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/- Copyright (c) 2020 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 Lean.Util.CollectFVars public import Lean.Util.CollectLevelParams public import Lean.Util.CollectMVars public import Lean.Util....
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/- Copyright (c) 2025 Lean FRO. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sebastian Ullrich -/ module prelude public import Lean.CoreM public import Lean.Compiler.MetaAttr -- TODO: public because of specializations import Init.Data.Range.Polymorphic.Stream /-! ...
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/- Copyright (c) 2019 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.Data.Array.BinSearch public import Init.Data.Stream public import Init.System.Promise public import Lean.Data.NameTrie pu...
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Container of asynchronously elaborated declarations. For consistency, `Lean.addDecl` makes sure this contains constants added even synchronously, i.e. `base ⨃ asyncConsts` is the set of constants known on the current environment branch, which is a subset of `checked`. Private view should correspond to kernel map...
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if sig.levelParams != info.levelParams then throw <| .userError s!"AddConstAsyncResult.commitConst: constant has level params {info.levelParams} but expected {sig.levelParams}" if sig.type != info.type then throw <| .userError s!"AddConstAsyncResult.commitConst: constant has type {info.type} but expected {sig...
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name : Name addImportedFn : Array (Array α) → ImportM σ addEntryFn : σ → β → σ /-- Function to transform state into data that should be imported into other modules. Returns entries for all three olean levels at once so that expensive computations can be shared. When using the module system...
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* needsIRTrans(A) ∧ A `(public)? (meta)? import (all)?` B → needsIRTrans(B) Note that in particular, A `meta import` B `import` C implies A `meta import` C, but A `import` B `meta import` C does not. As a final special case, we also load IR for `import all`, but non-transitively, to provide the same information as fo...
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-- This line should not affect the result value but it avoids potential blocking in `isUnsafe` as -- there is a fast path for theorems, so we want to make sure we do not perceive them merely as -- axioms (for imported theorems this does not matter as there is nothing to block on). let env := env.setExporting fals...
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/- Copyright (c) 2019 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Sebastian Ullrich, Leonardo de Moura -/ module prelude public import Init.Data.Slice public import Init.Data.Hashable public import Lean.Data.Format public import Init.Data.Opti...
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| _ => none def isAntiquotSplice (stx : Syntax) : Bool := antiquotSpliceKind? stx |>.isSome def getAntiquotSpliceContents (stx : Syntax) : Array Syntax := stx[3].getArgs -- `$[..],*` or `$x,*` ~> `,*` def getAntiquotSpliceSuffix (stx : Syntax) : Syntax := if stx.isAntiquotSplice then stx[5] else stx[...
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/- Copyright (c) 2019 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 Lean.ToLevel public import Init.Data.Rat.Basic public section universe u namespace Lean /-- We use the `ToExpr` type class to ...
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/- Copyright (c) 2025 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joachim Breitner -/ module prelude public import Lean.Meta.Basic import Lean.Meta.Check import Lean.Meta.WHNF public section namespace Lean open Meta /-- There are defeq theorems t...
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/- Copyright (c) 2019 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 Lean.Meta.Basic public import Lean.Meta.LevelDefEq public import Lean.Meta.WHNF public import Lean.Meta.InferType public import...
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/- Copyright (c) 2018 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Sebastian Ullrich, Leonardo de Moura Message type used by the Lean frontend -/ module prelude public import Init.Data.Slice.Array public import Lean.Util.PPExt public import Le...
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def msgs : MessageLog → PersistentArray Message := unreported def reportedPlusUnreported : MessageLog → PersistentArray Message | { reported := r, unreported := u, .. } => r ++ u def hasUnreported (log : MessageLog) : Bool := !log.unreported.isEmpty def add (msg : Message) (log : MessageLog) : MessageLog := { ...
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/- Copyright (c) 2019 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 Lean.CoreM public import Lean.Compiler.MetaAttr public section namespace Lean inductive AttributeApplicationTime where | ...
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/- Copyright (c) 2020 Sebastian Ullrich. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sebastian Ullrich -/ module prelude public import Lean.PrettyPrinter.Delaborator.Basic import Lean.PrettyPrinter.Delaborator public import Lean.Parser.Module public import Lean.Par...
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/- Copyright (c) 2024 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ module prelude public import Lean.Compiler.InitAttr public section namespace Lean def declareBuiltinDocStringAndRanges (declName : Name) : AttrM Unit := do if l...
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/- Copyright (c) 2026 Lean FRO. All Rights Reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sebastian Ullrich -/ module prelude public import Lean.Environment import Lean.EnvExtension namespace Lean -- No public mutating interface as this is an implementation detail of `addDecl`...
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/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude public import Lean.DocString public meta import Init.Data.String.Extra public meta import Init.Data.ToString.Name public section /-! # "Label" attribute...
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/- Copyright (c) 2018 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.Data.Array.QSort public import Lean.Data.PersistentHashSet public import Lean.Hygiene public import Init.Data.Option.Coe ...
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/- Copyright (c) 2021 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sebastian Ullrich, Daniel Selsam, Wojciech Nawrocki, E.W.Ayers -/ module prelude public import Lean.Meta.Basic public import Init.Data.Format.Macro public section namespace L...
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/- Copyright (c) 2021 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Wojciech Nawrocki -/ module prelude public import Lean.Widget.InteractiveCode public import Lean.Widget.InteractiveDiagnostic public import Lean.Widget.InteractiveGoal public ...
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/- Copyright (c) 2021 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 Lean.DocString.Extension public import Lean.DocString.Links public import Lean.Parser.Tactic.Doc public import Lean.Parser.Ter...
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/- Copyright (c) 2019 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.Prelude public section namespace Lean @[extern "lean_closure_max_args"] opaque closureMaxArgsFn : Unit → Nat @[extern...
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/- Copyright (c) 2019 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sebastian Ullrich -/ module prelude public import Lean.Data.Format public section namespace Lean /-! Remark: `MonadQuotation` class is part of the `Init` package and loaded b...
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/- Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ module prelude public import Lean.Meta.Sorry public import Lean.Util.CollectAxioms public import Lean.OriginalConstKind import Lean.Compiler.M...
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/- Copyright (c) 2022 Lars König. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Lars König -/ module prelude public import Lean.Linter.Util public import Lean.Linter.Builtin public import Lean.Linter.ConstructorAsVariable public import Lean.Linter.Deprecated public i...
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/- Copyright (c) 2020 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Leonardo de Moura -/ module prelude public import Lean.Expr public section namespace Lean /-- Datastructure for representing the "head symbol" of an expression. It is the key...
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/- Copyright (c) 2025 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rob Simmons -/ module prelude public import Lean.Elab.DeclModifiers import all Lean.Elab.ErrorUtils import Init.Omega namespace Lean open Elab.Term set_option doc.verso true ...
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/- Copyright (c) 2019 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Mac Malone -/ module prelude public import Lean.Data.Json.Parser public import Lean.Util.LeanOptions set_option doc.verso true public section /-! # Module...
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/- Copyright (c) 2019 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 Lean.Elab.Import public import Lean.Elab.Exception public import Lean.Elab.Config public import Lean.Elab.Command public impor...
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/- Copyright (c) 2020 Marc Huisinga. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Marc Huisinga, Wojciech Nawrocki -/ module prelude public import Lean.Server.Watchdog public import Lean.Server.FileWorker public import Lean.Server.Rpc public import Lean.Server.Code...
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/- Copyright (c) 2021 Mac Malone. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mac Malone -/ module prelude public import Init.System.IO import Init.Data.String.TakeDrop import Init.Data.ToString.Macro public section namespace Lean private opaque DynlibImpl : Non...
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/- Copyright (c) 2018 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.Data.Hashable public import Lean.Level import Init.Omega public section namespace Lean /-- Literal values for `Expr`. ...
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`.proj structName idx struct` is now the preferred form. -/ def mkProj (structName : Name) (idx : Nat) (struct : Expr) : Expr := .proj structName idx struct /-- `.app f a` is now the preferred form. -/ @[match_pattern, expose] def mkApp (f a : Expr) : Expr := .app f a /-- `.lam x t b bi` is now the preferred form...
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Instantiates the loose bound variables in `e` using the `subst` array, where a loose `Expr.bvar i` at "binding depth" `d` is instantiated with `subst[i - d]` if `0 <= i - d < subst.size`, and otherwise it is replaced with `Expr.bvar (i - subst.size)`; non-loose bound variables are not touched. If we imagine all expres...
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let args := e.getAppArgs.map fun arg => if arg.hasMVar then arg else arg.setPPExplicit false mkAppN f args |>.setPPExplicit true | _ => e /-- Maps `f` on each immediate child of the given expression. -/ @[specialize] def traverseChildren [Applicative M] (f : Expr → M Expr) : Expr → M Expr | e@(forallE _ d...
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/- Copyright (c) 2019 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.Notation public import Init.Data.Option.Coe public section namespace Lean /-! # Private name support. Suppose the ...
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/- Copyright (c) 2019 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 Lean.EnvExtension public section namespace Lean /-- Given a structure `S`, Lean automatically creates an auxiliary definiti...
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/- Copyright (c) 2019 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ module prelude -- This import is necessary to ensure that any users of the `logNamedError` macros have access to -- all declared explanations: public impor...
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/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude import Lean.CoreM public import Lean.AddDecl import Lean.Util.FoldConsts /-! # `Lean.Environment.replay` `replay env constantMap` will "replay" all the ...
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/- Copyright (c) 2018 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 Lean.Expr import Init.Data.Ord.UInt import Init.Data.ToString.Macro public section namespace Lean /-- Reducibility hints gui...
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/- Copyright (c) 2020 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ module prelude import Init.Control.Do public import Lean.Elab.Exception public import Lean.Log public import Lean.AuxRecursor public import Lean.Compiler.O...
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/- Copyright (c) 2019 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.ShareCommon public import Lean.Util.MonadCache public import Lean.LocalContext import Init.Data.Slice import Init.Data.To...
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def hasAssignableMVar [Monad m] [MonadMCtx m] : Expr → m Bool | .const _ lvls => lvls.anyM hasAssignableLevelMVar | .sort lvl => hasAssignableLevelMVar lvl | .app f a => (pure f.hasMVar <&&> hasAssignableMVar f) <||> (pure a.hasMVar <&&> hasAssignableMVar a) | .letE _ t v b _ => (pure t.hasMV...
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If we kept using the Lean3 approach, we would get the `Exception.revertFailure` exception because we are reverting the auxiliary definition `f`. Note that <https://github.com/leanprover/lean/issues/1258> is not an issue in Lean4 because we have changed how we compile recursive definitions. -/ def collectForwardD...
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def setFVarBinderInfo [MonadMCtx m] (mvarId : MVarId) (fvarId : FVarId) (bi : BinderInfo) : m Unit := modifyMCtx (·.setFVarBinderInfo mvarId fvarId bi) end MVarId end Lean
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/- Copyright (c) 2020 Sebastian Ullrich. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sebastian Ullrich -/ module prelude public import Lean.Meta.ReduceEval public import Lean.Meta.WHNF public import Lean.KeyedDeclsAttribute public import Lean.ParserCompiler.Attribu...
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/- Copyright (c) 2024 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ module prelude public import Std.Data.DHashMap public import Std.Data.HashMap public import Std.Data.HashSet public import Std.Data.DTreeMap public import Std.Data.Tre...
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/- Copyright (c) 2024 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sofia Rodrigues -/ module prelude public import Std.Time.Time public import Std.Time.Date public import Std.Time.Zoned public import Std.Time.Format public import Std.Time.DateTime pub...
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/- Copyright (c) 2024 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Henrik Böving -/ module prelude public import Std.Internal.Async public import Std.Internal.Http public import Std.Internal.Parsec public import Std.Internal.UV @[expose] public secti...
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/- Copyright (c) 2025 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Henrik Böving -/ module prelude public import Std.Net.Addr
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/- Copyright (c) 2025 Lean FRO LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sebastian Graf -/ module prelude public import Std.Do.SPred public import Std.Do.WP public import Std.Do.Triple public import Std.Do.PredTrans public import Std.Do.PostCond
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/- Copyright (c) 2024 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Henrik Böving -/ module prelude public import Std.Tactic.BVDecide public import Std.Tactic.Do @[expose] public section /-! This directory is mainly used for bootstrapping reasons. Su...
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/- Copyright (c) 2024 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Henrik Böving -/ module prelude public import Std.Sat.AIG public import Std.Sat.CNF
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/- Copyright (c) 2024 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Henrik Böving -/ module prelude public import Std.Sync.Basic public import Std.Sync.Channel public import Std.Sync.Mutex public import Std.Sync.RecursiveMutex public import Std.Sync.Ba...
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/- Copyright (c) 2021 Mac Malone. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mac Malone -/ module prelude public import Lake.Build public import Lake.CLI.Actions public import Lake.Config public import Lake.DSL public import Lake.Toml public import Lake.Util publi...
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/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, Sebastian Ullrich, Mac Malone -/ module prelude public import Init.System.IO import Lake.DSL -- shake: keep (registers builtins) import Lake.CLI.Main public def...
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/- Copyright (c) 2026 Amazon.com, Inc. or its affiliates. All Rights Reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ module prelude public import Init.Data.Rat.Basic public import Init.Data.SInt.Basic public import Init.Data.Int.DivMod.Lemmas public import Ini...
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/- Copyright (c) 2025 Lean FRO, LLC. or its affiliates. All Rights Reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude public import Init.GrindInstances.Ring.Nat public import Init.GrindInstances.Ring.Int public import Init.GrindInstances.Ring.UInt publ...
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/- Copyright (c) 2025 Lean FRO, LLC. or its affiliates. All Rights Reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude public import Init.Grind.Ordered.Module import Init.Omega public section namespace Lean.Grind instance : AddRightCancel Nat where ...
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/- Copyright (c) 2025 Lean FRO, LLC. or its affiliates. All Rights Reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude import all Init.Grind.ToInt public import Init.Data.SInt.Basic public import Init.Grind.ToInt import Init.Data.BitVec.Bootstrap import...
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/- Copyright (c) 2024 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joachim Breitner -/ module prelude public import Init.Internal.Order.Basic public import Init.Internal.Order.Lemmas public import Init.Internal.Order.Tactic
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/- Copyright (c) 2019 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura and Sebastian Ullrich Additional goodies for writing macros -/ module prelude import all Init.Prelude -- for unfolding `Name.beq` public import Init.Data.Arr...
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match (← getRef).getHead? with | none => x | some ref => withRef ref x /-- Expand macros in the given syntax. A node with kind `k` is visited only if `p k` is true. Note that the default value for `p` returns false for `by ...` nodes. This is a "hack". The tactic framework abuses the macro system to imple...
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def getNat (s : NumLit) : Nat := s.raw.isNatLit?.getD 0 private def isHexNum? (stx : Syntax) : Option Nat := match Syntax.isLit? hexnumKind stx with | some val => Syntax.decodeHexLitAux val 0 0 | _ => none /-- Returns the value of the hexadecimal numeral as a natural number. -/ def getHexNumVal (s : Sy...
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/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Luke Nelson, Jared Roesch, Leonardo de Moura, Sebastian Ullrich, Mac Malone, Henrik Böving -/ module prelude public import Init.Control.Do public import Init.System.IOError pub...
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@[extern "lean_io_get_num_heartbeats"] opaque getNumHeartbeats : BaseIO Nat /-- Sets the heartbeat counter of the current thread to the given amount. This can be used to avoid counting heartbeats of code whose execution time is non-deterministic. -/ @[extern "lean_io_set_heartbeats"] opaque setNumHeartbeats (count : N...
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| throw <| IO.userError s!"IO.appDir: unexpected filename '{p}'" FS.realPath p namespace FS /-- Creates a directory at the specified path, creating all missing parents as directories. -/ partial def createDirAll (p : FilePath) : IO Unit := do if ← p.isDir then return () if let some parent := p.parent then ...
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/- Copyright (c) 2022 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner -/ module prelude public import Init.System.IO public section set_option linter.missingDocs true namespace IO private opaque PromisePointed : NonemptyType.{0}...
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/- Copyright (c) 2020 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.Control.Except public import Init.NotationExtra import Init.Classical public section opaque Void.nonemptyType (σ : Type...
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/- Copyright (c) 2019 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Lovett -/ module prelude public import Init.System.FilePath import Init.Data.String.TakeDrop import Init.Data.String.Modify import Init.Data.String.Search import Init.Ome...
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/- Copyright (c) 2019 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Sebastian Ullrich -/ module prelude import Init.Data.String.Modify import Init.Data.String.Search public import Init.Data.ToString.Basic import Init.Data.Ite...
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/- Copyright (c) 2018 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.Data.Nat.Div.Basic public import Init.SimpLemmas import Init.Data.Nat.Basic import Init.Data.String.Bootstrap public sec...
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/- Copyright (c) 2019 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ module prelude public import Init.Data.ToString.Basic import Init.Data.String.Modify public section /-- Exceptions that may be thrown in the `IO` monad. Many...
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/- Copyright (c) 2023 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude public import Init.Data.Fin.Basic public import Init.Data.Int.DivMod.Basic public import Init.WF import Init.ByCases import Init.Data.Int.Lemmas import I...
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/- Copyright (c) 2023 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude public import Init.Omega.IntList import all Init.Omega.IntList public section /-! # `Coeffs` as a wrapper for `IntList` Currently `omega` uses a dense...
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/- Copyright (c) 2023 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude public import Init.Grind.Tactics import Init.PropLemmas public section /-! # Specializations of basic logic lemmas These are useful for `omega` while c...
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/- Copyright (c) 2023 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude public import Init.Data.Int.DivMod.Bootstrap public import Init.Data.Nat.Gcd import Init.Data.Int.Lemmas import Init.Data.Int.Order import Init.Data.Nat....
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/- Copyright (c) 2023 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude public import Init.Omega.Coeffs import Init.Data.Int.Lemmas import Init.Data.Int.Order import Init.Data.ToString.Macro import Init.Omega.Int import Init....
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/- Copyright (c) 2023 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude public import Init.Omega.Coeffs import Init.Data.Int.Lemmas import Init.Data.ToString.Macro import Init.RCases public section /-! # Linear combinations...
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/- 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 import Init.Data.Array.Basic public import Init.Data.UInt.Basic public section universe u instance : Hashable Nat where hash n := UInt64...
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/- Copyright (c) 2025 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Paul Reichert -/ module prelude public import Init.Data.Subtype.Basic public import Init.Data.Subtype.Order public import Init.Data.Subtype.OrderExtra
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/- Copyright (c) 2024 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joachim Breitner -/ module prelude public import Init.GetElem import Init.PropLemmas public section @[expose] section namespace Lean /-- A `RArray` can model `Fin n → α` or `Array...
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/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Yury G. Kudryashov -/ module prelude public import Init.Data.Sum.Basic public import Init.Data.Sum.Lemmas
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/- 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.Data.String.Basic public import Init.Data.String.Bootstrap public import Init.Data.String.Decode public import Init.Data....
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/- Copyright (c) 2023 Amazon.com, Inc. or its affiliates. All Rights Reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ module prelude public import Init.Data.Float public section -- Just show FloatSpec is inhabited. opaque float32Spec : FloatSpec := { float...
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/- Copyright (c) 2019 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Daniel Selsam Simple queue implemented using two lists. Note: this is only a temporary placeholder. -/ module prelude public import Init.Data.List.Control public section nam...
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/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Leonardo de Moura -/ module prelude public import Init.Data.Fin.Basic public import Init.Data.Fin.Log2 public import Init.Data.Fin.Iterate public import Init.Data.Fin.Fold publi...
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/- Copyright (c) 2020 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.Data.ToString.Basic public section structure FloatSpec where float : Type val : float lt : float → float → P...
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/- 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.Data.Int.Basic public import Init.Data.Int.Bitwise public import Init.Data.Int.Compare public import Init.Data.Int.DivMod...
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/- Copyright (c) 2025 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude public import Init.Data.Dyadic.Basic public import Init.Data.Dyadic.Instances public import Init.Data.Dyadic.Round public import Init.Data.Dyadic.Inv
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/- Copyright (c) 2019 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.Data.Option.Basic public import Init.Data.Option.BasicAux public import Init.Data.Option.Coe public import Init.Data.Opti...
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/- Copyright (c) 2025 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ module prelude public import Init.Data.Rat.Basic public import Init.Data.Rat.Lemmas
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/- Copyright (c) 2020 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Leonardo de Moura -/ module prelude public import Init.Data.FloatArray.Basic
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/- 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.Data.List.Attach public import Init.Data.List.Basic public import Init.Data.List.BasicAux public import Init.Data.List.Co...
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/- 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 `a == b` implies ...
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/- Copyright (c) 2022 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Leonardo de Moura -/ module prelude public import Init.NotationExtra public section namespace Prod attribute [grind =] Prod.map_fst Prod.map_snd instance [BEq α] [BEq β] [Re...
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/- 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.Data.Nat.Basic public import Init.Data.Nat.Div public import Init.Data.Nat.Dvd public import Init.Data.Nat.Gcd public imp...