (a : Vector α n) (i : Nat) (x : α) (hi : i < n) (j : Nat) (hj : j < n) :
(a.set i x hi)[j] = if i = j then x else a[j] := by
cases a
split <;> simp_all [Array.getElem_set]
@[simp] theorem getElem_set_eq (a : Vector α n) (i : Nat) (x : α) (hi : i < n) :
(a.set i x hi)[i] = x := by simp [getElem_set]
@[simp] theorem getElem_set_ne (a : Vector α n) (i : Nat) (x : α) (hi : i < n) (j : Nat)
(hj : j < n) (h : i j) : (a.set i x hi)[j] = a[j] := by simp [getElem_set, h]
/-! ### setIfInBounds -/
theorem getElem_setIfInBounds (a : Vector α n) (i : Nat) (x : α) (j : Nat)
(hj : j < n) : (a.setIfInBounds i x)[j] = if i = j then x else a[j] := by
cases a
split <;> simp_all [Array.getElem_setIfInBounds]
@[simp] theorem getElem_setIfInBounds_eq (a : Vector α n) (i : Nat) (x : α) (hj : i < n) :
(a.setIfInBounds i x)[i] = x := by simp [getElem_setIfInBounds]
@[simp] theorem getElem_setIfInBounds_ne (a : Vector α n) (i : Nat) (x : α) (j : Nat)
(hj : j < n) (h : i j) : (a.setIfInBounds i x)[j] = a[j] := by simp [getElem_setIfInBounds, h]
/-! ### append -/
theorem getElem_append (a : Vector α n) (b : Vector α m) (i : Nat) (hi : i < n + m) :
(a ++ b)[i] = if h : i < n then a[i] else b[i - n] := by
rcases a with a, rfl
rcases b with b, rfl
simp [Array.getElem_append, hi]
theorem getElem_append_left {a : Vector α n} {b : Vector α m} {i : Nat} (hi : i < n) :
(a ++ b)[i] = a[i] := by simp [getElem_append, hi]
theorem getElem_append_right {a : Vector α n} {b : Vector α m} {i : Nat} (h : i < n + m) (hi : n i) :
(a ++ b)[i] = b[i - n] := by
rw [getElem_append, dif_neg (by omega)]
/-! ### cast -/
@[simp] theorem getElem_cast (a : Vector α n) (h : n = m) (i : Nat) (hi : i < m) :
(a.cast h)[i] = a[i] := by
cases a
simp
/-! ### extract -/
@[simp] theorem getElem_extract (a : Vector α n) (start stop) (i : Nat) (hi : i < min stop n - start) :
(a.extract start stop)[i] = a[start + i] := by
cases a
simp
/-! ### map -/
@[simp] theorem getElem_map (f : α β) (a : Vector α n) (i : Nat) (hi : i < n) :
(a.map f)[i] = f a[i] := by
cases a
simp
/-! ### zipWith -/
@[simp] theorem getElem_zipWith (f : α β γ) (a : Vector α n) (b : Vector β n) (i : Nat)
(hi : i < n) : (zipWith a b f)[i] = f a[i] b[i] := by
cases a
cases b
simp
/-! ### swap -/
theorem getElem_swap (a : Vector α n) (i j : Nat) {hi hj} (k : Nat) (hk : k < n) :
(a.swap i j hi hj)[k] = if k = i then a[j] else if k = j then a[i] else a[k] := by
cases a
simp_all [Array.getElem_swap]
@[simp] theorem getElem_swap_right (a : Vector α n) {i j : Nat} {hi hj} :
(a.swap i j hi hj)[j]'(by simpa using hj) = a[i] := by
simp +contextual [getElem_swap]
@[simp] theorem getElem_swap_left (a : Vector α n) {i j : Nat} {hi hj} :
(a.swap i j hi hj)[i]'(by simpa using hi) = a[j] := by
simp [getElem_swap]
@[simp] theorem getElem_swap_of_ne (a : Vector α n) {i j : Nat} {hi hj} (hp : p < n)
(hi' : p i) (hj' : p j) : (a.swap i j hi hj)[p] = a[p] := by
simp_all [getElem_swap]
@[simp] theorem swap_swap (a : Vector α n) {i j : Nat} {hi hj} :
(a.swap i j hi hj).swap i j hi hj = a := by
cases a
simp_all [Array.swap_swap]
theorem swap_comm (a : Vector α n) {i j : Nat} {hi hj} :
a.swap i j hi hj = a.swap j i hj hi := by
cases a
simp only [swap_mk, mk.injEq]
rw [Array.swap_comm]
/-! ### range -/
@[simp] theorem getElem_range (i : Nat) (hi : i < n) : (Vector.range n)[i] = i := by
simp [Vector.range]
/-! ### take -/
@[simp] theorem getElem_take (a : Vector α n) (m : Nat) (hi : i < min n m) :
(a.take m)[i] = a[i] := by
cases a
simp
/-! ### drop -/
@[simp] theorem getElem_drop (a : Vector α n) (m : Nat) (hi : i < n - m) :
(a.drop m)[i] = a[m + i] := by
cases a
simp
/-! ### reverse -/
@[simp] theorem getElem_reverse (a : Vector α n) (i : Nat) (hi : i < n) :
(a.reverse)[i] = a[n - 1 - i] := by
rcases a with a, rfl
simp
/-! ### Decidable quantifiers. -/
theorem forall_zero_iff {P : Vector α 0 Prop} :

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@@ -118,16 +118,12 @@ instance (priority := low) [GetElem coll idx elem valid] [∀ xs i, Decidable (v
GetElem? coll idx elem valid where
getElem? xs i := decidableGetElem? xs i
theorem getElem_congr [GetElem coll idx elem valid] {c d : coll} (h : c = d)
{i j : idx} (h' : i = j) (w : valid c i) : c[i] = d[j]'(h' h w) := by
cases h; cases h'; rfl
theorem getElem_congr_coll [GetElem coll idx elem valid] {c d : coll} {i : idx} {h : valid c i}
(h' : c = d) : c[i] = d[i]'(h' h) := by
cases h'; rfl
theorem getElem_congr_coll [GetElem coll idx elem valid] {c d : coll} {i : idx} {w : valid c i}
(h : c = d) : c[i] = d[i]'(h w) := by
cases h; rfl
theorem getElem_congr_idx [GetElem coll idx elem valid] {c : coll} {i j : idx} {w : valid c i}
(h' : i = j) : c[i] = c[j]'(h' w) := by
theorem getElem_congr [GetElem coll idx elem valid] {c : coll} {i j : idx} {h : valid c i}
(h' : i = j) : c[i] = c[j]'(h' h) := by
cases h'; rfl
class LawfulGetElem (cont : Type u) (idx : Type v) (elem : outParam (Type w))
@@ -220,9 +216,13 @@ instance : GetElem (List α) Nat α fun as i => i < as.length where
@[simp] theorem getElem_cons_zero (a : α) (as : List α) (h : 0 < (a :: as).length) : getElem (a :: as) 0 h = a := by
rfl
@[deprecated getElem_cons_zero (since := "2024-06-12")] abbrev cons_getElem_zero := @getElem_cons_zero
@[simp] theorem getElem_cons_succ (a : α) (as : List α) (i : Nat) (h : i + 1 < (a :: as).length) : getElem (a :: as) (i+1) h = getElem as i (Nat.lt_of_succ_lt_succ h) := by
rfl
@[deprecated getElem_cons_succ (since := "2024-06-12")] abbrev cons_getElem_succ := @getElem_cons_succ
@[simp] theorem getElem_mem : {l : List α} {n} (h : n < l.length), l[n]'h l
| _ :: _, 0, _ => .head ..
| _ :: l, _+1, _ => .tail _ (getElem_mem (l := l) ..)
@@ -231,7 +231,7 @@ theorem getElem_cons_drop_succ_eq_drop {as : List α} {i : Nat} (h : i < as.leng
as[i] :: as.drop (i+1) = as.drop i :=
match as, i with
| _::_, 0 => rfl
| _::_, i+1 => getElem_cons_drop_succ_eq_drop (i := i) (Nat.add_one_lt_add_one_iff.mp h)
| _::_, i+1 => getElem_cons_drop_succ_eq_drop (i := i) _
@[deprecated getElem_cons_drop_succ_eq_drop (since := "2024-11-05")]
abbrev get_drop_eq_drop := @getElem_cons_drop_succ_eq_drop
@@ -243,12 +243,6 @@ namespace Array
instance : GetElem (Array α) Nat α fun xs i => i < xs.size where
getElem xs i h := xs.get i h
@[simp] theorem get_eq_getElem (a : Array α) (i : Nat) (h) : a.get i h = a[i] := rfl
@[simp] theorem get!_eq_getElem! [Inhabited α] (a : Array α) (i : Nat) : a.get! i = a[i]! := by
simp only [get!, getD, get_eq_getElem, getElem!_def]
split <;> simp_all [getElem?_pos, getElem?_neg]
end Array
namespace Lean.Syntax

View File

@@ -679,7 +679,6 @@ private partial def decodeBinLitAux (s : String) (i : String.Pos) (val : Nat) :
let c := s.get i
if c == '0' then decodeBinLitAux s (s.next i) (2*val)
else if c == '1' then decodeBinLitAux s (s.next i) (2*val + 1)
else if c == '_' then decodeBinLitAux s (s.next i) val
else none
private partial def decodeOctalLitAux (s : String) (i : String.Pos) (val : Nat) : Option Nat :=
@@ -687,7 +686,6 @@ private partial def decodeOctalLitAux (s : String) (i : String.Pos) (val : Nat)
else
let c := s.get i
if '0' c && c '7' then decodeOctalLitAux s (s.next i) (8*val + c.toNat - '0'.toNat)
else if c == '_' then decodeOctalLitAux s (s.next i) val
else none
private def decodeHexDigit (s : String) (i : String.Pos) : Option (Nat × String.Pos) :=
@@ -702,16 +700,13 @@ private partial def decodeHexLitAux (s : String) (i : String.Pos) (val : Nat) :
if s.atEnd i then some val
else match decodeHexDigit s i with
| some (d, i) => decodeHexLitAux s i (16*val + d)
| none =>
if s.get i == '_' then decodeHexLitAux s (s.next i) val
else none
| none => none
private partial def decodeDecimalLitAux (s : String) (i : String.Pos) (val : Nat) : Option Nat :=
if s.atEnd i then some val
else
let c := s.get i
if '0' c && c '9' then decodeDecimalLitAux s (s.next i) (10*val + c.toNat - '0'.toNat)
else if c == '_' then decodeDecimalLitAux s (s.next i) val
else none
def decodeNatLitVal? (s : String) : Option Nat :=
@@ -778,8 +773,6 @@ where
let c := s.get i
if '0' c && c '9' then
decodeAfterExp (s.next i) val e sign (10*exp + c.toNat - '0'.toNat)
else if c == '_' then
decodeAfterExp (s.next i) val e sign exp
else
none
@@ -800,8 +793,6 @@ where
let c := s.get i
if '0' c && c '9' then
decodeAfterDot (s.next i) (10*val + c.toNat - '0'.toNat) (e+1)
else if c == '_' then
decodeAfterDot (s.next i) val e
else if c == 'e' || c == 'E' then
decodeExp (s.next i) val e
else
@@ -814,8 +805,6 @@ where
let c := s.get i
if '0' c && c '9' then
decode (s.next i) (10*val + c.toNat - '0'.toNat)
else if c == '_' then
decode (s.next i) val
else if c == '.' then
decodeAfterDot (s.next i) val 0
else if c == 'e' || c == 'E' then

View File

@@ -250,13 +250,6 @@ def neutralConfig : Simp.Config := {
zetaDelta := false
}
structure NormCastConfig extends Simp.Config where
zeta := false
beta := false
eta := false
proj := false
iota := false
end Simp
/-- Configuration for which occurrences that match an expression should be rewritten. -/

View File

@@ -386,15 +386,6 @@ theorem exists_comm {p : α → β → Prop} : (∃ a b, p a b) ↔ (∃ b a, p
theorem forall_prop_of_false {p : Prop} {q : p Prop} (hn : ¬p) : ( h' : p, q h') True :=
iff_true_intro fun h => hn.elim h
@[simp] theorem and_exists_self (P : Prop) (Q : P Prop) : (P p, Q p) p, Q p :=
fun _, h => h, fun p, q => p, p, q
@[simp] theorem exists_and_self (P : Prop) (Q : P Prop) : (( p, Q p) P) p, Q p :=
fun h, _ => h, fun p, q => p, q, p
@[simp] theorem forall_self_imp (P : Prop) (Q : P Prop) : ( p : P, P Q p) p, Q p :=
fun h p => h p p, fun h _ p => h p
end quantifiers
/-! ## membership -/

View File

@@ -981,14 +981,3 @@ not used concurrently or which are already persistent.
-/
@[extern "lean_runtime_mark_persistent"]
unsafe def Runtime.markPersistent (a : α) : BaseIO α := return a
set_option linter.unusedVariables false in
/--
Discards the passed owned reference. This leads to `a` any any object reachable from it never being
freed. This can be a useful optimization for eliding deallocation time of big object graphs that are
kept alive close to the end of the process anyway (in which case calling `Runtime.markPersistent`
would be similarly costly to deallocation). It is still considered a safe operation as it cannot
lead to undefined behavior.
-/
@[extern "lean_runtime_forget"]
def Runtime.forget (a : α) : BaseIO Unit := return

View File

@@ -7,9 +7,6 @@ prelude
import Init.System.IO
import Init.Control.StateRef
set_option linter.deprecated false
namespace IO
private opaque BaseMutexImpl : NonemptyType.{0}
@@ -19,13 +16,12 @@ Mutual exclusion primitive (a lock).
If you want to guard shared state, use `Mutex α` instead.
-/
@[deprecated "Use Std.BaseMutex from Std.Sync.Mutex instead" (since := "2024-12-02")]
def BaseMutex : Type := BaseMutexImpl.type
instance : Nonempty BaseMutex := BaseMutexImpl.property
/-- Creates a new `BaseMutex`. -/
@[extern "lean_io_basemutex_new", deprecated "Use Std.BaseMutex.new from Std.Sync.Mutex instead" (since := "2024-12-02")]
@[extern "lean_io_basemutex_new"]
opaque BaseMutex.new : BaseIO BaseMutex
/--
@@ -34,7 +30,7 @@ Locks a `BaseMutex`. Waits until no other thread has locked the mutex.
The current thread must not have already locked the mutex.
Reentrant locking is undefined behavior (inherited from the C++ implementation).
-/
@[extern "lean_io_basemutex_lock", deprecated "Use Std.BaseMutex.lock from Std.Sync.Mutex instead" (since := "2024-12-02")]
@[extern "lean_io_basemutex_lock"]
opaque BaseMutex.lock (mutex : @& BaseMutex) : BaseIO Unit
/--
@@ -43,35 +39,33 @@ Unlocks a `BaseMutex`.
The current thread must have already locked the mutex.
Unlocking an unlocked mutex is undefined behavior (inherited from the C++ implementation).
-/
@[extern "lean_io_basemutex_unlock", deprecated "Use Std.BaseMutex.unlock from Std.Sync.Mutex instead" (since := "2024-12-02")]
@[extern "lean_io_basemutex_unlock"]
opaque BaseMutex.unlock (mutex : @& BaseMutex) : BaseIO Unit
private opaque CondvarImpl : NonemptyType.{0}
/-- Condition variable. -/
@[deprecated "Use Std.Condvar from Std.Sync.Mutex instead" (since := "2024-12-02")]
def Condvar : Type := CondvarImpl.type
instance : Nonempty Condvar := CondvarImpl.property
/-- Creates a new condition variable. -/
@[extern "lean_io_condvar_new", deprecated "Use Std.Condvar.new from Std.Sync.Mutex instead" (since := "2024-12-02")]
@[extern "lean_io_condvar_new"]
opaque Condvar.new : BaseIO Condvar
/-- Waits until another thread calls `notifyOne` or `notifyAll`. -/
@[extern "lean_io_condvar_wait", deprecated "Use Std.Condvar.wait from Std.Sync.Mutex instead" (since := "2024-12-02")]
@[extern "lean_io_condvar_wait"]
opaque Condvar.wait (condvar : @& Condvar) (mutex : @& BaseMutex) : BaseIO Unit
/-- Wakes up a single other thread executing `wait`. -/
@[extern "lean_io_condvar_notify_one", deprecated "Use Std.Condvar.notifyOne from Std.Sync.Mutex instead" (since := "2024-12-02")]
@[extern "lean_io_condvar_notify_one"]
opaque Condvar.notifyOne (condvar : @& Condvar) : BaseIO Unit
/-- Wakes up all other threads executing `wait`. -/
@[extern "lean_io_condvar_notify_all", deprecated "Use Std.Condvar.notifyAll from Std.Sync.Mutex instead" (since := "2024-12-02")]
@[extern "lean_io_condvar_notify_all"]
opaque Condvar.notifyAll (condvar : @& Condvar) : BaseIO Unit
/-- Waits on the condition variable until the predicate is true. -/
@[deprecated "Use Std.Condvar.waitUntil from Std.Sync.Mutex instead" (since := "2024-12-02")]
def Condvar.waitUntil [Monad m] [MonadLift BaseIO m]
(condvar : Condvar) (mutex : BaseMutex) (pred : m Bool) : m Unit := do
while !( pred) do
@@ -84,7 +78,6 @@ The type `Mutex α` is similar to `IO.Ref α`,
except that concurrent accesses are guarded by a mutex
instead of atomic pointer operations and busy-waiting.
-/
@[deprecated "Use Std.Mutex from Std.Sync.Mutex instead" (since := "2024-12-02")]
structure Mutex (α : Type) where private mk ::
private ref : IO.Ref α
mutex : BaseMutex
@@ -93,7 +86,6 @@ structure Mutex (α : Type) where private mk ::
instance : CoeOut (Mutex α) BaseMutex where coe := Mutex.mutex
/-- Creates a new mutex. -/
@[deprecated "Use Std.Mutex.new from Std.Sync.Mutex instead" (since := "2024-12-02")]
def Mutex.new (a : α) : BaseIO (Mutex α) :=
return { ref := mkRef a, mutex := BaseMutex.new }
@@ -102,11 +94,9 @@ def Mutex.new (a : α) : BaseIO (Mutex α) :=
with outside monad `m`.
The action has access to the state `α` of the mutex (via `get` and `set`).
-/
@[deprecated "Use Std.AtomicT from Std.Sync.Mutex instead" (since := "2024-12-02")]
abbrev AtomicT := StateRefT' IO.RealWorld
/-- `mutex.atomically k` runs `k` with access to the mutex's state while locking the mutex. -/
@[deprecated "Use Std.Mutex.atomically from Std.Sync.Mutex instead" (since := "2024-12-02")]
def Mutex.atomically [Monad m] [MonadLiftT BaseIO m] [MonadFinally m]
(mutex : Mutex α) (k : AtomicT α m β) : m β := do
try
@@ -120,7 +110,6 @@ def Mutex.atomically [Monad m] [MonadLiftT BaseIO m] [MonadFinally m]
waiting on `condvar` until `pred` returns true.
Both `k` and `pred` have access to the mutex's state.
-/
@[deprecated "Use Std.Mutex.atomicallyOnce from Std.Sync.Mutex instead" (since := "2024-12-02")]
def Mutex.atomicallyOnce [Monad m] [MonadLiftT BaseIO m] [MonadFinally m]
(mutex : Mutex α) (condvar : Condvar)
(pred : AtomicT α m Bool) (k : AtomicT α m β) : m β :=

View File

@@ -1309,7 +1309,7 @@ macro "bv_omega" : tactic => `(tactic| (try simp only [bv_toNat] at *) <;> omega
syntax (name := acNf0) "ac_nf0" (location)? : tactic
/-- Implementation of `norm_cast` (the full `norm_cast` calls `trivial` afterwards). -/
syntax (name := normCast0) "norm_cast0" optConfig (location)? : tactic
syntax (name := normCast0) "norm_cast0" (location)? : tactic
/-- `assumption_mod_cast` is a variant of `assumption` that solves the goal
using a hypothesis. Unlike `assumption`, it first pre-processes the goal and
@@ -1318,7 +1318,7 @@ in more situations.
Concretely, it runs `norm_cast` on the goal. For each local hypothesis `h`, it also
normalizes `h` with `norm_cast` and tries to use that to close the goal. -/
macro "assumption_mod_cast" cfg:optConfig : tactic => `(tactic| norm_cast0 $cfg at * <;> assumption)
macro "assumption_mod_cast" : tactic => `(tactic| norm_cast0 at * <;> assumption)
/--
The `norm_cast` family of tactics is used to normalize certain coercions (*casts*) in expressions.
@@ -1355,9 +1355,26 @@ their operation, to make them more flexible about the expressions they accept
See also `push_cast`, which moves casts inwards rather than lifting them outwards.
-/
macro "norm_cast" cfg:optConfig loc:(location)? : tactic =>
`(tactic| norm_cast0 $cfg $[$loc]? <;> try trivial)
macro "norm_cast" loc:(location)? : tactic =>
`(tactic| norm_cast0 $[$loc]? <;> try trivial)
/--
`ac_nf` normalizes equalities up to application of an associative and commutative operator.
- `ac_nf` normalizes all hypotheses and the goal target of the goal.
- `ac_nf at l` normalizes at location(s) `l`, where `l` is either `*` or a
list of hypotheses in the local context. In the latter case, a turnstile `⊢` or `|-`
can also be used, to signify the target of the goal.
```
instance : Associative (α := Nat) (.+.) := ⟨Nat.add_assoc⟩
instance : Commutative (α := Nat) (.+.) := ⟨Nat.add_comm⟩
example (a b c d : Nat) : a + b + c + d = d + (b + c) + a := by
ac_nf
-- goal: a + (b + (c + d)) = a + (b + (c + d))
```
-/
macro "ac_nf" loc:(location)? : tactic =>
`(tactic| ac_nf0 $[$loc]? <;> try trivial)
/--
`push_cast` rewrites the goal to move certain coercions (*casts*) inward, toward the leaf nodes.
@@ -1400,24 +1417,6 @@ syntax (name := pushCast) "push_cast" optConfig (discharger)? (&" only")?
-/
syntax (name := normCastAddElim) "norm_cast_add_elim" ident : command
/--
`ac_nf` normalizes equalities up to application of an associative and commutative operator.
- `ac_nf` normalizes all hypotheses and the goal target of the goal.
- `ac_nf at l` normalizes at location(s) `l`, where `l` is either `*` or a
list of hypotheses in the local context. In the latter case, a turnstile `⊢` or `|-`
can also be used, to signify the target of the goal.
```
instance : Associative (α := Nat) (.+.) := ⟨Nat.add_assoc⟩
instance : Commutative (α := Nat) (.+.) := ⟨Nat.add_comm⟩
example (a b c d : Nat) : a + b + c + d = d + (b + c) + a := by
ac_nf
-- goal: a + (b + (c + d)) = a + (b + (c + d))
```
-/
macro "ac_nf" loc:(location)? : tactic =>
`(tactic| ac_nf0 $[$loc]? <;> try trivial)
/--
* `symm` applies to a goal whose target has the form `t ~ u` where `~` is a symmetric relation,
that is, a relation which has a symmetry lemma tagged with the attribute [symm].

View File

@@ -81,7 +81,6 @@ then one of the following must hold in each (execution) branch.
inductive IRType where
| float | uint8 | uint16 | uint32 | uint64 | usize
| irrelevant | object | tobject
| float32
| struct (leanTypeName : Option Name) (types : Array IRType) : IRType
| union (leanTypeName : Name) (types : Array IRType) : IRType
deriving Inhabited, Repr
@@ -90,7 +89,6 @@ namespace IRType
partial def beq : IRType IRType Bool
| float, float => true
| float32, float32 => true
| uint8, uint8 => true
| uint16, uint16 => true
| uint32, uint32 => true
@@ -106,14 +104,13 @@ partial def beq : IRType → IRType → Bool
instance : BEq IRType := beq
def isScalar : IRType Bool
| float => true
| float32 => true
| uint8 => true
| uint16 => true
| uint32 => true
| uint64 => true
| usize => true
| _ => false
| float => true
| uint8 => true
| uint16 => true
| uint32 => true
| uint64 => true
| usize => true
| _ => false
def isObj : IRType Bool
| object => true
@@ -614,11 +611,10 @@ def mkIf (x : VarId) (t e : FnBody) : FnBody :=
def getUnboxOpName (t : IRType) : String :=
match t with
| IRType.usize => "lean_unbox_usize"
| IRType.uint32 => "lean_unbox_uint32"
| IRType.uint64 => "lean_unbox_uint64"
| IRType.float => "lean_unbox_float"
| IRType.float32 => "lean_unbox_float32"
| _ => "lean_unbox"
| IRType.usize => "lean_unbox_usize"
| IRType.uint32 => "lean_unbox_uint32"
| IRType.uint64 => "lean_unbox_uint64"
| IRType.float => "lean_unbox_float"
| _ => "lean_unbox"
end Lean.IR

View File

@@ -55,7 +55,6 @@ def emitArg (x : Arg) : M Unit :=
def toCType : IRType String
| IRType.float => "double"
| IRType.float32 => "float"
| IRType.uint8 => "uint8_t"
| IRType.uint16 => "uint16_t"
| IRType.uint32 => "uint32_t"
@@ -312,13 +311,12 @@ def emitUSet (x : VarId) (n : Nat) (y : VarId) : M Unit := do
def emitSSet (x : VarId) (n : Nat) (offset : Nat) (y : VarId) (t : IRType) : M Unit := do
match t with
| IRType.float => emit "lean_ctor_set_float"
| IRType.float32 => emit "lean_ctor_set_float32"
| IRType.uint8 => emit "lean_ctor_set_uint8"
| IRType.uint16 => emit "lean_ctor_set_uint16"
| IRType.uint32 => emit "lean_ctor_set_uint32"
| IRType.uint64 => emit "lean_ctor_set_uint64"
| _ => throw "invalid instruction";
| IRType.float => emit "lean_ctor_set_float"
| IRType.uint8 => emit "lean_ctor_set_uint8"
| IRType.uint16 => emit "lean_ctor_set_uint16"
| IRType.uint32 => emit "lean_ctor_set_uint32"
| IRType.uint64 => emit "lean_ctor_set_uint64"
| _ => throw "invalid instruction";
emit "("; emit x; emit ", "; emitOffset n offset; emit ", "; emit y; emitLn ");"
def emitJmp (j : JoinPointId) (xs : Array Arg) : M Unit := do
@@ -388,13 +386,12 @@ def emitUProj (z : VarId) (i : Nat) (x : VarId) : M Unit := do
def emitSProj (z : VarId) (t : IRType) (n offset : Nat) (x : VarId) : M Unit := do
emitLhs z;
match t with
| IRType.float => emit "lean_ctor_get_float"
| IRType.float32 => emit "lean_ctor_get_float32"
| IRType.uint8 => emit "lean_ctor_get_uint8"
| IRType.uint16 => emit "lean_ctor_get_uint16"
| IRType.uint32 => emit "lean_ctor_get_uint32"
| IRType.uint64 => emit "lean_ctor_get_uint64"
| _ => throw "invalid instruction"
| IRType.float => emit "lean_ctor_get_float"
| IRType.uint8 => emit "lean_ctor_get_uint8"
| IRType.uint16 => emit "lean_ctor_get_uint16"
| IRType.uint32 => emit "lean_ctor_get_uint32"
| IRType.uint64 => emit "lean_ctor_get_uint64"
| _ => throw "invalid instruction"
emit "("; emit x; emit ", "; emitOffset n offset; emitLn ");"
def toStringArgs (ys : Array Arg) : List String :=
@@ -449,12 +446,11 @@ def emitApp (z : VarId) (f : VarId) (ys : Array Arg) : M Unit :=
def emitBoxFn (xType : IRType) : M Unit :=
match xType with
| IRType.usize => emit "lean_box_usize"
| IRType.uint32 => emit "lean_box_uint32"
| IRType.uint64 => emit "lean_box_uint64"
| IRType.float => emit "lean_box_float"
| IRType.float32 => emit "lean_box_float32"
| _ => emit "lean_box"
| IRType.usize => emit "lean_box_usize"
| IRType.uint32 => emit "lean_box_uint32"
| IRType.uint64 => emit "lean_box_uint64"
| IRType.float => emit "lean_box_float"
| _ => emit "lean_box"
def emitBox (z : VarId) (x : VarId) (xType : IRType) : M Unit := do
emitLhs z; emitBoxFn xType; emit "("; emit x; emitLn ");"

View File

@@ -315,7 +315,6 @@ def callLeanCtorSetTag (builder : LLVM.Builder llvmctx)
def toLLVMType (t : IRType) : M llvmctx (LLVM.LLVMType llvmctx) := do
match t with
| IRType.float => LLVM.doubleTypeInContext llvmctx
| IRType.float32 => LLVM.floatTypeInContext llvmctx
| IRType.uint8 => LLVM.intTypeInContext llvmctx 8
| IRType.uint16 => LLVM.intTypeInContext llvmctx 16
| IRType.uint32 => LLVM.intTypeInContext llvmctx 32
@@ -818,13 +817,12 @@ def emitSProj (builder : LLVM.Builder llvmctx)
(z : VarId) (t : IRType) (n offset : Nat) (x : VarId) : M llvmctx Unit := do
let (fnName, retty)
match t with
| IRType.float => pure ("lean_ctor_get_float", LLVM.doubleTypeInContext llvmctx)
| IRType.float32 => pure ("lean_ctor_get_float32", LLVM.floatTypeInContext llvmctx)
| IRType.uint8 => pure ("lean_ctor_get_uint8", LLVM.i8Type llvmctx)
| IRType.uint16 => pure ("lean_ctor_get_uint16", LLVM.i16Type llvmctx)
| IRType.uint32 => pure ("lean_ctor_get_uint32", LLVM.i32Type llvmctx)
| IRType.uint64 => pure ("lean_ctor_get_uint64", LLVM.i64Type llvmctx)
| _ => throw s!"Invalid type for lean_ctor_get: '{t}'"
| IRType.float => pure ("lean_ctor_get_float", LLVM.doubleTypeInContext llvmctx)
| IRType.uint8 => pure ("lean_ctor_get_uint8", LLVM.i8Type llvmctx)
| IRType.uint16 => pure ("lean_ctor_get_uint16", LLVM.i16Type llvmctx)
| IRType.uint32 => pure ("lean_ctor_get_uint32", LLVM.i32Type llvmctx)
| IRType.uint64 => pure ("lean_ctor_get_uint64", LLVM.i64Type llvmctx)
| _ => throw s!"Invalid type for lean_ctor_get: '{t}'"
let argtys := #[ LLVM.voidPtrType llvmctx, LLVM.unsignedType llvmctx]
let fn getOrCreateFunctionPrototype ( getLLVMModule) retty fnName argtys
let xval emitLhsVal builder x
@@ -864,12 +862,11 @@ def emitBox (builder : LLVM.Builder llvmctx) (z : VarId) (x : VarId) (xType : IR
let xv emitLhsVal builder x
let (fnName, argTy, xv)
match xType with
| IRType.usize => pure ("lean_box_usize", LLVM.size_tType llvmctx, xv)
| IRType.uint32 => pure ("lean_box_uint32", LLVM.i32Type llvmctx, xv)
| IRType.uint64 => pure ("lean_box_uint64", LLVM.size_tType llvmctx, xv)
| IRType.float => pure ("lean_box_float", LLVM.doubleTypeInContext llvmctx, xv)
| IRType.float32 => pure ("lean_box_float32", LLVM.floatTypeInContext llvmctx, xv)
| _ =>
| IRType.usize => pure ("lean_box_usize", LLVM.size_tType llvmctx, xv)
| IRType.uint32 => pure ("lean_box_uint32", LLVM.i32Type llvmctx, xv)
| IRType.uint64 => pure ("lean_box_uint64", LLVM.size_tType llvmctx, xv)
| IRType.float => pure ("lean_box_float", LLVM.doubleTypeInContext llvmctx, xv)
| _ => do
-- sign extend smaller values into i64
let xv LLVM.buildSext builder xv ( LLVM.size_tType llvmctx)
pure ("lean_box", LLVM.size_tType llvmctx, xv)
@@ -895,12 +892,11 @@ def callUnboxForType (builder : LLVM.Builder llvmctx)
(retName : String := "") : M llvmctx (LLVM.Value llvmctx) := do
let (fnName, retty)
match t with
| IRType.usize => pure ("lean_unbox_usize", toLLVMType t)
| IRType.uint32 => pure ("lean_unbox_uint32", toLLVMType t)
| IRType.uint64 => pure ("lean_unbox_uint64", toLLVMType t)
| IRType.float => pure ("lean_unbox_float", toLLVMType t)
| IRType.float32 => pure ("lean_unbox_float32", toLLVMType t)
| _ => pure ("lean_unbox", LLVM.size_tType llvmctx)
| IRType.usize => pure ("lean_unbox_usize", toLLVMType t)
| IRType.uint32 => pure ("lean_unbox_uint32", toLLVMType t)
| IRType.uint64 => pure ("lean_unbox_uint64", toLLVMType t)
| IRType.float => pure ("lean_unbox_float", toLLVMType t)
| _ => pure ("lean_unbox", LLVM.size_tType llvmctx)
let argtys := #[ LLVM.voidPtrType llvmctx ]
let fn getOrCreateFunctionPrototype ( getLLVMModule) retty fnName argtys
let fnty LLVM.functionType retty argtys
@@ -1045,13 +1041,12 @@ def emitJmp (builder : LLVM.Builder llvmctx) (jp : JoinPointId) (xs : Array Arg)
def emitSSet (builder : LLVM.Builder llvmctx) (x : VarId) (n : Nat) (offset : Nat) (y : VarId) (t : IRType) : M llvmctx Unit := do
let (fnName, setty)
match t with
| IRType.float => pure ("lean_ctor_set_float", LLVM.doubleTypeInContext llvmctx)
| IRType.float32 => pure ("lean_ctor_set_float32", LLVM.floatTypeInContext llvmctx)
| IRType.uint8 => pure ("lean_ctor_set_uint8", LLVM.i8Type llvmctx)
| IRType.uint16 => pure ("lean_ctor_set_uint16", LLVM.i16Type llvmctx)
| IRType.uint32 => pure ("lean_ctor_set_uint32", LLVM.i32Type llvmctx)
| IRType.uint64 => pure ("lean_ctor_set_uint64", LLVM.i64Type llvmctx)
| _ => throw s!"invalid type for 'lean_ctor_set': '{t}'"
| IRType.float => pure ("lean_ctor_set_float", LLVM.doubleTypeInContext llvmctx)
| IRType.uint8 => pure ("lean_ctor_set_uint8", LLVM.i8Type llvmctx)
| IRType.uint16 => pure ("lean_ctor_set_uint16", LLVM.i16Type llvmctx)
| IRType.uint32 => pure ("lean_ctor_set_uint32", LLVM.i32Type llvmctx)
| IRType.uint64 => pure ("lean_ctor_set_uint64", LLVM.i64Type llvmctx)
| _ => throw s!"invalid type for 'lean_ctor_set': '{t}'"
let argtys := #[ LLVM.voidPtrType llvmctx, LLVM.unsignedType llvmctx, setty]
let retty LLVM.voidType llvmctx
let fn getOrCreateFunctionPrototype ( getLLVMModule) retty fnName argtys

View File

@@ -55,7 +55,6 @@ instance : ToString Expr := ⟨fun e => Format.pretty (format e)⟩
private partial def formatIRType : IRType Format
| IRType.float => "float"
| IRType.float32 => "float32"
| IRType.uint8 => "u8"
| IRType.uint16 => "u16"
| IRType.uint32 => "u32"

View File

@@ -593,14 +593,6 @@ where
let minor visit minor
mkOverApplication minor args arity
visitHEqRec (e : Expr) : M Arg :=
let arity := 7
etaIfUnderApplied e arity do
let args := e.getAppArgs
let minor := if e.isAppOf ``HEq.rec || e.isAppOf ``HEq.ndrec then args[3]! else args[6]!
let minor visit minor
mkOverApplication minor args arity
visitFalseRec (e : Expr) : M Arg :=
let arity := 2
etaIfUnderApplied e arity do
@@ -677,8 +669,6 @@ where
visitCtor 3 e
else if declName == ``Eq.casesOn || declName == ``Eq.rec || declName == ``Eq.ndrec then
visitEqRec e
else if declName == ``HEq.casesOn || declName == ``HEq.rec || declName == ``HEq.ndrec then
visitHEqRec e
else if declName == ``And.rec || declName == ``Iff.rec then
visitAndIffRecCore e (minorPos := 3)
else if declName == ``And.casesOn || declName == ``Iff.casesOn then

View File

@@ -33,15 +33,7 @@ register_builtin_option maxHeartbeats : Nat := {
register_builtin_option Elab.async : Bool := {
defValue := false
descr := "perform elaboration using multiple threads where possible\
\n\
\nThis option defaults to `false` but (when not explicitly set) is overridden to `true` in \
`Lean.Language.Lean.process` as used by the cmdline driver and language server. \
Metaprogramming users driving elaboration directly via e.g. \
`Lean.Elab.Command.elabCommandTopLevel` can opt into asynchronous elaboration by setting \
this option but then are responsible for processing messages and other data not only in the \
resulting command state but also from async tasks in `Lean.Command.Context.snap?` and \
`Lean.Command.State.snapshotTasks`."
descr := "perform elaboration using multiple threads where possible"
}
/--
@@ -364,7 +356,9 @@ Returns the current log and then resets its messages while adjusting `MessageLog
for incremental reporting during elaboration of a single command.
-/
def getAndEmptyMessageLog : CoreM MessageLog :=
modifyGet fun s => (s.messages, { s with messages := s.messages.markAllReported })
modifyGet fun s => (s.messages, { s with
messages.unreported := {}
messages.hadErrors := s.messages.hasErrors })
instance : MonadLog CoreM where
getRef := getRef
@@ -423,7 +417,7 @@ def wrapAsyncAsSnapshot (act : Unit → CoreM Unit) (desc : String := by exact d
IO.FS.withIsolatedStreams (isolateStderr := stderrAsMessages.get ( getOptions)) do
let tid IO.getTID
-- reset trace state and message log so as not to report them twice
modify fun st => { st with messages := st.messages.markAllReported, traceState := { tid } }
modify ({ · with messages := {}, traceState := { tid } })
try
withTraceNode `Elab.async (fun _ => return desc) do
act ()

View File

@@ -35,7 +35,7 @@ theorem RArray.get_ofFn {n : Nat} (f : Fin n → α) (h : 0 < n) (i : Fin n) :
go 0 n h (Nat.le_refl _) (Nat.zero_le _) i.2
where
go lb ub h1 h2 (h3 : lb i.val) (h3 : i.val < ub) : (ofFn.go f lb ub h1 h2).get i = f i := by
induction lb, ub, h1, h2 using RArray.ofFn.go.induct (n := n)
induction lb, ub, h1, h2 using RArray.ofFn.go.induct (f := f) (n := n)
case case1 =>
simp [ofFn.go, RArray.get_eq_getImpl, RArray.getImpl]
congr
@@ -53,7 +53,7 @@ theorem RArray.size_ofFn {n : Nat} (f : Fin n → α) (h : 0 < n) :
go 0 n h (Nat.le_refl _)
where
go lb ub h1 h2 : (ofFn.go f lb ub h1 h2).size = ub - lb := by
induction lb, ub, h1, h2 using RArray.ofFn.go.induct (n := n)
induction lb, ub, h1, h2 using RArray.ofFn.go.induct (f := f) (n := n)
case case1 => simp [ofFn.go, size]; omega
case case2 ih1 ih2 hiu => rw [ofFn.go]; simp [size, *]; omega

View File

@@ -488,9 +488,6 @@ where
let mut lines : Array MessageData := #[]
let decls getOptionDecls
for (name, val) in opts do
-- `#guard_msgs` sets this option internally, we don't want it to end up in its output
if name == `Elab.async then
continue
let (isSet, isUnknown) :=
match decls.find? name with
| some decl => (decl.defValue != val, false)

View File

@@ -101,7 +101,7 @@ structure Context where
(mutual) defs and contained tactics, in which case the `DynamicSnapshot` is a
`HeadersParsedSnapshot`.
Definitely resolved in `Lean.Elab.Command.elabCommandTopLevel`.
Definitely resolved in `Language.Lean.process.doElab`.
Invariant: if the bundle's `old?` is set, the context and state at the beginning of current and
old elaboration are identical.
@@ -287,9 +287,7 @@ def runLinters (stx : Syntax) : CommandElabM Unit := do
| Exception.internal _ _ =>
logException ex
finally
-- TODO: it would be good to preserve even more state (#4363) but preserving info
-- trees currently breaks from linters adding context-less info nodes
modify fun s => { savedState with messages := s.messages, traceState := s.traceState }
modify fun s => { savedState with messages := s.messages }
/--
Catches and logs exceptions occurring in `x`. Unlike `try catch` in `CommandElabM`, this function
@@ -313,7 +311,7 @@ def wrapAsyncAsSnapshot (act : Unit → CommandElabM Unit)
IO.FS.withIsolatedStreams (isolateStderr := Core.stderrAsMessages.get ( getOptions)) do
let tid IO.getTID
-- reset trace state and message log so as not to report them twice
modify fun st => { st with messages := st.messages.markAllReported, traceState := { tid } }
modify ({ · with messages := {}, traceState := { tid } })
try
withTraceNode `Elab.async (fun _ => return desc) do
act ()
@@ -346,17 +344,6 @@ def wrapAsyncAsSnapshot (act : Unit → CommandElabM Unit)
def logSnapshotTask (task : Language.SnapshotTask Language.SnapshotTree) : CommandElabM Unit :=
modify fun s => { s with snapshotTasks := s.snapshotTasks.push task }
def runLintersAsync (stx : Syntax) : CommandElabM Unit := do
if !Elab.async.get ( getOptions) then
withoutModifyingEnv do
runLinters stx
return
-- We only start one task for all linters for now as most linters are fast and we simply want
-- to unblock elaboration of the next command
let lintAct wrapAsyncAsSnapshot fun _ => runLinters stx
logSnapshotTask { range? := none, task := ( BaseIO.asTask lintAct) }
protected def getCurrMacroScope : CommandElabM Nat := do pure ( read).currMacroScope
protected def getMainModule : CommandElabM Name := do pure ( getEnv).mainModule
@@ -560,13 +547,8 @@ def elabCommandTopLevel (stx : Syntax) : CommandElabM Unit := withRef stx do pro
-- rather than engineer a general solution.
unless (stx.find? (·.isOfKind ``Lean.guardMsgsCmd)).isSome do
withLogging do
runLintersAsync stx
runLinters stx
finally
-- Make sure `snap?` is definitely resolved; we do not use it for reporting as `#guard_msgs` may
-- be the caller of this function and add new messages and info trees
if let some snap := ( read).snap? then
snap.new.resolve default
-- note the order: first process current messages & info trees, then add back old messages & trees,
-- then convert new traces to messages
let mut msgs := ( get).messages

View File

@@ -169,8 +169,6 @@ def runFrontend
IO.FS.writeFile out <| Json.compress <| toJson profile
let hasErrors := snaps.getAll.any (·.diagnostics.msgLog.hasErrors)
-- no point in freeing the snapshot graph and all referenced data this close to process exit
Runtime.forget snaps
pure (cmdState.env, !hasErrors)

View File

@@ -140,15 +140,9 @@ def MessageOrdering.apply (mode : MessageOrdering) (msgs : List String) : List S
|>.trim |> removeTrailingWhitespaceMarker
let (whitespace, ordering, specFn) parseGuardMsgsSpec spec?
let initMsgs modifyGet fun st => (st.messages, { st with messages := {} })
-- do not forward snapshot as we don't want messages assigned to it to leak outside
withReader ({ · with snap? := none }) do
-- The `#guard_msgs` command is special-cased in `elabCommandTopLevel` to ensure linters only run once.
elabCommandTopLevel cmd
-- collect sync and async messages
let msgs := ( get).messages ++
( get).snapshotTasks.foldl (· ++ ·.get.getAll.foldl (· ++ ·.diagnostics.msgLog) {}) {}
-- clear async messages as we don't want them to leak outside
modify ({ · with snapshotTasks := #[] })
-- The `#guard_msgs` command is special-cased in `elabCommandTopLevel` to ensure linters only run once.
elabCommandTopLevel cmd
let msgs := ( get).messages
let mut toCheck : MessageLog := .empty
let mut toPassthrough : MessageLog := .empty
for msg in msgs.toList do

View File

@@ -399,20 +399,6 @@ register_builtin_option linter.unusedSectionVars : Bool := {
descr := "enable the 'unused section variables in theorem body' linter"
}
register_builtin_option debug.proofAsSorry : Bool := {
defValue := false
group := "debug"
descr := "replace the bodies (proofs) of theorems with `sorry`"
}
/-- Returns true if `k` is a theorem, option `debug.proofAsSorry` is set to true, and the environment contains the axiom `sorryAx`. -/
private def useProofAsSorry (k : DefKind) : CoreM Bool := do
if k.isTheorem then
if debug.proofAsSorry.get ( getOptions) then
if ( getEnv).contains ``sorryAx then
return true
return false
private def elabFunValues (headers : Array DefViewElabHeader) (vars : Array Expr) (sc : Command.Scope) : TermElabM (Array Expr) :=
headers.mapM fun header => do
let mut reusableResult? := none
@@ -434,9 +420,7 @@ private def elabFunValues (headers : Array DefViewElabHeader) (vars : Array Expr
for h : i in [0:header.binderIds.size] do
-- skip auto-bound prefix in `xs`
addLocalVarInfo header.binderIds[i] xs[header.numParams - header.binderIds.size + i]!
let val if ( useProofAsSorry header.kind) then
mkSorry type false
else withReader ({ · with tacSnap? := header.tacSnap? }) do
let val withReader ({ · with tacSnap? := header.tacSnap? }) do
-- Store instantiated body in info tree for the benefit of the unused variables linter
-- and other metaprograms that may want to inspect it without paying for the instantiation
-- again

View File

@@ -8,7 +8,6 @@ import Std.Data.HashMap
import Std.Tactic.BVDecide.Bitblast.BVExpr.Basic
import Lean.Meta.AppBuilder
import Lean.ToExpr
import Lean.Data.RArray
/-!
This module contains the implementation of the reflection monad, used by all other components of this
@@ -139,11 +138,9 @@ structure State where
-/
atoms : Std.HashMap Expr Atom := {}
/--
A cache for `atomsAssignment`. We maintain the invariant that this value is only used if
`atoms` is non empty. The reason for not using an `Option` is that it would pollute a lot of code
with error handling that is never hit as this invariant is enforced before all of this code.
A cache for `atomsAssignment`.
-/
atomsAssignmentCache : Expr := mkConst `illegal
atomsAssignmentCache : Expr := mkConst ``List.nil [.zero]
/--
The reflection monad, used to track `BitVec` variables that we see as we traverse the context.
@@ -160,9 +157,9 @@ structure ReifiedBVExpr where
-/
bvExpr : BVExpr width
/--
A proof that `bvExpr.eval atomsAssignment = originalBVExpr`, none if it holds by `rfl`.
A proof that `bvExpr.eval atomsAssignment = originalBVExpr`.
-/
evalsAtAtoms : M (Option Expr)
evalsAtAtoms : M Expr
/--
A cache for `toExpr bvExpr`.
-/
@@ -177,9 +174,9 @@ structure ReifiedBVPred where
-/
bvPred : BVPred
/--
A proof that `bvPred.eval atomsAssignment = originalBVPredExpr`, none if it holds by `rfl`.
A proof that `bvPred.eval atomsAssignment = originalBVPredExpr`.
-/
evalsAtAtoms : M (Option Expr)
evalsAtAtoms : M Expr
/--
A cache for `toExpr bvPred`
-/
@@ -194,9 +191,9 @@ structure ReifiedBVLogical where
-/
bvExpr : BVLogicalExpr
/--
A proof that `bvExpr.eval atomsAssignment = originalBVLogicalExpr`, none if it holds by `rfl`.
A proof that `bvExpr.eval atomsAssignment = originalBVLogicalExpr`.
-/
evalsAtAtoms : M (Option Expr)
evalsAtAtoms : M Expr
/--
A cache for `toExpr bvExpr`
-/
@@ -231,9 +228,9 @@ def run (m : M α) : MetaM α :=
/--
Retrieve the atoms as pairs of their width and expression.
-/
def atoms : M (Array (Nat × Expr)) := do
def atoms : M (List (Nat × Expr)) := do
let sortedAtoms := ( getThe State).atoms.toArray.qsort (·.2.atomNumber < ·.2.atomNumber)
return sortedAtoms.map (fun (expr, {width, ..}) => (width, expr))
return sortedAtoms.map (fun (expr, {width, ..}) => (width, expr)) |>.toList
/--
Retrieve a `BitVec.Assignment` representing the atoms we found so far.
@@ -260,37 +257,11 @@ def lookup (e : Expr) (width : Nat) (synthetic : Bool) : M Nat := do
where
updateAtomsAssignment : M Unit := do
let as atoms
if h : 0 < as.size then
let ras := Lean.RArray.ofArray as h
let packedType := mkConst ``BVExpr.PackedBitVec
let pack := fun (width, expr) => mkApp2 (mkConst ``BVExpr.PackedBitVec.mk) (toExpr width) expr
let newAtomsAssignment := ras.toExpr packedType pack
modify fun s => { s with atomsAssignmentCache := newAtomsAssignment }
else
throwError "updateAtomsAssignment should only be called when there is an atom"
@[specialize]
def simplifyBinaryProof' (mkFRefl : Expr Expr) (fst : Expr) (fproof : Option Expr)
(mkSRefl : Expr Expr) (snd : Expr) (sproof : Option Expr) : Option (Expr × Expr) := do
match fproof, sproof with
| some fproof, some sproof => some (fproof, sproof)
| some fproof, none => some (fproof, mkSRefl snd)
| none, some sproof => some (mkFRefl fst, sproof)
| none, none => none
@[specialize]
def simplifyBinaryProof (mkRefl : Expr Expr) (fst : Expr) (fproof : Option Expr) (snd : Expr)
(sproof : Option Expr) : Option (Expr × Expr) := do
simplifyBinaryProof' mkRefl fst fproof mkRefl snd sproof
@[specialize]
def simplifyTernaryProof (mkRefl : Expr Expr) (fst : Expr) (fproof : Option Expr) (snd : Expr)
(sproof : Option Expr) (thd : Expr) (tproof : Option Expr) : Option (Expr × Expr × Expr) := do
match fproof, simplifyBinaryProof mkRefl snd sproof thd tproof with
| some fproof, some stproof => some (fproof, stproof)
| some fproof, none => some (fproof, mkRefl snd, mkRefl thd)
| none, some stproof => some (mkRefl fst, stproof)
| none, none => none
let packed :=
as.map (fun (width, expr) => mkApp2 (mkConst ``BVExpr.PackedBitVec.mk) (toExpr width) expr)
let packedType := mkConst ``BVExpr.PackedBitVec
let newAtomsAssignment mkListLit packedType packed
modify fun s => { s with atomsAssignmentCache := newAtomsAssignment }
end M

View File

@@ -37,8 +37,9 @@ Register `e` as an atom of `width` that might potentially be `synthetic`.
def mkAtom (e : Expr) (width : Nat) (synthetic : Bool) : M ReifiedBVExpr := do
let ident M.lookup e width synthetic
let expr := mkApp2 (mkConst ``BVExpr.var) (toExpr width) (toExpr ident)
-- This is safe because this proof always holds definitionally.
let proof := pure none
let proof := do
let evalExpr mkEvalExpr width expr
return mkBVRefl width evalExpr
return width, .var ident, proof, expr
/--
@@ -69,8 +70,9 @@ Build a reified version of the constant `val`.
def mkBVConst (val : BitVec w) : M ReifiedBVExpr := do
let bvExpr : BVExpr w := .const val
let expr := mkApp2 (mkConst ``BVExpr.const) (toExpr w) (toExpr val)
-- This is safe because this proof always holds definitionally.
let proof := pure none
let proof := do
let evalExpr ReifiedBVExpr.mkEvalExpr w expr
return ReifiedBVExpr.mkBVRefl w evalExpr
return w, bvExpr, proof, expr
end ReifiedBVExpr

View File

@@ -49,8 +49,7 @@ Build a reified version of the constant `val`.
def mkBoolConst (val : Bool) : M ReifiedBVLogical := do
let boolExpr := .const val
let expr := mkApp2 (mkConst ``BoolExpr.const) (mkConst ``BVPred) (toExpr val)
-- This is safe because this proof always holds definitionally.
let proof := pure none
let proof := pure <| ReifiedBVLogical.mkRefl (toExpr val)
return boolExpr, proof, expr
/--
@@ -72,13 +71,8 @@ def mkGate (lhs rhs : ReifiedBVLogical) (lhsExpr rhsExpr : Expr) (gate : Gate) :
let proof := do
let lhsEvalExpr ReifiedBVLogical.mkEvalExpr lhs.expr
let rhsEvalExpr ReifiedBVLogical.mkEvalExpr rhs.expr
let lhsProof? lhs.evalsAtAtoms
let rhsProof? rhs.evalsAtAtoms
let some (lhsProof, rhsProof) :=
M.simplifyBinaryProof
ReifiedBVLogical.mkRefl
lhsEvalExpr lhsProof?
rhsEvalExpr rhsProof? | return none
let lhsProof lhs.evalsAtAtoms
let rhsProof rhs.evalsAtAtoms
return mkApp6
(mkConst congrThm)
lhsExpr rhsExpr
@@ -101,9 +95,8 @@ def mkNot (sub : ReifiedBVLogical) (subExpr : Expr) : M ReifiedBVLogical := do
let boolExpr := .not sub.bvExpr
let expr := mkApp2 (mkConst ``BoolExpr.not) (mkConst ``BVPred) sub.expr
let proof := do
-- This is safe as `not_congr` holds definitionally if the arguments are defeq.
let some subProof sub.evalsAtAtoms | return none
let subEvalExpr ReifiedBVLogical.mkEvalExpr sub.expr
let subProof sub.evalsAtAtoms
return mkApp3 (mkConst ``Std.Tactic.BVDecide.Reflect.Bool.not_congr) subExpr subEvalExpr subProof
return boolExpr, proof, expr
@@ -126,15 +119,9 @@ def mkIte (discr lhs rhs : ReifiedBVLogical) (discrExpr lhsExpr rhsExpr : Expr)
let discrEvalExpr ReifiedBVLogical.mkEvalExpr discr.expr
let lhsEvalExpr ReifiedBVLogical.mkEvalExpr lhs.expr
let rhsEvalExpr ReifiedBVLogical.mkEvalExpr rhs.expr
let discrProof? discr.evalsAtAtoms
let lhsProof? lhs.evalsAtAtoms
let rhsProof? rhs.evalsAtAtoms
let some (discrProof, lhsProof, rhsProof) :=
M.simplifyTernaryProof
ReifiedBVLogical.mkRefl
discrEvalExpr discrProof?
lhsEvalExpr lhsProof?
rhsEvalExpr rhsProof? | return none
let discrProof discr.evalsAtAtoms
let lhsProof lhs.evalsAtAtoms
let rhsProof rhs.evalsAtAtoms
return mkApp9
(mkConst ``Std.Tactic.BVDecide.Reflect.Bool.ite_congr)
discrExpr lhsExpr rhsExpr

View File

@@ -35,10 +35,8 @@ def boolAtom (t : Expr) : M (Option ReifiedBVPred) := do
let bvExpr : BVPred := .getLsbD atom.bvExpr 0
let expr := mkApp3 (mkConst ``BVPred.getLsbD) (toExpr 1) atom.expr (toExpr 0)
let proof := do
-- ofBool_congr does not hold definitionally, if this ever becomes an issue we need to find
-- a more clever encoding for boolean atoms
let atomEval ReifiedBVExpr.mkEvalExpr atom.width atom.expr
let atomProof := ( atom.evalsAtAtoms).getD (ReifiedBVExpr.mkBVRefl atom.width atomEval)
let atomProof atom.evalsAtAtoms
return mkApp3
(mkConst ``Std.Tactic.BVDecide.Reflect.BitVec.ofBool_congr)
t
@@ -65,14 +63,9 @@ def mkBinPred (lhs rhs : ReifiedBVExpr) (lhsExpr rhsExpr : Expr) (pred : BVBinPr
rhs.expr
let proof := do
let lhsEval ReifiedBVExpr.mkEvalExpr lhs.width lhs.expr
let lhsProof lhs.evalsAtAtoms
let rhsEval ReifiedBVExpr.mkEvalExpr rhs.width rhs.expr
let lhsProof? lhs.evalsAtAtoms
let rhsProof? rhs.evalsAtAtoms
let some (lhsProof, rhsProof) :=
M.simplifyBinaryProof
(ReifiedBVExpr.mkBVRefl lhs.width)
lhsEval lhsProof?
rhsEval rhsProof? | return none
let rhsProof rhs.evalsAtAtoms
return mkApp7
(mkConst congrThm)
(toExpr lhs.width)
@@ -97,9 +90,8 @@ def mkGetLsbD (sub : ReifiedBVExpr) (subExpr : Expr) (idx : Nat) : M ReifiedBVPr
let idxExpr := toExpr idx
let expr := mkApp3 (mkConst ``BVPred.getLsbD) (toExpr sub.width) sub.expr idxExpr
let proof := do
-- This is safe as `getLsbD_congr` holds definitionally if the arguments are defeq.
let some subProof sub.evalsAtAtoms | return none
let subEval ReifiedBVExpr.mkEvalExpr sub.width sub.expr
let subProof sub.evalsAtAtoms
return mkApp5
(mkConst ``Std.Tactic.BVDecide.Reflect.BitVec.getLsbD_congr)
idxExpr

View File

@@ -62,7 +62,7 @@ where
let proof := do
let evalExpr ReifiedBVLogical.mkEvalExpr imp.expr
let congrProof := ( imp.evalsAtAtoms).getD (ReifiedBVLogical.mkRefl evalExpr)
let congrProof imp.evalsAtAtoms
let lemmaProof := mkApp4 (mkConst lemmaName) (toExpr lhs.width) discrExpr lhsExpr rhsExpr
let trueExpr := mkConst ``Bool.true

View File

@@ -112,8 +112,7 @@ where
inner.expr
let proof := do
let innerEval ReifiedBVExpr.mkEvalExpr inner.width inner.expr
-- This is safe as `zeroExtend_congr` holds definitionally if the arguments are defeq.
let some innerProof inner.evalsAtAtoms | return none
let innerProof inner.evalsAtAtoms
return mkApp5 (mkConst ``Std.Tactic.BVDecide.Reflect.BitVec.zeroExtend_congr)
newWidthExpr
(toExpr inner.width)
@@ -133,8 +132,7 @@ where
inner.expr
let proof := do
let innerEval ReifiedBVExpr.mkEvalExpr inner.width inner.expr
-- This is safe as `zeroExtend_congr` holds definitionally if the arguments are defeq.
let some innerProof inner.evalsAtAtoms | return none
let innerProof inner.evalsAtAtoms
return mkApp5 (mkConst ``Std.Tactic.BVDecide.Reflect.BitVec.signExtend_congr)
newWidthExpr
(toExpr inner.width)
@@ -152,13 +150,9 @@ where
lhs.expr rhs.expr
let proof := do
let lhsEval ReifiedBVExpr.mkEvalExpr lhs.width lhs.expr
let lhsProof lhs.evalsAtAtoms
let rhsProof rhs.evalsAtAtoms
let rhsEval ReifiedBVExpr.mkEvalExpr rhs.width rhs.expr
let lhsProof? lhs.evalsAtAtoms
let rhsProof? rhs.evalsAtAtoms
let some (lhsProof, rhsProof) :=
M.simplifyBinaryProof'
(ReifiedBVExpr.mkBVRefl lhs.width) lhsEval lhsProof?
(ReifiedBVExpr.mkBVRefl rhs.width) rhsEval rhsProof? | return none
return mkApp8 (mkConst ``Std.Tactic.BVDecide.Reflect.BitVec.append_congr)
(toExpr lhs.width) (toExpr rhs.width)
lhsExpr lhsEval
@@ -175,8 +169,7 @@ where
inner.expr
let proof := do
let innerEval ReifiedBVExpr.mkEvalExpr inner.width inner.expr
-- This is safe as `zeroExtend_congr` holds definitionally if the arguments are defeq.
let some innerProof inner.evalsAtAtoms | return none
let innerProof inner.evalsAtAtoms
return mkApp5 (mkConst ``Std.Tactic.BVDecide.Reflect.BitVec.replicate_congr)
(toExpr n)
(toExpr inner.width)
@@ -196,8 +189,7 @@ where
inner.expr
let proof := do
let innerEval ReifiedBVExpr.mkEvalExpr inner.width inner.expr
-- This is safe as `zeroExtend_congr` holds definitionally if the arguments are defeq.
let some innerProof inner.evalsAtAtoms | return none
let innerProof inner.evalsAtAtoms
return mkApp6 (mkConst ``Std.Tactic.BVDecide.Reflect.BitVec.extract_congr)
startExpr
lenExpr
@@ -309,16 +301,11 @@ where
return none
binaryCongrProof (lhs rhs : ReifiedBVExpr) (lhsExpr rhsExpr : Expr) (congrThm : Expr) :
M (Option Expr) := do
M Expr := do
let lhsEval ReifiedBVExpr.mkEvalExpr lhs.width lhs.expr
let lhsProof lhs.evalsAtAtoms
let rhsProof rhs.evalsAtAtoms
let rhsEval ReifiedBVExpr.mkEvalExpr rhs.width rhs.expr
let lhsProof? lhs.evalsAtAtoms
let rhsProof? rhs.evalsAtAtoms
let some (lhsProof, rhsProof) :=
M.simplifyBinaryProof
(ReifiedBVExpr.mkBVRefl lhs.width)
lhsEval lhsProof?
rhsEval rhsProof? | return none
return mkApp6 congrThm lhsExpr rhsExpr lhsEval rhsEval lhsProof rhsProof
unaryReflection (innerExpr : Expr) (op : BVUnOp) (congrThm : Name) :
@@ -329,9 +316,9 @@ where
let proof := unaryCongrProof inner innerExpr (mkConst congrThm)
return some inner.width, bvExpr, proof, expr
unaryCongrProof (inner : ReifiedBVExpr) (innerExpr : Expr) (congrProof : Expr) : M (Option Expr) := do
unaryCongrProof (inner : ReifiedBVExpr) (innerExpr : Expr) (congrProof : Expr) : M Expr := do
let innerEval ReifiedBVExpr.mkEvalExpr inner.width inner.expr
let some innerProof inner.evalsAtAtoms | return none
let innerProof inner.evalsAtAtoms
return mkApp4 congrProof (toExpr inner.width) innerExpr innerEval innerProof
goBvLit (x : Expr) : M (Option ReifiedBVExpr) := do

View File

@@ -37,7 +37,7 @@ partial def of (h : Expr) : LemmaM (Option SatAtBVLogical) := do
let proof := do
let evalLogic ReifiedBVLogical.mkEvalExpr bvLogical.expr
-- this is evalLogic = lhsExpr
let evalProof := ( bvLogical.evalsAtAtoms).getD (ReifiedBVLogical.mkRefl evalLogic)
let evalProof bvLogical.evalsAtAtoms
-- h is lhsExpr = true
-- we prove evalLogic = true by evalLogic = lhsExpr = true
return ReifiedBVLogical.mkTrans evalLogic lhsExpr (mkConst ``Bool.true) evalProof h
@@ -61,16 +61,13 @@ def and (x y : SatAtBVLogical) : SatAtBVLogical where
/-- Given a proof that `x.expr.Unsat`, produce a proof of `False`. -/
def proveFalse (x : SatAtBVLogical) (h : Expr) : M Expr := do
if ( get).atoms.isEmpty then
throwError "Unable to identify any relevant atoms."
else
let atomsList M.atomsAssignment
let evalExpr := mkApp2 (mkConst ``BVLogicalExpr.eval) atomsList x.expr
return mkApp3
(mkConst ``Std.Tactic.BVDecide.Reflect.Bool.false_of_eq_true_of_eq_false)
evalExpr
( x.satAtAtoms)
(.app h atomsList)
let atomsList M.atomsAssignment
let evalExpr := mkApp2 (mkConst ``BVLogicalExpr.eval) atomsList x.expr
return mkApp3
(mkConst ``Std.Tactic.BVDecide.Reflect.Bool.false_of_eq_true_of_eq_false)
evalExpr
( x.satAtAtoms)
(.app h atomsList)
end SatAtBVLogical

View File

@@ -168,16 +168,20 @@ def numeralToCoe (e : Expr) : MetaM Simp.Result := do
let some pr proveEqUsingDown e newE | failure
return pr
declare_config_elab elabNormCastConfig NormCastConfig
/--
The core simplification routine of `normCast`.
-/
def derive (e : Expr) (config : NormCastConfig := {}) : MetaM Simp.Result := do
def derive (e : Expr) : MetaM Simp.Result := do
withTraceNode `Tactic.norm_cast (fun _ => return m!"{e}") do
let e instantiateMVars e
let config := config.toConfig
let config : Simp.Config := {
zeta := false
beta := false
eta := false
proj := false
iota := false
}
let congrTheorems Meta.getSimpCongrTheorems
let r : Simp.Result := { expr := e }
@@ -189,13 +193,13 @@ def derive (e : Expr) (config : NormCastConfig := {}) : MetaM Simp.Result := do
-- step 1: pre-processing of numerals
let r withTrace "pre-processing numerals" do
let post e := return Simp.Step.done ( try numeralToCoe e catch _ => pure {expr := e})
let ctx Simp.mkContext config (congrTheorems := congrTheorems)
let ctx Simp.mkContext (config := config) (congrTheorems := congrTheorems)
r.mkEqTrans ( Simp.main r.expr ctx (methods := { post })).1
-- step 2: casts are moved upwards and eliminated
let r withTrace "moving upward, splitting and eliminating" do
let post := upwardAndElim ( normCastExt.up.getTheorems)
let ctx Simp.mkContext config (congrTheorems := congrTheorems)
let ctx Simp.mkContext (config := config) (congrTheorems := congrTheorems)
r.mkEqTrans ( Simp.main r.expr ctx (methods := { post })).1
let simprocs ({} : Simp.SimprocsArray).add `reduceCtorEq false
@@ -230,33 +234,32 @@ open Term
| _ => throwUnsupportedSyntax
/-- Implementation of the `norm_cast` tactic when operating on the main goal. -/
def normCastTarget (cfg : NormCastConfig) : TacticM Unit :=
def normCastTarget : TacticM Unit :=
liftMetaTactic1 fun goal => do
let tgt instantiateMVars ( goal.getType)
let prf derive tgt cfg
let prf derive tgt
applySimpResultToTarget goal tgt prf
/-- Implementation of the `norm_cast` tactic when operating on a hypothesis. -/
def normCastHyp (cfg : NormCastConfig) (fvarId : FVarId) : TacticM Unit :=
def normCastHyp (fvarId : FVarId) : TacticM Unit :=
liftMetaTactic1 fun goal => do
let hyp instantiateMVars ( fvarId.getDecl).type
let prf derive hyp cfg
let prf derive hyp
return ( applySimpResultToLocalDecl goal fvarId prf false).map (·.snd)
@[builtin_tactic normCast0]
def evalNormCast0 : Tactic := fun stx => do
match stx with
| `(tactic| norm_cast0 $cfg $[$loc?]?) =>
| `(tactic| norm_cast0 $[$loc?]?) =>
let loc := if let some loc := loc? then expandLocation loc else Location.targets #[] true
let cfg elabNormCastConfig cfg
withMainContext do
match loc with
| Location.targets hyps target =>
if target then (normCastTarget cfg)
( getFVarIds hyps).forM (normCastHyp cfg)
if target then normCastTarget
( getFVarIds hyps).forM normCastHyp
| Location.wildcard =>
normCastTarget cfg
( ( getMainGoal).getNondepPropHyps).forM (normCastHyp cfg)
normCastTarget
( ( getMainGoal).getNondepPropHyps).forM normCastHyp
| _ => throwUnsupportedSyntax
@[builtin_tactic Lean.Parser.Tactic.Conv.normCast]

View File

@@ -228,7 +228,6 @@ partial def asLinearComboImpl (e : Expr) : OmegaM (LinearCombo × OmegaM Expr ×
| .app (.app (.app (.app (.const ``Prod.mk [u, v]) _) _) x) y =>
rewrite e (mkApp4 (.const ``Prod.snd_mk [u, v]) α x β y)
| _ => mkAtomLinearCombo e
| (``Int.negSucc, #[n]) => rewrite e (mkApp (.const ``Int.negSucc_eq []) n)
| _ => mkAtomLinearCombo e
where
/--

View File

@@ -1235,9 +1235,6 @@ def getRevArg!' : Expr → Nat → Expr
@[inline] def getArgD (e : Expr) (i : Nat) (v₀ : Expr) (n := e.getAppNumArgs) : Expr :=
getRevArgD e (n - i - 1) v₀
/-- Return `true` if `e` contains any loose bound variables.
This is a constant time operation. -/
def hasLooseBVars (e : Expr) : Bool :=
e.looseBVarRange > 0
@@ -1250,11 +1247,6 @@ def isArrow (e : Expr) : Bool :=
| forallE _ _ b _ => !b.hasLooseBVars
| _ => false
/--
Return `true` if `e` contains the specified loose bound variable with index `bvarIdx`.
This operation traverses the expression tree.
-/
@[extern "lean_expr_has_loose_bvar"]
opaque hasLooseBVar (e : @& Expr) (bvarIdx : @& Nat) : Bool

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@@ -433,8 +433,6 @@ where
}
-- now that imports have been loaded, check options again
let opts reparseOptions setup.opts
-- default to async elaboration; see also `Elab.async` docs
let opts := Elab.async.setIfNotSet opts true
let cmdState := Elab.Command.mkState headerEnv msgLog opts
let cmdState := { cmdState with
infoState := {

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@@ -51,8 +51,8 @@ def checkDeprecated [Monad m] [MonadEnv m] [MonadLog m] [AddMessageContext m] [M
if getLinterValue linter.deprecated ( getOptions) then
let some attr := deprecatedAttr.getParam? ( getEnv) declName | pure ()
logWarning <| .tagged ``deprecatedAttr <|
m!"`{.ofConstName declName true}` has been deprecated" ++ match attr.text? with
s!"`{declName}` has been deprecated" ++ match attr.text? with
| some text => s!": {text}"
| none => match attr.newName? with
| some newName => m!": use `{.ofConstName newName true}` instead"
| some newName => s!": use `{newName}` instead"
| none => ""

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@@ -441,10 +441,6 @@ instance : Append MessageLog :=
def hasErrors (log : MessageLog) : Bool :=
log.hadErrors || log.unreported.any (·.severity matches .error)
/-- Clears unreported messages while preserving `hasErrors`. -/
def markAllReported (log : MessageLog) : MessageLog :=
{ log with unreported := {}, hadErrors := log.hasErrors }
def errorsToWarnings (log : MessageLog) : MessageLog :=
{ unreported := log.unreported.map (fun m => match m.severity with | MessageSeverity.error => { m with severity := MessageSeverity.warning } | _ => m) }

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@@ -35,27 +35,11 @@ def isConstructorApp? (e : Expr) : MetaM (Option ConstructorVal) := do
/--
Similar to `isConstructorApp?`, but uses `whnf`.
It also uses `isOffset?` for `Nat`.
See also `Lean.Meta.constructorApp'?`.
-/
def isConstructorApp'? (e : Expr) : MetaM (Option ConstructorVal) := do
if let some (_, k) isOffset? e then
if k = 0 then
return none
else
let .ctorInfo val getConstInfo ``Nat.succ | return none
return some val
else if let some r isConstructorApp? e then
if let some r isConstructorApp? e then
return r
else try
/-
We added the `try` block here because `whnf` fails at terms `n ^ m`
when `m` is a big numeral, and `n` is a numeral. This is a little bit hackish.
-/
isConstructorApp? ( whnf e)
catch _ =>
return none
isConstructorApp? ( whnf e)
/--
Returns `true`, if `e` is constructor application of builtin literal defeq to
@@ -86,9 +70,7 @@ def constructorApp? (e : Expr) : MetaM (Option (ConstructorVal × Array Expr)) :
/--
Similar to `constructorApp?`, but on failure it puts `e` in WHNF and tries again.
It also uses `isOffset?` for `Nat`.
See also `Lean.Meta.isConstructorApp'?`.
It also `isOffset?`
-/
def constructorApp'? (e : Expr) : MetaM (Option (ConstructorVal × Array Expr)) := do
if let some (e, k) isOffset? e then

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@@ -62,7 +62,7 @@ def getStringValue? (e : Expr) : (Option String) :=
| .lit (.strVal s) => some s
| _ => none
/-- Return `some ⟨n, v⟩` if `e` is an `OfNat.ofNat` application encoding a `Fin n` with value `v` -/
/-- Return `some ⟨n, v⟩` if `e` is af `OfNat.ofNat` application encoding a `Fin n` with value `v` -/
def getFinValue? (e : Expr) : MetaM (Option ((n : Nat) × Fin n)) := OptionT.run do
let (v, type) getOfNatValue? e ``Fin
let n getNatValue? ( whnfD type.appArg!)

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@@ -719,11 +719,13 @@ def deriveUnaryInduction (name : Name) : MetaM Name := do
let e' abstractIndependentMVars mvars ( motive.fvarId!.getDecl).index e'
let e' mkLambdaFVars #[motive] e'
-- We used to pass (usedOnly := false) below in the hope that the types of the
-- induction principle match the type of the function better.
-- But this leads to avoidable parameters that make functional induction strictly less
-- useful (e.g. when the unsued parameter mentions bound variables in the users' goal)
let e' mkLambdaFVars (binderInfoForMVars := .default) (usedOnly := true) fixedParams e'
-- We could pass (usedOnly := true) below, and get nicer induction principles that
-- do not mention odd unused parameters.
-- But the downside is that automatic instantiation of the principle (e.g. in a tactic
-- that derives them from an function application in the goal) is harder, as
-- one would have to infer or keep track of which parameters to pass.
-- So for now lets just keep them around.
let e' mkLambdaFVars (binderInfoForMVars := .default) fixedParams e'
instantiateMVars e'
| _ =>
if funBody.isAppOf ``WellFounded.fix then
@@ -1060,11 +1062,13 @@ def deriveInductionStructural (names : Array Name) (numFixed : Nat) : MetaM Unit
let e' abstractIndependentMVars mvars ( motives.back!.fvarId!.getDecl).index e'
let e' mkLambdaFVars motives e'
-- We used to pass (usedOnly := false) below in the hope that the types of the
-- induction principle match the type of the function better.
-- But this leads to avoidable parameters that make functional induction strictly less
-- useful (e.g. when the unsued parameter mentions bound variables in the users' goal)
let e' mkLambdaFVars (binderInfoForMVars := .default) (usedOnly := true) xs e'
-- We could pass (usedOnly := true) below, and get nicer induction principles that
-- do not mention odd unused parameters.
-- But the downside is that automatic instantiation of the principle (e.g. in a tactic
-- that derives them from an function application in the goal) is harder, as
-- one would have to infer or keep track of which parameters to pass.
-- So for now lets just keep them around.
let e' mkLambdaFVars (binderInfoForMVars := .default) xs e'
let e' instantiateMVars e'
trace[Meta.FunInd] "complete body of mutual induction principle:{indentExpr e'}"
pure e'

View File

@@ -20,18 +20,6 @@ def fromExpr? (e : Expr) : SimpM (Option Value) := do
let some n, value getFinValue? e | return none
return some { n, value }
@[inline] def reduceOp (declName : Name) (arity : Nat) (f : Nat Nat) (op : {n : Nat} Fin n Fin (f n)) (e : Expr) : SimpM DStep := do
unless e.isAppOfArity declName arity do return .continue
let some v fromExpr? e.appArg! | return .continue
let v' := op v.value
return .done <| toExpr v'
@[inline] def reduceNatOp (declName : Name) (arity : Nat) (f : Nat Nat) (op : (n : Nat) Fin (f n)) (e : Expr) : SimpM DStep := do
unless e.isAppOfArity declName arity do return .continue
let some v getNatValue? e.appArg! | return .continue
let v' := op v
return .done <| toExpr v'
@[inline] def reduceBin (declName : Name) (arity : Nat) (op : {n : Nat} Fin n Fin n Fin n) (e : Expr) : SimpM DStep := do
unless e.isAppOfArity declName arity do return .continue
let some v₁ fromExpr? e.appFn!.appArg! | return .continue
@@ -59,23 +47,12 @@ The following code assumes users did not override the `Fin n` instances for the
If they do, they must disable the following `simprocs`.
-/
builtin_dsimproc [simp, seval] reduceSucc (Fin.succ _) := reduceOp ``Fin.succ 2 (· + 1) Fin.succ
builtin_dsimproc [simp, seval] reduceRev (Fin.rev _) := reduceOp ``Fin.rev 2 (·) Fin.rev
builtin_dsimproc [simp, seval] reduceLast (Fin.last _) := reduceNatOp ``Fin.last 1 (· + 1) Fin.last
builtin_dsimproc [simp, seval] reduceAdd ((_ + _ : Fin _)) := reduceBin ``HAdd.hAdd 6 (· + ·)
builtin_dsimproc [simp, seval] reduceMul ((_ * _ : Fin _)) := reduceBin ``HMul.hMul 6 (· * ·)
builtin_dsimproc [simp, seval] reduceSub ((_ - _ : Fin _)) := reduceBin ``HSub.hSub 6 (· - ·)
builtin_dsimproc [simp, seval] reduceDiv ((_ / _ : Fin _)) := reduceBin ``HDiv.hDiv 6 (· / ·)
builtin_dsimproc [simp, seval] reduceMod ((_ % _ : Fin _)) := reduceBin ``HMod.hMod 6 (· % ·)
builtin_dsimproc [simp, seval] reduceAnd ((_ &&& _ : Fin _)) := reduceBin ``HAnd.hAnd 6 (· &&& ·)
builtin_dsimproc [simp, seval] reduceOr ((_ ||| _ : Fin _)) := reduceBin ``HOr.hOr 6 (· ||| ·)
builtin_dsimproc [simp, seval] reduceXor ((_ ^^^ _ : Fin _)) := reduceBin ``HXor.hXor 6 (· ^^^ ·)
builtin_dsimproc [simp, seval] reduceShiftLeft ((_ <<< _ : Fin _)) := reduceBin ``HShiftLeft.hShiftLeft 6 (· <<< ·)
builtin_dsimproc [simp, seval] reduceShiftRight ((_ >>> _ : Fin _)) := reduceBin ``HShiftRight.hShiftRight 6 (· >>> ·)
builtin_simproc [simp, seval] reduceLT (( _ : Fin _) < _) := reduceBinPred ``LT.lt 4 (. < .)
builtin_simproc [simp, seval] reduceLE (( _ : Fin _) _) := reduceBinPred ``LE.le 4 (. .)
builtin_simproc [simp, seval] reduceGT (( _ : Fin _) > _) := reduceBinPred ``GT.gt 4 (. > .)
@@ -106,70 +83,4 @@ builtin_dsimproc [simp, seval] reduceFinMk (Fin.mk _ _) := fun e => do
else
return .continue
builtin_dsimproc [simp, seval] reduceOfNat' (Fin.ofNat' _ _) := fun e => do
unless e.isAppOfArity ``Fin.ofNat' 3 do return .continue
let some (n + 1) getNatValue? e.appFn!.appFn!.appArg! | return .continue
let some k getNatValue? e.appArg! | return .continue
return .done <| toExpr (Fin.ofNat' (n + 1) k)
builtin_dsimproc [simp, seval] reduceCastSucc (Fin.castSucc _) := fun e => do
unless e.isAppOfArity ``Fin.castSucc 2 do return .continue
let some k fromExpr? e.appArg! | return .continue
return .done <| toExpr (castSucc k.value)
builtin_dsimproc [simp, seval] reduceCastAdd (Fin.castAdd _ _) := fun e => do
unless e.isAppOfArity ``Fin.castAdd 3 do return .continue
let some m getNatValue? e.appFn!.appArg! | return .continue
let some k fromExpr? e.appArg! | return .continue
return .done <| toExpr (castAdd m k.value)
builtin_dsimproc [simp, seval] reduceAddNat (Fin.addNat _ _) := fun e => do
unless e.isAppOfArity ``Fin.addNat 3 do return .continue
let some k fromExpr? e.appFn!.appArg! | return .continue
let some m getNatValue? e.appArg! | return .continue
return .done <| toExpr (addNat k.value m)
builtin_dsimproc [simp, seval] reduceNatAdd (Fin.natAdd _ _) := fun e => do
unless e.isAppOfArity ``Fin.natAdd 3 do return .continue
let some m getNatValue? e.appFn!.appArg! | return .continue
let some k fromExpr? e.appArg! | return .continue
return .done <| toExpr (natAdd m k.value)
builtin_dsimproc [simp, seval] reduceCastLT (Fin.castLT _ _) := fun e => do
unless e.isAppOfArity ``Fin.castLT 4 do return .continue
let some n getNatValue? e.appFn!.appFn!.appFn!.appArg! | return .continue
let some i fromExpr? e.appFn!.appArg! | return .continue
if h : i.value < n then
return .done <| toExpr (castLT i.value h)
else
return .continue
builtin_dsimproc [simp, seval] reduceCastLE (Fin.castLE _ _) := fun e => do
unless e.isAppOfArity ``Fin.castLE 4 do return .continue
let some m getNatValue? e.appFn!.appFn!.appArg! | return .continue
let some i fromExpr? e.appArg! | return .continue
if h : i.n m then
return .done <| toExpr (castLE h i.value)
else
return .continue
-- No simproc is needed for `Fin.cast`, as for explicit numbers `Fin.cast_refl` will apply.
builtin_dsimproc [simp, seval] reduceSubNat (Fin.subNat _ _ _) := fun e => do
unless e.isAppOfArity ``Fin.subNat 4 do return .continue
let some m getNatValue? e.appFn!.appFn!.appArg! | return .continue
let some i fromExpr? e.appFn!.appArg! | return .continue
if h : m i.value then
return .done <| toExpr (subNat m (i.value.cast (by omega : i.n = (i.n - m) + m)) h)
else
return .continue
builtin_dsimproc [simp, seval] reducePred (Fin.pred _ _) := fun e => do
unless e.isAppOfArity ``Fin.pred 3 do return .continue
let some (_ + 1), i fromExpr? e.appFn!.appArg! | return .continue
if h : i 0 then
return .done <| toExpr (pred i h)
else
return .continue
end Fin

View File

@@ -71,8 +71,8 @@ builtin_dsimproc [simp, seval] reduceMul ((_ * _ : Int)) := reduceBin ``HMul.hMu
builtin_dsimproc [simp, seval] reduceSub ((_ - _ : Int)) := reduceBin ``HSub.hSub 6 (· - ·)
builtin_dsimproc [simp, seval] reduceDiv ((_ / _ : Int)) := reduceBin ``HDiv.hDiv 6 (· / ·)
builtin_dsimproc [simp, seval] reduceMod ((_ % _ : Int)) := reduceBin ``HMod.hMod 6 (· % ·)
builtin_dsimproc [simp, seval] reduceTDiv (tdiv _ _) := reduceBin ``Int.tdiv 2 Int.tdiv
builtin_dsimproc [simp, seval] reduceTMod (tmod _ _) := reduceBin ``Int.tmod 2 Int.tmod
builtin_dsimproc [simp, seval] reduceTDiv (tdiv _ _) := reduceBin ``Int.div 2 Int.tdiv
builtin_dsimproc [simp, seval] reduceTMod (tmod _ _) := reduceBin ``Int.mod 2 Int.tmod
builtin_dsimproc [simp, seval] reduceFDiv (fdiv _ _) := reduceBin ``Int.fdiv 2 Int.fdiv
builtin_dsimproc [simp, seval] reduceFMod (fmod _ _) := reduceBin ``Int.fmod 2 Int.fmod
builtin_dsimproc [simp, seval] reduceBdiv (bdiv _ _) := reduceBinIntNatOp ``bdiv bdiv

View File

@@ -804,45 +804,18 @@ where
else
normalState num c s
/--
Parses a sequence of the form `many (many '_' >> many1 digit)`, but if `needDigit` is true the parsed result must be nonempty.
Note: this does not report that it is expecting `_` if we reach EOI or an unexpected character.
Rationale: this error happens if there is already a `_`, and while sequences of `_` are allowed, it's a bit perverse to suggest extending the sequence.
-/
partial def takeDigitsFn (isDigit : Char → Bool) (expecting : String) (needDigit : Bool) : ParserFn := fun c s =>
let input := c.input
let i := s.pos
if h : input.atEnd i then
if needDigit then
s.mkEOIError [expecting]
else
s
else
let curr := input.get' i h
if curr == '_' then takeDigitsFn isDigit expecting true c (s.next' c.input i h)
else if isDigit curr then takeDigitsFn isDigit expecting false c (s.next' c.input i h)
else if needDigit then s.mkUnexpectedError "unexpected character" (expected := [expecting])
else s
def decimalNumberFn (startPos : String.Pos) (c : ParserContext) : ParserState → ParserState := fun s =>
let s := takeDigitsFn (fun c => c.isDigit) "decimal number" false c s
let s := takeWhileFn (fun c => c.isDigit) c s
let input := c.input
let i := s.pos
if h : input.atEnd i then
mkNodeToken numLitKind startPos c s
else
let curr := input.get' i h
if curr == '.' || curr == 'e' || curr == 'E' then
parseScientific s
else
mkNodeToken numLitKind startPos c s
where
parseScientific s :=
let curr := input.get i
if curr == '.' || curr == 'e' || curr == 'E' then
let s := parseOptDot s
let s := parseOptExp s
mkNodeToken scientificLitKind startPos c s
else
mkNodeToken numLitKind startPos c s
where
parseOptDot s :=
let input := c.input
let i := s.pos
@@ -851,7 +824,7 @@ where
let i := input.next i
let curr := input.get i
if curr.isDigit then
takeDigitsFn (fun c => c.isDigit) "decimal number" false c (s.setPos i)
takeWhileFn (fun c => c.isDigit) c (s.setPos i)
else
s.setPos i
else
@@ -866,22 +839,22 @@ where
let i := if input.get i == '-' || input.get i == '+' then input.next i else i
let curr := input.get i
if curr.isDigit then
takeDigitsFn (fun c => c.isDigit) "decimal number" false c (s.setPos i)
takeWhileFn (fun c => c.isDigit) c (s.setPos i)
else
s.mkUnexpectedError "missing exponent digits in scientific literal"
else
s
def binNumberFn (startPos : String.Pos) : ParserFn := fun c s =>
let s := takeDigitsFn (fun c => c == '0' || c == '1') "binary number" true c s
let s := takeWhile1Fn (fun c => c == '0' || c == '1') "binary number" c s
mkNodeToken numLitKind startPos c s
def octalNumberFn (startPos : String.Pos) : ParserFn := fun c s =>
let s := takeDigitsFn (fun c => '0' ≤ c && c ≤ '7') "octal number" true c s
let s := takeWhile1Fn (fun c => '0' ≤ c && c ≤ '7') "octal number" c s
mkNodeToken numLitKind startPos c s
def hexNumberFn (startPos : String.Pos) : ParserFn := fun c s =>
let s := takeDigitsFn (fun c => ('0' ≤ c && c ≤ '9') || ('a' ≤ c && c ≤ 'f') || ('A' ≤ c && c ≤ 'F')) "hexadecimal number" true c s
let s := takeWhile1Fn (fun c => ('0' ≤ c && c ≤ '9') || ('a' ≤ c && c ≤ 'f') || ('A' ≤ c && c ≤ 'F')) "hexadecimal number" c s
mkNodeToken numLitKind startPos c s
def numberFnAux : ParserFn := fun c s =>

View File

@@ -100,6 +100,20 @@ private def findSyntheticIdentifierCompletion?
HoverInfo.after
some { hoverInfo, ctx, info := .id stx id danglingDot info.lctx none }
private partial def getIndentationAmount (fileMap : FileMap) (line : Nat) : Nat := Id.run do
let lineStartPos := fileMap.lineStart line
let lineEndPos := fileMap.lineStart (line + 1)
let mut it : String.Iterator := fileMap.source, lineStartPos
let mut indentationAmount := 0
while it.pos < lineEndPos do
let c := it.curr
if c = ' ' || c = '\t' then
indentationAmount := indentationAmount + 1
else
break
it := it.next
return indentationAmount
private partial def isCursorOnWhitespace (fileMap : FileMap) (hoverPos : String.Pos) : Bool :=
fileMap.source.atEnd hoverPos || (fileMap.source.get hoverPos).isWhitespace
@@ -113,10 +127,15 @@ private partial def isSyntheticTacticCompletion
(cmdStx : Syntax)
: Bool := Id.run do
let hoverFilePos := fileMap.toPosition hoverPos
go hoverFilePos cmdStx 0
let mut hoverLineIndentation := getIndentationAmount fileMap hoverFilePos.line
if hoverFilePos.column < hoverLineIndentation then
-- Ignore trailing whitespace after the cursor
hoverLineIndentation := hoverFilePos.column
go hoverFilePos hoverLineIndentation cmdStx 0
where
go
(hoverFilePos : Position)
(hoverLineIndentation : Nat)
(stx : Syntax)
(leadingWs : Nat)
: Bool := Id.run do
@@ -129,7 +148,7 @@ where
return false
let mut wsBeforeArg := leadingWs
for arg in stx.getArgs do
if go hoverFilePos arg wsBeforeArg then
if go hoverFilePos hoverLineIndentation arg wsBeforeArg then
return true
-- We must account for the whitespace before an argument because the syntax nodes we use
-- to identify tactic blocks only start *after* the whitespace following a `by`, and we
@@ -139,7 +158,7 @@ where
wsBeforeArg := arg.getTrailingSize
return isCompletionInEmptyTacticBlock stx
|| isCompletionAfterSemicolon stx
|| isCompletionOnTacticBlockIndentation hoverFilePos stx
|| isCompletionOnTacticBlockIndentation hoverFilePos hoverLineIndentation stx
| _, _ =>
-- Empty tactic blocks typically lack ranges since they do not contain any tokens.
-- We do not perform more precise range checking in this case because we assume that empty
@@ -150,17 +169,24 @@ where
isCompletionOnTacticBlockIndentation
(hoverFilePos : Position)
(hoverLineIndentation : Nat)
(stx : Syntax)
: Bool := Id.run do
let isCursorInIndentation := hoverFilePos.column <= hoverLineIndentation
if ! isCursorInIndentation then
-- Do not trigger tactic completion at the end of a properly indented tactic block line since
-- that line might already have entered term mode by that point.
return false
let some tacticsNode := getTacticsNode? stx
| return false
let some firstTacticPos := tacticsNode.getPos?
| return false
let firstTacticColumn := fileMap.toPosition firstTacticPos |>.column
let firstTacticLine := fileMap.toPosition firstTacticPos |>.line
let firstTacticIndentation := getIndentationAmount fileMap firstTacticLine
-- This ensures that we do not accidentally provide tactic completions in a term mode proof -
-- tactic completions are only provided at the same indentation level as the other tactics in
-- that tactic block.
let isCursorInTacticBlock := hoverFilePos.column == firstTacticColumn
let isCursorInTacticBlock := hoverLineIndentation == firstTacticIndentation
return isCursorInProperWhitespace fileMap hoverPos && isCursorInTacticBlock
isCompletionAfterSemicolon (stx : Syntax) : Bool := Id.run do
@@ -289,6 +315,10 @@ private def isSyntheticStructFieldCompletion
return false
let hoverFilePos := fileMap.toPosition hoverPos
let mut hoverLineIndentation := getIndentationAmount fileMap hoverFilePos.line
if hoverFilePos.column < hoverLineIndentation then
-- Ignore trailing whitespace after the cursor
hoverLineIndentation := hoverFilePos.column
return Option.isSome <| findWithLeadingToken? (stx := cmdStx) fun leadingToken? stx => Id.run do
let some leadingToken := leadingToken?
@@ -325,10 +355,14 @@ private def isSyntheticStructFieldCompletion
let isCompletionOnIndentation := Id.run do
if ! isCursorInProperWhitespace then
return false
let isCursorInIndentation := hoverFilePos.column <= hoverLineIndentation
if ! isCursorInIndentation then
return false
let some firstFieldPos := stx.getPos?
| return false
let firstFieldColumn := fileMap.toPosition firstFieldPos |>.column
let isCursorInBlock := hoverFilePos.column == firstFieldColumn
let firstFieldLine := fileMap.toPosition firstFieldPos |>.line
let firstFieldIndentation := getIndentationAmount fileMap firstFieldLine
let isCursorInBlock := hoverLineIndentation == firstFieldIndentation
return isCursorInBlock
return isCompletionOnIndentation

View File

@@ -6,7 +6,7 @@ Authors: Marc Huisinga, Wojciech Nawrocki
-/
prelude
import Init.System.IO
import Std.Sync.Channel
import Init.Data.Channel
import Lean.Data.RBMap
import Lean.Environment
@@ -64,7 +64,7 @@ open Widget in
structure WorkerContext where
/-- Synchronized output channel for LSP messages. Notifications for outdated versions are
discarded on read. -/
chanOut : Std.Channel JsonRpc.Message
chanOut : IO.Channel JsonRpc.Message
/--
Latest document version received by the client, used for filtering out notifications from
previous versions.
@@ -75,7 +75,7 @@ structure WorkerContext where
Channel that receives a message for every a `$/lean/fileProgress` notification, indicating whether
the notification suggests that the file is currently being processed.
-/
chanIsProcessing : Std.Channel Bool
chanIsProcessing : IO.Channel Bool
/--
Diagnostics that are included in every single `textDocument/publishDiagnostics` notification.
-/
@@ -271,7 +271,7 @@ open Language Lean in
Callback from Lean language processor after parsing imports that requests necessary information from
Lake for processing imports.
-/
def setupImports (meta : DocumentMeta) (cmdlineOpts : Options) (chanOut : Std.Channel JsonRpc.Message)
def setupImports (meta : DocumentMeta) (cmdlineOpts : Options) (chanOut : Channel JsonRpc.Message)
(srcSearchPathPromise : Promise SearchPath) (stx : Syntax) :
Language.ProcessingT IO (Except Language.Lean.HeaderProcessedSnapshot SetupImportsResult) := do
let importsAlreadyLoaded importsLoadedRef.modifyGet ((·, true))
@@ -337,7 +337,7 @@ section Initialization
let clientHasWidgets := initParams.initializationOptions?.bind (·.hasWidgets?) |>.getD false
let maxDocVersionRef IO.mkRef 0
let freshRequestIdRef IO.mkRef (0 : Int)
let chanIsProcessing Std.Channel.new
let chanIsProcessing IO.Channel.new
let stickyDiagnosticsRef IO.mkRef
let chanOut mkLspOutputChannel maxDocVersionRef chanIsProcessing
let srcSearchPathPromise IO.Promise.new
@@ -380,8 +380,8 @@ section Initialization
the output FS stream after discarding outdated notifications. This is the only component of
the worker with access to the output stream, so we can synchronize messages from parallel
elaboration tasks here. -/
mkLspOutputChannel maxDocVersion chanIsProcessing : IO (Std.Channel JsonRpc.Message) := do
let chanOut Std.Channel.new
mkLspOutputChannel maxDocVersion chanIsProcessing : IO (IO.Channel JsonRpc.Message) := do
let chanOut IO.Channel.new
let _ chanOut.forAsync (prio := .dedicated) fun msg => do
-- discard outdated notifications; note that in contrast to responses, notifications can
-- always be silently discarded

View File

@@ -6,7 +6,7 @@ Authors: Marc Huisinga, Wojciech Nawrocki
-/
prelude
import Init.System.IO
import Std.Sync.Mutex
import Init.System.Mutex
import Init.Data.ByteArray
import Lean.Data.RBMap
@@ -113,7 +113,7 @@ section FileWorker
structure FileWorker where
doc : DocumentMeta
proc : Process.Child workerCfg
exitCode : Std.Mutex (Option UInt32)
exitCode : IO.Mutex (Option UInt32)
commTask : Task WorkerEvent
state : WorkerState
-- This should not be mutated outside of namespace FileWorker,
@@ -392,7 +392,7 @@ section ServerM
-- open session for `kill` above
setsid := true
}
let exitCode Std.Mutex.new none
let exitCode IO.Mutex.new none
let pendingRequestsRef IO.mkRef (RBMap.empty : PendingRequestMap)
let initialDependencyBuildMode := m.dependencyBuildMode
let updatedDependencyBuildMode :=

View File

@@ -5,7 +5,6 @@ Authors: Leonardo de Moura
-/
prelude
import Lean.Expr
import Lean.ToLevel
import Init.Data.BitVec.Basic
universe u
@@ -139,35 +138,34 @@ instance : ToExpr Name where
toExpr := Name.toExprAux
toTypeExpr := mkConst ``Name
instance {α : Type u} [ToLevel.{u}] [ToExpr α] : ToExpr (Option α) :=
instance [ToExpr α] : ToExpr (Option α) :=
let type := toTypeExpr α
{ toExpr := fun o => match o with
| none => mkApp (mkConst ``Option.none [toLevel.{u}]) type
| some a => mkApp2 (mkConst ``Option.some [toLevel.{u}]) type (toExpr a),
toTypeExpr := mkApp (mkConst ``Option [toLevel.{u}]) type }
| none => mkApp (mkConst ``Option.none [levelZero]) type
| some a => mkApp2 (mkConst ``Option.some [levelZero]) type (toExpr a),
toTypeExpr := mkApp (mkConst ``Option [levelZero]) type }
private def List.toExprAux [ToExpr α] (nilFn : Expr) (consFn : Expr) : List α Expr
| [] => nilFn
| a::as => mkApp2 consFn (toExpr a) (toExprAux nilFn consFn as)
instance {α : Type u} [ToLevel.{u}] [ToExpr α] : ToExpr (List α) :=
instance [ToExpr α] : ToExpr (List α) :=
let type := toTypeExpr α
let nil := mkApp (mkConst ``List.nil [toLevel.{u}]) type
let cons := mkApp (mkConst ``List.cons [toLevel.{u}]) type
let nil := mkApp (mkConst ``List.nil [levelZero]) type
let cons := mkApp (mkConst ``List.cons [levelZero]) type
{ toExpr := List.toExprAux nil cons,
toTypeExpr := mkApp (mkConst ``List [toLevel.{u}]) type }
toTypeExpr := mkApp (mkConst ``List [levelZero]) type }
instance {α : Type u} [ToLevel.{u}] [ToExpr α] : ToExpr (Array α) :=
instance [ToExpr α] : ToExpr (Array α) :=
let type := toTypeExpr α
{ toExpr := fun as => mkApp2 (mkConst ``List.toArray [toLevel.{u}]) type (toExpr as.toList),
toTypeExpr := mkApp (mkConst ``Array [toLevel.{u}]) type }
{ toExpr := fun as => mkApp2 (mkConst ``List.toArray [levelZero]) type (toExpr as.toList),
toTypeExpr := mkApp (mkConst ``Array [levelZero]) type }
instance {α : Type u} {β : Type v} [ToLevel.{u}] [ToLevel.{v}]
[ToExpr α] [ToExpr β] : ToExpr (α × β) :=
instance [ToExpr α] [ToExpr β] : ToExpr (α × β) :=
let αType := toTypeExpr α
let βType := toTypeExpr β
{ toExpr := fun a, b => mkApp4 (mkConst ``Prod.mk [toLevel.{u}, toLevel.{v}]) αType βType (toExpr a) (toExpr b),
toTypeExpr := mkApp2 (mkConst ``Prod [toLevel.{u}, toLevel.{v}]) αType βType }
{ toExpr := fun a, b => mkApp4 (mkConst ``Prod.mk [levelZero, levelZero]) αType βType (toExpr a) (toExpr b),
toTypeExpr := mkApp2 (mkConst ``Prod [levelZero, levelZero]) αType βType }
instance : ToExpr Literal where
toTypeExpr := mkConst ``Literal

View File

@@ -1,40 +0,0 @@
/-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Alex Keizer
-/
prelude
import Lean.Expr
/-!
# `ToLevel` class
This module defines `Lean.ToLevel`, which is the `Lean.Level` analogue to `Lean.ToExpr`.
-/
namespace Lean
/-- A class to create `Level` expressions that denote particular universe levels in Lean.
`Lean.ToLevel.toLevel.{u}` evaluates to a `Lean.Level` term representing `u` -/
class ToLevel.{u} : Type where
/-- A `Level` that represents the universe level `u`. -/
toLevel : Level
/-- A hack to avoid the "unused universe parameter" error.
We can remove this field pending issue https://github.com/leanprover/lean4/issues/2116 -/
univ : (_ : Sort u), True := fun _ => trivial
export ToLevel (toLevel)
instance : ToLevel.{0} where
toLevel := .zero
instance [ToLevel.{u}] : ToLevel.{u+1} where
toLevel := .succ toLevel.{u}
/-- `ToLevel` for `max u v`. This is not an instance since it causes divergence. -/
def ToLevel.max [ToLevel.{u}] [ToLevel.{v}] : ToLevel.{max u v} where
toLevel := .max toLevel.{u} toLevel.{v}
/-- `ToLevel` for `imax u v`. This is not an instance since it causes divergence. -/
def ToLevel.imax [ToLevel.{u}] [ToLevel.{v}] : ToLevel.{imax u v} where
toLevel := .imax toLevel.{u} toLevel.{v}
end Lean

View File

@@ -6,7 +6,6 @@ Authors: Sebastian Ullrich
prelude
import Std.Data
import Std.Sat
import Std.Sync
import Std.Time
import Std.Tactic
import Std.Internal

View File

@@ -10,11 +10,6 @@ import Init.NotationExtra
This is an internal implementation file of the hash map. Users of the hash map should not rely on
the contents of this file.
Note that some functions in this file (in particular, `foldrM`, `foldr`, `toList`, `replace`, and
`erase`) are not tail-recursive. This is not a problem because they are only used internally by
`HashMap`, where `AssocList` is always small. Before making this API public, we would need to add
`@[csimp]` lemmas for tail-recursive implementations.
File contents: Operations on associative lists
-/
@@ -51,17 +46,6 @@ namespace AssocList
@[inline] def foldl (f : δ (α : α) β α δ) (init : δ) (as : AssocList α β) : δ :=
Id.run (foldlM f init as)
/-- Internal implementation detail of the hash map -/
@[specialize] def foldrM (f : (a : α) β a δ m δ) : (init : δ) AssocList α β m δ
| d, nil => pure d
| d, cons a b es => do
let d foldrM f d es
f a b d
/-- Internal implementation detail of the hash map -/
@[inline] def foldr (f : (a : α) β a δ δ) (init : δ) (as : AssocList α β) : δ :=
Id.run (foldrM f init as)
/-- Internal implementation detail of the hash map -/
@[inline] def forM (f : (a : α) β a m PUnit) (as : AssocList α β) : m PUnit :=
as.foldlM (fun _ => f)

View File

@@ -204,9 +204,4 @@ theorem foldl_apply {l : AssocList α β} {acc : List δ} (f : (a : α) → β a
(l.toList.map (fun p => f p.1 p.2)).reverse ++ acc := by
induction l generalizing acc <;> simp_all [AssocList.foldl, AssocList.foldlM, Id.run]
theorem foldr_apply {l : AssocList α β} {acc : List δ} (f : (a : α) β a δ) :
l.foldr (fun k v acc => f k v :: acc) acc =
(l.toList.map (fun p => f p.1 p.2)) ++ acc := by
induction l generalizing acc <;> simp_all [AssocList.foldr, AssocList.foldrM, Id.run]
end Std.DHashMap.Internal.AssocList

View File

@@ -46,11 +46,19 @@ cf. https://github.com/leanprover/lean4/issues/4157
@[irreducible, inline] def mkIdx (sz : Nat) (h : 0 < sz) (hash : UInt64) :
{ u : USize // u.toNat < sz } :=
(scrambleHash hash).toUSize &&& (sz.toUSize - 1), by
-- This proof is a good test for our USize API
-- Making this proof significantly less painful will be a good test for our USize API
by_cases h' : sz < USize.size
· rw [USize.toNat_and, USize.toNat_sub_of_le, USize.toNat_ofNat_of_lt h']
· exact Nat.lt_of_le_of_lt Nat.and_le_right (Nat.sub_lt h (by simp))
· simp [USize.le_iff_toNat_le, Nat.mod_eq_of_lt h', Nat.succ_le_of_lt h]
· rw [USize.and_toNat, USize.ofNat_one, USize.toNat_sub_of_le, USize.toNat_ofNat_of_lt]
· refine Nat.lt_of_le_of_lt Nat.and_le_right (Nat.sub_lt h ?_)
rw [USize.toNat_ofNat_of_lt]
· exact Nat.one_pos
· exact Nat.lt_of_le_of_lt h h'
· exact h'
· rw [USize.le_def, BitVec.le_def]
change _ (_ % _)
rw [Nat.mod_eq_of_lt h', USize.ofNat, BitVec.toNat_ofNat, Nat.mod_eq_of_lt]
· exact h
· exact Nat.lt_of_le_of_lt h h'
· exact Nat.lt_of_lt_of_le (USize.toNat_lt_size _) (Nat.le_of_not_lt h')
end Std.DHashMap.Internal

View File

@@ -83,36 +83,12 @@ theorem fold_cons_key {l : Raw α β} {acc : List α} :
l.fold (fun acc k _ => k :: acc) acc = List.keys (toListModel l.buckets).reverse ++ acc := by
rw [fold_cons_apply, keys_eq_map, map_reverse]
theorem foldRev_eq {l : Raw α β} {f : γ (a : α) β a γ} {init : γ} :
l.foldRev f init = l.buckets.foldr (fun l acc => l.foldr (fun a b g => f g a b) acc) init := by
simp only [Raw.foldRev, Raw.foldRevM, Array.foldrM_toList, Array.foldr_toList,
List.foldr_eq_foldrM, Id.run, AssocList.foldr]
theorem foldRev_cons_apply {l : Raw α β} {acc : List γ} (f : (a : α) β a γ) :
l.foldRev (fun acc k v => f k v :: acc) acc =
((toListModel l.buckets).map (fun p => f p.1 p.2)) ++ acc := by
rw [foldRev_eq, Array.foldr_toList, toListModel]
generalize l.buckets.toList = l
induction l generalizing acc with
| nil => simp
| cons x xs ih =>
rw [foldr_cons, ih, AssocList.foldr_apply]
simp
theorem foldRev_cons {l : Raw α β} {acc : List ((a : α) × β a)} :
l.foldRev (fun acc k v => k, v :: acc) acc = toListModel l.buckets ++ acc := by
simp [foldRev_cons_apply]
theorem foldRev_cons_key {l : Raw α β} {acc : List α} :
l.foldRev (fun acc k _ => k :: acc) acc = List.keys (toListModel l.buckets) ++ acc := by
rw [foldRev_cons_apply, keys_eq_map]
theorem toList_perm_toListModel {m : Raw α β} : Perm m.toList (toListModel m.buckets) := by
simp [Raw.toList, foldRev_cons]
simp [Raw.toList, fold_cons]
theorem keys_perm_keys_toListModel {m : Raw α β} :
Perm m.keys (List.keys (toListModel m.buckets)) := by
simp [Raw.keys, foldRev_cons_key, keys_eq_map]
simp [Raw.keys, fold_cons_key, keys_eq_map]
theorem length_keys_eq_length_keys {m : Raw α β} :
m.keys.length = (List.keys (toListModel m.buckets)).length :=
@@ -216,7 +192,7 @@ theorem expand.go_eq [BEq α] [Hashable α] [PartialEquivBEq α] (source : Array
refine ih.trans ?_
simp only [Array.get_eq_getElem, AssocList.foldl_eq, Array.toList_set]
rw [List.drop_eq_getElem_cons hi, List.flatMap_cons, List.foldl_append,
List.drop_set_of_lt _ _ (by omega), Array.getElem_toList]
List.drop_set_of_lt _ _ (by omega), Array.getElem_eq_getElem_toList]
· next i source target hi =>
rw [expand.go_neg hi, List.drop_eq_nil_of_le, flatMap_nil, foldl_nil]
rwa [Array.size_eq_length_toList, Nat.not_lt] at hi

View File

@@ -333,19 +333,6 @@ map in some order.
@[inline] def fold (f : δ (a : α) β a δ) (init : δ) (b : Raw α β) : δ :=
Id.run (b.foldM f init)
/--
Monadically computes a value by folding the given function over the mappings in the hash
map in the reverse order used by `foldM`.
-/
@[inline] def foldRevM (f : δ (a : α) β a m δ) (init : δ) (b : Raw α β) : m δ :=
b.buckets.foldrM (fun l acc => l.foldrM (fun a b d => f d a b) acc) init
/--
Folds the given function over the mappings in the hash map in the reverse order used
by `foldM`. -/
@[inline] def foldRev (f : δ (a : α) β a δ) (init : δ) (b : Raw α β) : δ :=
Id.run (b.foldRevM f init)
/-- Carries out a monadic action on each mapping in the hash map in some order. -/
@[inline] def forM (f : (a : α) β a m PUnit) (b : Raw α β) : m PUnit :=
b.buckets.forM (AssocList.forM f)
@@ -362,7 +349,7 @@ instance : ForIn m (Raw α β) ((a : α) × β a) where
/-- Transforms the hash map into a list of mappings in some order. -/
@[inline] def toList (m : Raw α β) : List ((a : α) × β a) :=
m.foldRev (fun acc k v => k, v :: acc) []
m.fold (fun acc k v => k, v :: acc) []
/-- Transforms the hash map into an array of mappings in some order. -/
@[inline] def toArray (m : Raw α β) : Array ((a : α) × β a) :=
@@ -370,7 +357,7 @@ instance : ForIn m (Raw α β) ((a : α) × β a) where
@[inline, inherit_doc Raw.toList] def Const.toList {β : Type v} (m : Raw α (fun _ => β)) :
List (α × β) :=
m.foldRev (fun acc k v => k, v :: acc) []
m.fold (fun acc k v => k, v :: acc) []
@[inline, inherit_doc Raw.toArray] def Const.toArray {β : Type v} (m : Raw α (fun _ => β)) :
Array (α × β) :=
@@ -382,7 +369,7 @@ instance : ForIn m (Raw α β) ((a : α) × β a) where
/-- Returns a list of all values present in the hash map in some order. -/
@[inline] def values {β : Type v} (m : Raw α (fun _ => β)) : List β :=
m.foldRev (fun acc _ v => v :: acc) []
m.fold (fun acc _ v => v :: acc) []
/-- Returns an array of all values present in the hash map in some order. -/
@[inline] def valuesArray {β : Type v} (m : Raw α (fun _ => β)) : Array β :=
@@ -468,7 +455,7 @@ end Unverified
/-- Returns a list of all keys present in the hash map in some order. -/
@[inline] def keys (m : Raw α β) : List α :=
m.foldRev (fun acc k _ => k :: acc) []
m.fold (fun acc k _ => k :: acc) []
section WF

View File

@@ -354,7 +354,7 @@ theorem containsThenInsert_snd {k : α} : (m.containsThenInsert k).2 = m.insert
ext HashMap.containsThenInsertIfNew_snd
@[simp]
theorem length_toList [EquivBEq α] [LawfulHashable α] :
theorem length_toList [EquivBEq α] [LawfulHashable α] :
m.toList.length = m.size :=
HashMap.length_keys
@@ -369,7 +369,7 @@ theorem contains_toList [EquivBEq α] [LawfulHashable α] {k : α}:
HashMap.contains_keys
@[simp]
theorem mem_toList [LawfulBEq α] [LawfulHashable α] {k : α} :
theorem mem_toList [LawfulBEq α] [LawfulHashable α] {k : α}:
k m.toList k m :=
HashMap.mem_keys

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