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1 Commits

Author SHA1 Message Date
Leonardo de Moura
c35ec8668d fix: grind sort internalization
This PR ensures sorts are internalized by `grind`.
2025-09-20 11:24:22 -07:00
2909 changed files with 9755 additions and 38433 deletions

View File

@@ -116,10 +116,10 @@ jobs:
build/stage1/**/*.ir
build/stage1/**/*.c
build/stage1/**/*.c.o*' || '' }}
key: ${{ matrix.name }}-build-v4-${{ github.sha }}
key: ${{ matrix.name }}-build-v3-${{ github.sha }}
# fall back to (latest) previous cache
restore-keys: |
${{ matrix.name }}-build-v4
${{ matrix.name }}-build-v3
# open nix-shell once for initial setup
- name: Setup
run: |

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@@ -213,7 +213,7 @@ jobs:
},*/
{
"name": "macOS",
"os": "macos-15-intel",
"os": "macos-13",
"release": true,
"check-level": 2,
"shell": "bash -euxo pipefail {0}",
@@ -226,7 +226,7 @@ jobs:
{
"name": "macOS aarch64",
// standard GH runner only comes with 7GB so use large runner if possible when running tests
"os": large && !isPr ? "nscloud-macos-sequoia-arm64-6x14" : "macos-15",
"os": large && !isPr ? "nscloud-macos-sonoma-arm64-6x14" : "macos-14",
"CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
"release": true,
"shell": "bash -euxo pipefail {0}",

View File

@@ -69,10 +69,10 @@ jobs:
build/stage1/**/*.ir
build/stage1/**/*.c
build/stage1/**/*.c.o*
key: Linux Lake-build-v4-${{ github.sha }}
key: Linux Lake-build-v3-${{ github.sha }}
# fall back to (latest) previous cache
restore-keys: |
Linux Lake-build-v4
Linux Lake-build-v3
- if: env.should_update_stage0 == 'yes'
# sync options with `Linux Lake` to ensure cache reuse
run: |

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@@ -59,7 +59,7 @@ All these tests are included by [src/shell/CMakeLists.txt](https://github.com/le
open Foo in
theorem tst2 (h : a ≤ b) : a + 2 ≤ b + 2 :=
Bla.
--^ completion
--^ textDocument/completion
```
In this example, the test driver [`test_single.sh`](https://github.com/leanprover/lean4/tree/master/tests/lean/interactive/test_single.sh) will simulate an
auto-completion request at `Bla.`. The expected output is stored in

View File

@@ -8,9 +8,6 @@
},
{
"path": "tests"
},
{
"path": "script"
}
],
"settings": {

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@@ -1,91 +0,0 @@
import Lake.CLI.Main
/-!
A simple script that inserts `module` and `@[expose] public section` into un-modulized files and
bumps their imports to `public`.
-/
open Lean Parser.Module
def main (args : List String) : IO Unit := do
initSearchPath ( findSysroot)
-- the list of root modules
let mut mods := args.toArray.map (·.toName)
if mods.isEmpty then
-- Determine default module(s) to run modulize on
mods try
let (elanInstall?, leanInstall?, lakeInstall?) Lake.findInstall?
let config Lake.MonadError.runEIO <| Lake.mkLoadConfig { elanInstall?, leanInstall?, lakeInstall? }
let some workspace Lake.loadWorkspace config |>.toBaseIO
| throw <| IO.userError "failed to load Lake workspace"
let defaultTargetModules := workspace.root.defaultTargets.flatMap fun target =>
if let some lib := workspace.root.findLeanLib? target then
lib.roots
else if let some exe := workspace.root.findLeanExe? target then
#[exe.config.root]
else
#[]
pure defaultTargetModules
catch _ =>
pure #[]
-- Only submodules of `pkg` will be edited or have info reported on them
let pkg := mods[0]!.components.head!
-- Load all the modules
let imps := mods.map ({ module := · })
let env importModules imps {}
let srcSearchPath getSrcSearchPath
for mod in env.header.moduleNames do
if !pkg.isPrefixOf mod then
continue
-- Parse the input file
let some path srcSearchPath.findModuleWithExt "lean" mod
| throw <| .userError "error: failed to find source file for {mod}"
let mut text IO.FS.readFile path
let inputCtx := Parser.mkInputContext text path.toString
let (header, parserState, msgs) Parser.parseHeader inputCtx
if !msgs.toList.isEmpty then -- skip this file if there are parse errors
msgs.forM fun msg => msg.toString >>= IO.println
throw <| .userError "parse errors in file"
let `(header| $[module%$moduleTk?]? $imps:import*) := header
| throw <| .userError s!"unexpected header syntax of {path}"
if moduleTk?.isSome then
continue
let looksMeta := mod.components.any (· [`Tactic, `Linter])
-- initial whitespace if empty header
let startPos := header.raw.getPos? |>.getD parserState.pos
-- insert section if any trailing text
if header.raw.getTrailingTailPos?.all (· < text.endPos) then
let insertPos := header.raw.getTailPos? |>.getD startPos -- empty header
let mut sec := if looksMeta then
"public meta section"
else
"@[expose] public section"
if !imps.isEmpty then
sec := "\n\n" ++ sec
if header.raw.getTailPos?.isNone then
sec := sec ++ "\n\n"
text := text.extract 0 insertPos ++ sec ++ text.extract insertPos text.endPos
-- prepend each import with `public `
for imp in imps.reverse do
let insertPos := imp.raw.getPos?.get!
let prfx := if looksMeta then "public meta " else "public "
text := text.extract 0 insertPos ++ prfx ++ text.extract insertPos text.endPos
-- insert `module` header
let mut initText := text.extract 0 startPos
if !initText.trim.isEmpty then
-- If there is a header comment, preserve it and put `module` in the line after
initText := initText.trimRight ++ "\n"
text := initText ++ "module\n\n" ++ text.extract startPos text.endPos
IO.FS.writeFile path text

View File

@@ -1,584 +0,0 @@
/-
Copyright (c) 2023 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Sebastian Ullrich
-/
import Lake.CLI.Main
import Lean.ExtraModUses
/-! # `lake exe shake` command
This command will check the current project (or a specified target module) and all dependencies for
unused imports. This works by looking at generated `.olean` files to deduce required imports and
ensuring that every import is used to contribute some constant or other elaboration dependency
recorded by `recordExtraModUse`. Because recompilation is not needed this is quite fast (about 8
seconds to check `Mathlib` and all dependencies).
-/
/-- help string for the command line interface -/
def help : String := "Lean project tree shaking tool
Usage: lake exe shake [OPTIONS] <MODULE>..
Arguments:
<MODULE>
A module path like `Mathlib`. All files transitively reachable from the
provided module(s) will be checked.
Options:
--force
Skips the `lake build --no-build` sanity check
--fix
Apply the suggested fixes directly. Make sure you have a clean checkout
before running this, so you can review the changes.
"
open Lean
/-- We use `Nat` as a bitset for doing efficient set operations.
The bit indexes will usually be a module index. -/
structure Bitset where
toNat : Nat
deriving Inhabited, DecidableEq, Repr
namespace Bitset
instance : EmptyCollection Bitset where
emptyCollection := { toNat := 0 }
instance : Insert Nat Bitset where
insert i s := { toNat := s.toNat ||| (1 <<< i) }
instance : Singleton Nat Bitset where
singleton i := insert i
instance : Inter Bitset where
inter a b := { toNat := a.toNat &&& b.toNat }
instance : Union Bitset where
union a b := { toNat := a.toNat ||| b.toNat }
instance : XorOp Bitset where
xor a b := { toNat := a.toNat ^^^ b.toNat }
def has (s : Bitset) (i : Nat) : Bool := s {i}
end Bitset
/-- The kind of a module dependency, corresponding to the homonymous `ExtraModUse` fields. -/
structure NeedsKind where
isExported : Bool
isMeta : Bool
deriving Inhabited, BEq, Repr, Hashable
namespace NeedsKind
@[match_pattern] abbrev priv : NeedsKind := { isExported := false, isMeta := false }
@[match_pattern] abbrev pub : NeedsKind := { isExported := true, isMeta := false }
@[match_pattern] abbrev metaPriv : NeedsKind := { isExported := false, isMeta := true }
@[match_pattern] abbrev metaPub : NeedsKind := { isExported := true, isMeta := true }
def all : Array NeedsKind := #[pub, priv, metaPub, metaPriv]
def ofImport : Lean.Import NeedsKind
| { isExported := true, isMeta := true, .. } => .metaPub
| { isExported := true, isMeta := false, .. } => .pub
| { isExported := false, isMeta := true, .. } => .metaPriv
| { isExported := false, isMeta := false, .. } => .priv
end NeedsKind
/-- Logically, a map `NeedsKind → Bitset`. -/
structure Needs where
pub : Bitset
priv : Bitset
metaPub : Bitset
metaPriv : Bitset
deriving Inhabited, Repr
def Needs.empty : Needs := default
def Needs.get (needs : Needs) (k : NeedsKind) : Bitset :=
match k with
| .pub => needs.pub
| .priv => needs.priv
| .metaPub => needs.metaPub
| .metaPriv => needs.metaPriv
def Needs.has (needs : Needs) (k : NeedsKind) (i : ModuleIdx) : Bool :=
needs.get k |>.has i
def Needs.set (needs : Needs) (k : NeedsKind) (s : Bitset) : Needs :=
match k with
| .pub => { needs with pub := s }
| .priv => { needs with priv := s }
| .metaPub => { needs with metaPub := s }
| .metaPriv => { needs with metaPriv := s }
def Needs.modify (needs : Needs) (k : NeedsKind) (f : Bitset Bitset) : Needs :=
needs.set k (f (needs.get k))
def Needs.union (needs : Needs) (k : NeedsKind) (s : Bitset) : Needs :=
needs.modify k (· s)
def Needs.sub (needs : Needs) (k : NeedsKind) (s : Bitset) : Needs :=
needs.modify k (fun s' => s' ^^^ (s' s))
/-- The main state of the checker, containing information on all loaded modules. -/
structure State where
env : Environment
/--
`transDeps[i]` is the (non-reflexive) transitive closure of `mods[i].imports`. More specifically,
* `j ∈ transDeps[i].pub` if `i -(public import)->+ j`
* `j ∈ transDeps[i].priv` if `i -(import ...)-> _ -(public import)->* j`
* `j ∈ transDeps[i].priv` if `i -(import all)->+ -(public import ...)-> _ -(public import)->* j`
* `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import ...)->* j`
* `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import ...)->* j`
* `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ -(public meta import ...)-> _ -(public (meta)? import ...)->* j`
-/
transDeps : Array Needs := #[]
/--
`transDepsOrig` is the initial value of `transDeps` before changes potentially resulting from
changes to upstream headers.
-/
transDepsOrig : Array Needs := #[]
def State.mods (s : State) := s.env.header.moduleData
def State.modNames (s : State) := s.env.header.moduleNames
/--
Given module `j`'s transitive dependencies, computes the union of `transImps` and the transitive
dependencies resulting from importing the module via `imp` according to the rules of
`State.transDeps`.
-/
def addTransitiveImps (transImps : Needs) (imp : Import) (j : Nat) (impTransImps : Needs) : Needs := Id.run do
let mut transImps := transImps
-- `j ∈ transDeps[i].pub` if `i -(public import)->+ j`
if imp.isExported && !imp.isMeta then
transImps := transImps.union .pub {j} |>.union .pub (impTransImps.get .pub)
if !imp.isExported && !imp.isMeta then
-- `j ∈ transDeps[i].priv` if `i -(import ...)-> _ -(public import)->* j`
transImps := transImps.union .priv {j} |>.union .priv (impTransImps.get .pub)
if imp.importAll then
-- `j ∈ transDeps[i].priv` if `i -(import all)->+ -(public import ...)-> _ -(public import)->* j`
transImps := transImps.union .priv (impTransImps.get .pub)
-- `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import ...)->* j`
if imp.isExported then
transImps := transImps.union .metaPub (impTransImps.get .metaPub)
if imp.isMeta then
transImps := transImps.union .metaPub {j} |>.union .metaPub (impTransImps.get .pub impTransImps.get .metaPub)
if !imp.isExported then
if imp.isMeta then
-- `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import ...)->* j`
transImps := transImps.union .metaPriv {j} |>.union .metaPriv (impTransImps.get .pub impTransImps.get .metaPub)
if imp.importAll then
-- `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ -(public meta import ...)-> _ -(public (meta)? import ...)->* j`
transImps := transImps.union .metaPriv (impTransImps.get .metaPub)
transImps
/-- Calculates the needs for a given module `mod` from constants and recorded extra uses. -/
def calcNeeds (env : Environment) (i : ModuleIdx) : Needs := Id.run do
let mut needs := default
for ci in env.header.moduleData[i]!.constants do
let pubCI? := env.setExporting true |>.find? ci.name
let k := { isExported := pubCI?.isSome, isMeta := isMeta env ci.name }
needs := visitExpr k ci.type needs
if let some e := ci.value? (allowOpaque := true) then
-- type and value has identical visibility under `meta`
let k := if k.isMeta then k else
if pubCI?.any (·.hasValue (allowOpaque := true)) then .pub else .priv
needs := visitExpr k e needs
for use in getExtraModUses env i do
let j := env.getModuleIdx? use.module |>.get!
needs := needs.union { use with } {j}
return needs
where
/-- Accumulate the results from expression `e` into `deps`. -/
visitExpr (k : NeedsKind) e deps :=
Lean.Expr.foldConsts e deps fun c deps => match env.getModuleIdxFor? c with
| some j =>
let k := { k with isMeta := k.isMeta && !isMeta env c }
if j != i then deps.union k {j} else deps
| _ => deps
/--
Calculates the same as `calcNeeds` but tracing each module to a use-def declaration pair or
`none` if merely a recorded extra use.
-/
def getExplanations (env : Environment) (i : ModuleIdx) :
Std.HashMap (ModuleIdx × NeedsKind) (Option (Name × Name)) := Id.run do
let mut deps := default
for ci in env.header.moduleData[i]!.constants do
let pubCI? := env.setExporting true |>.find? ci.name
let k := { isExported := pubCI?.isSome, isMeta := isMeta env ci.name }
deps := visitExpr k ci.name ci.type deps
if let some e := ci.value? (allowOpaque := true) then
let k := if k.isMeta then k else
if pubCI?.any (·.hasValue (allowOpaque := true)) then .pub else .priv
deps := visitExpr k ci.name e deps
for use in getExtraModUses env i do
let j := env.getModuleIdx? use.module |>.get!
if !deps.contains (j, { use with }) then
deps := deps.insert (j, { use with }) none
return deps
where
/-- Accumulate the results from expression `e` into `deps`. -/
visitExpr (k : NeedsKind) name e deps :=
Lean.Expr.foldConsts e deps fun c deps => match env.getModuleIdxFor? c with
| some i =>
let k := { k with isMeta := k.isMeta && !isMeta env c }
if
if let some (some (name', _)) := deps[(i, k)]? then
decide (name.toString.length < name'.toString.length)
else true
then
deps.insert (i, k) (name, c)
else
deps
| _ => deps
partial def initStateFromEnv (env : Environment) : State := Id.run do
let mut s := { env }
for i in 0...env.header.moduleData.size do
let mod := env.header.moduleData[i]!
let mut imps := #[]
let mut transImps := Needs.empty
for imp in mod.imports do
let j := env.getModuleIdx? imp.module |>.get!
imps := imps.push j
transImps := addTransitiveImps transImps imp j s.transDeps[j]!
s := { s with transDeps := s.transDeps.push transImps }
s := { s with transDepsOrig := s.transDeps }
return s
/-- The list of edits that will be applied in `--fix`. `edits[i] = (removed, added)` where:
* If `j ∈ removed` then we want to delete module named `j` from the imports of `i`
* If `j ∈ added` then we want to add module index `j` to the imports of `i`.
-/
abbrev Edits := Std.HashMap Name (Array Import × Array Import)
/-- Register that we want to remove `tgt` from the imports of `src`. -/
def Edits.remove (ed : Edits) (src : Name) (tgt : Import) : Edits :=
match ed.get? src with
| none => ed.insert src (#[tgt], #[])
| some (a, b) => ed.insert src (a.push tgt, b)
/-- Register that we want to add `tgt` to the imports of `src`. -/
def Edits.add (ed : Edits) (src : Name) (tgt : Import) : Edits :=
match ed.get? src with
| none => ed.insert src (#[], #[tgt])
| some (a, b) => ed.insert src (a, b.push tgt)
/-- Parse a source file to extract the location of the import lines, for edits and error messages.
Returns `(path, inputCtx, imports, endPos)` where `imports` is the `Lean.Parser.Module.import` list
and `endPos` is the position of the end of the header.
-/
def parseHeaderFromString (text path : String) :
IO (System.FilePath × Parser.InputContext ×
TSyntaxArray ``Parser.Module.import × String.Pos) := do
let inputCtx := Parser.mkInputContext text path
let (header, parserState, msgs) Parser.parseHeader inputCtx
if !msgs.toList.isEmpty then -- skip this file if there are parse errors
msgs.forM fun msg => msg.toString >>= IO.println
throw <| .userError "parse errors in file"
-- the insertion point for `add` is the first newline after the imports
let insertion := header.raw.getTailPos?.getD parserState.pos
let insertion := text.findAux (· == '\n') text.endPos insertion + 1
pure (path, inputCtx, .mk header.raw[2].getArgs, insertion)
/-- Parse a source file to extract the location of the import lines, for edits and error messages.
Returns `(path, inputCtx, imports, endPos)` where `imports` is the `Lean.Parser.Module.import` list
and `endPos` is the position of the end of the header.
-/
def parseHeader (srcSearchPath : SearchPath) (mod : Name) :
IO (System.FilePath × Parser.InputContext ×
TSyntaxArray ``Parser.Module.import × String.Pos) := do
-- Parse the input file
let some path srcSearchPath.findModuleWithExt "lean" mod
| throw <| .userError s!"error: failed to find source file for {mod}"
let text IO.FS.readFile path
parseHeaderFromString text path.toString
def decodeImport : TSyntax ``Parser.Module.import Import
| `(Parser.Module.import| $[public%$pubTk?]? $[meta%$metaTk?]? import $[all%$allTk?]? $id) =>
{ module := id.getId, isExported := pubTk?.isSome, isMeta := metaTk?.isSome, importAll := allTk?.isSome }
| stx => panic! s!"unexpected syntax {stx}"
/-- Analyze and report issues from module `i`. Arguments:
* `srcSearchPath`: Used to find the path for error reporting purposes
* `i`: the module index
* `needs`: the module's calculated needs
* `pinned`: dependencies that should be preserved even if unused
* `edits`: accumulates the list of edits to apply if `--fix` is true
* `addOnly`: if true, only add missing imports, do not remove unused ones
-/
def visitModule (srcSearchPath : SearchPath)
(i : Nat) (needs : Needs) (preserve : Needs) (edits : Edits)
(addOnly := false) (githubStyle := false) (explain := false) : StateT State IO Edits := do
let s get
-- Do transitive reduction of `needs` in `deps`.
let mut deps := needs
for j in [0:s.mods.size] do
let transDeps := s.transDeps[j]!
for k in NeedsKind.all do
if s.transDepsOrig[i]!.has k j && preserve.has k j then
deps := deps.union k {j}
if deps.has k j then
let transDeps := addTransitiveImps .empty { k with module := .anonymous } j transDeps
for k' in NeedsKind.all do
deps := deps.sub k' (transDeps.sub k' {j} |>.get k')
-- Any import which is not in `transDeps` was unused.
-- Also accumulate `newDeps` which is the transitive closure of the remaining imports
let mut toRemove : Array Import := #[]
let mut newDeps := Needs.empty
for imp in s.mods[i]!.imports do
let j := s.env.getModuleIdx? imp.module |>.get!
if
-- skip folder-nested imports
s.modNames[i]!.isPrefixOf imp.module ||
imp.importAll then
newDeps := addTransitiveImps newDeps imp j s.transDeps[j]!
else
let k := NeedsKind.ofImport imp
if !addOnly && !deps.has k j && !deps.has { k with isExported := false } j then
toRemove := toRemove.push imp
else
newDeps := addTransitiveImps newDeps imp j s.transDeps[j]!
-- If `newDeps` does not cover `deps`, then we have to add back some imports until it does.
-- To minimize new imports we pick only new imports which are not transitively implied by
-- another new import
let mut toAdd : Array Import := #[]
for j in [0:s.mods.size] do
for k in NeedsKind.all do
if deps.has k j && !newDeps.has k j && !newDeps.has { k with isExported := true } j then
let imp := { k with module := s.modNames[j]! }
toAdd := toAdd.push imp
newDeps := addTransitiveImps newDeps imp j s.transDeps[j]!
-- mark and report the removals
let mut edits := toRemove.foldl (init := edits) fun edits imp =>
edits.remove s.modNames[i]! imp
if !toAdd.isEmpty || !toRemove.isEmpty || explain then
if let some path srcSearchPath.findModuleWithExt "lean" s.modNames[i]! then
println! "{path}:"
else
println! "{s.modNames[i]!}:"
if !toRemove.isEmpty then
println! " remove {toRemove}"
if githubStyle then
try
let (path, inputCtx, imports, endHeader) parseHeader srcSearchPath s.modNames[i]!
for stx in imports do
if toRemove.any fun imp => imp == decodeImport stx then
let pos := inputCtx.fileMap.toPosition stx.raw.getPos?.get!
println! "{path}:{pos.line}:{pos.column+1}: warning: unused import \
(use `lake exe shake --fix` to fix this, or `lake exe shake --update` to ignore)"
if !toAdd.isEmpty then
-- we put the insert message on the beginning of the last import line
let pos := inputCtx.fileMap.toPosition endHeader
println! "{path}:{pos.line-1}:1: warning: \
add {toAdd} instead"
catch _ => pure ()
-- mark and report the additions
edits := toAdd.foldl (init := edits) fun edits imp =>
edits.add s.modNames[i]! imp
if !toAdd.isEmpty then
println! " add {toAdd}"
-- recalculate transitive dependencies of downstream modules
let mut newTransDepsI := Needs.empty
for imp in s.mods[i]!.imports do
if !toRemove.contains imp then
let j := s.env.getModuleIdx? imp.module |>.get!
newTransDepsI := addTransitiveImps newTransDepsI imp j s.transDeps[j]!
for imp in toAdd do
let j := s.env.getModuleIdx? imp.module |>.get!
newTransDepsI := addTransitiveImps newTransDepsI imp j s.transDeps[j]!
set { s with transDeps := s.transDeps.set! i newTransDepsI }
if explain then
let explanation := getExplanations s.env i
let sanitize n := if n.hasMacroScopes then (sanitizeName n).run' { options := {} } else n
let run (imp : Import) := do
let j := s.env.getModuleIdx? imp.module |>.get!
if let some exp? := explanation[(j, NeedsKind.ofImport imp)]? then
println! " note: `{imp}` required"
if let some (n, c) := exp? then
println! " because `{sanitize n}` refers to `{sanitize c}`"
else
println! " because of additional compile-time dependencies"
for j in s.mods[i]!.imports do
if !toRemove.contains j then
run j
for i in toAdd do run i
return edits
/-- Convert a list of module names to a bitset of module indexes -/
def toBitset (s : State) (ns : List Name) : Bitset :=
ns.foldl (init := ) fun c name =>
match s.env.getModuleIdxFor? name with
| some i => c {i}
| none => c
/-- The parsed CLI arguments. See `help` for more information -/
structure Args where
/-- `--help`: shows the help -/
help : Bool := false
/-- `--force`: skips the `lake build --no-build` sanity check -/
force : Bool := false
/-- `--gh-style`: output messages that can be parsed by `gh-problem-matcher-wrap` -/
githubStyle : Bool := false
/-- `--explain`: give constants explaining why each module is needed -/
explain : Bool := false
/-- `--fix`: apply the fixes directly -/
fix : Bool := false
/-- `<MODULE>..`: the list of root modules to check -/
mods : Array Name := #[]
local instance : Ord Import where
compare a b :=
if a.isExported && !b.isExported then
Ordering.lt
else if !a.isExported && b.isExported then
Ordering.gt
else
a.module.cmp b.module
/-- The main entry point. See `help` for more information on arguments. -/
def main (args : List String) : IO UInt32 := do
initSearchPath ( findSysroot)
-- Parse the arguments
let rec parseArgs (args : Args) : List String Args
| [] => args
| "--help" :: rest => parseArgs { args with help := true } rest
| "--force" :: rest => parseArgs { args with force := true } rest
| "--fix" :: rest => parseArgs { args with fix := true } rest
| "--explain" :: rest => parseArgs { args with explain := true } rest
| "--gh-style" :: rest => parseArgs { args with githubStyle := true } rest
| "--" :: rest => { args with mods := args.mods ++ rest.map (·.toName) }
| other :: rest => parseArgs { args with mods := args.mods.push other.toName } rest
let args := parseArgs {} args
-- Bail if `--help` is passed
if args.help then
IO.println help
IO.Process.exit 0
if !args.force then
if ( IO.Process.output { cmd := "lake", args := #["build", "--no-build"] }).exitCode != 0 then
IO.println "There are out of date oleans. Run `lake build` or `lake exe cache get` first"
IO.Process.exit 1
-- Determine default module(s) to run shake on
let defaultTargetModules : Array Name try
let (elanInstall?, leanInstall?, lakeInstall?) Lake.findInstall?
let config Lake.MonadError.runEIO <| Lake.mkLoadConfig { elanInstall?, leanInstall?, lakeInstall? }
let some workspace Lake.loadWorkspace config |>.toBaseIO
| throw <| IO.userError "failed to load Lake workspace"
let defaultTargetModules := workspace.root.defaultTargets.flatMap fun target =>
if let some lib := workspace.root.findLeanLib? target then
lib.roots
else if let some exe := workspace.root.findLeanExe? target then
#[exe.config.root]
else
#[]
pure defaultTargetModules
catch _ =>
pure #[]
let srcSearchPath getSrcSearchPath
-- the list of root modules
let mods := if args.mods.isEmpty then defaultTargetModules else args.mods
-- Only submodules of `pkg` will be edited or have info reported on them
let pkg := mods[0]!.components.head!
-- Load all the modules
let imps := mods.map ({ module := · })
let (_, s) importModulesCore imps (isExported := true) |>.run
let s := s.markAllExported
let env finalizeImport s (isModule := true) imps {} (leakEnv := false) (loadExts := false)
StateT.run' (s := initStateFromEnv env) do
let s get
-- Parse the config file
-- Run the calculation of the `needs` array in parallel
let needs := s.mods.mapIdx fun i _ =>
Task.spawn fun _ => calcNeeds s.env i
if args.fix then
println! "The following changes will be made automatically:"
-- Check all selected modules
let mut edits : Edits :=
let mut revNeeds : Needs := default
for i in [0:s.mods.size], t in needs do
edits visitModule (addOnly := !pkg.isPrefixOf s.modNames[i]!) srcSearchPath i t.get revNeeds edits args.githubStyle args.explain
if isExtraRevModUse s.env i then
revNeeds := revNeeds.union .priv {i}
if !args.fix then
-- return error if any issues were found
return if edits.isEmpty then 0 else 1
-- Apply the edits to existing files
let count edits.foldM (init := 0) fun count mod (remove, add) => do
let add : Array Import := add.qsortOrd
-- Parse the input file
let (path, inputCtx, imports, insertion)
try parseHeader srcSearchPath mod
catch e => println! e.toString; return count
let text := inputCtx.fileMap.source
-- Calculate the edit result
let mut pos : String.Pos := 0
let mut out : String := ""
let mut seen : Std.HashSet Import := {}
for stx in imports do
let mod := decodeImport stx
if remove.contains mod || seen.contains mod then
out := out ++ text.extract pos stx.raw.getPos?.get!
-- We use the end position of the syntax, but include whitespace up to the first newline
pos := text.findAux (· == '\n') text.endPos stx.raw.getTailPos?.get! + 1
seen := seen.insert mod
out := out ++ text.extract pos insertion
for mod in add do
if !seen.contains mod then
seen := seen.insert mod
out := out ++ s!"{mod}\n"
out := out ++ text.extract insertion text.endPos
IO.FS.writeFile path out
return count + 1
-- Since we throw an error upon encountering issues, we can be sure that everything worked
-- if we reach this point of the script.
if count > 0 then
println! "Successfully applied {count} suggestions."
else
println! "No edits required."
return 0

View File

@@ -1,9 +0,0 @@
name = "scripts"
[[lean_exe]]
name = "modulize"
root = "Modulize"
[[lean_exe]]
name = "shake"
root = "Shake"

View File

@@ -1 +0,0 @@
lean4

View File

@@ -797,9 +797,6 @@ install(DIRECTORY "${CMAKE_BINARY_DIR}/lib/" DESTINATION lib
# symlink source into expected installation location for go-to-definition, if file system allows it
file(MAKE_DIRECTORY ${CMAKE_BINARY_DIR}/src)
# get rid of all files in `src/lean` that may have been loaded from the cache
# (at the time of writing this, this is the case for some lake test .c files)
file(REMOVE_RECURSE ${CMAKE_BINARY_DIR}/src/lean)
if(${STAGE} EQUAL 0)
file(CREATE_LINK ${CMAKE_SOURCE_DIR}/../../src ${CMAKE_BINARY_DIR}/src/lean RESULT _IGNORE_RES SYMBOLIC)
else()
@@ -847,13 +844,15 @@ endfunction()
string(REPLACE "ROOT" "${CMAKE_BINARY_DIR}" LEANC_CC "${LEANC_CC}")
string(REPLACE "ROOT" "${CMAKE_BINARY_DIR}" LEANC_INTERNAL_FLAGS "${LEANC_INTERNAL_FLAGS}")
string(REPLACE "ROOT" "${CMAKE_BINARY_DIR}" LEANC_INTERNAL_LINKER_FLAGS "${LEANC_INTERNAL_LINKER_FLAGS}")
set(LEANC_OPTS_TOML "${LEANC_OPTS} ${LEANC_EXTRA_CC_FLAGS} ${LEANC_INTERNAL_FLAGS}")
set(LINK_OPTS_TOML "${LEANC_INTERNAL_LINKER_FLAGS} -L${CMAKE_BINARY_DIR}/lib/lean ${LEAN_EXTRA_LINKER_FLAGS}")
toml_escape("${LEAN_EXTRA_MAKE_OPTS}" LEAN_EXTRA_OPTS_TOML)
toml_escape("${LEANC_OPTS_TOML}" LEANC_OPTS_TOML)
toml_escape("${LINK_OPTS_TOML}" LINK_OPTS_TOML)
if(${CMAKE_BUILD_TYPE} MATCHES "Debug|Release|RelWithDebInfo|MinSizeRel")
set(CMAKE_BUILD_TYPE_TOML "${CMAKE_BUILD_TYPE}")
else()
set(CMAKE_BUILD_TYPE_TOML "Release")
if(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
set(LAKE_LIB_PREFIX "lib")
endif()
if(USE_LAKE)

View File

@@ -8,7 +8,7 @@ module
prelude
public import Init.PropLemmas
@[expose] public section
public section
universe u v

View File

@@ -16,3 +16,5 @@ public import Init.Control.Option
public import Init.Control.Lawful
public import Init.Control.StateCps
public import Init.Control.ExceptCps
public section

View File

@@ -10,3 +10,5 @@ public import Init.Control.Lawful.Basic
public import Init.Control.Lawful.Instances
public import Init.Control.Lawful.Lemmas
public import Init.Control.Lawful.MonadLift
public section

View File

@@ -9,8 +9,6 @@ prelude
public import Init.Control.Lawful.Basic
public import Init.Control.Except
import all Init.Control.Except
public import Init.Control.Option
import all Init.Control.Option
public import Init.Control.State
import all Init.Control.State
public import Init.Control.StateRef
@@ -112,121 +110,6 @@ instance : LawfulMonad (Except ε) := LawfulMonad.mk'
instance : LawfulApplicative (Except ε) := inferInstance
instance : LawfulFunctor (Except ε) := inferInstance
/-! # OptionT -/
namespace OptionT
@[ext] theorem ext {x y : OptionT m α} (h : x.run = y.run) : x = y := by
simp [run] at h
assumption
@[simp, grind =] theorem run_mk {m : Type u Type v} (x : m (Option α)) :
OptionT.run (OptionT.mk x) = x := by rfl
@[simp, grind =] theorem run_pure [Monad m] (x : α) : run (pure x : OptionT m α) = pure (some x) := by
simp [run, pure, OptionT.pure, OptionT.mk]
@[simp, grind =] theorem run_lift [Monad.{u, v} m] (x : m α) : run (OptionT.lift x : OptionT m α) = (return some ( x) : m (Option α)) := by
simp [run, OptionT.lift, OptionT.mk]
@[simp, grind =] theorem run_throw [Monad m] : run (throw e : OptionT m β) = pure none := by
simp [run, throw, throwThe, MonadExceptOf.throw, OptionT.fail, OptionT.mk]
@[simp, grind =] theorem run_bind_lift [Monad m] [LawfulMonad m] (x : m α) (f : α OptionT m β) : run (OptionT.lift x >>= f : OptionT m β) = x >>= fun a => run (f a) := by
simp [OptionT.run, OptionT.lift, bind, OptionT.bind, OptionT.mk]
@[simp, grind =] theorem bind_throw [Monad m] [LawfulMonad m] (f : α OptionT m β) : (throw e >>= f) = throw e := by
simp [throw, throwThe, MonadExceptOf.throw, bind, OptionT.bind, OptionT.mk, OptionT.fail]
@[simp, grind =] theorem run_bind (f : α OptionT m β) [Monad m] :
(x >>= f).run = Option.elimM x.run (pure none) (fun x => (f x).run) := by
change x.run >>= _ = _
simp [Option.elimM]
exact bind_congr fun |some _ => rfl | none => rfl
@[simp, grind =] theorem lift_pure [Monad m] [LawfulMonad m] {α : Type u} (a : α) : OptionT.lift (pure a : m α) = pure a := by
simp only [OptionT.lift, OptionT.mk, bind_pure_comp, map_pure, pure, OptionT.pure]
@[simp, grind =] theorem run_map [Monad m] [LawfulMonad m] (f : α β) (x : OptionT m α)
: (f <$> x).run = Option.map f <$> x.run := by
simp [Functor.map, Option.map, bind_pure_comp]
apply bind_congr
intro a; cases a <;> simp [OptionT.pure, OptionT.mk]
protected theorem seq_eq {α β : Type u} [Monad m] (mf : OptionT m (α β)) (x : OptionT m α) : mf <*> x = mf >>= fun f => f <$> x :=
rfl
protected theorem bind_pure_comp [Monad m] (f : α β) (x : OptionT m α) : x >>= pure f = f <$> x := by
intros; rfl
protected theorem seqLeft_eq {α β : Type u} {m : Type u Type v} [Monad m] [LawfulMonad m] (x : OptionT m α) (y : OptionT m β) : x <* y = const β <$> x <*> y := by
change (x >>= fun a => y >>= fun _ => pure a) = (const (α := α) β <$> x) >>= fun f => f <$> y
rw [ OptionT.bind_pure_comp]
apply ext
simp [Option.elimM, Option.elim]
apply bind_congr
intro
| none => simp
| some _ =>
simp [bind_pure_comp]; apply bind_congr; intro b;
cases b <;> simp [const]
protected theorem seqRight_eq [Monad m] [LawfulMonad m] (x : OptionT m α) (y : OptionT m β) : x *> y = const α id <$> x <*> y := by
change (x >>= fun _ => y) = (const α id <$> x) >>= fun f => f <$> y
rw [ OptionT.bind_pure_comp]
apply ext
simp [Option.elimM, Option.elim]
apply bind_congr
intro a; cases a <;> simp
instance [Monad m] [LawfulMonad m] : LawfulMonad (OptionT m) where
id_map := by intros; apply ext; simp
map_const := by intros; rfl
seqLeft_eq := OptionT.seqLeft_eq
seqRight_eq := OptionT.seqRight_eq
pure_seq := by intros; apply ext; simp [OptionT.seq_eq, Option.elimM, Option.elim]
bind_pure_comp := OptionT.bind_pure_comp
bind_map := by intros; rfl
pure_bind := by intros; apply ext; simp [Option.elimM, Option.elim]
bind_assoc := by intros; apply ext; simp [Option.elimM, Option.elim]; apply bind_congr; intro a; cases a <;> simp
@[simp] theorem run_seq [Monad m] [LawfulMonad m] (f : OptionT m (α β)) (x : OptionT m α) :
(f <*> x).run = Option.elimM f.run (pure none) (fun f => Option.map f <$> x.run) := by
simp [seq_eq_bind, Option.elimM, Option.elim]
@[simp] theorem run_seqLeft [Monad m] [LawfulMonad m] (x : OptionT m α) (y : OptionT m β) :
(x <* y).run = Option.elimM x.run (pure none)
(fun x => Option.map (Function.const β x) <$> y.run) := by
simp [seqLeft_eq, seq_eq_bind, Option.elimM, OptionT.run_bind]
@[simp] theorem run_seqRight [Monad m] [LawfulMonad m] (x : OptionT m α) (y : OptionT m β) :
(x *> y).run = Option.elimM x.run (pure none) (Function.const α y.run) := by
simp only [seqRight_eq, run_seq, Option.elimM, run_map, Option.elim, bind_map_left]
refine bind_congr (fun | some _ => by simp | none => by simp)
@[simp, grind =] theorem run_failure [Monad m] : (failure : OptionT m α).run = pure none := by rfl
@[simp] theorem map_failure [Monad m] [LawfulMonad m] {α β : Type _} (f : α β) :
f <$> (failure : OptionT m α) = (failure : OptionT m β) := by
simp [OptionT.mk, Functor.map, Alternative.failure, OptionT.fail, OptionT.bind]
@[simp] theorem run_orElse [Monad m] (x : OptionT m α) (y : OptionT m α) :
(x <|> y).run = Option.elimM x.run y.run (fun x => pure (some x)) :=
bind_congr fun | some _ => by rfl | none => by rfl
end OptionT
/-! # Option -/
instance : LawfulMonad Option := LawfulMonad.mk'
(id_map := fun x => by cases x <;> rfl)
(pure_bind := fun _ _ => by rfl)
(bind_assoc := fun a _ _ => by cases a <;> rfl)
(bind_pure_comp := bind_pure_comp)
instance : LawfulApplicative Option := inferInstance
instance : LawfulFunctor Option := inferInstance
/-! # ReaderT -/
namespace ReaderT

View File

@@ -9,3 +9,5 @@ prelude
public import Init.Control.Lawful.MonadLift.Basic
public import Init.Control.Lawful.MonadLift.Lemmas
public import Init.Control.Lawful.MonadLift.Instances
public section

View File

@@ -64,6 +64,10 @@ namespace OptionT
variable [Monad m] [LawfulMonad m]
@[simp]
theorem lift_pure {α : Type u} (a : α) : OptionT.lift (pure a : m α) = pure a := by
simp only [OptionT.lift, OptionT.mk, bind_pure_comp, map_pure, pure, OptionT.pure]
@[simp]
theorem lift_bind {α β : Type u} (ma : m α) (f : α m β) :
OptionT.lift (ma >>= f) = OptionT.lift ma >>= (fun a => OptionT.lift (f a)) := by

View File

@@ -39,14 +39,13 @@ variable {m : Type u → Type v} [Monad m] {α β : Type u}
Converts an action that returns an `Option` into one that might fail, with `none` indicating
failure.
-/
@[always_inline, inline, expose]
protected def mk (x : m (Option α)) : OptionT m α :=
x
/--
Sequences two potentially-failing actions. The second action is run only if the first succeeds.
-/
@[always_inline, inline, expose]
@[always_inline, inline]
protected def bind (x : OptionT m α) (f : α OptionT m β) : OptionT m β := OptionT.mk do
match ( x) with
| some a => f a
@@ -55,7 +54,7 @@ protected def bind (x : OptionT m α) (f : α → OptionT m β) : OptionT m β :
/--
Succeeds with the provided value.
-/
@[always_inline, inline, expose]
@[always_inline, inline]
protected def pure (a : α) : OptionT m α := OptionT.mk do
pure (some a)

View File

@@ -144,9 +144,8 @@ Computed values are cached, so the value is not recomputed.
x.fn ()
-- Ensure `Thunk.fn` is still computable even if it shouldn't be accessed directly.
/-- Implementation detail. -/
@[inline] def Thunk.fnImpl (x : Thunk α) : Unit α := fun _ => x.get
@[csimp] theorem Thunk.fn_eq_fnImpl : @Thunk.fn = @Thunk.fnImpl := rfl
@[inline] private def Thunk.fnImpl (x : Thunk α) : Unit α := fun _ => x.get
@[csimp] private theorem Thunk.fn_eq_fnImpl : @Thunk.fn = @Thunk.fnImpl := rfl
/--
Constructs a new thunk that forces `x` and then applies `x` to the result. Upon forcing, the result
@@ -1606,7 +1605,7 @@ gen_injective_theorems% PSigma
gen_injective_theorems% PSum
gen_injective_theorems% Sigma
gen_injective_theorems% String
gen_injective_theorems% String.Pos.Raw
gen_injective_theorems% String.Pos
gen_injective_theorems% Substring
gen_injective_theorems% Subtype
gen_injective_theorems% Sum

View File

@@ -30,7 +30,6 @@ public import Init.Data.Random
public import Init.Data.ToString
public import Init.Data.Range
public import Init.Data.Hashable
public import Init.Data.LawfulHashable
public import Init.Data.OfScientific
public import Init.Data.Format
public import Init.Data.Stream
@@ -53,3 +52,5 @@ public import Init.Data.Slice
public import Init.Data.Order
public import Init.Data.Rat
public import Init.Data.Dyadic
public section

View File

@@ -30,3 +30,5 @@ public import Init.Data.Array.Erase
public import Init.Data.Array.Zip
public import Init.Data.Array.InsertIdx
public import Init.Data.Array.Extract
public section

View File

@@ -84,10 +84,10 @@ well-founded recursion mechanism to prove that the function terminates.
simp [pmap]
/-- Implementation of `pmap` using the zero-copy version of `attach`. -/
@[inline] def pmapImpl {P : α Prop} (f : a, P a β) (xs : Array α) (H : a xs, P a) :
@[inline] private def pmapImpl {P : α Prop} (f : a, P a β) (xs : Array α) (H : a xs, P a) :
Array β := (xs.attachWith _ H).map fun x, h' => f x h'
@[csimp] theorem pmap_eq_pmapImpl : @pmap = @pmapImpl := by
@[csimp] private theorem pmap_eq_pmapImpl : @pmap = @pmapImpl := by
funext α β p f xs H
cases xs
simp only [pmap, pmapImpl, List.attachWith_toArray, List.map_toArray, mk.injEq, List.map_attachWith_eq_pmap]
@@ -95,16 +95,16 @@ well-founded recursion mechanism to prove that the function terminates.
intro a m h₁ h₂
congr
@[simp] theorem pmap_empty {P : α Prop} (f : a, P a β) : pmap f #[] (by simp) = #[] := rfl
@[simp, grind =] theorem pmap_empty {P : α Prop} (f : a, P a β) : pmap f #[] (by simp) = #[] := rfl
@[simp] theorem pmap_push {P : α Prop} (f : a, P a β) (a : α) (xs : Array α) (h : b xs.push a, P b) :
@[simp, grind =] theorem pmap_push {P : α Prop} (f : a, P a β) (a : α) (xs : Array α) (h : b xs.push a, P b) :
pmap f (xs.push a) h =
(pmap f xs (fun a m => by simp at h; exact h a (.inl m))).push (f a (h a (by simp))) := by
simp [pmap]
@[simp] theorem attach_empty : (#[] : Array α).attach = #[] := rfl
@[simp, grind =] theorem attach_empty : (#[] : Array α).attach = #[] := rfl
@[simp] theorem attachWith_empty {P : α Prop} (H : x #[], P x) : (#[] : Array α).attachWith P H = #[] := rfl
@[simp, grind =] theorem attachWith_empty {P : α Prop} (H : x #[], P x) : (#[] : Array α).attachWith P H = #[] := rfl
@[simp] theorem _root_.List.attachWith_mem_toArray {l : List α} :
l.attachWith (fun x => x l.toArray) (fun x h => by simpa using h) =
@@ -125,11 +125,13 @@ theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a,
simp only [List.pmap_toArray, mk.injEq]
rw [List.pmap_congr_left _ h]
@[grind =]
theorem map_pmap {p : α Prop} {g : β γ} {f : a, p a β} {xs : Array α} (H) :
map g (pmap f xs H) = pmap (fun a h => g (f a h)) xs H := by
cases xs
simp [List.map_pmap]
@[grind =]
theorem pmap_map {p : β Prop} {g : b, p b γ} {f : α β} {xs : Array α} (H) :
pmap g (map f xs) H = pmap (fun a h => g (f a) h) xs fun _ h => H _ (mem_map_of_mem h) := by
cases xs
@@ -145,14 +147,14 @@ theorem attachWith_congr {xs ys : Array α} (w : xs = ys) {P : α → Prop} {H :
subst w
simp
@[simp] theorem attach_push {a : α} {xs : Array α} :
@[simp, grind =] theorem attach_push {a : α} {xs : Array α} :
(xs.push a).attach =
(xs.attach.map (fun x, h => x, mem_push_of_mem a h)).push a, by simp := by
cases xs
rw [attach_congr (List.push_toArray _ _)]
simp [Function.comp_def]
@[simp] theorem attachWith_push {a : α} {xs : Array α} {P : α Prop} {H : x xs.push a, P x} :
@[simp, grind =] theorem attachWith_push {a : α} {xs : Array α} {P : α Prop} {H : x xs.push a, P x} :
(xs.push a).attachWith P H =
(xs.attachWith P (fun x h => by simp at H; exact H x (.inl h))).push a, H a (by simp) := by
cases xs
@@ -174,6 +176,9 @@ theorem attach_map_val (xs : Array α) (f : α → β) :
cases xs
simp
@[deprecated attach_map_val (since := "2025-02-17")]
abbrev attach_map_coe := @attach_map_val
-- The argument `xs : Array α` is explicit to allow rewriting from right to left.
theorem attach_map_subtype_val (xs : Array α) : xs.attach.map Subtype.val = xs := by
cases xs; simp
@@ -182,6 +187,9 @@ theorem attachWith_map_val {p : α → Prop} {f : α → β} {xs : Array α} (H
((xs.attachWith p H).map fun (i : { i // p i}) => f i) = xs.map f := by
cases xs; simp
@[deprecated attachWith_map_val (since := "2025-02-17")]
abbrev attachWith_map_coe := @attachWith_map_val
theorem attachWith_map_subtype_val {p : α Prop} {xs : Array α} (H : a xs, p a) :
(xs.attachWith p H).map Subtype.val = xs := by
cases xs; simp
@@ -286,23 +294,25 @@ theorem getElem_attach {xs : Array α} {i : Nat} (h : i < xs.attach.size) :
xs.attach[i] = xs[i]'(by simpa using h), getElem_mem (by simpa using h) :=
getElem_attachWith h
@[simp] theorem pmap_attach {xs : Array α} {p : {x // x xs} Prop} {f : a, p a β} (H) :
@[simp, grind =] theorem pmap_attach {xs : Array α} {p : {x // x xs} Prop} {f : a, p a β} (H) :
pmap f xs.attach H =
xs.pmap (P := fun a => h : a xs, p a, h)
(fun a h => f a, h.1 h.2) (fun a h => h, H a, h (by simp)) := by
ext <;> simp
@[simp] theorem pmap_attachWith {xs : Array α} {p : {x // q x} Prop} {f : a, p a β} (H₁ H₂) :
@[simp, grind =] theorem pmap_attachWith {xs : Array α} {p : {x // q x} Prop} {f : a, p a β} (H₁ H₂) :
pmap f (xs.attachWith q H₁) H₂ =
xs.pmap (P := fun a => h : q a, p a, h)
(fun a h => f a, h.1 h.2) (fun a h => H₁ _ h, H₂ a, H₁ _ h (by simpa)) := by
ext <;> simp
@[grind =]
theorem foldl_pmap {xs : Array α} {P : α Prop} {f : (a : α) P a β}
(H : (a : α), a xs P a) (g : γ β γ) (x : γ) :
(xs.pmap f H).foldl g x = xs.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
rw [pmap_eq_map_attach, foldl_map]
@[grind =]
theorem foldr_pmap {xs : Array α} {P : α Prop} {f : (a : α) P a β}
(H : (a : α), a xs P a) (g : β γ γ) (x : γ) :
(xs.pmap f H).foldr g x = xs.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by
@@ -360,18 +370,20 @@ theorem foldr_attach {xs : Array α} {f : α → β → β} {b : β} :
ext
simpa using fun a => List.mem_of_getElem? a
@[grind =]
theorem attach_map {xs : Array α} {f : α β} :
(xs.map f).attach = xs.attach.map (fun x, h => f x, mem_map_of_mem h) := by
cases xs
ext <;> simp
@[grind =]
theorem attachWith_map {xs : Array α} {f : α β} {P : β Prop} (H : (b : β), b xs.map f P b) :
(xs.map f).attachWith P H = (xs.attachWith (P f) (fun _ h => H _ (mem_map_of_mem h))).map
fun x, h => f x, h := by
cases xs
simp [List.attachWith_map]
@[simp] theorem map_attachWith {xs : Array α} {P : α Prop} {H : (a : α), a xs P a}
@[simp, grind =] theorem map_attachWith {xs : Array α} {P : α Prop} {H : (a : α), a xs P a}
{f : { x // P x } β} :
(xs.attachWith P H).map f = xs.attach.map fun x, h => f x, H _ h := by
cases xs <;> simp_all
@@ -389,6 +401,9 @@ theorem map_attach_eq_pmap {xs : Array α} {f : { x // x ∈ xs } → β} :
cases xs
ext <;> simp
@[deprecated map_attach_eq_pmap (since := "2025-02-09")]
abbrev map_attach := @map_attach_eq_pmap
@[grind =]
theorem attach_filterMap {xs : Array α} {f : α Option β} :
(xs.filterMap f).attach = xs.attach.filterMap
@@ -424,6 +439,7 @@ theorem filter_attachWith {q : α → Prop} {xs : Array α} {p : {x // q x} →
cases xs
simp [Function.comp_def, List.filter_map]
@[grind =]
theorem pmap_pmap {p : α Prop} {q : β Prop} {g : a, p a β} {f : b, q b γ} {xs} (H₁ H₂) :
pmap f (pmap g xs H₁) H₂ =
pmap (α := { x // x xs }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) xs.attach
@@ -431,7 +447,7 @@ theorem pmap_pmap {p : α → Prop} {q : β → Prop} {g : ∀ a, p a → β} {f
cases xs
simp [List.pmap_pmap, List.pmap_map]
@[simp] theorem pmap_append {p : ι Prop} {f : a : ι, p a α} {xs ys : Array ι}
@[simp, grind =] theorem pmap_append {p : ι Prop} {f : a : ι, p a α} {xs ys : Array ι}
(h : a xs ++ ys, p a) :
(xs ++ ys).pmap f h =
(xs.pmap f fun a ha => h a (mem_append_left ys ha)) ++
@@ -446,7 +462,7 @@ theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {xs ys : Arr
xs.pmap f h₁ ++ ys.pmap f h₂ :=
pmap_append _
@[simp] theorem attach_append {xs ys : Array α} :
@[simp, grind =] theorem attach_append {xs ys : Array α} :
(xs ++ ys).attach = xs.attach.map (fun x, h => x, mem_append_left ys h) ++
ys.attach.map fun x, h => x, mem_append_right xs h := by
cases xs
@@ -454,59 +470,62 @@ theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {xs ys : Arr
rw [attach_congr (List.append_toArray _ _)]
simp [List.attach_append, Function.comp_def]
@[simp] theorem attachWith_append {P : α Prop} {xs ys : Array α}
@[simp, grind =] theorem attachWith_append {P : α Prop} {xs ys : Array α}
{H : (a : α), a xs ++ ys P a} :
(xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_left ys h)) ++
ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
simp [attachWith]
@[simp] theorem pmap_reverse {P : α Prop} {f : (a : α) P a β} {xs : Array α}
@[simp, grind =] theorem pmap_reverse {P : α Prop} {f : (a : α) P a β} {xs : Array α}
(H : (a : α), a xs.reverse P a) :
xs.reverse.pmap f H = (xs.pmap f (fun a h => H a (by simpa using h))).reverse := by
induction xs <;> simp_all
@[grind =]
theorem reverse_pmap {P : α Prop} {f : (a : α) P a β} {xs : Array α}
(H : (a : α), a xs P a) :
(xs.pmap f H).reverse = xs.reverse.pmap f (fun a h => H a (by simpa using h)) := by
rw [pmap_reverse]
@[simp] theorem attachWith_reverse {P : α Prop} {xs : Array α}
@[simp, grind =] theorem attachWith_reverse {P : α Prop} {xs : Array α}
{H : (a : α), a xs.reverse P a} :
xs.reverse.attachWith P H =
(xs.attachWith P (fun a h => H a (by simpa using h))).reverse := by
cases xs
simp
@[grind =]
theorem reverse_attachWith {P : α Prop} {xs : Array α}
{H : (a : α), a xs P a} :
(xs.attachWith P H).reverse = (xs.reverse.attachWith P (fun a h => H a (by simpa using h))) := by
cases xs
simp
@[simp] theorem attach_reverse {xs : Array α} :
@[simp, grind =] theorem attach_reverse {xs : Array α} :
xs.reverse.attach = xs.attach.reverse.map fun x, h => x, by simpa using h := by
cases xs
rw [attach_congr List.reverse_toArray]
simp
@[grind =]
theorem reverse_attach {xs : Array α} :
xs.attach.reverse = xs.reverse.attach.map fun x, h => x, by simpa using h := by
cases xs
simp
@[simp] theorem back?_pmap {P : α Prop} {f : (a : α) P a β} {xs : Array α}
@[simp, grind =] theorem back?_pmap {P : α Prop} {f : (a : α) P a β} {xs : Array α}
(H : (a : α), a xs P a) :
(xs.pmap f H).back? = xs.attach.back?.map fun a, m => f a (H a m) := by
cases xs
simp
@[simp] theorem back?_attachWith {P : α Prop} {xs : Array α}
@[simp, grind =] theorem back?_attachWith {P : α Prop} {xs : Array α}
{H : (a : α), a xs P a} :
(xs.attachWith P H).back? = xs.back?.pbind (fun a h => some a, H _ (mem_of_back? h)) := by
cases xs
simp
@[simp]
@[simp, grind =]
theorem back?_attach {xs : Array α} :
xs.attach.back? = xs.back?.pbind fun a h => some a, mem_of_back? h := by
cases xs

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@@ -129,11 +129,20 @@ end Array
namespace List
@[deprecated Array.toArray_toList (since := "2025-02-17")]
abbrev toArray_toList := @Array.toArray_toList
-- This does not need to be a simp lemma, as already after the `whnfR` the right hand side is `as`.
theorem toList_toArray {as : List α} : as.toArray.toList = as := rfl
@[deprecated toList_toArray (since := "2025-02-17")]
abbrev _root_.Array.toList_toArray := @List.toList_toArray
@[simp, grind =] theorem size_toArray {as : List α} : as.toArray.size = as.length := by simp [Array.size]
@[deprecated size_toArray (since := "2025-02-17")]
abbrev _root_.Array.size_toArray := @List.size_toArray
@[simp, grind =] theorem getElem_toArray {xs : List α} {i : Nat} (h : i < xs.toArray.size) :
xs.toArray[i] = xs[i]'(by simpa using h) := rfl
@@ -403,6 +412,10 @@ that requires a proof the array is non-empty.
def back? (xs : Array α) : Option α :=
xs[xs.size - 1]?
@[deprecated "Use `a[i]?` instead." (since := "2025-02-12"), expose]
def get? (xs : Array α) (i : Nat) : Option α :=
if h : i < xs.size then some xs[i] else none
/--
Swaps a new element with the element at the given index.
@@ -1799,6 +1812,7 @@ Examples:
* `#["apple", "pear", "orange"].eraseIdxIfInBounds 3 = #["apple", "pear", "orange"]`
* `#["apple", "pear", "orange"].eraseIdxIfInBounds 5 = #["apple", "pear", "orange"]`
-/
@[grind]
def eraseIdxIfInBounds (xs : Array α) (i : Nat) : Array α :=
if h : i < xs.size then xs.eraseIdx i h else xs

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@@ -24,6 +24,29 @@ set_option linter.indexVariables true -- Enforce naming conventions for index va
namespace Array
/--
Use the indexing notation `a[i]` instead.
Access an element from an array without needing a runtime bounds checks,
using a `Nat` index and a proof that it is in bounds.
This function does not use `get_elem_tactic` to automatically find the proof that
the index is in bounds. This is because the tactic itself needs to look up values in
arrays.
-/
@[deprecated "Use indexing notation `as[i]` instead" (since := "2025-02-17")]
def get {α : Type u} (xs : @& Array α) (i : @& Nat) (h : LT.lt i xs.size) : α :=
xs.toList.get i, h
/--
Use the indexing notation `a[i]!` instead.
Access an element from an array, or panic if the index is out of bounds.
-/
@[deprecated "Use indexing notation `as[i]!` instead" (since := "2025-02-17"), expose]
def get! {α : Type u} [Inhabited α] (xs : @& Array α) (i : @& Nat) : α :=
Array.getD xs i default
theorem foldlM_toList.aux [Monad m]
{f : β α m β} {xs : Array α} {i j} (H : xs.size i + j) {b} :
foldlM.loop f xs xs.size (Nat.le_refl _) i j b = (xs.toList.drop j).foldlM f b := by
@@ -85,6 +108,9 @@ abbrev push_toList := @toList_push
@[simp, grind =] theorem toList_pop {xs : Array α} : xs.pop.toList = xs.toList.dropLast := rfl
@[deprecated toList_pop (since := "2025-02-17")]
abbrev pop_toList := @Array.toList_pop
@[simp] theorem append_eq_append {xs ys : Array α} : xs.append ys = xs ++ ys := rfl
@[simp, grind =] theorem toList_append {xs ys : Array α} :

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@@ -63,7 +63,7 @@ theorem size_eq_countP_add_countP {xs : Array α} : xs.size = countP p xs + coun
rcases xs with xs
simp [List.length_eq_countP_add_countP (p := p)]
@[grind =]
@[grind _=_]
theorem countP_eq_size_filter {xs : Array α} : countP p xs = (filter p xs).size := by
rcases xs with xs
simp [List.countP_eq_length_filter]

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@@ -324,13 +324,6 @@ abbrev erase_mkArray_ne := @erase_replicate_ne
end erase
/-! ### eraseIdxIfInBounds -/
@[grind =]
theorem eraseIdxIfInBounds_eq {xs : Array α} {i : Nat} :
xs.eraseIdxIfInBounds i = if h : i < xs.size then xs.eraseIdx i else xs := by
simp [eraseIdxIfInBounds]
/-! ### eraseIdx -/
theorem eraseIdx_eq_eraseIdxIfInBounds {xs : Array α} {i : Nat} (h : i < xs.size) :

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@@ -278,6 +278,9 @@ theorem find?_flatten_eq_none_iff {xss : Array (Array α)} {p : α → Bool} :
xss.flatten.find? p = none ys xss, x ys, !p x := by
simp
@[deprecated find?_flatten_eq_none_iff (since := "2025-02-03")]
abbrev find?_flatten_eq_none := @find?_flatten_eq_none_iff
/--
If `find? p` returns `some a` from `xs.flatten`, then `p a` holds, and
some array in `xs` contains `a`, and no earlier element of that array satisfies `p`.
@@ -303,6 +306,9 @@ theorem find?_flatten_eq_some_iff {xss : Array (Array α)} {p : α → Bool} {a
zs.toList, bs.toList.map Array.toList, by simpa using h,
by simpa using h₁, by simpa using h₂
@[deprecated find?_flatten_eq_some_iff (since := "2025-02-03")]
abbrev find?_flatten_eq_some := @find?_flatten_eq_some_iff
@[simp, grind =] theorem find?_flatMap {xs : Array α} {f : α Array β} {p : β Bool} :
(xs.flatMap f).find? p = xs.findSome? (fun x => (f x).find? p) := by
cases xs
@@ -312,11 +318,17 @@ theorem find?_flatMap_eq_none_iff {xs : Array α} {f : α → Array β} {p : β
(xs.flatMap f).find? p = none x xs, y f x, !p y := by
simp
@[deprecated find?_flatMap_eq_none_iff (since := "2025-02-03")]
abbrev find?_flatMap_eq_none := @find?_flatMap_eq_none_iff
@[grind =]
theorem find?_replicate :
find? p (replicate n a) = if n = 0 then none else if p a then some a else none := by
simp [ List.toArray_replicate, List.find?_replicate]
@[deprecated find?_replicate (since := "2025-03-18")]
abbrev find?_mkArray := @find?_replicate
@[simp] theorem find?_replicate_of_size_pos (h : 0 < n) :
find? p (replicate n a) = if p a then some a else none := by
simp [find?_replicate, Nat.ne_of_gt h]
@@ -334,19 +346,34 @@ abbrev find?_mkArray_of_pos := @find?_replicate_of_pos
@[simp] theorem find?_replicate_of_neg (h : ¬ p a) : find? p (replicate n a) = none := by
simp [find?_replicate, h]
@[deprecated find?_replicate_of_neg (since := "2025-03-18")]
abbrev find?_mkArray_of_neg := @find?_replicate_of_neg
-- This isn't a `@[simp]` lemma since there is already a lemma for `l.find? p = none` for any `l`.
theorem find?_replicate_eq_none_iff {n : Nat} {a : α} {p : α Bool} :
(replicate n a).find? p = none n = 0 !p a := by
simp [ List.toArray_replicate, Classical.or_iff_not_imp_left]
@[deprecated find?_replicate_eq_none_iff (since := "2025-03-18")]
abbrev find?_mkArray_eq_none_iff := @find?_replicate_eq_none_iff
@[simp] theorem find?_replicate_eq_some_iff {n : Nat} {a b : α} {p : α Bool} :
(replicate n a).find? p = some b n 0 p a a = b := by
simp [ List.toArray_replicate]
@[deprecated find?_replicate_eq_some_iff (since := "2025-03-18")]
abbrev find?_mkArray_eq_some_iff := @find?_replicate_eq_some_iff
@[deprecated find?_replicate_eq_some_iff (since := "2025-02-03")]
abbrev find?_mkArray_eq_some := @find?_replicate_eq_some_iff
@[simp] theorem get_find?_replicate {n : Nat} {a : α} {p : α Bool} (h) :
((replicate n a).find? p).get h = a := by
simp [ List.toArray_replicate]
@[deprecated get_find?_replicate (since := "2025-03-18")]
abbrev get_find?_mkArray := @get_find?_replicate
@[grind =]
theorem find?_pmap {P : α Prop} {f : (a : α) P a β} {xs : Array α}
(H : (a : α), a xs P a) {p : β Bool} :

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@@ -80,6 +80,9 @@ theorem ne_empty_of_size_pos (h : 0 < xs.size) : xs ≠ #[] := by
@[simp] theorem size_eq_zero_iff : xs.size = 0 xs = #[] :=
eq_empty_of_size_eq_zero, fun h => h rfl
@[deprecated size_eq_zero_iff (since := "2025-02-24")]
abbrev size_eq_zero := @size_eq_zero_iff
theorem eq_empty_iff_size_eq_zero : xs = #[] xs.size = 0 :=
size_eq_zero_iff.symm
@@ -104,10 +107,17 @@ theorem exists_mem_of_size_eq_add_one {xs : Array α} (h : xs.size = n + 1) :
theorem size_pos_iff {xs : Array α} : 0 < xs.size xs #[] :=
Nat.pos_iff_ne_zero.trans (not_congr size_eq_zero_iff)
@[deprecated size_pos_iff (since := "2025-02-24")]
abbrev size_pos := @size_pos_iff
theorem size_eq_one_iff {xs : Array α} : xs.size = 1 a, xs = #[a] := by
cases xs
simpa using List.length_eq_one_iff
@[deprecated size_eq_one_iff (since := "2025-02-24")]
abbrev size_eq_one := @size_eq_one_iff
/-! ## L[i] and L[i]? -/
theorem getElem?_eq_none_iff {xs : Array α} : xs[i]? = none xs.size i := by
@@ -361,7 +371,6 @@ abbrev getElem?_mkArray := @getElem?_replicate
/-! ### mem -/
@[grind ]
theorem not_mem_empty (a : α) : ¬ a #[] := by simp
@[simp, grind =] theorem mem_push {xs : Array α} {x y : α} : x xs.push y x xs x = y := by
@@ -533,12 +542,18 @@ theorem isEmpty_eq_false_iff_exists_mem {xs : Array α} :
@[simp] theorem isEmpty_iff {xs : Array α} : xs.isEmpty xs = #[] := by
cases xs <;> simp
@[deprecated isEmpty_iff (since := "2025-02-17")]
abbrev isEmpty_eq_true := @isEmpty_iff
@[grind ]
theorem empty_of_isEmpty {xs : Array α} (h : xs.isEmpty) : xs = #[] := Array.isEmpty_iff.mp h
@[simp] theorem isEmpty_eq_false_iff {xs : Array α} : xs.isEmpty = false xs #[] := by
cases xs <;> simp
@[deprecated isEmpty_eq_false_iff (since := "2025-02-17")]
abbrev isEmpty_eq_false := @isEmpty_eq_false_iff
theorem isEmpty_iff_size_eq_zero {xs : Array α} : xs.isEmpty xs.size = 0 := by
rw [isEmpty_iff, size_eq_zero_iff]
@@ -2981,6 +2996,11 @@ theorem _root_.List.toArray_drop {l : List α} {k : Nat} :
(l.drop k).toArray = l.toArray.extract k := by
rw [List.drop_eq_extract, List.extract_toArray, List.size_toArray]
@[deprecated extract_size (since := "2025-02-27")]
theorem take_size {xs : Array α} : xs.take xs.size = xs := by
cases xs
simp
/-! ### shrink -/
@[simp] private theorem size_shrink_loop {xs : Array α} {n : Nat} : (shrink.loop n xs).size = xs.size - n := by
@@ -3566,6 +3586,8 @@ theorem foldr_eq_foldl_reverse {xs : Array α} {f : α → β → β} {b} :
subst w
rw [foldr_eq_foldl_reverse, foldl_push_eq_append rfl, map_reverse]
@[deprecated foldr_push_eq_append (since := "2025-02-09")] abbrev foldr_flip_push_eq_append := @foldr_push_eq_append
theorem foldl_assoc {op : α α α} [ha : Std.Associative op] {xs : Array α} {a₁ a₂} :
xs.foldl op (op a₁ a₂) = op a₁ (xs.foldl op a₂) := by
rcases xs with l
@@ -4690,3 +4712,44 @@ namespace List
simp_all
end List
/-! ### Deprecations -/
namespace Array
set_option linter.deprecated false in
@[deprecated "`get?` is deprecated" (since := "2025-02-12"), simp]
theorem get?_eq_getElem? (xs : Array α) (i : Nat) : xs.get? i = xs[i]? := rfl
@[deprecated getD_eq_getD_getElem? (since := "2025-02-12")] abbrev getD_eq_get? := @getD_eq_getD_getElem?
set_option linter.deprecated false in
@[deprecated getElem!_eq_getD (since := "2025-02-12")]
theorem get!_eq_getD [Inhabited α] (xs : Array α) : xs.get! n = xs.getD n default := rfl
set_option linter.deprecated false in
@[deprecated "Use `a[i]!` instead of `a.get! i`." (since := "2025-02-12")]
theorem get!_eq_getD_getElem? [Inhabited α] (xs : Array α) (i : Nat) :
xs.get! i = xs[i]?.getD default := by
by_cases p : i < xs.size <;>
simp [get!, getD_eq_getD_getElem?, p]
set_option linter.deprecated false in
@[deprecated get!_eq_getD_getElem? (since := "2025-02-12")] abbrev get!_eq_getElem? := @get!_eq_getD_getElem?
set_option linter.deprecated false in
@[deprecated "`Array.get?` is deprecated, use `a[i]?` instead." (since := "2025-02-12")]
theorem get?_eq_get?_toList (xs : Array α) (i : Nat) : xs.get? i = xs.toList.get? i := by
simp [ getElem?_toList]
set_option linter.deprecated false in
@[deprecated get!_eq_getD_getElem? (since := "2025-02-12")] abbrev get!_eq_get? := @get!_eq_getD_getElem?
/-! ### set -/
@[deprecated getElem?_set_self (since := "2025-02-27")] abbrev get?_set_eq := @getElem?_set_self
@[deprecated getElem?_set_ne (since := "2025-02-27")] abbrev get?_set_ne := @getElem?_set_ne
@[deprecated getElem?_set (since := "2025-02-27")] abbrev get?_set := @getElem?_set
@[deprecated get_set (since := "2025-02-27")] abbrev get_set := @getElem_set
@[deprecated get_set_ne (since := "2025-02-27")] abbrev get_set_ne := @getElem_set_ne
end Array

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@@ -8,3 +8,5 @@ module
prelude
public import Init.Data.Array.Lex.Basic
public import Init.Data.Array.Lex.Lemmas
public section

View File

@@ -9,8 +9,8 @@ prelude
public import Init.Core
import Init.Data.Array.Basic
import Init.Data.Nat.Lemmas
public import Init.Data.Range.Polymorphic.Iterators
public import Init.Data.Range.Polymorphic.Nat
import Init.Data.Range.Polymorphic.Iterators
import Init.Data.Range.Polymorphic.Nat
import Init.Data.Iterators.Consumers
public section
@@ -31,7 +31,7 @@ Specifically, `Array.lex as bs lt` is true if
def lex [BEq α] (as bs : Array α) (lt : α α Bool := by exact (· < ·)) : Bool := Id.run do
for h : i in 0...(min as.size bs.size) do
-- TODO: `get_elem_tactic` should be able to find this itself.
have : i < min as.size bs.size := Std.Rco.lt_upper_of_mem h
have : i < min as.size bs.size := Std.PRange.lt_upper_of_mem h
if lt as[i] bs[i] then
return true
else if as[i] != bs[i] then

View File

@@ -42,7 +42,8 @@ protected theorem not_le_iff_gt [LT α] {xs ys : Array α} :
Classical.not_not
@[simp] theorem lex_empty [BEq α] {lt : α α Bool} {xs : Array α} : xs.lex #[] lt = false := by
simp [lex, Std.Rco.forIn'_eq_if]
rw [lex, Std.PRange.forIn'_eq_match]
simp [Std.PRange.SupportsUpperBound.IsSatisfied]
private theorem cons_lex_cons.forIn'_congr_aux [Monad m] {as bs : ρ} {_ : Membership α ρ}
[ForIn' m ρ α inferInstance] (w : as = bs)
@@ -63,13 +64,13 @@ private theorem cons_lex_cons [BEq α] {lt : αα → Bool} {a b : α} {xs
(#[a] ++ xs).lex (#[b] ++ ys) lt =
(lt a b || a == b && xs.lex ys lt) := by
simp only [lex, size_append, List.size_toArray, List.length_cons, List.length_nil, Nat.zero_add,
Nat.add_min_add_left, Nat.add_lt_add_iff_left, Std.Rco.forIn'_eq_forIn'_toList]
Nat.add_min_add_left, Nat.add_lt_add_iff_left, Std.PRange.forIn'_eq_forIn'_toList]
conv =>
lhs; congr; congr
rw [cons_lex_cons.forIn'_congr_aux Std.Rco.toList_eq_if rfl (fun _ _ _ => rfl)]
simp only [bind_pure_comp, map_pure]
rw [cons_lex_cons.forIn'_congr_aux Std.PRange.toList_eq_match rfl (fun _ _ _ => rfl)]
simp only [Std.PRange.SupportsUpperBound.IsSatisfied, bind_pure_comp, map_pure]
rw [cons_lex_cons.forIn'_congr_aux (if_pos (by omega)) rfl (fun _ _ _ => rfl)]
simp only [Std.toList_Roo_eq_toList_Rco_of_isSome_succ? (lo := 0) (h := rfl),
simp only [Std.PRange.toList_Rox_eq_toList_Rcx_of_isSome_succ? (lo := 0) (h := rfl),
Std.PRange.UpwardEnumerable.succ?, Nat.add_comm 1, Std.PRange.Nat.toList_Rco_succ_succ,
Option.get_some, List.forIn'_cons, List.size_toArray, List.length_cons, List.length_nil,
Nat.lt_add_one, getElem_append_left, List.getElem_toArray, List.getElem_cons_zero]
@@ -82,10 +83,16 @@ private theorem cons_lex_cons [BEq α] {lt : αα → Bool} {a b : α} {xs
l₁.toArray.lex l₂.toArray lt = l₁.lex l₂ lt := by
induction l₁ generalizing l₂ with
| nil =>
cases l₂ <;> simp [lex, Std.Rco.forIn'_eq_if]
cases l₂
· rw [lex, Std.PRange.forIn'_eq_match]
simp [Std.PRange.SupportsUpperBound.IsSatisfied]
· rw [lex, Std.PRange.forIn'_eq_match]
simp [Std.PRange.SupportsUpperBound.IsSatisfied]
| cons x l₁ ih =>
cases l₂ with
| nil => simp [lex, Std.Rco.forIn'_eq_if]
| nil =>
rw [lex, Std.PRange.forIn'_eq_match]
simp [Std.PRange.SupportsUpperBound.IsSatisfied]
| cons y l₂ =>
rw [List.toArray_cons, List.toArray_cons y, cons_lex_cons, List.lex, ih]

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@@ -7,3 +7,5 @@ module
prelude
public import Init.Data.Array.QSort.Basic
public section

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@@ -7,7 +7,6 @@ module
prelude
public import Init.GetElem
public import Init.Data.Array.Basic
import Init.Data.Array.GetLit
public import Init.Data.Slice.Basic

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@@ -16,3 +16,5 @@ public import Init.Data.UInt
public import Init.Data.Repr
public import Init.Data.ToString.Basic
public import Init.Data.String.Extra
public section

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@@ -13,3 +13,5 @@ public import Init.Data.BitVec.Bitblast
public import Init.Data.BitVec.Decidable
public import Init.Data.BitVec.Lemmas
public import Init.Data.BitVec.Folds
public section

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@@ -29,6 +29,10 @@ set_option linter.missingDocs true
namespace BitVec
@[inline, deprecated BitVec.ofNatLT (since := "2025-02-13"), inherit_doc BitVec.ofNatLT]
protected def ofNatLt {n : Nat} (i : Nat) (p : i < 2 ^ n) : BitVec n :=
BitVec.ofNatLT i p
section Nat
/--

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@@ -17,7 +17,6 @@ import all Init.Data.BitVec.Basic
public import Init.Data.BitVec.Decidable
public import Init.Data.BitVec.Lemmas
public import Init.Data.BitVec.Folds
import Init.BinderPredicates
@[expose] public section

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@@ -9,7 +9,6 @@ prelude
public import Init.Data.BitVec.Basic
import all Init.Data.BitVec.Basic
import Init.Data.Int.Bitwise.Lemmas
import Init.Ext
public section

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@@ -8,7 +8,6 @@ module
prelude
public import Init.Data.BitVec.Bootstrap
import Init.Ext
public section
@@ -50,11 +49,11 @@ instance instDecidableForallBitVecSucc (P : BitVec (n+1) → Prop) [DecidablePre
instance instDecidableExistsBitVecZero (P : BitVec 0 Prop) [Decidable (P 0#0)] :
Decidable ( v, P v) :=
decidable_of_iff (¬ v, ¬ P v) (by exact Classical.not_forall_not)
decidable_of_iff (¬ v, ¬ P v) Classical.not_forall_not
instance instDecidableExistsBitVecSucc (P : BitVec (n+1) Prop) [DecidablePred P]
[Decidable ( (x : Bool) (v : BitVec n), ¬ P (v.cons x))] : Decidable ( v, P v) :=
decidable_of_iff (¬ v, ¬ P v) (by exact Classical.not_forall_not)
decidable_of_iff (¬ v, ¬ P v) Classical.not_forall_not
/--
For small numerals this isn't necessary (as typeclass search can use the above two instances),

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@@ -22,9 +22,6 @@ public import Init.Data.Int.Pow
public import Init.Data.Int.LemmasAux
public import Init.Data.BitVec.Bootstrap
public import Init.Data.Order.Factories
public import Init.Data.List.BasicAux
import Init.Data.List.Lemmas
import Init.Data.BEq
public section
@@ -77,6 +74,10 @@ theorem some_eq_getElem?_iff {l : BitVec w} : some a = l[n]? ↔ ∃ h : n < w,
theorem getElem_of_getElem? {l : BitVec w} : l[n]? = some a h : n < w, l[n] = a :=
getElem?_eq_some_iff.mp
set_option linter.missingDocs false in
@[deprecated getElem?_eq_some_iff (since := "2025-02-17")]
abbrev getElem?_eq_some := @getElem?_eq_some_iff
theorem getElem?_eq_none_iff {l : BitVec w} : l[n]? = none w n := by
simp
@@ -349,14 +350,25 @@ theorem ofBool_eq_iff_eq : ∀ {b b' : Bool}, BitVec.ofBool b = BitVec.ofBool b'
@[simp] theorem ofBool_xor_ofBool : ofBool b ^^^ ofBool b' = ofBool (b ^^ b') := by
cases b <;> cases b' <;> rfl
@[deprecated toNat_ofNatLT (since := "2025-02-13")]
theorem toNat_ofNatLt (x : Nat) (p : x < 2^w) : (x#'p).toNat = x := rfl
@[simp, grind =] theorem getLsbD_ofNatLT {n : Nat} (x : Nat) (lt : x < 2^n) (i : Nat) :
getLsbD (x#'lt) i = x.testBit i := by
simp [getLsbD, BitVec.ofNatLT]
@[deprecated getLsbD_ofNatLT (since := "2025-02-13")]
theorem getLsbD_ofNatLt {n : Nat} (x : Nat) (lt : x < 2^n) (i : Nat) :
getLsbD (x#'lt) i = x.testBit i := getLsbD_ofNatLT x lt i
@[simp, grind =] theorem getMsbD_ofNatLT {n x i : Nat} (h : x < 2^n) :
getMsbD (x#'h) i = (decide (i < n) && x.testBit (n - 1 - i)) := by
simp [getMsbD, getLsbD]
@[deprecated getMsbD_ofNatLT (since := "2025-02-13")]
theorem getMsbD_ofNatLt {n x i : Nat} (h : x < 2^n) :
getMsbD (x#'h) i = (decide (i < n) && x.testBit (n - 1 - i)) := getMsbD_ofNatLT h
@[grind =]
theorem ofNatLT_eq_ofNat {w : Nat} {n : Nat} (hn) : BitVec.ofNatLT n hn = BitVec.ofNat w n :=
eq_of_toNat_eq (by simp [Nat.mod_eq_of_lt hn])
@@ -6349,4 +6361,15 @@ theorem two_pow_ctz_le_toNat_of_ne_zero {x : BitVec w} (hx : x ≠ 0#w) :
have hclz := getLsbD_true_ctz_of_ne_zero (x := x) hx
exact Nat.ge_two_pow_of_testBit hclz
/-! ### Deprecations -/
set_option linter.missingDocs false
@[deprecated toFin_uShiftRight (since := "2025-02-18")]
abbrev toFin_uShiftRight := @toFin_ushiftRight
end BitVec

View File

@@ -10,3 +10,5 @@ public import Init.Data.ByteArray.Basic
public import Init.Data.ByteArray.Bootstrap
public import Init.Data.ByteArray.Extra
public import Init.Data.ByteArray.Lemmas
public section

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@@ -13,8 +13,6 @@ import all Init.Data.UInt.BasicAux
public import Init.Data.Option.Basic
public import Init.Data.Array.Extract
set_option doc.verso true
@[expose] public section
universe u
@@ -36,40 +34,18 @@ instance : Inhabited ByteArray where
instance : EmptyCollection ByteArray where
emptyCollection := ByteArray.empty
/--
Retrieves the size of the array as a platform-specific fixed-width integer.
Because {name}`USize` is big enough to address all memory on every platform that Lean supports,
there are in practice no {name}`ByteArray`s that have more elements that {name}`USize` can count.
-/
@[extern "lean_sarray_size", simp]
def usize (a : @& ByteArray) : USize :=
a.size.toUSize
/--
Retrieves the byte at the indicated index. Callers must prove that the index is in bounds. The index
is represented by a platform-specific fixed-width integer (either 32 or 64 bits).
Because {name}`USize` is big enough to address all memory on every platform that Lean supports, there are
in practice no {name}`ByteArray`s for which {name}`uget` cannot retrieve all elements.
-/
@[extern "lean_byte_array_uget"]
def uget : (a : @& ByteArray) (i : USize) (h : i.toNat < a.size := by get_elem_tactic) UInt8
| bs, i, h => bs[i]
/--
Retrieves the byte at the indicated index. Panics if the index is out of bounds.
-/
@[extern "lean_byte_array_get"]
def get! : (@& ByteArray) (@& Nat) UInt8
| bs, i => bs[i]!
/--
Retrieves the byte at the indicated index. Callers must prove that the index is in bounds.
Use {name}`uget` for a more efficient alternative or {name}`get!` for a variant that panics if the
index is out of bounds.
-/
@[extern "lean_byte_array_fget"]
def get : (a : @& ByteArray) (i : @& Nat) (h : i < a.size := by get_elem_tactic) UInt8
| bs, i, _ => bs[i]
@@ -80,65 +56,37 @@ instance : GetElem ByteArray Nat UInt8 fun xs i => i < xs.size where
instance : GetElem ByteArray USize UInt8 fun xs i => i.toFin < xs.size where
getElem xs i h := xs.uget i h
/--
Replaces the byte at the given index.
The array is modified in-place if there are no other references to it.
If the index is out of bounds, the array is returned unmodified.
-/
@[extern "lean_byte_array_set"]
def set! : ByteArray (@& Nat) UInt8 ByteArray
| bs, i, b => bs.set! i b
/--
Replaces the byte at the given index.
No bounds check is performed, but the function requires a proof that the index is in bounds. This
proof can usually be omitted, and will be synthesized automatically.
The array is modified in-place if there are no other references to it.
-/
@[extern "lean_byte_array_fset"]
def set : (a : ByteArray) (i : @& Nat) UInt8 (h : i < a.size := by get_elem_tactic) ByteArray
| bs, i, b, h => bs.set i b h
@[extern "lean_byte_array_uset", inherit_doc ByteArray.set]
@[extern "lean_byte_array_uset"]
def uset : (a : ByteArray) (i : USize) UInt8 (h : i.toNat < a.size := by get_elem_tactic) ByteArray
| bs, i, v, h => bs.uset i v h
/--
Computes a hash for a {name}`ByteArray`.
-/
@[extern "lean_byte_array_hash"]
protected opaque hash (a : @& ByteArray) : UInt64
instance : Hashable ByteArray where
hash := ByteArray.hash
/--
Returns {name}`true` when {name}`s` contains zero bytes.
-/
def isEmpty (s : ByteArray) : Bool :=
s.size == 0
/--
Copies the slice at `[srcOff, srcOff + len)` in {name}`src` to `[destOff, destOff + len)` in
{name}`dest`, growing {name}`dest` if necessary. If {name}`exact` is {name}`false`, the capacity
will be doubled when grown.
-/
Copy the slice at `[srcOff, srcOff + len)` in `src` to `[destOff, destOff + len)` in `dest`, growing `dest` if necessary.
If `exact` is `false`, the capacity will be doubled when grown. -/
@[extern "lean_byte_array_copy_slice"]
def copySlice (src : @& ByteArray) (srcOff : Nat) (dest : ByteArray) (destOff len : Nat) (exact : Bool := true) : ByteArray :=
dest.data.extract 0 destOff ++ src.data.extract srcOff (srcOff + len) ++ dest.data.extract (destOff + min len (src.data.size - srcOff)) dest.data.size
/--
Copies the bytes with indices {name}`b` (inclusive) to {name}`e` (exclusive) to a new
{name}`ByteArray`.
-/
def extract (a : ByteArray) (b e : Nat) : ByteArray :=
a.copySlice b empty 0 (e - b)
@[inline]
protected def fastAppend (a : ByteArray) (b : ByteArray) : ByteArray :=
-- we assume that `append`s may be repeated, so use asymptotic growing; use `copySlice` directly to customize
b.copySlice 0 a a.size b.size false
@@ -165,9 +113,6 @@ theorem append_eq {a b : ByteArray} : a.append b = a ++ b := rfl
theorem fastAppend_eq {a b : ByteArray} : a.fastAppend b = a ++ b := by
simp [ append_eq_fastAppend]
/--
Converts a packed array of bytes to a linked list.
-/
def toList (bs : ByteArray) : List UInt8 :=
let rec loop (i : Nat) (r : List UInt8) :=
if i < bs.size then
@@ -178,12 +123,16 @@ def toList (bs : ByteArray) : List UInt8 :=
decreasing_by decreasing_trivial_pre_omega
loop 0 []
/--
Finds the index of the first byte in {name}`a` for which {name}`p` returns {name}`true`. If no byte
in {name}`a` satisfies {name}`p`, then the result is {name}`none`.
@[inline] def findIdx? (a : ByteArray) (p : UInt8 Bool) (start := 0) : Option Nat :=
let rec @[specialize] loop (i : Nat) :=
if h : i < a.size then
if p a[i] then some i else loop (i+1)
else
none
termination_by a.size - i
decreasing_by decreasing_trivial_pre_omega
loop start
The index is returned along with a proof that it is a valid index in the array.
-/
@[inline] def findFinIdx? (a : ByteArray) (p : UInt8 Bool) (start := 0) : Option (Fin a.size) :=
let rec @[specialize] loop (i : Nat) :=
if h : i < a.size then
@@ -195,29 +144,11 @@ The index is returned along with a proof that it is a valid index in the array.
loop start
/--
Finds the index of the first byte in {name}`a` for which {name}`p` returns {name}`true`. If no byte
in {name}`a` satisfies {name}`p`, then the result is {name}`none`.
We claim this unsafe implementation is correct because an array cannot have more than `usizeSz` elements in our runtime.
This is similar to the `Array` version.
The variant {name}`findFinIdx?` additionally returns a proof that the found index is in bounds.
TODO: avoid code duplication in the future after we improve the compiler.
-/
@[inline] def findIdx? (a : ByteArray) (p : UInt8 Bool) (start := 0) : Option Nat :=
let rec @[specialize] loop (i : Nat) :=
if h : i < a.size then
if p a[i] then some i else loop (i+1)
else
none
termination_by a.size - i
decreasing_by decreasing_trivial_pre_omega
loop start
/--
An efficient implementation of {name}`ForIn.forIn` for {name}`ByteArray` that uses {name}`USize`
rather than {name}`Nat` for indices.
We claim this unsafe implementation is correct because an array cannot have more than
{name}`USize.size` elements in our runtime. This is similar to the {name}`Array` version.
-/
-- TODO: avoid code duplication in the future after we improve the compiler.
@[inline] unsafe def forInUnsafe {β : Type v} {m : Type v Type w} [Monad m] (as : ByteArray) (b : β) (f : UInt8 β m (ForInStep β)) : m β :=
let sz := as.usize
let rec @[specialize] loop (i : USize) (b : β) : m β := do
@@ -230,11 +161,7 @@ We claim this unsafe implementation is correct because an array cannot have more
pure b
loop 0 b
/--
The reference implementation of {name}`ForIn.forIn` for {name}`ByteArray`.
In compiled code, this is replaced by the more efficient {name}`ByteArray.forInUnsafe`.
-/
/-- Reference implementation for `forIn` -/
@[implemented_by ByteArray.forInUnsafe]
protected def forIn {β : Type v} {m : Type v Type w} [Monad m] (as : ByteArray) (b : β) (f : UInt8 β m (ForInStep β)) : m β :=
let rec loop (i : Nat) (h : i as.size) (b : β) : m β := do
@@ -252,13 +179,7 @@ protected def forIn {β : Type v} {m : Type v → Type w} [Monad m] (as : ByteAr
instance : ForIn m ByteArray UInt8 where
forIn := ByteArray.forIn
/--
An efficient implementation of a monadic left fold on for {name}`ByteArray` that uses {name}`USize`
rather than {name}`Nat` for indices.
We claim this unsafe implementation is correct because an array cannot have more than
{name}`USize.size` elements in our runtime. This is similar to the {name}`Array` version.
-/
/-- See comment at `forInUnsafe` -/
-- TODO: avoid code duplication.
@[inline]
unsafe def foldlMUnsafe {β : Type v} {m : Type v Type w} [Monad m] (f : β UInt8 m β) (init : β) (as : ByteArray) (start := 0) (stop := as.size) : m β :=
@@ -275,14 +196,7 @@ unsafe def foldlMUnsafe {β : Type v} {m : Type v → Type w} [Monad m] (f : β
else
pure init
/--
A monadic left fold on {name}`ByteArray` that iterates over an array from low to high indices,
computing a running value.
Each element of the array is combined with the value from the prior elements using a monadic
function {name}`f`. The initial value {name}`init` is the starting value before any elements have
been processed.
-/
/-- Reference implementation for `foldlM` -/
@[implemented_by foldlMUnsafe]
def foldlM {β : Type v} {m : Type v Type w} [Monad m] (f : β UInt8 m β) (init : β) (as : ByteArray) (start := 0) (stop := as.size) : m β :=
let fold (stop : Nat) (h : stop as.size) :=
@@ -300,23 +214,11 @@ def foldlM {β : Type v} {m : Type v → Type w} [Monad m] (f : β → UInt8 →
else
fold as.size (Nat.le_refl _)
/--
A left fold on {name}`ByteArray` that iterates over an array from low to high indices, computing a
running value.
Each element of the array is combined with the value from the prior elements using a function
{name}`f`. The initial value {name}`init` is the starting value before any elements have been
processed.
{name}`ByteArray.foldlM` is a monadic variant of this function.
-/
@[inline]
def foldl {β : Type v} (f : β UInt8 β) (init : β) (as : ByteArray) (start := 0) (stop := as.size) : β :=
Id.run <| as.foldlM (pure <| f · ·) init start stop
set_option doc.verso false -- Awaiting intra-module forward reference support
/--
Iterator over the bytes (`UInt8`) of a `ByteArray`.
/-- Iterator over the bytes (`UInt8`) of a `ByteArray`.
Typically created by `arr.iter`, where `arr` is a `ByteArray`.
@@ -340,7 +242,6 @@ structure Iterator where
current byte is `(default : UInt8)`. -/
idx : Nat
deriving Inhabited
set_option doc.verso true
/-- Creates an iterator at the beginning of an array. -/
def mkIterator (arr : ByteArray) : Iterator :=
@@ -358,25 +259,16 @@ theorem Iterator.sizeOf_eq (i : Iterator) : sizeOf i = i.array.size - i.idx :=
namespace Iterator
/--
The number of bytes remaining in the iterator.
-/
/-- Number of bytes remaining in the iterator. -/
def remainingBytes : Iterator Nat
| arr, i => arr.size - i
@[inherit_doc Iterator.idx]
def pos := Iterator.idx
/-- True if the iterator is past the array's last byte. -/
@[inline]
def atEnd : Iterator Bool
| arr, i => i arr.size
/-- The byte at the current position.
/--
The byte at the current position.
On an invalid position, returns {lean}`(default : UInt8)`.
-/
On an invalid position, returns `(default : UInt8)`. -/
@[inline]
def curr : Iterator UInt8
| arr, i =>
@@ -385,28 +277,27 @@ def curr : Iterator → UInt8
else
default
/--
Moves the iterator's position forward by one byte, unconditionally.
/-- Moves the iterator's position forward by one byte, unconditionally.
It is only valid to call this function if the iterator is not at the end of the array, *i.e.*
{name}`Iterator.atEnd` is {name}`false`; otherwise, the resulting iterator will be invalid.
-/
`Iterator.atEnd` is `false`; otherwise, the resulting iterator will be invalid. -/
@[inline]
def next : Iterator Iterator
| arr, i => arr, i + 1
/--
Decreases the iterator's position.
/-- Decreases the iterator's position.
If the position is zero, this function is the identity.
-/
If the position is zero, this function is the identity. -/
@[inline]
def prev : Iterator Iterator
| arr, i => arr, i - 1
/--
True if the iterator is valid; that is, it is not past the array's last byte.
-/
/-- True if the iterator is past the array's last byte. -/
@[inline]
def atEnd : Iterator Bool
| arr, i => i arr.size
/-- True if the iterator is not past the array's last byte. -/
@[inline]
def hasNext : Iterator Bool
| arr, i => i < arr.size
@@ -432,21 +323,17 @@ def next' (it : Iterator) (_h : it.hasNext) : Iterator :=
def hasPrev : Iterator Bool
| _, i => i > 0
/--
Moves the iterator's position to the end of the array.
/-- Moves the iterator's position to the end of the array.
Given {given}`i : ByteArray.Iterator`, note that {lean}`i.toEnd.atEnd` is always {name}`true`.
-/
Note that `i.toEnd.atEnd` is always `true`. -/
@[inline]
def toEnd : Iterator Iterator
| arr, _ => arr, arr.size
/--
Moves the iterator's position several bytes forward.
/-- Moves the iterator's position several bytes forward.
The resulting iterator is only valid if the number of bytes to skip is less than or equal to
the number of bytes left in the iterator.
-/
the number of bytes left in the iterator. -/
@[inline]
def forward : Iterator Nat Iterator
| arr, i, f => arr, i + f
@@ -454,11 +341,9 @@ def forward : Iterator → Nat → Iterator
@[inherit_doc forward, inline]
def nextn : Iterator Nat Iterator := forward
/--
Moves the iterator's position several bytes back.
/-- Moves the iterator's position several bytes back.
If asked to go back more bytes than available, stops at the beginning of the array.
-/
If asked to go back more bytes than available, stops at the beginning of the array. -/
@[inline]
def prevn : Iterator Nat Iterator
| arr, i, f => arr, i - f

View File

@@ -10,19 +10,12 @@ public import Init.Prelude
public import Init.Data.List.Basic
public section
set_option doc.verso true
namespace ByteArray
@[simp]
theorem data_push {a : ByteArray} {b : UInt8} : (a.push b).data = a.data.push b := rfl
/--
Appends two byte arrays.
In compiled code, calls to {name}`ByteArray.append` are replaced with the much more efficient
{name (scope:="Init.Data.ByteArray.Basic")}`ByteArray.fastAppend`.
-/
@[expose]
protected def append (a b : ByteArray) : ByteArray :=
a.data.toList ++ b.data.toList

View File

@@ -9,13 +9,7 @@ prelude
public import Init.Data.ByteArray.Basic
import Init.Data.String.Basic
set_option doc.verso true
/--
Interprets a {name}`ByteArray` of size 8 as a little-endian {name}`UInt64`.
Panics if the array's size is not 8.
-/
/-- Interpret a `ByteArray` of size 8 as a little-endian `UInt64`. -/
public def ByteArray.toUInt64LE! (bs : ByteArray) : UInt64 :=
assert! bs.size == 8
(bs.get! 7).toUInt64 <<< 0x38 |||
@@ -27,11 +21,7 @@ public def ByteArray.toUInt64LE! (bs : ByteArray) : UInt64 :=
(bs.get! 1).toUInt64 <<< 0x8 |||
(bs.get! 0).toUInt64
/--
Interprets a {name}`ByteArray` of size 8 as a big-endian {name}`UInt64`.
Panics if the array's size is not 8.
-/
/-- Interpret a `ByteArray` of size 8 as a big-endian `UInt64`. -/
public def ByteArray.toUInt64BE! (bs : ByteArray) : UInt64 :=
assert! bs.size == 8
(bs.get! 0).toUInt64 <<< 0x38 |||

View File

@@ -11,13 +11,6 @@ public import Init.Data.Array.Extract
public section
-- At present the preferred normal form for empty byte arrays is `ByteArray.empty`
@[simp]
theorem emptyc_eq_empty : ( : ByteArray) = ByteArray.empty := rfl
@[simp]
theorem emptyWithCapacity_eq_empty : ByteArray.emptyWithCapacity 0 = ByteArray.empty := rfl
@[simp]
theorem ByteArray.data_empty : ByteArray.empty.data = #[] := rfl
@@ -167,9 +160,9 @@ theorem ByteArray.append_inj_left {xs₁ xs₂ ys₁ ys₂ : ByteArray} (h : xs
simp only [ByteArray.ext_iff, ByteArray.size_data, ByteArray.data_append] at *
exact Array.append_inj_left h hl
theorem ByteArray.extract_append_eq_right {a b : ByteArray} {i j : Nat} (hi : i = a.size) (hj : j = a.size + b.size) :
(a ++ b).extract i j = b := by
subst hi hj
theorem ByteArray.extract_append_eq_right {a b : ByteArray} {i : Nat} (hi : i = a.size) :
(a ++ b).extract i (a ++ b).size = b := by
subst hi
ext1
simp [ size_data]

View File

@@ -9,3 +9,5 @@ prelude
public import Init.Data.Char.Basic
public import Init.Data.Char.Lemmas
public import Init.Data.Char.Order
public section

View File

@@ -11,3 +11,5 @@ public import Init.Data.Fin.Log2
public import Init.Data.Fin.Iterate
public import Init.Data.Fin.Fold
public import Init.Data.Fin.Lemmas
public section

View File

@@ -140,7 +140,7 @@ Modulus of bounded numbers, usually invoked via the `%` operator.
The resulting value is that computed by the `%` operator on `Nat`.
-/
protected def mod : Fin n Fin n Fin n
| a, h, b, _ => a % b, by exact Nat.lt_of_le_of_lt (Nat.mod_le _ _) h
| a, h, b, _ => a % b, Nat.lt_of_le_of_lt (Nat.mod_le _ _) h
/--
Division of bounded numbers, usually invoked via the `/` operator.
@@ -154,7 +154,7 @@ Examples:
* `(5 : Fin 10) / (7 : Fin 10) = (0 : Fin 10)`
-/
protected def div : Fin n Fin n Fin n
| a, h, b, _ => a / b, by exact Nat.lt_of_le_of_lt (Nat.div_le_self _ _) h
| a, h, b, _ => a / b, Nat.lt_of_le_of_lt (Nat.div_le_self _ _) h
/--
Modulus of bounded numbers with respect to a `Nat`.
@@ -162,7 +162,7 @@ Modulus of bounded numbers with respect to a `Nat`.
The resulting value is that computed by the `%` operator on `Nat`.
-/
def modn : Fin n Nat Fin n
| a, h, m => a % m, by exact Nat.lt_of_le_of_lt (Nat.mod_le _ _) h
| a, h, m => a % m, Nat.lt_of_le_of_lt (Nat.mod_le _ _) h
/--
Bitwise and.

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@@ -7,6 +7,7 @@ module
prelude
public import Init.Data.Nat.Lemmas
public import Init.Data.Int.DivMod.Lemmas
public import Init.Ext
public import Init.ByCases
public import Init.Conv
@@ -326,9 +327,7 @@ theorem subsingleton_iff_le_one : Subsingleton (Fin n) ↔ n ≤ 1 := by
(match n with | 0 | 1 | n+2 => ?_) <;> try simp
· exact nofun
· exact fun 0, _ 0, _ => rfl
· have : ¬ n + 2 1 := by simp [Nat.not_le]
simp only [this, iff_false]
exact fun h => by have := zero_lt_one (n := n); simp_all [h.elim 0 1]
· exact fun h => by have := zero_lt_one (n := n); simp_all [h.elim 0 1]
instance subsingleton_zero : Subsingleton (Fin 0) := subsingleton_iff_le_one.2 (by decide)

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@@ -7,3 +7,5 @@ module
prelude
public import Init.Data.FloatArray.Basic
public section

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@@ -10,3 +10,5 @@ public import Init.Data.Format.Basic
public import Init.Data.Format.Macro
public import Init.Data.Format.Instances
public import Init.Data.Format.Syntax
public section

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@@ -51,5 +51,5 @@ Converts a string to a pretty-printer document, replacing newlines in the string
def String.toFormat (s : String) : Std.Format :=
Std.Format.joinSep (s.splitOn "\n") Std.Format.line
instance : ToFormat String.Pos.Raw where
instance : ToFormat String.Pos where
format p := format p.byteIdx

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@@ -16,7 +16,7 @@ universe u
instance : Hashable Nat where
hash n := UInt64.ofNat n
instance : Hashable String.Pos.Raw where
instance : Hashable String.Pos where
hash p := UInt64.ofNat p.byteIdx
instance [Hashable α] [Hashable β] : Hashable (α × β) where
@@ -76,3 +76,22 @@ instance (P : Prop) : Hashable P where
/-- An opaque (low-level) hash operation used to implement hashing for pointers. -/
@[always_inline, inline] def hash64 (u : UInt64) : UInt64 :=
mixHash u 11
/--
The `BEq α` and `Hashable α` instances on `α` are compatible. This means that that `a == b` implies
`hash a = hash b`.
This is automatic if the `BEq` instance is lawful.
-/
class LawfulHashable (α : Type u) [BEq α] [Hashable α] where
/-- If `a == b`, then `hash a = hash b`. -/
hash_eq (a b : α) : a == b hash a = hash b
/--
A lawful hash function respects its Boolean equality test.
-/
theorem hash_eq [BEq α] [Hashable α] [LawfulHashable α] {a b : α} : a == b hash a = hash b :=
LawfulHashable.hash_eq a b
instance (priority := low) [BEq α] [Hashable α] [LawfulBEq α] : LawfulHashable α where
hash_eq _ _ h := eq_of_beq h rfl

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@@ -18,3 +18,5 @@ public import Init.Data.Int.Pow
public import Init.Data.Int.Cooper
public import Init.Data.Int.Linear
public import Init.Data.Int.OfNat
public section

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@@ -8,3 +8,5 @@ module
prelude
public import Init.Data.Int.Bitwise.Basic
public import Init.Data.Int.Bitwise.Lemmas
public section

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@@ -9,7 +9,6 @@ prelude
public import Init.Data.Ord.Basic
import all Init.Data.Ord.Basic
public import Init.Data.Int.Order
import Init.Omega
public section

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@@ -9,3 +9,5 @@ prelude
public import Init.Data.Int.DivMod.Basic
public import Init.Data.Int.DivMod.Bootstrap
public import Init.Data.Int.DivMod.Lemmas
public section

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@@ -206,6 +206,9 @@ theorem ediv_nonneg_iff_of_pos {a b : Int} (h : 0 < b) : 0 ≤ a / b ↔ 0 ≤ a
| Int.ofNat (b+1), _ =>
rcases a with a <;> simp [Int.ediv, -natCast_ediv]
@[deprecated ediv_nonneg_iff_of_pos (since := "2025-02-28")]
abbrev div_nonneg_iff_of_pos := @ediv_nonneg_iff_of_pos
/-! ### emod -/
theorem emod_nonneg : (a : Int) {b : Int}, b 0 0 a % b

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@@ -13,7 +13,6 @@ public import Init.Data.Int.Order
public import Init.Data.Int.Lemmas
public import Init.Data.Nat.Dvd
public import Init.RCases
import Init.TacticsExtra
public section
@@ -123,8 +122,8 @@ theorem eq_one_of_mul_eq_one_right {a b : Int} (H : 0 ≤ a) (H' : a * b = 1) :
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']
instance decidableDvd : DecidableRel (α := Int) (· ·) := fun a b =>
decidable_of_decidable_of_iff (p := b % a = 0) (by exact (dvd_iff_emod_eq_zero ..).symm)
instance decidableDvd : DecidableRel (α := Int) (· ·) := fun _ _ =>
decidable_of_decidable_of_iff (dvd_iff_emod_eq_zero ..).symm
protected theorem mul_dvd_mul_iff_left {a b c : Int} (h : a 0) : (a * b) (a * c) b c :=
by rintro d, h'; exact d, by rw [Int.mul_assoc] at h'; exact (mul_eq_mul_left_iff h).mp h',

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@@ -8,6 +8,7 @@ module
prelude
public import Init.Data.Int.Order
public import Init.Data.Int.Pow
public import Init.Data.Int.DivMod.Lemmas
public import Init.Omega
public section

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@@ -88,20 +88,6 @@ theorem finVal {n : Nat} {a : Fin n} {a' : Int}
(h₁ : Lean.Grind.ToInt.toInt a = a') : NatCast.natCast (a.val) = a' := by
rw [ h₁, Lean.Grind.ToInt.toInt, Lean.Grind.instToIntFinCoOfNatIntCast]
theorem eq_eq {a b : Nat} {a' b' : Int}
(h₁ : NatCast.natCast a = a') (h₂ : NatCast.natCast b = b') : (a = b) = (a' = b') := by
simp [ h₁, h₂]; constructor
next => intro; subst a; rfl
next => simp [Int.natCast_inj]
theorem lt_eq {a b : Nat} {a' b' : Int}
(h₁ : NatCast.natCast a = a') (h₂ : NatCast.natCast b = b') : (a < b) = (a' < b') := by
simp only [ h₁, h₂, Int.ofNat_lt]
theorem le_eq {a b : Nat} {a' b' : Int}
(h₁ : NatCast.natCast a = a') (h₂ : NatCast.natCast b = b') : (a b) = (a' b') := by
simp only [ h₁, h₂, Int.ofNat_le]
end Nat.ToInt
namespace Int.Nonneg

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@@ -1347,6 +1347,8 @@ theorem neg_of_sign_eq_neg_one : ∀ {a : Int}, sign a = -1 → a < 0
| 0 => Int.mul_zero _
| -[_+1] => Int.mul_neg_one _
@[deprecated mul_sign_self (since := "2025-02-24")] abbrev mul_sign := @mul_sign_self
@[simp] theorem sign_mul_self (i : Int) : sign i * i = natAbs i := by
rw [Int.mul_comm, mul_sign_self]

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@@ -50,9 +50,14 @@ protected theorem pow_ne_zero {n : Int} {m : Nat} : n ≠ 0 → n ^ m ≠ 0 := b
instance {n : Int} {m : Nat} [NeZero n] : NeZero (n ^ m) := Int.pow_ne_zero (NeZero.ne _)
-- This can't be removed until the next update-stage0
@[deprecated Nat.pow_le_pow_left (since := "2025-02-17")]
abbrev pow_le_pow_of_le_left := @Nat.pow_le_pow_left
@[deprecated Nat.pow_le_pow_right (since := "2025-02-17")]
abbrev pow_le_pow_of_le_right := @Nat.pow_le_pow_right
@[deprecated Nat.pow_pos (since := "2025-02-17")]
abbrev _root_.Nat.pos_pow_of_pos := @Nat.pow_pos
abbrev pos_pow_of_pos := @Nat.pow_pos
@[simp, norm_cast]
protected theorem natCast_pow (b n : Nat) : ((b^n : Nat) : Int) = (b : Int) ^ n := by

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@@ -9,3 +9,5 @@ prelude
public import Init.Data.Iterators.Combinators.Monadic
public import Init.Data.Iterators.Combinators.FilterMap
public import Init.Data.Iterators.Combinators.ULift
public section

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@@ -8,3 +8,5 @@ module
prelude
public import Init.Data.Iterators.Combinators.Monadic.FilterMap
public import Init.Data.Iterators.Combinators.Monadic.ULift
public section

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@@ -13,3 +13,5 @@ public import Init.Data.Iterators.Consumers.Loop
public import Init.Data.Iterators.Consumers.Partial
public import Init.Data.Iterators.Consumers.Stream
public section

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@@ -10,3 +10,5 @@ public import Init.Data.Iterators.Consumers.Monadic.Access
public import Init.Data.Iterators.Consumers.Monadic.Collect
public import Init.Data.Iterators.Consumers.Monadic.Loop
public import Init.Data.Iterators.Consumers.Monadic.Partial
public section

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@@ -8,3 +8,5 @@ module
prelude
public import Init.Data.Iterators.Internal.LawfulMonadLiftFunction
public import Init.Data.Iterators.Internal.Termination
public section

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@@ -8,3 +8,5 @@ module
prelude
public import Init.Data.Iterators.Lemmas.Consumers
public import Init.Data.Iterators.Lemmas.Combinators
public section

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@@ -10,3 +10,5 @@ public import Init.Data.Iterators.Lemmas.Combinators.Attach
public import Init.Data.Iterators.Lemmas.Combinators.Monadic
public import Init.Data.Iterators.Lemmas.Combinators.FilterMap
public import Init.Data.Iterators.Lemmas.Combinators.ULift
public section

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@@ -195,7 +195,8 @@ theorem Iter.step_mapM {f : β → n γ}
match step with
| .yield it' out h =>
simp only [bind_pure_comp]
simp only [Functor.map]
simp only [Functor.map,
]
rfl
| .skip it' h => rfl
| .done h => rfl
@@ -316,119 +317,4 @@ theorem Iter.toArray_filter
(it.filter f).toArray = it.toArray.filter f := by
simp [filter_eq_toIter_filter_toIterM, IterM.toArray_filter, Iter.toArray_eq_toArray_toIterM]
section Fold
theorem Iter.foldM_filterMapM {α β γ δ : Type w} {m : Type w Type w'} {n : Type w Type w''}
[Iterator α Id β] [Finite α Id] [Monad m] [Monad n] [LawfulMonad m] [LawfulMonad n]
[IteratorLoop α Id Id] [IteratorLoop α Id m] [IteratorLoop α Id n]
[MonadLiftT m n] [LawfulMonadLiftT m n]
[LawfulIteratorLoop α Id Id] [LawfulIteratorLoop α Id m] [LawfulIteratorLoop α Id n]
{f : β m (Option γ)} {g : δ γ n δ} {init : δ} {it : Iter (α := α) β} :
(it.filterMapM f).foldM (init := init) g =
it.foldM (init := init) (fun d b => do
let some c f b | pure d
g d c) := by
rw [foldM_eq_foldM_toIterM, filterMapM_eq_toIter_filterMapM_toIterM, IterM.foldM_filterMapM]
congr
simp [instMonadLiftTOfMonadLift, Id.instMonadLiftTOfPure]
theorem Iter.foldM_mapM {α β γ δ : Type w} {m : Type w Type w'} {n : Type w Type w''}
[Iterator α Id β] [Finite α Id] [Monad m] [Monad n] [LawfulMonad m] [LawfulMonad n]
[IteratorLoop α Id m] [IteratorLoop α Id n]
[LawfulIteratorLoop α Id m] [LawfulIteratorLoop α Id n]
[MonadLiftT m n] [LawfulMonadLiftT m n]
{f : β m γ} {g : δ γ n δ} {init : δ} {it : Iter (α := α) β} :
(it.mapM f).foldM (init := init) g =
it.foldM (init := init) (fun d b => do let c f b; g d c) := by
rw [foldM_eq_foldM_toIterM, mapM_eq_toIter_mapM_toIterM, IterM.foldM_mapM]
congr
simp [instMonadLiftTOfMonadLift, Id.instMonadLiftTOfPure]
theorem Iter.foldM_filterMap {α β γ : Type w} {δ : Type x} {m : Type x Type w'}
[Iterator α Id β] [Finite α Id] [Monad m] [LawfulMonad m]
[IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
{f : β Option γ} {g : δ γ m δ} {init : δ} {it : Iter (α := α) β} :
(it.filterMap f).foldM (init := init) g =
it.foldM (init := init) (fun d b => do
let some c := f b | pure d
g d c) := by
induction it using Iter.inductSteps generalizing init with | step it ihy ihs
rw [foldM_eq_match_step, foldM_eq_match_step, step_filterMap]
-- There seem to be some type dependencies that, combined with nested match expressions,
-- force us to split a lot.
split <;> rename_i h
· split at h
· split at h
· cases h
· cases h; simp [*, ihy _]
· cases h
· cases h
· split at h
· split at h
· cases h; simp [*, ihy _]
· cases h
· cases h; simp [*, ihs _]
· cases h
· split at h
· split at h
· cases h
· cases h
· cases h
· simp [*]
theorem Iter.foldM_map {α β γ : Type w} {δ : Type x} {m : Type x Type w'}
[Iterator α Id β] [Finite α Id] [Monad m] [LawfulMonad m]
[IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
{f : β γ} {g : δ γ m δ} {init : δ} {it : Iter (α := α) β} :
(it.map f).foldM (init := init) g =
it.foldM (init := init) (fun d b => g d (f b)) := by
induction it using Iter.inductSteps generalizing init with | step it ihy ihs
rw [foldM_eq_match_step, foldM_eq_match_step, step_map]
cases it.step using PlausibleIterStep.casesOn
· simp [*, ihy _]
· simp [*, ihs _]
· simp
theorem Iter.fold_filterMapM {α β γ δ : Type w} {m : Type w Type w'}
[Iterator α Id β] [Finite α Id] [Monad m] [LawfulMonad m]
[IteratorLoop α Id Id.{w}] [IteratorLoop α Id m]
[LawfulIteratorLoop α Id Id] [LawfulIteratorLoop α Id m]
{f : β m (Option γ)} {g : δ γ δ} {init : δ} {it : Iter (α := α) β} :
(it.filterMapM f).fold (init := init) g =
it.foldM (init := init) (fun d b => do
let some c f b | pure d
return g d c) := by
rw [foldM_eq_foldM_toIterM, filterMapM_eq_toIter_filterMapM_toIterM, IterM.fold_filterMapM]
rfl
theorem Iter.fold_mapM {α β γ δ : Type w} {m : Type w Type w'}
[Iterator α Id β] [Finite α Id] [Monad m] [LawfulMonad m]
[IteratorLoop α Id Id.{w}] [IteratorLoop α Id m]
[LawfulIteratorLoop α Id Id] [LawfulIteratorLoop α Id m]
{f : β m γ} {g : δ γ δ} {init : δ} {it : Iter (α := α) β} :
(it.mapM f).fold (init := init) g =
it.foldM (init := init) (fun d b => do return g d ( f b)) := by
rw [foldM_eq_foldM_toIterM, mapM_eq_toIter_mapM_toIterM, IterM.fold_mapM]
theorem Iter.fold_filterMap {α β γ : Type w} {δ : Type x}
[Iterator α Id β] [Finite α Id] [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
{f : β Option γ} {g : δ γ δ} {init : δ} {it : Iter (α := α) β} :
(it.filterMap f).fold (init := init) g =
it.fold (init := init) (fun d b =>
match f b with
| some c => g d c
| _ => d) := by
simp only [fold_eq_foldM, foldM_filterMap]
rfl
theorem Iter.fold_map {α β γ : Type w} {δ : Type x}
[Iterator α Id β] [Finite α Id]
[IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
{f : β γ} {g : δ γ δ} {init : δ} {it : Iter (α := α) β} :
(it.map f).fold (init := init) g =
it.fold (init := init) (fun d b => g d (f b)) := by
simp [fold_eq_foldM, foldM_map]
end Fold
end Std.Iterators

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@@ -9,3 +9,5 @@ prelude
public import Init.Data.Iterators.Lemmas.Combinators.Monadic.Attach
public import Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
public import Init.Data.Iterators.Lemmas.Combinators.Monadic.ULift
public section

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@@ -414,129 +414,4 @@ theorem IterM.toArray_filter {α : Type w} {m : Type w → Type w'} [Monad m] [L
end ToArray
section Fold
theorem IterM.foldM_filterMapM {α β γ δ : Type w}
{m : Type w Type w'} {n : Type w Type w''} {o : Type w Type w'''}
[Iterator α m β] [Finite α m]
[Monad m] [Monad n] [Monad o] [LawfulMonad m] [LawfulMonad n] [LawfulMonad o]
[IteratorLoop α m n] [IteratorLoop α m o]
[LawfulIteratorLoop α m n] [LawfulIteratorLoop α m o]
[MonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT m n] [LawfulMonadLiftT n o]
{f : β n (Option γ)} {g : δ γ o δ} {init : δ} {it : IterM (α := α) m β} :
haveI : MonadLift n o := MonadLiftT.monadLift
(it.filterMapM f).foldM (init := init) g =
it.foldM (init := init) (fun d b => do
let some c f b | pure d
g d c) := by
letI : MonadLift n o := MonadLiftT.monadLift
induction it using IterM.inductSteps generalizing init with | step it ihy ihs
rw [foldM_eq_match_step, foldM_eq_match_step, step_filterMapM, liftM_bind, bind_assoc]
apply bind_congr; intro step
split
· simp only [PlausibleIterStep.skip, PlausibleIterStep.yield, liftM_bind, bind_assoc]
apply bind_congr; intro c?
split <;> simp [ihy _]
· simp [ihs _]
· simp
theorem IterM.foldM_mapM {α β γ δ : Type w}
{m : Type w Type w'} {n : Type w Type w''} {o : Type w Type w'''}
[Iterator α m β] [Finite α m]
[Monad m] [Monad n] [Monad o] [LawfulMonad m] [LawfulMonad n] [LawfulMonad o]
[IteratorLoop α m n] [IteratorLoop α m o]
[LawfulIteratorLoop α m n] [LawfulIteratorLoop α m o]
[MonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT m n] [LawfulMonadLiftT n o]
{f : β n γ} {g : δ γ o δ} {init : δ} {it : IterM (α := α) m β} :
haveI : MonadLift n o := MonadLiftT.monadLift
(it.mapM f).foldM (init := init) g =
it.foldM (init := init) (fun d b => do let c f b; g d c) := by
letI : MonadLift n o := MonadLiftT.monadLift
induction it using IterM.inductSteps generalizing init with | step it ihy ihs
rw [foldM_eq_match_step, foldM_eq_match_step, step_mapM, liftM_bind, bind_assoc]
apply bind_congr; intro step
split
· simp [ihy _]
· simp [ihs _]
· simp
theorem IterM.foldM_filterMap {α β γ δ : Type w} {m : Type w Type w'} {n : Type w Type w''}
[Iterator α m β] [Finite α m] [Monad m] [Monad n] [LawfulMonad m] [LawfulMonad n]
[IteratorLoop α m m] [IteratorLoop α m n]
[LawfulIteratorLoop α m m] [LawfulIteratorLoop α m n]
[MonadLiftT m n] [LawfulMonadLiftT m n]
{f : β Option γ} {g : δ γ n δ} {init : δ} {it : IterM (α := α) m β} :
(it.filterMap f).foldM (init := init) g =
it.foldM (init := init) (fun d b => do
let some c := f b | pure d
g d c) := by
induction it using IterM.inductSteps generalizing init with | step it ihy ihs
rw [foldM_eq_match_step, foldM_eq_match_step, step_filterMap, liftM_bind, bind_assoc]
apply bind_congr; intro step
split
· split <;> simp [ihy _, *]
· simp [ihs _]
· simp
theorem IterM.foldM_map {α β γ δ : Type w} {m : Type w Type w'} {n : Type w Type w''}
[Iterator α m β] [Finite α m] [Monad m] [Monad n] [LawfulMonad m] [LawfulMonad n]
[IteratorLoop α m m] [IteratorLoop α m n]
[LawfulIteratorLoop α m m] [LawfulIteratorLoop α m n]
[MonadLiftT m n] [LawfulMonadLiftT m n]
{f : β γ} {g : δ γ n δ} {init : δ} {it : IterM (α := α) m β} :
(it.map f).foldM (init := init) g =
it.foldM (init := init) (fun d b => do g d (f b)) := by
induction it using IterM.inductSteps generalizing init with | step it ihy ihs
rw [foldM_eq_match_step, foldM_eq_match_step, step_map, liftM_bind, bind_assoc]
apply bind_congr; intro step
split
· simp [ihy _]
· simp [ihs _]
· simp
theorem IterM.fold_filterMapM {α β γ δ : Type w} {m : Type w Type w'} {n : Type w Type w''}
[Iterator α m β] [Finite α m] [Monad m] [Monad n] [LawfulMonad m] [LawfulMonad n]
[IteratorLoop α m m] [IteratorLoop α m n]
[LawfulIteratorLoop α m m] [LawfulIteratorLoop α m n]
[MonadLiftT m n] [LawfulMonadLiftT m n]
{f : β n (Option γ)} {g : δ γ δ} {init : δ} {it : IterM (α := α) m β} :
(it.filterMapM f).fold (init := init) g =
it.foldM (init := init) (fun d b => do
let some c f b | pure d
return g d c) := by
simp [fold_eq_foldM, foldM_filterMapM]
theorem IterM.fold_mapM {α β γ δ : Type w} {m : Type w Type w'} {n : Type w Type w''}
[Iterator α m β] [Finite α m] [Monad m] [Monad n] [LawfulMonad m] [LawfulMonad n]
[IteratorLoop α m m] [IteratorLoop α m n]
[LawfulIteratorLoop α m m] [LawfulIteratorLoop α m n]
[MonadLiftT m n] [LawfulMonadLiftT m n]
{f : β n γ} {g : δ γ δ} {init : δ} {it : IterM (α := α) m β} :
(it.mapM f).fold (init := init) g =
it.foldM (init := init) (fun d b => do let c f b; return g d c) := by
simp [fold_eq_foldM, foldM_mapM]
theorem IterM.fold_filterMap {α β γ δ : Type w} {m : Type w Type w'}
[Iterator α m β] [Finite α m] [Monad m] [LawfulMonad m]
[IteratorLoop α m m] [LawfulIteratorLoop α m m]
{f : β Option γ} {g : δ γ δ} {init : δ} {it : IterM (α := α) m β} :
(it.filterMap f).fold (init := init) g =
it.fold (init := init) (fun d b =>
match f b with
| some c => g d c
| _ => d) := by
simp [fold_eq_foldM, foldM_filterMap]
congr; ext
split <;> simp
theorem IterM.fold_map {α β γ δ : Type w} {m : Type w Type w'}
[Iterator α m β] [Finite α m] [Monad m] [LawfulMonad m]
[IteratorLoop α m m] [LawfulIteratorLoop α m m]
{f : β γ} {g : δ γ δ} {init : δ} {it : IterM (α := α) m β} :
(it.map f).fold (init := init) g =
it.fold (init := init) (fun d b => g d (f b)) := by
simp [fold_eq_foldM, foldM_map]
end Fold
end Std.Iterators

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@@ -9,3 +9,5 @@ prelude
public import Init.Data.Iterators.Lemmas.Consumers.Monadic
public import Init.Data.Iterators.Lemmas.Consumers.Collect
public import Init.Data.Iterators.Lemmas.Consumers.Loop
public section

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@@ -44,32 +44,20 @@ theorem Iter.forIn_eq {α β : Type w} [Iterator α Id β] [Finite α Id]
f out acc) := by
simp [ForIn.forIn, forIn'_eq, -forIn'_eq_forIn]
@[congr] theorem Iter.forIn'_congr {α β : Type w} {m : Type w Type w'} [Monad m]
[Iterator α Id β] [Finite α Id] [IteratorLoop α Id m]
@[congr] theorem Iter.forIn'_congr {α β : Type w}
[Iterator α Id β] [Finite α Id] [IteratorLoop α Id Id]
{ita itb : Iter (α := α) β} (w : ita = itb)
{b b' : γ} (hb : b = b')
{f : (a' : β) _ γ m (ForInStep γ)}
{g : (a' : β) _ γ m (ForInStep γ)}
{f : (a' : β) _ γ Id (ForInStep γ)}
{g : (a' : β) _ γ Id (ForInStep γ)}
(h : a m b, f a (by simpa [w] using m) b = g a m b) :
letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
letI : ForIn' Id (Iter (α := α) β) β _ := Iter.instForIn'
forIn' ita b f = forIn' itb b' g := by
subst_eqs
simp only [ funext_iff] at h
rw [ h]
rfl
@[congr] theorem Iter.forIn_congr {α β : Type w} {m : Type w Type w'} [Monad m]
[Iterator α Id β] [Finite α Id] [IteratorLoop α Id m]
{ita itb : Iter (α := α) β} (w : ita = itb)
{b b' : γ} (hb : b = b')
{f : (a' : β) γ m (ForInStep γ)}
{g : (a' : β) γ m (ForInStep γ)}
(h : a b, f a b = g a b) :
forIn ita b f = forIn itb b' g := by
subst_eqs
simp only [ funext_iff] at h
rw [ h]
theorem Iter.forIn'_eq_forIn'_toIterM {α β : Type w} [Iterator α Id β]
[Finite α Id] {m : Type w Type w''} [Monad m] [LawfulMonad m]
[IteratorLoop α Id m] [LawfulIteratorLoop α Id m]

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@@ -8,3 +8,5 @@ module
prelude
public import Init.Data.Iterators.Lemmas.Consumers.Monadic.Collect
public import Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop
public section

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@@ -60,34 +60,20 @@ theorem IterM.forIn_eq {α β : Type w} {m : Type w → Type w'} [Iterator α m
IteratorLoop.wellFounded_of_finite it init _ (fun _ => id) (fun out _ acc => (·, .intro) <$> f out acc) := by
simp only [ForIn.forIn, forIn'_eq]
@[congr] theorem IterM.forIn'_congr {α β : Type w} {m : Type w Type w'}
{n : Type w Type w''} [Monad n] [Monad m]
[Iterator α m β] [Finite α m] [IteratorLoop α m n] [MonadLiftT m n]
@[congr] theorem IterM.forIn'_congr {α β : Type w} {m : Type w Type w'} [Monad m]
[Iterator α m β] [Finite α m] [IteratorLoop α m m]
{ita itb : IterM (α := α) m β} (w : ita = itb)
{b b' : γ} (hb : b = b')
{f : (a' : β) _ γ n (ForInStep γ)}
{g : (a' : β) _ γ n (ForInStep γ)}
{f : (a' : β) _ γ m (ForInStep γ)}
{g : (a' : β) _ γ m (ForInStep γ)}
(h : a m b, f a (by simpa [w] using m) b = g a m b) :
letI : ForIn' n (IterM (α := α) m β) β _ := IterM.instForIn'
letI : ForIn' m (IterM (α := α) m β) β _ := IterM.instForIn'
forIn' ita b f = forIn' itb b' g := by
subst_eqs
simp only [ funext_iff] at h
rw [ h]
rfl
@[congr] theorem IterM.forIn_congr {α β : Type w} {m : Type w Type w'}
{n : Type w Type w''} [Monad n] [Monad m]
[Iterator α m β] [Finite α m] [IteratorLoop α m n] [MonadLiftT m n]
{ita itb : IterM (α := α) m β} (w : ita = itb)
{b b' : γ} (hb : b = b')
{f : (a' : β) γ n (ForInStep γ)}
{g : (a' : β) γ n (ForInStep γ)}
(h : a b, f a b = g a b) :
forIn ita b f = forIn itb b' g := by
subst_eqs
simp only [ funext_iff] at h
rw [ h]
theorem IterM.forIn'_eq_match_step {α β : Type w} {m : Type w Type w'} [Iterator α m β]
[Finite α m] {n : Type w Type w''} [Monad m] [Monad n] [LawfulMonad n]
[IteratorLoop α m n] [LawfulIteratorLoop α m n]

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@@ -1,30 +0,0 @@
/-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
prelude
public import Init.Core
public section
/--
The `BEq α` and `Hashable α` instances on `α` are compatible. This means that that `a == b` implies
`hash a = hash b`.
This is automatic if the `BEq` instance is lawful.
-/
class LawfulHashable (α : Type u) [BEq α] [Hashable α] where
/-- If `a == b`, then `hash a = hash b`. -/
hash_eq (a b : α) : a == b hash a = hash b
/--
A lawful hash function respects its Boolean equality test.
-/
theorem hash_eq [BEq α] [Hashable α] [LawfulHashable α] {a b : α} : a == b hash a = hash b :=
LawfulHashable.hash_eq a b
instance (priority := low) [BEq α] [Hashable α] [LawfulBEq α] : LawfulHashable α where
hash_eq _ _ h := eq_of_beq h rfl

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@@ -31,3 +31,5 @@ public import Init.Data.List.MapIdx
public import Init.Data.List.OfFn
public import Init.Data.List.FinRange
public import Init.Data.List.Lex
public section

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@@ -61,10 +61,10 @@ well-founded recursion mechanism to prove that the function terminates.
@[inline, expose] def attach (l : List α) : List {x // x l} := attachWith l _ fun _ => id
/-- Implementation of `pmap` using the zero-copy version of `attach`. -/
@[inline] def pmapImpl {P : α Prop} (f : a, P a β) (l : List α) (H : a l, P a) :
@[inline] private def pmapImpl {P : α Prop} (f : a, P a β) (l : List α) (H : a l, P a) :
List β := (l.attachWith _ H).map fun x, h' => f x h'
@[csimp] theorem pmap_eq_pmapImpl : @pmap = @pmapImpl := by
@[csimp] private theorem pmap_eq_pmapImpl : @pmap = @pmapImpl := by
funext α β p f l h'
let rec go : l' (hL' : x, x l' p x),
pmap f l' hL' = map (fun x, hx => f x hx) (pmap Subtype.mk l' hL')
@@ -95,12 +95,14 @@ theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a,
| cons x l ih =>
rw [pmap, pmap, h _ mem_cons_self, ih fun a ha => h a (mem_cons_of_mem _ ha)]
@[grind =]
theorem map_pmap {p : α Prop} {g : β γ} {f : a, p a β} {l : List α} (H) :
map g (pmap f l H) = pmap (fun a h => g (f a h)) l H := by
induction l
· rfl
· simp only [*, pmap, map]
@[grind =]
theorem pmap_map {p : β Prop} {g : b, p b γ} {f : α β} {l : List α} (H) :
pmap g (map f l) H = pmap (fun a h => g (f a) h) l fun _ h => H _ (mem_map_of_mem h) := by
induction l
@@ -147,6 +149,9 @@ theorem attach_map_val {l : List α} {f : α → β} :
(l.attach.map fun (i : {i // i l}) => f i) = l.map f := by
rw [attach, attachWith, map_pmap]; exact pmap_eq_map _
@[deprecated attach_map_val (since := "2025-02-17")]
abbrev attach_map_coe := @attach_map_val
-- The argument `l : List α` is explicit to allow rewriting from right to left.
theorem attach_map_subtype_val (l : List α) : l.attach.map Subtype.val = l :=
attach_map_val.trans (List.map_id _)
@@ -155,6 +160,9 @@ theorem attachWith_map_val {p : α → Prop} {f : α → β} {l : List α} (H :
((l.attachWith p H).map fun (i : { i // p i}) => f i) = l.map f := by
rw [attachWith, map_pmap]; exact pmap_eq_map _
@[deprecated attachWith_map_val (since := "2025-02-17")]
abbrev attachWith_map_coe := @attachWith_map_val
theorem attachWith_map_subtype_val {p : α Prop} {l : List α} (H : a l, p a) :
(l.attachWith p H).map Subtype.val = l :=
(attachWith_map_val _).trans (List.map_id _)
@@ -246,6 +254,13 @@ theorem getElem?_pmap {p : α → Prop} {f : ∀ a, p a → β} {l : List α} (h
· simp
· simp only [pmap, getElem?_cons_succ, hl]
set_option linter.deprecated false in
@[deprecated List.getElem?_pmap (since := "2025-02-12")]
theorem get?_pmap {p : α Prop} (f : a, p a β) {l : List α} (h : a l, p a) (n : Nat) :
get? (pmap f l h) n = Option.pmap f (get? l n) fun x H => h x (mem_of_get? H) := by
simp only [get?_eq_getElem?]
simp [getElem?_pmap]
-- The argument `f` is explicit to allow rewriting from right to left.
@[simp, grind =]
theorem getElem_pmap {p : α Prop} (f : a, p a β) {l : List α} (h : a l, p a) {i : Nat}
@@ -262,6 +277,15 @@ theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h
· simp
· simp [hl]
@[deprecated getElem_pmap (since := "2025-02-13")]
theorem get_pmap {p : α Prop} (f : a, p a β) {l : List α} (h : a l, p a) {n : Nat}
(hn : n < (pmap f l h).length) :
get (pmap f l h) n, hn =
f (get l n, @length_pmap _ _ p f l h hn)
(h _ (getElem_mem (@length_pmap _ _ p f l h hn))) := by
simp only [get_eq_getElem]
simp [getElem_pmap]
@[simp, grind =]
theorem getElem?_attachWith {xs : List α} {i : Nat} {P : α Prop} {H : a xs, P a} :
(xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (mem_of_getElem? a)) :=
@@ -283,13 +307,13 @@ theorem getElem_attach {xs : List α} {i : Nat} (h : i < xs.attach.length) :
xs.attach[i] = xs[i]'(by simpa using h), getElem_mem (by simpa using h) :=
getElem_attachWith h
@[simp] theorem pmap_attach {l : List α} {p : {x // x l} Prop} {f : a, p a β} (H) :
@[simp, grind =] theorem pmap_attach {l : List α} {p : {x // x l} Prop} {f : a, p a β} (H) :
pmap f l.attach H =
l.pmap (P := fun a => h : a l, p a, h)
(fun a h => f a, h.1 h.2) (fun a h => h, H a, h (by simp)) := by
apply ext_getElem <;> simp
@[simp] theorem pmap_attachWith {l : List α} {p : {x // q x} Prop} {f : a, p a β} (H₁ H₂) :
@[simp, grind =] theorem pmap_attachWith {l : List α} {p : {x // q x} Prop} {f : a, p a β} (H₁ H₂) :
pmap f (l.attachWith q H₁) H₂ =
l.pmap (P := fun a => h : q a, p a, h)
(fun a h => f a, h.1 h.2) (fun a h => H₁ _ h, H₂ a, H₁ _ h (by simpa)) := by
@@ -347,24 +371,26 @@ theorem getElem_attach {xs : List α} {i : Nat} (h : i < xs.attach.length) :
xs.attach.tail = xs.tail.attach.map (fun x, h => x, mem_of_mem_tail h) := by
cases xs <;> simp
@[grind =]
theorem foldl_pmap {l : List α} {P : α Prop} {f : (a : α) P a β}
(H : (a : α), a l P a) (g : γ β γ) (x : γ) :
(l.pmap f H).foldl g x = l.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
rw [pmap_eq_map_attach, foldl_map]
@[grind =]
theorem foldr_pmap {l : List α} {P : α Prop} {f : (a : α) P a β}
(H : (a : α), a l P a) (g : β γ γ) (x : γ) :
(l.pmap f H).foldr g x = l.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by
rw [pmap_eq_map_attach, foldr_map]
@[simp] theorem foldl_attachWith
@[simp, grind =] theorem foldl_attachWith
{l : List α} {q : α Prop} (H : a, a l q a) {f : β { x // q x } β} {b} :
(l.attachWith q H).foldl f b = l.attach.foldl (fun b a, h => f b a, H _ h) b := by
induction l generalizing b with
| nil => simp
| cons a l ih => simp [ih, foldl_map]
@[simp] theorem foldr_attachWith
@[simp, grind =] theorem foldr_attachWith
{l : List α} {q : α Prop} (H : a, a l q a) {f : { x // q x } β β} {b} :
(l.attachWith q H).foldr f b = l.attach.foldr (fun a acc => f a.1, H _ a.2 acc) b := by
induction l generalizing b with
@@ -403,16 +429,18 @@ theorem foldr_attach {l : List α} {f : α → β → β} {b : β} :
| nil => simp
| cons a l ih => rw [foldr_cons, attach_cons, foldr_cons, foldr_map, ih]
@[grind =]
theorem attach_map {l : List α} {f : α β} :
(l.map f).attach = l.attach.map (fun x, h => f x, mem_map_of_mem h) := by
induction l <;> simp [*]
@[grind =]
theorem attachWith_map {l : List α} {f : α β} {P : β Prop} (H : (b : β), b l.map f P b) :
(l.map f).attachWith P H = (l.attachWith (P f) (fun _ h => H _ (mem_map_of_mem h))).map
fun x, h => f x, h := by
induction l <;> simp [*]
@[simp] theorem map_attachWith {l : List α} {P : α Prop} {H : (a : α), a l P a}
@[simp, grind =] theorem map_attachWith {l : List α} {P : α Prop} {H : (a : α), a l P a}
{f : { x // P x } β} :
(l.attachWith P H).map f = l.attach.map fun x, h => f x, H _ h := by
induction l <;> simp_all
@@ -438,6 +466,10 @@ theorem map_attach_eq_pmap {l : List α} {f : { x // x ∈ l } → β} :
apply pmap_congr_left
simp
@[deprecated map_attach_eq_pmap (since := "2025-02-09")]
abbrev map_attach := @map_attach_eq_pmap
@[grind =]
theorem attach_filterMap {l : List α} {f : α Option β} :
(l.filterMap f).attach = l.attach.filterMap
fun x, h => (f x).pbind (fun b m => some b, mem_filterMap.mpr x, h, m) := by
@@ -468,6 +500,7 @@ theorem attach_filterMap {l : List α} {f : α → Option β} :
ext
simp
@[grind =]
theorem attach_filter {l : List α} (p : α Bool) :
(l.filter p).attach = l.attach.filterMap
fun x => if w : p x.1 then some x.1, mem_filter.mpr x.2, w else none := by
@@ -479,7 +512,7 @@ theorem attach_filter {l : List α} (p : α → Bool) :
-- We are still missing here `attachWith_filterMap` and `attachWith_filter`.
@[simp]
@[simp, grind =]
theorem filterMap_attachWith {q : α Prop} {l : List α} {f : {x // q x} Option β} (H) :
(l.attachWith q H).filterMap f = l.attach.filterMap (fun x, h => f x, H _ h) := by
induction l with
@@ -488,7 +521,7 @@ theorem filterMap_attachWith {q : α → Prop} {l : List α} {f : {x // q x} →
simp only [attachWith_cons, filterMap_cons]
split <;> simp_all [Function.comp_def]
@[simp]
@[simp, grind =]
theorem filter_attachWith {q : α Prop} {l : List α} {p : {x // q x} Bool} (H) :
(l.attachWith q H).filter p =
(l.attach.filter (fun x, h => p x, H _ h)).map (fun x, h => x, H _ h) := by
@@ -498,13 +531,14 @@ theorem filter_attachWith {q : α → Prop} {l : List α} {p : {x // q x} → Bo
simp only [attachWith_cons, filter_cons]
split <;> simp_all [Function.comp_def, filter_map]
@[grind =]
theorem pmap_pmap {p : α Prop} {q : β Prop} {g : a, p a β} {f : b, q b γ} {l} (H₁ H₂) :
pmap f (pmap g l H₁) H₂ =
pmap (α := { x // x l }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) l.attach
(fun a _ => H₁ a a.2) := by
simp [pmap_eq_map_attach, attach_map]
@[simp] theorem pmap_append {p : ι Prop} {f : a : ι, p a α} {l₁ l₂ : List ι}
@[simp, grind =] theorem pmap_append {p : ι Prop} {f : a : ι, p a α} {l₁ l₂ : List ι}
(h : a l₁ ++ l₂, p a) :
(l₁ ++ l₂).pmap f h =
(l₁.pmap f fun a ha => h a (mem_append_left l₂ ha)) ++
@@ -521,47 +555,50 @@ theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {l₁ l₂ :
l₁.pmap f h₁ ++ l₂.pmap f h₂ :=
pmap_append _
@[simp] theorem attach_append {xs ys : List α} :
@[simp, grind =] theorem attach_append {xs ys : List α} :
(xs ++ ys).attach = xs.attach.map (fun x, h => x, mem_append_left ys h) ++
ys.attach.map fun x, h => x, mem_append_right xs h := by
simp only [attach, attachWith, map_pmap, pmap_append]
congr 1 <;>
exact pmap_congr_left _ fun _ _ _ _ => rfl
@[simp] theorem attachWith_append {P : α Prop} {xs ys : List α}
@[simp, grind =] theorem attachWith_append {P : α Prop} {xs ys : List α}
{H : (a : α), a xs ++ ys P a} :
(xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_left ys h)) ++
ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
simp only [attachWith, pmap_append]
@[simp] theorem pmap_reverse {P : α Prop} {f : (a : α) P a β} {xs : List α}
@[simp, grind =] theorem pmap_reverse {P : α Prop} {f : (a : α) P a β} {xs : List α}
(H : (a : α), a xs.reverse P a) :
xs.reverse.pmap f H = (xs.pmap f (fun a h => H a (by simpa using h))).reverse := by
induction xs <;> simp_all
@[grind =]
theorem reverse_pmap {P : α Prop} {f : (a : α) P a β} {xs : List α}
(H : (a : α), a xs P a) :
(xs.pmap f H).reverse = xs.reverse.pmap f (fun a h => H a (by simpa using h)) := by
rw [pmap_reverse]
@[simp] theorem attachWith_reverse {P : α Prop} {xs : List α}
@[simp, grind =] theorem attachWith_reverse {P : α Prop} {xs : List α}
{H : (a : α), a xs.reverse P a} :
xs.reverse.attachWith P H =
(xs.attachWith P (fun a h => H a (by simpa using h))).reverse :=
pmap_reverse ..
@[grind =]
theorem reverse_attachWith {P : α Prop} {xs : List α}
{H : (a : α), a xs P a} :
(xs.attachWith P H).reverse = (xs.reverse.attachWith P (fun a h => H a (by simpa using h))) :=
reverse_pmap ..
@[simp] theorem attach_reverse {xs : List α} :
@[simp, grind =] theorem attach_reverse {xs : List α} :
xs.reverse.attach = xs.attach.reverse.map fun x, h => x, by simpa using h := by
simp only [attach, attachWith, reverse_pmap, map_pmap]
apply pmap_congr_left
intros
rfl
@[grind =]
theorem reverse_attach {xs : List α} :
xs.attach.reverse = xs.reverse.attach.map fun x, h => x, by simpa using h := by
simp only [attach, attachWith, reverse_pmap, map_pmap]
@@ -615,7 +652,7 @@ theorem countP_attachWith {p : α → Prop} {q : α → Bool} {l : List α} (H :
(l.attachWith p H).countP (fun a : {x // p x} => q a) = l.countP q := by
simp only [ Function.comp_apply (g := Subtype.val), countP_map, attachWith_map_subtype_val]
@[simp, grind =]
@[simp]
theorem count_attach [BEq α] {l : List α} {a : {x // x l}} :
l.attach.count a = l.count a :=
Eq.trans (countP_congr fun _ _ => by simp) <| countP_attach

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@@ -289,6 +289,16 @@ theorem cons_lex_nil [BEq α] {a} {as : List α} : lex (a :: as) [] lt = false :
@[simp] theorem lex_nil [BEq α] {as : List α} : lex as [] lt = false := by
cases as <;> simp [nil_lex_nil, cons_lex_nil]
@[deprecated nil_lex_nil (since := "2025-02-10")]
theorem lex_nil_nil [BEq α] : lex ([] : List α) [] lt = false := rfl
@[deprecated nil_lex_cons (since := "2025-02-10")]
theorem lex_nil_cons [BEq α] {b} {bs : List α} : lex [] (b :: bs) lt = true := rfl
@[deprecated cons_lex_nil (since := "2025-02-10")]
theorem lex_cons_nil [BEq α] {a} {as : List α} : lex (a :: as) [] lt = false := rfl
@[deprecated cons_lex_cons (since := "2025-02-10")]
theorem lex_cons_cons [BEq α] {a b} {as bs : List α} :
lex (a :: as) (b :: bs) lt = (lt a b || (a == b && lex as bs lt)) := rfl
/-! ## Alternative getters -/
/-! ### getLast -/

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@@ -21,6 +21,65 @@ namespace List
/-! ## Alternative getters -/
/-! ### get? -/
/--
Returns the `i`-th element in the list (zero-based).
If the index is out of bounds (`i ≥ as.length`), this function returns `none`.
Also see `get`, `getD` and `get!`.
-/
@[deprecated "Use `a[i]?` instead." (since := "2025-02-12"), expose]
def get? : (as : List α) (i : Nat) Option α
| a::_, 0 => some a
| _::as, n+1 => get? as n
| _, _ => none
set_option linter.deprecated false in
@[deprecated "Use `a[i]?` instead." (since := "2025-02-12"), simp]
theorem get?_nil : @get? α [] n = none := rfl
set_option linter.deprecated false in
@[deprecated "Use `a[i]?` instead." (since := "2025-02-12"), simp]
theorem get?_cons_zero : @get? α (a::l) 0 = some a := rfl
set_option linter.deprecated false in
@[deprecated "Use `a[i]?` instead." (since := "2025-02-12"), simp]
theorem get?_cons_succ : @get? α (a::l) (n+1) = get? l n := rfl
set_option linter.deprecated false in
@[deprecated "Use `List.ext_getElem?`." (since := "2025-02-12")]
theorem ext_get? : {l₁ l₂ : List α}, ( n, l₁.get? n = l₂.get? n) l₁ = l₂
| [], [], _ => rfl
| _ :: _, [], h => nomatch h 0
| [], _ :: _, h => nomatch h 0
| a :: l₁, a' :: l₂, h => by
have h0 : some a = some a' := h 0
injection h0 with aa; simp only [aa, ext_get? fun n => h (n+1)]
/-! ### get! -/
/--
Returns the `i`-th element in the list (zero-based).
If the index is out of bounds (`i ≥ as.length`), this function panics when executed, and returns
`default`. See `get?` and `getD` for safer alternatives.
-/
@[deprecated "Use `a[i]!` instead." (since := "2025-02-12"), expose]
def get! [Inhabited α] : (as : List α) (i : Nat) α
| a::_, 0 => a
| _::as, n+1 => get! as n
| _, _ => panic! "invalid index"
set_option linter.deprecated false in
@[deprecated "Use `a[i]!` instead." (since := "2025-02-12")]
theorem get!_nil [Inhabited α] (n : Nat) : [].get! n = (default : α) := rfl
set_option linter.deprecated false in
@[deprecated "Use `a[i]!` instead." (since := "2025-02-12")]
theorem get!_cons_succ [Inhabited α] (l : List α) (a : α) (n : Nat) :
(a::l).get! (n+1) = get! l n := rfl
set_option linter.deprecated false in
@[deprecated "Use `a[i]!` instead." (since := "2025-02-12")]
theorem get!_cons_zero [Inhabited α] (l : List α) (a : α) : (a::l).get! 0 = a := rfl
/-! ### getD -/
/--
@@ -222,6 +281,17 @@ theorem getElem_append_right {as bs : List α} {i : Nat} (h₁ : as.length ≤ i
cases i with simp [Nat.succ_sub_succ] <;> simp at h₁
| succ i => apply ih; simp [h₁]
@[deprecated "Deprecated without replacement." (since := "2025-02-13")]
theorem get_last {as : List α} {i : Fin (length (as ++ [a]))} (h : ¬ i.1 < as.length) : (as ++ [a] : List _).get i = a := by
cases i; rename_i i h'
induction as generalizing i with
| nil => cases i with
| zero => simp [List.get]
| succ => simp +arith at h'
| cons a as ih =>
cases i with simp at h
| succ i => apply ih; simp [h]
theorem sizeOf_lt_of_mem [SizeOf α] {as : List α} (h : a as) : sizeOf a < sizeOf as := by
induction h with
| head => simp +arith

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@@ -13,7 +13,7 @@ public section
/-!
# Lemmas about `List.countP` and `List.count`.
Because we mark `countP_eq_length_filter` with `@[grind =]`,
Because we mark `countP_eq_length_filter` and `count_eq_countP` with `@[grind _=_]`,
we don't need many other `@[grind]` annotations here.
-/
@@ -66,7 +66,7 @@ theorem length_eq_countP_add_countP (p : α → Bool) {l : List α} : length l =
· rfl
· simp [h]
@[grind =] -- This to quite aggressive, as it introduces `filter` based reasoning whenever we see `countP`.
@[grind _=_] -- This to quite aggressive, as it introduces `filter` based reasoning whenever we see `countP`.
theorem countP_eq_length_filter {l : List α} : countP p l = (filter p l).length := by
induction l with
| nil => rfl

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@@ -360,6 +360,9 @@ theorem find?_flatten_eq_none_iff {xs : List (List α)} {p : α → Bool} :
xs.flatten.find? p = none ys xs, x ys, !p x := by
simp
@[deprecated find?_flatten_eq_none_iff (since := "2025-02-03")]
abbrev find?_flatten_eq_none := @find?_flatten_eq_none_iff
/--
If `find? p` returns `some a` from `xs.flatten`, then `p a` holds, and
some list in `xs` contains `a`, and no earlier element of that list satisfies `p`.
@@ -400,6 +403,9 @@ theorem find?_flatten_eq_some_iff {xs : List (List α)} {p : α → Bool} {a :
· exact h₁ l ml a m
· exact h₂ a m
@[deprecated find?_flatten_eq_some_iff (since := "2025-02-03")]
abbrev find?_flatten_eq_some := @find?_flatten_eq_some_iff
@[simp, grind =] theorem find?_flatMap {xs : List α} {f : α List β} {p : β Bool} :
(xs.flatMap f).find? p = xs.findSome? (fun x => (f x).find? p) := by
simp [flatMap_def, findSome?_map]; rfl
@@ -428,10 +434,16 @@ theorem find?_replicate_eq_none_iff {n : Nat} {a : α} {p : α → Bool} :
(replicate n a).find? p = none n = 0 !p a := by
simp [Classical.or_iff_not_imp_left]
@[deprecated find?_replicate_eq_none_iff (since := "2025-02-03")]
abbrev find?_replicate_eq_none := @find?_replicate_eq_none_iff
@[simp] theorem find?_replicate_eq_some_iff {n : Nat} {a b : α} {p : α Bool} :
(replicate n a).find? p = some b n 0 p a a = b := by
cases n <;> simp
@[deprecated find?_replicate_eq_some_iff (since := "2025-02-03")]
abbrev find?_replicate_eq_some := @find?_replicate_eq_some_iff
@[simp] theorem get_find?_replicate {n : Nat} {a : α} {p : α Bool} (h) : ((replicate n a).find? p).get h = a := by
cases n with
| zero => simp at h
@@ -824,6 +836,9 @@ theorem of_findIdx?_eq_some {xs : List α} {p : α → Bool} (w : xs.findIdx? p
simp_all only [findIdx?_cons]
split at w <;> cases i <;> simp_all
@[deprecated of_findIdx?_eq_some (since := "2025-02-02")]
abbrev findIdx?_of_eq_some := @of_findIdx?_eq_some
theorem of_findIdx?_eq_none {xs : List α} {p : α Bool} (w : xs.findIdx? p = none) :
i : Nat, match xs[i]? with | some a => ¬ p a | none => true := by
intro i
@@ -839,6 +854,9 @@ theorem of_findIdx?_eq_none {xs : List α} {p : α → Bool} (w : xs.findIdx? p
apply ih
split at w <;> simp_all
@[deprecated of_findIdx?_eq_none (since := "2025-02-02")]
abbrev findIdx?_of_eq_none := @of_findIdx?_eq_none
@[simp, grind _=_] theorem findIdx?_map {f : β α} {l : List β} : findIdx? p (l.map f) = l.findIdx? (p f) := by
induction l with
| nil => simp

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@@ -107,6 +107,9 @@ theorem ne_nil_of_length_pos (_ : 0 < length l) : l ≠ [] := fun _ => nomatch l
@[simp] theorem length_eq_zero_iff : length l = 0 l = [] :=
eq_nil_of_length_eq_zero, fun h => h rfl
@[deprecated length_eq_zero_iff (since := "2025-02-24")]
abbrev length_eq_zero := @length_eq_zero_iff
theorem eq_nil_iff_length_eq_zero : l = [] length l = 0 :=
length_eq_zero_iff.symm
@@ -139,12 +142,18 @@ theorem exists_cons_of_length_eq_add_one :
theorem length_pos_iff {l : List α} : 0 < length l l [] :=
Nat.pos_iff_ne_zero.trans (not_congr length_eq_zero_iff)
@[deprecated length_pos_iff (since := "2025-02-24")]
abbrev length_pos := @length_pos_iff
theorem ne_nil_iff_length_pos {l : List α} : l [] 0 < length l :=
length_pos_iff.symm
theorem length_eq_one_iff {l : List α} : length l = 1 a, l = [a] :=
fun h => match l, h with | [_], _ => _, rfl, fun _, h => by simp [h]
@[deprecated length_eq_one_iff (since := "2025-02-24")]
abbrev length_eq_one := @length_eq_one_iff
/-! ### cons -/
-- The arguments here are intentionally explicit.
@@ -189,6 +198,38 @@ We simplify `l.get i` to `l[i.1]'i.2` and `l.get? i` to `l[i]?`.
@[simp, grind =]
theorem get_eq_getElem {l : List α} {i : Fin l.length} : l.get i = l[i.1]'i.2 := rfl
set_option linter.deprecated false in
@[deprecated "Use `a[i]?` instead." (since := "2025-02-12")]
theorem get?_eq_none : {l : List α} {n}, length l n l.get? n = none
| [], _, _ => rfl
| _ :: l, _+1, h => get?_eq_none (l := l) <| Nat.le_of_succ_le_succ h
set_option linter.deprecated false in
@[deprecated "Use `a[i]?` instead." (since := "2025-02-12")]
theorem get?_eq_get : {l : List α} {n} (h : n < l.length), l.get? n = some (get l n, h)
| _ :: _, 0, _ => rfl
| _ :: l, _+1, _ => get?_eq_get (l := l) _
set_option linter.deprecated false in
@[deprecated "Use `a[i]?` instead." (since := "2025-02-12")]
theorem get?_eq_some_iff : l.get? n = some a h, get l n, h = a :=
fun e =>
have : n < length l := Nat.gt_of_not_le fun hn => by cases get?_eq_none hn e
this, by rwa [get?_eq_get this, Option.some.injEq] at e,
fun _, e => e get?_eq_get _
set_option linter.deprecated false in
@[deprecated "Use `a[i]?` instead." (since := "2025-02-12")]
theorem get?_eq_none_iff : l.get? n = none length l n :=
fun e => Nat.ge_of_not_lt (fun h' => by cases e get?_eq_some_iff.2 h', rfl), get?_eq_none
set_option linter.deprecated false in
@[deprecated "Use `a[i]?` instead." (since := "2025-02-12"), simp]
theorem get?_eq_getElem? {l : List α} {i : Nat} : l.get? i = l[i]? := by
simp only [getElem?_def]; split
· exact (get?_eq_get _)
· exact (get?_eq_none_iff.2 <| Nat.not_lt.1 _)
/-! ### getElem!
We simplify `l[i]!` to `(l[i]?).getD default`.
@@ -332,9 +373,26 @@ theorem getD_eq_getElem?_getD {l : List α} {i : Nat} {a : α} : getD l i a = (l
theorem getD_cons_zero : getD (x :: xs) 0 d = x := by simp
theorem getD_cons_succ : getD (x :: xs) (n + 1) d = getD xs n d := by simp
/-! ### get!
We simplify `l.get! i` to `l[i]!`.
-/
set_option linter.deprecated false in
@[deprecated "Use `a[i]!` instead." (since := "2025-02-12")]
theorem get!_eq_getD [Inhabited α] : (l : List α) i, l.get! i = l.getD i default
| [], _ => rfl
| _a::_, 0 => by simp [get!]
| _a::l, n+1 => by simpa using get!_eq_getD l n
set_option linter.deprecated false in
@[deprecated "Use `a[i]!` instead." (since := "2025-02-12"), simp]
theorem get!_eq_getElem! [Inhabited α] (l : List α) (i) : l.get! i = l[i]! := by
simp [get!_eq_getD]
/-! ### mem -/
@[simp, grind ] theorem not_mem_nil {a : α} : ¬ a [] := nofun
@[simp] theorem not_mem_nil {a : α} : ¬ a [] := nofun
@[simp, grind =] theorem mem_cons : a b :: l a = b a l :=
fun h => by cases h <;> simp [Membership.mem, *],
@@ -523,9 +581,15 @@ theorem elem_eq_mem [BEq α] [LawfulBEq α] (a : α) (as : List α) :
@[grind ]
theorem nil_of_isEmpty {l : List α} (h : l.isEmpty) : l = [] := List.isEmpty_iff.mp h
@[deprecated isEmpty_iff (since := "2025-02-17")]
abbrev isEmpty_eq_true := @isEmpty_iff
@[simp] theorem isEmpty_eq_false_iff {l : List α} : l.isEmpty = false l [] := by
cases l <;> simp
@[deprecated isEmpty_eq_false_iff (since := "2025-02-17")]
abbrev isEmpty_eq_false := @isEmpty_eq_false_iff
theorem isEmpty_eq_false_iff_exists_mem {xs : List α} :
xs.isEmpty = false x, x xs := by
cases xs <;> simp
@@ -2817,6 +2881,9 @@ theorem getLast_eq_head_reverse {l : List α} (h : l ≠ []) :
l.getLast h = l.reverse.head (by simp_all) := by
rw [ head_reverse]
@[deprecated getLast_eq_iff_getLast?_eq_some (since := "2025-02-17")]
abbrev getLast_eq_iff_getLast_eq_some := @getLast_eq_iff_getLast?_eq_some
@[simp] theorem getLast?_eq_none_iff {xs : List α} : xs.getLast? = none xs = [] := by
rw [getLast?_eq_head?_reverse, head?_eq_none_iff, reverse_eq_nil_iff]
@@ -3620,6 +3687,10 @@ theorem get_cons_succ' {as : List α} {i : Fin as.length} :
theorem get_mk_zero : {l : List α} (h : 0 < l.length), l.get 0, h = l.head (length_pos_iff.mp h)
| _::_, _ => rfl
set_option linter.deprecated false in
@[deprecated "Use `a[0]?` instead." (since := "2025-02-12")]
theorem get?_zero (l : List α) : l.get? 0 = l.head? := by cases l <;> rfl
/--
If one has `l.get i` in an expression (with `i : Fin l.length`) and `h : l = l'`,
`rw [h]` will give a "motive is not type correct" error, as it cannot rewrite the
@@ -3629,6 +3700,18 @@ such a rewrite, with `rw [get_of_eq h]`.
theorem get_of_eq {l l' : List α} (h : l = l') (i : Fin l.length) :
get l i = get l' i, h i.2 := by cases h; rfl
set_option linter.deprecated false in
@[deprecated "Use `a[i]?` instead." (since := "2025-02-12")]
theorem get!_of_get? [Inhabited α] : {l : List α} {n}, get? l n = some a get! l n = a
| _a::_, 0, rfl => rfl
| _::l, _+1, e => get!_of_get? (l := l) e
set_option linter.deprecated false in
@[deprecated "Use `a[i]!` instead." (since := "2025-02-12")]
theorem get!_len_le [Inhabited α] : {l : List α} {n}, length l n l.get! n = (default : α)
| [], _, _ => rfl
| _ :: l, _+1, h => get!_len_le (l := l) <| Nat.le_of_succ_le_succ h
theorem getElem!_nil [Inhabited α] {n : Nat} : ([] : List α)[n]! = default := rfl
theorem getElem!_cons_zero [Inhabited α] {l : List α} : (a::l)[0]! = a := by
@@ -3654,11 +3737,30 @@ theorem get_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n, get l n = a := by
obtain n, h, e := getElem_of_mem h
exact n, h, e
set_option linter.deprecated false in
@[deprecated getElem?_of_mem (since := "2025-02-12")]
theorem get?_of_mem {a} {l : List α} (h : a l) : n, l.get? n = some a :=
let n, _, e := get_of_mem h; n, e get?_eq_get _
theorem get_mem : (l : List α) n, get l n l
| _ :: _, 0, _ => .head ..
| _ :: l, _+1, _ => .tail _ (get_mem l ..)
set_option linter.deprecated false in
@[deprecated mem_of_getElem? (since := "2025-02-12")]
theorem mem_of_get? {l : List α} {n a} (e : l.get? n = some a) : a l :=
let _, e := get?_eq_some_iff.1 e; e get_mem ..
theorem mem_iff_get {a} {l : List α} : a l n, get l n = a :=
get_of_mem, fun _, e => e get_mem ..
set_option linter.deprecated false in
@[deprecated mem_iff_getElem? (since := "2025-02-12")]
theorem mem_iff_get? {a} {l : List α} : a l n, l.get? n = some a := by
simp [getElem?_eq_some_iff, Fin.exists_iff, mem_iff_get]
/-! ### Deprecations -/
end List

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@@ -18,3 +18,5 @@ public import Init.Data.List.Nat.BEq
public import Init.Data.List.Nat.Modify
public import Init.Data.List.Nat.InsertIdx
public import Init.Data.List.Nat.Perm
public section

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@@ -8,7 +8,6 @@ module
prelude
public import Init.Data.Nat.Lemmas
public import Init.Data.List.Basic
import Init.Data.List.Lemmas
public section

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@@ -105,6 +105,9 @@ theorem length_leftpad {n : Nat} {a : α} {l : List α} :
(leftpad n a l).length = max n l.length := by
simp only [leftpad, length_append, length_replicate, Nat.sub_add_eq_max]
@[deprecated length_leftpad (since := "2025-02-24")]
abbrev leftpad_length := @length_leftpad
theorem length_rightpad {n : Nat} {a : α} {l : List α} :
(rightpad n a l).length = max n l.length := by
simp [rightpad]

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@@ -14,19 +14,10 @@ public section
set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
set_option linter.indexVariables true -- Enforce naming conventions for index variables.
protected theorem Nat.sum_pos_iff_exists_pos {l : List Nat} : 0 < l.sum x l, 0 < x := by
induction l with
| nil => simp
| cons x xs ih =>
simp [ ih]
omega
namespace List
open Nat
/-! ### Results about `List.sum` specialized to `Nat` -/
theorem find?_eq_some_iff_getElem {xs : List α} {p : α Bool} {b : α} :
xs.find? p = some b p b i h, xs[i] = b j : Nat, (hj : j < i) !p xs[j] := by
rw [find?_eq_some_iff_append]

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@@ -196,6 +196,9 @@ theorem getElem_insertIdx_of_gt {l : List α} {x : α} {i j : Nat} (hn : i < j)
| zero => omega
| succ j => simp
@[deprecated getElem_insertIdx_of_gt (since := "2025-02-04")]
abbrev getElem_insertIdx_of_ge := @getElem_insertIdx_of_gt
@[grind =]
theorem getElem_insertIdx {l : List α} {x : α} {i j : Nat} (h : j < (l.insertIdx i x).length) :
(l.insertIdx i x)[j] =
@@ -258,6 +261,9 @@ theorem getElem?_insertIdx_of_gt {l : List α} {x : α} {i j : Nat} (h : i < j)
(l.insertIdx i x)[j]? = l[j - 1]? := by
rw [getElem?_insertIdx, if_neg (by omega), if_neg (by omega)]
@[deprecated getElem?_insertIdx_of_gt (since := "2025-02-04")]
abbrev getElem?_insertIdx_of_ge := @getElem?_insertIdx_of_gt
end InsertIdx
end List

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@@ -176,7 +176,7 @@ theorem modifyHead_eq_modify_zero (f : αα) (l : List α) :
| n, [], _+1 => by cases n <;> rfl
| 0, _ :: l, j+1 => by cases h : l[j]? <;> simp [h, modify]
| i+1, a :: l, j+1 => by
simp only [modify_succ_cons, getElem?_cons_succ, Option.map_eq_map]
simp only [modify_succ_cons, getElem?_cons_succ, Nat.reduceEqDiff, Option.map_eq_map]
refine (getElem?_modify f i l j).trans ?_
cases h' : l[j]? <;> by_cases h : i = j <;>
simp [h, Option.map]

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@@ -103,14 +103,14 @@ theorem range'_eq_append_iff : range' s n step = xs ++ ys ↔ ∃ k, k ≤ n ∧
· simp only [ih] at h
obtain k, h, rfl, rfl := h
refine k + 1, ?_
simp_all [range'_succ, Nat.add_assoc, (by omega : n + 1 - (k + 1) = n - k)]
simp_all [range'_succ, Nat.add_assoc]
· rintro k, h, rfl, rfl
cases k with
| zero => simp [range'_succ]
| succ k =>
simp only [range'_succ, reduceCtorEq, false_and, cons.injEq, true_and, ih, exists_eq_left', false_or]
refine k, ?_
simp_all [Nat.add_assoc, (by omega : n + 1 - (k + 1) = n - k)]
simp_all [Nat.add_assoc]
@[simp] theorem find?_range'_eq_some {s n : Nat} {i : Nat} {p : Nat Bool} :
(range' s n).find? p = some i p i i range' s n j, s j j < i !p j := by
@@ -203,13 +203,7 @@ theorem sum_range' : (range' start n step).sum = n * start + n * (n - 1) * step
theorem drop_range' : (List.range' start n step).drop k = List.range' (start + k * step) (n - k) step := by
induction k generalizing start n with
| zero => simp
| succ =>
cases n
· simp [*, Nat.add_mul, Nat.add_assoc, Nat.add_right_comm]
· simp only [range'_succ, drop_succ_cons, Nat.add_mul, Nat.one_mul, Nat.add_assoc,
Nat.add_right_comm, *]
rename_i n₁ _ n₂
rw [(by omega : n₂ + 1 - (n₁ + 1) = n₂ - n₁)]
| succ => cases n <;> simp [*, List.range'_succ, Nat.add_mul, Nat.add_assoc, Nat.add_right_comm]
@[simp, grind =]
theorem take_range'_of_length_le (h : n k) : (List.range' start n step).take k = List.range' start n step := by

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@@ -117,6 +117,9 @@ theorem take_set_of_le {a : α} {i j : Nat} {l : List α} (h : j ≤ i) :
next h' => rw [getElem?_set_ne (by omega)]
· rfl
@[deprecated take_set_of_le (since := "2025-02-04")]
abbrev take_set_of_lt := @take_set_of_le
@[simp, grind =] theorem take_replicate {a : α} : {i n : Nat}, take i (replicate n a) = replicate (min i n) a
| n, 0 => by simp
| 0, m => by simp
@@ -162,8 +165,8 @@ theorem take_eq_take_iff :
| x :: xs, 0, j + 1 => by simp [succ_min_succ]
| x :: xs, i + 1, j + 1 => by simp [succ_min_succ, take_eq_take_iff]
theorem take_eq_take_min {l : List α} {i : Nat} : l.take i = l.take (min i l.length) := by
simp
@[deprecated take_eq_take_iff (since := "2025-02-16")]
abbrev take_eq_take := @take_eq_take_iff
@[grind =]
theorem take_add {l : List α} {i j : Nat} : l.take (i + j) = l.take i ++ (l.drop i).take j := by
@@ -370,8 +373,7 @@ theorem drop_take : ∀ {i j : Nat} {l : List α}, drop i (take j l) = take (j -
| _, 0, _ => by simp
| _, _, [] => by simp
| i+1, j+1, h :: t => by
simp only [take_succ_cons, drop_succ_cons, drop_take, take_eq_take_iff, length_drop]
omega
simp [take_succ_cons, drop_succ_cons, drop_take]
@[simp] theorem drop_take_self : drop i (take i l) = [] := by
rw [drop_take]

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@@ -6,8 +6,8 @@ Authors: Mario Carneiro, Kim Morrison
module
prelude
public import Init.Data.List.Basic
public import Init.Data.Fin.Fold
public import Init.Data.List.Lemmas
public section
@@ -114,7 +114,7 @@ theorem mem_ofFn {n} {f : Fin n → α} {a : α} : a ∈ ofFn f ↔ ∃ i, f i =
rw [ getElem_zero (length_ofFn Nat.pos_of_ne_zero (mt ofFn_eq_nil_iff.2 h)),
List.getElem_ofFn]
@[grind =] theorem getLast_ofFn {n} {f : Fin n α} (h : ofFn f []) :
@[grind =]theorem getLast_ofFn {n} {f : Fin n α} (h : ofFn f []) :
(ofFn f).getLast h = f n - 1, Nat.sub_one_lt (mt ofFn_eq_nil_iff.2 h) := by
simp [getLast_eq_getElem, length_ofFn, List.getElem_ofFn]

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@@ -9,3 +9,5 @@ prelude
public import Init.Data.List.Sort.Basic
public import Init.Data.List.Sort.Impl
public import Init.Data.List.Sort.Lemmas
public section

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@@ -165,6 +165,9 @@ theorem take_set {l : List α} {i j : Nat} {a : α} :
| nil => simp
| cons hd tl => cases j <;> simp_all
@[deprecated take_set (since := "2025-02-17")]
abbrev set_take := @take_set
theorem drop_set {l : List α} {i j : Nat} {a : α} :
(l.set j a).drop i = if j < i then l.drop i else (l.drop i).set (j - i) a := by
induction i generalizing l j with

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@@ -26,3 +26,5 @@ public import Init.Data.Nat.Compare
public import Init.Data.Nat.Simproc
public import Init.Data.Nat.Fold
public import Init.Data.Nat.Order
public section

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@@ -19,12 +19,12 @@ namespace Nat
/-- Compiled version of `Nat.rec` so that we can define `Nat.recAux` to be defeq to `Nat.rec`.
This is working around the fact that the compiler does not currently support recursors. -/
def recCompiled {motive : Nat Sort u} (zero : motive zero) (succ : (n : Nat) motive n motive (Nat.succ n)) : (t : Nat) motive t
private def recCompiled {motive : Nat Sort u} (zero : motive zero) (succ : (n : Nat) motive n motive (Nat.succ n)) : (t : Nat) motive t
| .zero => zero
| .succ n => succ n (recCompiled zero succ n)
@[csimp]
theorem rec_eq_recCompiled : @Nat.rec = @Nat.recCompiled :=
private theorem rec_eq_recCompiled : @Nat.rec = @Nat.recCompiled :=
funext fun _ => funext fun _ => funext fun succ => funext fun t =>
Nat.recOn t rfl (fun n ih => congrArg (succ n) ih)
@@ -791,6 +791,18 @@ protected theorem pow_le_pow_right {n : Nat} (hx : n > 0) {i : Nat} : ∀ {j}, i
| Or.inr h =>
h.symm Nat.le_refl _
set_option linter.missingDocs false in
@[deprecated Nat.pow_le_pow_left (since := "2025-02-17")]
abbrev pow_le_pow_of_le_left := @Nat.pow_le_pow_left
set_option linter.missingDocs false in
@[deprecated Nat.pow_le_pow_right (since := "2025-02-17")]
abbrev pow_le_pow_of_le_right := @Nat.pow_le_pow_right
set_option linter.missingDocs false in
@[deprecated Nat.pow_pos (since := "2025-02-17")]
abbrev pos_pow_of_pos := @Nat.pow_pos
@[simp] theorem zero_pow_of_pos (n : Nat) (h : 0 < n) : 0 ^ n = 0 := by
cases n with
| zero => cases h
@@ -870,6 +882,9 @@ protected theorem ne_zero_of_lt (h : b < a) : a ≠ 0 := by
exact absurd h (Nat.not_lt_zero _)
apply Nat.noConfusion
@[deprecated Nat.ne_zero_of_lt (since := "2025-02-06")]
theorem not_eq_zero_of_lt (h : b < a) : a 0 := Nat.ne_zero_of_lt h
theorem pred_lt_of_lt {n m : Nat} (h : m < n) : pred n < n :=
pred_lt (Nat.ne_zero_of_lt h)

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@@ -8,3 +8,5 @@ module
prelude
public import Init.Data.Nat.Bitwise.Basic
public import Init.Data.Nat.Bitwise.Lemmas
public section

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@@ -14,7 +14,6 @@ import all Init.Data.Nat.Bitwise.Basic
public import Init.Data.Nat.Lemmas
public import Init.Data.Nat.Simproc
public import Init.TacticsExtra
import Init.BinderPredicates
public section

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@@ -8,3 +8,5 @@ module
prelude
public import Init.Data.Nat.Div.Basic
public import Init.Data.Nat.Div.Lemmas
public section

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