Basic.lean

/-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Data.LOption
import Lean.Environment
import Lean.Class
import Lean.ReducibilityAttrs
import Lean.Util.Trace
import Lean.Util.RecDepth
import Lean.Util.PPExt
import Lean.Util.ReplaceExpr
import Lean.Util.OccursCheck
import Lean.Util.MonadBacktrack
import Lean.Compiler.InlineAttrs
import Lean.Meta.TransparencyMode
import Lean.Meta.DiscrTreeTypes
import Lean.Eval
import Lean.CoreM

/-
This module provides four (mutually dependent) goodies that are needed for building the elaborator and tactic frameworks.
1- Weak head normal form computation with support for metavariables and transparency modes.
2- Definitionally equality checking with support for metavariables (aka unification modulo definitional equality).
3- Type inference.
4- Type class resolution.

They are packed into the MetaM monad.
-/

namespace Lean.Meta

builtin_initialize isDefEqStuckExceptionId : InternalExceptionId ← registerInternalExceptionId `isDefEqStuck

structure Config where
  foApprox           : Bool := false
  ctxApprox          : Bool := false
  quasiPatternApprox : Bool := false
  /-- When `constApprox` is set to true,
     we solve `?m t =?= c` using
     `?m := fun _ => c`
     when `?m t` is not a higher-order pattern and `c` is not an application as -/
  constApprox        : Bool := false
  /--
    When the following flag is set,
    `isDefEq` throws the exeption `Exeption.isDefEqStuck`
    whenever it encounters a constraint `?m ... =?= t` where
    `?m` is read only.
    This feature is useful for type class resolution where
    we may want to notify the caller that the TC problem may be solveable
    later after it assigns `?m`. -/
  isDefEqStuckEx     : Bool := false
  transparency       : TransparencyMode := TransparencyMode.default
  /-- If zetaNonDep == false, then non dependent let-decls are not zeta expanded. -/
  zetaNonDep         : Bool := true
  /-- When `trackZeta == true`, we store zetaFVarIds all free variables that have been zeta-expanded. -/
  trackZeta          : Bool := false
  unificationHints   : Bool := true
  /-- Enables proof irrelevance at `isDefEq` -/
  proofIrrelevance   : Bool := true
  /-- By default synthetic opaque metavariables are not assigned by `isDefEq`. Motivation: we want to make
      sure typing constraints resolved during elaboration should not "fill" holes that are supposed to be filled using tactics.
      However, this restriction is too restrictive for tactics such as `exact t`. When elaborating `t`, we dot not fill
      named holes when solving typing constraints or TC resolution. But, we ignore the restriction when we try to unify
      the type of `t` with the goal target type. We claim this is not a hack and is defensible behavior because
      this last unification step is not really part of the term elaboration. -/
  assignSyntheticOpaque : Bool := false
  /-- When `ignoreLevelDepth` is `false`, only universe level metavariables with depth == metavariable context depth
      can be assigned.
      We used to have `ignoreLevelDepth == false` always, but this setting produced counterintuitive behavior in a few
      cases. Recall that universe levels are often ignored by users, they may not even be aware they exist.
      We still use this restriction for regular metavariables. See discussion at the beginning of `MetavarContext.lean`.
      We claim it is reasonable to ignore this restriction for universe metavariables because their values are often
      contrained by the terms is instances and simp theorems.
      TODO: we should delete this configuration option and the method `isReadOnlyLevelMVar` after we have more tests.
  -/
  ignoreLevelMVarDepth  : Bool := true
  /-- Enable/Disable support for offset constraints such as `?x + 1 =?= e` -/
  offsetCnstrs          : Bool := true
  /-- Enable/Disable support for eta-structures. -/
  etaStruct             : Bool := true

structure ParamInfo where
  binderInfo     : BinderInfo := BinderInfo.default
  hasFwdDeps     : Bool       := false
  backDeps       : Array Nat  := #[]
  deriving Inhabited

def ParamInfo.isImplicit (p : ParamInfo) : Bool :=
  p.binderInfo == BinderInfo.implicit

def ParamInfo.isInstImplicit (p : ParamInfo) : Bool :=
  p.binderInfo == BinderInfo.instImplicit

def ParamInfo.isStrictImplicit (p : ParamInfo) : Bool :=
  p.binderInfo == BinderInfo.strictImplicit

def ParamInfo.isExplicit (p : ParamInfo) : Bool :=
  p.binderInfo == BinderInfo.default || p.binderInfo == BinderInfo.auxDecl

structure FunInfo where
  paramInfo  : Array ParamInfo := #[]
  resultDeps : Array Nat       := #[]

structure InfoCacheKey where
  transparency : TransparencyMode
  expr         : Expr
  nargs?       : Option Nat
  deriving Inhabited, BEq

namespace InfoCacheKey
instance : Hashable InfoCacheKey :=
  ⟨fun ⟨transparency, expr, nargs⟩ => mixHash (hash transparency) <| mixHash (hash expr) (hash nargs)⟩
end InfoCacheKey

open Std (PersistentArray PersistentHashMap)

abbrev SynthInstanceCache := PersistentHashMap Expr (Option Expr)

abbrev InferTypeCache := PersistentExprStructMap Expr
abbrev FunInfoCache   := PersistentHashMap InfoCacheKey FunInfo
abbrev WhnfCache      := PersistentExprStructMap Expr

/- A set of pairs. TODO: consider more efficient representations (e.g., a proper set) and caching policies (e.g., imperfect cache).
   We should also investigate the impact on memory consumption. -/
abbrev DefEqCache := PersistentHashMap (Expr × Expr) Unit

structure Cache where
  inferType     : InferTypeCache := {}
  funInfo       : FunInfoCache   := {}
  synthInstance : SynthInstanceCache := {}
  whnfDefault   : WhnfCache := {} -- cache for closed terms and `TransparencyMode.default`
  whnfAll       : WhnfCache := {} -- cache for closed terms and `TransparencyMode.all`
  defEqDefault  : DefEqCache := {}
  defEqAll      : DefEqCache := {}
  deriving Inhabited

/--
 "Context" for a postponed universe constraint.
 `lhs` and `rhs` are the surrounding `isDefEq` call when the postponed constraint was created.
-/
structure DefEqContext where
  lhs            : Expr
  rhs            : Expr
  lctx           : LocalContext
  localInstances : LocalInstances

/--
  Auxiliary structure for representing postponed universe constraints.
  Remark: the fields `ref` and `rootDefEq?` are used for error message generation only.
  Remark: we may consider improving the error message generation in the future.
-/
structure PostponedEntry where
  ref  : Syntax -- We save the `ref` at entry creation time
  lhs  : Level
  rhs  : Level
  ctx? : Option DefEqContext -- Context for the surrounding `isDefEq` call when entry was created
  deriving Inhabited

structure State where
  mctx        : MetavarContext := {}
  cache       : Cache := {}
  /- When `trackZeta == true`, then any let-decl free variable that is zeta expansion performed by `MetaM` is stored in `zetaFVarIds`. -/
  zetaFVarIds : FVarIdSet := {}
  postponed   : PersistentArray PostponedEntry := {}
  deriving Inhabited

structure SavedState where
  core        : Core.State
  meta        : State
  deriving Inhabited

structure Context where
  config            : Config               := {}
  lctx              : LocalContext         := {}
  localInstances    : LocalInstances       := #[]
  /-- Not `none` when inside of an `isDefEq` test. See `PostponedEntry`. -/
  defEqCtx?         : Option DefEqContext  := none
  /--
    Track the number of nested `synthPending` invocations. Nested invocations can happen
    when the type class resolution invokes `synthPending`.

    Remark: in the current implementation, `synthPending` fails if `synthPendingDepth > 0`.
    We will add a configuration option if necessary. -/
  synthPendingDepth : Nat                  := 0

abbrev MetaM  := ReaderT Context $ StateRefT State CoreM

-- Make the compiler generate specialized `pure`/`bind` so we do not have to optimize through the
-- whole monad stack at every use site. May eventually be covered by `deriving`.
instance : Monad MetaM := let i := inferInstanceAs (Monad MetaM); { pure := i.pure, bind := i.bind }

instance : Inhabited (MetaM α) where
  default := fun _ _ => arbitrary

instance : MonadLCtx MetaM where
  getLCtx := return (← read).lctx

instance : MonadMCtx MetaM where
  getMCtx    := return (← get).mctx
  modifyMCtx f := modify fun s => { s with mctx := f s.mctx }

instance : AddMessageContext MetaM where
  addMessageContext := addMessageContextFull

protected def saveState : MetaM SavedState :=
  return { core := (← getThe Core.State), meta := (← get) }

/-- Restore backtrackable parts of the state. -/
def SavedState.restore (b : SavedState) : MetaM Unit := do
  Core.restore b.core
  modify fun s => { s with mctx := b.meta.mctx, zetaFVarIds := b.meta.zetaFVarIds, postponed := b.meta.postponed }

instance : MonadBacktrack SavedState MetaM where
  saveState      := Meta.saveState
  restoreState s := s.restore

@[inline] def MetaM.run (x : MetaM α) (ctx : Context := {}) (s : State := {}) : CoreM (α × State) :=
  x ctx |>.run s

@[inline] def MetaM.run' (x : MetaM α) (ctx : Context := {}) (s : State := {}) : CoreM α :=
  Prod.fst <$> x.run ctx s

@[inline] def MetaM.toIO (x : MetaM α) (ctxCore : Core.Context) (sCore : Core.State) (ctx : Context := {}) (s : State := {}) : IO (α × Core.State × State) := do
  let ((a, s), sCore) ← (x.run ctx s).toIO ctxCore sCore
  pure (a, sCore, s)

instance [MetaEval α] : MetaEval (MetaM α) :=
  ⟨fun env opts x _ => MetaEval.eval env opts x.run' true⟩

protected def throwIsDefEqStuck : MetaM α :=
  throw <| Exception.internal isDefEqStuckExceptionId

builtin_initialize
  registerTraceClass `Meta
  registerTraceClass `Meta.debug

@[inline] def liftMetaM [MonadLiftT MetaM m] (x : MetaM α) : m α :=
  liftM x

@[inline] def mapMetaM [MonadControlT MetaM m] [Monad m] (f : forall {α}, MetaM α → MetaM α) {α} (x : m α) : m α :=
  controlAt MetaM fun runInBase => f <| runInBase x

@[inline] def map1MetaM [MonadControlT MetaM m] [Monad m] (f : forall {α}, (β → MetaM α) → MetaM α) {α} (k : β → m α) : m α :=
  controlAt MetaM fun runInBase => f fun b => runInBase <| k b

@[inline] def map2MetaM [MonadControlT MetaM m] [Monad m] (f : forall {α}, (β → γ → MetaM α) → MetaM α) {α} (k : β → γ → m α) : m α :=
  controlAt MetaM fun runInBase => f fun b c => runInBase <| k b c

section Methods
variable [MonadControlT MetaM n] [Monad n]

@[inline] def modifyCache (f : Cache → Cache) : MetaM Unit :=
  modify fun ⟨mctx, cache, zetaFVarIds, postponed⟩ => ⟨mctx, f cache, zetaFVarIds, postponed⟩

@[inline] def modifyInferTypeCache (f : InferTypeCache → InferTypeCache) : MetaM Unit :=
  modifyCache fun ⟨ic, c1, c2, c3, c4, c5, c6⟩ => ⟨f ic, c1, c2, c3, c4, c5, c6⟩

def getLocalInstances : MetaM LocalInstances :=
  return (← read).localInstances

def getConfig : MetaM Config :=
  return (← read).config

def setMCtx (mctx : MetavarContext) : MetaM Unit :=
  modify fun s => { s with mctx := mctx }

def resetZetaFVarIds : MetaM Unit :=
  modify fun s => { s with zetaFVarIds := {} }

def getZetaFVarIds : MetaM FVarIdSet :=
  return (← get).zetaFVarIds

def getPostponed : MetaM (PersistentArray PostponedEntry) :=
  return (← get).postponed

def setPostponed (postponed : PersistentArray PostponedEntry) : MetaM Unit :=
  modify fun s => { s with postponed := postponed }

@[inline] def modifyPostponed (f : PersistentArray PostponedEntry → PersistentArray PostponedEntry) : MetaM Unit :=
  modify fun s => { s with postponed := f s.postponed }

/- WARNING: The following 4 constants are a hack for simulating forward declarations.
   They are defined later using the `export` attribute. This is hackish because we
   have to hard-code the true arity of these definitions here, and make sure the C names match.
   We have used another hack based on `IO.Ref`s in the past, it was safer but less efficient. -/
@[extern 6 "lean_whnf"] constant whnf : Expr → MetaM Expr
@[extern 6 "lean_infer_type"] constant inferType : Expr → MetaM Expr
@[extern 7 "lean_is_expr_def_eq"] constant isExprDefEqAux : Expr → Expr → MetaM Bool
@[extern 7 "lean_is_level_def_eq"] constant isLevelDefEqAux : Level → Level → MetaM Bool
@[extern 6 "lean_synth_pending"] protected constant synthPending : MVarId → MetaM Bool

def whnfForall (e : Expr) : MetaM Expr := do
  let e' ← whnf e
  if e'.isForall then pure e' else pure e

-- withIncRecDepth for a monad `n` such that `[MonadControlT MetaM n]`
protected def withIncRecDepth (x : n α) : n α :=
  mapMetaM (withIncRecDepth (m := MetaM)) x

private def mkFreshExprMVarAtCore
    (mvarId : MVarId) (lctx : LocalContext) (localInsts : LocalInstances) (type : Expr) (kind : MetavarKind) (userName : Name) (numScopeArgs : Nat) : MetaM Expr := do
  modifyMCtx fun mctx => mctx.addExprMVarDecl mvarId userName lctx localInsts type kind numScopeArgs;
  return mkMVar mvarId

def mkFreshExprMVarAt
    (lctx : LocalContext) (localInsts : LocalInstances) (type : Expr)
    (kind : MetavarKind := MetavarKind.natural) (userName : Name := Name.anonymous) (numScopeArgs : Nat := 0)
    : MetaM Expr := do
  mkFreshExprMVarAtCore (← mkFreshMVarId) lctx localInsts type kind userName numScopeArgs

def mkFreshLevelMVar : MetaM Level := do
  let mvarId ← mkFreshMVarId
  modifyMCtx fun mctx => mctx.addLevelMVarDecl mvarId;
  return mkLevelMVar mvarId

private def mkFreshExprMVarCore (type : Expr) (kind : MetavarKind) (userName : Name) : MetaM Expr := do
  mkFreshExprMVarAt (← getLCtx) (← getLocalInstances) type kind userName

private def mkFreshExprMVarImpl (type? : Option Expr) (kind : MetavarKind) (userName : Name) : MetaM Expr :=
  match type? with
  | some type => mkFreshExprMVarCore type kind userName
  | none      => do
    let u ← mkFreshLevelMVar
    let type ← mkFreshExprMVarCore (mkSort u) MetavarKind.natural Name.anonymous
    mkFreshExprMVarCore type kind userName

def mkFreshExprMVar (type? : Option Expr) (kind := MetavarKind.natural) (userName := Name.anonymous) : MetaM Expr :=
  mkFreshExprMVarImpl type? kind userName

def mkFreshTypeMVar (kind := MetavarKind.natural) (userName := Name.anonymous) : MetaM Expr := do
  let u ← mkFreshLevelMVar
  mkFreshExprMVar (mkSort u) kind userName

/- Low-level version of `MkFreshExprMVar` which allows users to create/reserve a `mvarId` using `mkFreshId`, and then later create
   the metavar using this method. -/
private def mkFreshExprMVarWithIdCore (mvarId : MVarId) (type : Expr)
    (kind : MetavarKind := MetavarKind.natural) (userName : Name := Name.anonymous) (numScopeArgs : Nat := 0)
    : MetaM Expr := do
  mkFreshExprMVarAtCore mvarId (← getLCtx) (← getLocalInstances) type kind userName numScopeArgs

def mkFreshExprMVarWithId (mvarId : MVarId) (type? : Option Expr := none) (kind : MetavarKind := MetavarKind.natural) (userName := Name.anonymous) : MetaM Expr :=
  match type? with
  | some type => mkFreshExprMVarWithIdCore mvarId type kind userName
  | none      => do
    let u ← mkFreshLevelMVar
    let type ← mkFreshExprMVar (mkSort u)
    mkFreshExprMVarWithIdCore mvarId type kind userName

def mkFreshLevelMVars (num : Nat) : MetaM (List Level) :=
  num.foldM (init := []) fun _ us =>
    return (← mkFreshLevelMVar)::us

def mkFreshLevelMVarsFor (info : ConstantInfo) : MetaM (List Level) :=
  mkFreshLevelMVars info.numLevelParams

def mkConstWithFreshMVarLevels (declName : Name) : MetaM Expr := do
  let info ← getConstInfo declName
  return mkConst declName (← mkFreshLevelMVarsFor info)

def getTransparency : MetaM TransparencyMode :=
  return (← getConfig).transparency

def shouldReduceAll : MetaM Bool :=
  return (← getTransparency) == TransparencyMode.all

def shouldReduceReducibleOnly : MetaM Bool :=
  return (← getTransparency) == TransparencyMode.reducible

def getMVarDecl (mvarId : MVarId) : MetaM MetavarDecl := do
  match (← getMCtx).findDecl? mvarId with
  | some d => pure d
  | none   => throwError "unknown metavariable '?{mvarId.name}'"

def setMVarKind (mvarId : MVarId) (kind : MetavarKind) : MetaM Unit :=
  modifyMCtx fun mctx => mctx.setMVarKind mvarId kind

/- Update the type of the given metavariable. This function assumes the new type is
   definitionally equal to the current one -/
def setMVarType (mvarId : MVarId) (type : Expr) : MetaM Unit := do
  modifyMCtx fun mctx => mctx.setMVarType mvarId type

def isReadOnlyExprMVar (mvarId : MVarId) : MetaM Bool := do
  return (← getMVarDecl mvarId).depth != (← getMCtx).depth

def isReadOnlyOrSyntheticOpaqueExprMVar (mvarId : MVarId) : MetaM Bool := do
  let mvarDecl ← getMVarDecl mvarId
  match mvarDecl.kind with
  | MetavarKind.syntheticOpaque => return !(← getConfig).assignSyntheticOpaque
  | _ => return mvarDecl.depth != (← getMCtx).depth

def getLevelMVarDepth (mvarId : MVarId) : MetaM Nat := do
  match (← getMCtx).findLevelDepth? mvarId with
  | some depth => return depth
  | _          => throwError "unknown universe metavariable '?{mvarId.name}'"

def isReadOnlyLevelMVar (mvarId : MVarId) : MetaM Bool := do
  if (← getConfig).ignoreLevelMVarDepth then
    return false
  else
    return (← getLevelMVarDepth mvarId) != (← getMCtx).depth

def renameMVar (mvarId : MVarId) (newUserName : Name) : MetaM Unit :=
  modifyMCtx fun mctx => mctx.renameMVar mvarId newUserName

def isExprMVarAssigned (mvarId : MVarId) : MetaM Bool :=
  return (← getMCtx).isExprAssigned mvarId

def getExprMVarAssignment? (mvarId : MVarId) : MetaM (Option Expr) :=
  return (← getMCtx).getExprAssignment? mvarId

/-- Return true if `e` contains `mvarId` directly or indirectly -/
def occursCheck (mvarId : MVarId) (e : Expr) : MetaM Bool :=
  return (← getMCtx).occursCheck mvarId e

def assignExprMVar (mvarId : MVarId) (val : Expr) : MetaM Unit :=
  modifyMCtx fun mctx => mctx.assignExpr mvarId val

def isDelayedAssigned (mvarId : MVarId) : MetaM Bool :=
  return (← getMCtx).isDelayedAssigned mvarId

def getDelayedAssignment? (mvarId : MVarId) : MetaM (Option DelayedMetavarAssignment) :=
  return (← getMCtx).getDelayedAssignment? mvarId

def hasAssignableMVar (e : Expr) : MetaM Bool :=
  return (← getMCtx).hasAssignableMVar e

def throwUnknownFVar (fvarId : FVarId) : MetaM α :=
  throwError "unknown free variable '{mkFVar fvarId}'"

def findLocalDecl? (fvarId : FVarId) : MetaM (Option LocalDecl) :=
  return (← getLCtx).find? fvarId

def getLocalDecl (fvarId : FVarId) : MetaM LocalDecl := do
  match (← getLCtx).find? fvarId with
  | some d => pure d
  | none   => throwUnknownFVar fvarId

def getFVarLocalDecl (fvar : Expr) : MetaM LocalDecl :=
  getLocalDecl fvar.fvarId!

def getLocalDeclFromUserName (userName : Name) : MetaM LocalDecl := do
  match (← getLCtx).findFromUserName? userName with
  | some d => pure d
  | none   => throwError "unknown local declaration '{userName}'"

def instantiateLevelMVars (u : Level) : MetaM Level :=
  MetavarContext.instantiateLevelMVars u

def instantiateMVars (e : Expr) : MetaM Expr :=
  (MetavarContext.instantiateExprMVars e).run

def instantiateLocalDeclMVars (localDecl : LocalDecl) : MetaM LocalDecl :=
  match localDecl with
  | LocalDecl.cdecl idx id n type bi  =>
    return LocalDecl.cdecl idx id n (← instantiateMVars type) bi
  | LocalDecl.ldecl idx id n type val nonDep =>
    return LocalDecl.ldecl idx id n (← instantiateMVars type) (← instantiateMVars val) nonDep

@[inline] def liftMkBindingM (x : MetavarContext.MkBindingM α) : MetaM α := do
  match x (← getLCtx) { mctx := (← getMCtx), ngen := (← getNGen) } with
  | EStateM.Result.ok e newS => do
    setNGen newS.ngen;
    setMCtx newS.mctx;
    pure e
  | EStateM.Result.error (MetavarContext.MkBinding.Exception.revertFailure mctx lctx toRevert decl) newS => do
    setMCtx newS.mctx;
    setNGen newS.ngen;
    throwError "failed to create binder due to failure when reverting variable dependencies"

def abstractRange (e : Expr) (n : Nat) (xs : Array Expr) : MetaM Expr :=
  liftMkBindingM <| MetavarContext.abstractRange e n xs

def abstract (e : Expr) (xs : Array Expr) : MetaM Expr :=
  abstractRange e xs.size xs

def mkForallFVars (xs : Array Expr) (e : Expr) (usedOnly : Bool := false) (usedLetOnly : Bool := true) : MetaM Expr :=
  if xs.isEmpty then pure e else liftMkBindingM <| MetavarContext.mkForall xs e usedOnly usedLetOnly

def mkLambdaFVars (xs : Array Expr) (e : Expr) (usedOnly : Bool := false) (usedLetOnly : Bool := true) : MetaM Expr :=
  if xs.isEmpty then pure e else liftMkBindingM <| MetavarContext.mkLambda xs e usedOnly usedLetOnly

def mkLetFVars (xs : Array Expr) (e : Expr) (usedLetOnly := true) : MetaM Expr :=
  mkLambdaFVars xs e (usedLetOnly := usedLetOnly)

def mkArrow (d b : Expr) : MetaM Expr :=
  return Lean.mkForall (← mkFreshUserName `x) BinderInfo.default d b

/-- `fun _ : Unit => a` -/
def mkFunUnit (a : Expr) : MetaM Expr :=
  return Lean.mkLambda (← mkFreshUserName `x) BinderInfo.default (mkConst ``Unit) a

def elimMVarDeps (xs : Array Expr) (e : Expr) (preserveOrder : Bool := false) : MetaM Expr :=
  if xs.isEmpty then pure e else liftMkBindingM <| MetavarContext.elimMVarDeps xs e preserveOrder

@[inline] def withConfig (f : Config → Config) : n α → n α :=
  mapMetaM <| withReader (fun ctx => { ctx with config := f ctx.config })

@[inline] def withTrackingZeta (x : n α) : n α :=
  withConfig (fun cfg => { cfg with trackZeta := true }) x

@[inline] def withoutProofIrrelevance (x : n α) : n α :=
  withConfig (fun cfg => { cfg with proofIrrelevance := false }) x

@[inline] def withTransparency (mode : TransparencyMode) : n α → n α :=
  mapMetaM <| withConfig (fun config => { config with transparency := mode })

@[inline] def withDefault (x : n α) : n α :=
  withTransparency TransparencyMode.default x

@[inline] def withReducible (x : n α) : n α :=
  withTransparency TransparencyMode.reducible x

@[inline] def withReducibleAndInstances (x : n α) : n α :=
  withTransparency TransparencyMode.instances x

@[inline] def withAtLeastTransparency (mode : TransparencyMode) (x : n α) : n α :=
  withConfig
    (fun config =>
      let oldMode := config.transparency
      let mode    := if oldMode.lt mode then mode else oldMode
      { config with transparency := mode })
    x

/-- Execute `x` allowing `isDefEq` to assign synthetic opaque metavariables. -/
@[inline] def withAssignableSyntheticOpaque (x : n α) : n α :=
  withConfig (fun config => { config with assignSyntheticOpaque := true }) x

/-- Save cache, execute `x`, restore cache -/
@[inline] private def savingCacheImpl (x : MetaM α) : MetaM α := do
  let savedCache := (← get).cache
  try x finally modify fun s => { s with cache := savedCache }

@[inline] def savingCache : n α → n α :=
  mapMetaM savingCacheImpl

def getTheoremInfo (info : ConstantInfo) : MetaM (Option ConstantInfo) := do
  if (← shouldReduceAll) then
    return some info
  else
    return none

private def getDefInfoTemp (info : ConstantInfo) : MetaM (Option ConstantInfo) := do
  match (← getTransparency) with
  | TransparencyMode.all => return some info
  | TransparencyMode.default => return some info
  | _ =>
    if (← isReducible info.name) then
      return some info
    else
      return none

/- Remark: we later define `getConst?` at `GetConst.lean` after we define `Instances.lean`.
   This method is only used to implement `isClassQuickConst?`.
   It is very similar to `getConst?`, but it returns none when `TransparencyMode.instances` and
   `constName` is an instance. This difference should be irrelevant for `isClassQuickConst?`. -/
private def getConstTemp? (constName : Name) : MetaM (Option ConstantInfo) := do
  match (← getEnv).find? constName with
  | some (info@(ConstantInfo.thmInfo _))  => getTheoremInfo info
  | some (info@(ConstantInfo.defnInfo _)) => getDefInfoTemp info
  | some info                             => pure (some info)
  | none                                  => throwUnknownConstant constName

private def isClassQuickConst? (constName : Name) : MetaM (LOption Name) := do
  if isClass (← getEnv) constName then
    pure (LOption.some constName)
  else
    match (← getConstTemp? constName) with
    | some _ => pure LOption.undef
    | none   => pure LOption.none

private partial def isClassQuick? : Expr → MetaM (LOption Name)
  | Expr.bvar ..         => pure LOption.none
  | Expr.lit ..          => pure LOption.none
  | Expr.fvar ..         => pure LOption.none
  | Expr.sort ..         => pure LOption.none
  | Expr.lam ..          => pure LOption.none
  | Expr.letE ..         => pure LOption.undef
  | Expr.proj ..         => pure LOption.undef
  | Expr.forallE _ _ b _ => isClassQuick? b
  | Expr.mdata _ e _     => isClassQuick? e
  | Expr.const n _ _     => isClassQuickConst? n
  | Expr.mvar mvarId _   => do
    match (← getExprMVarAssignment? mvarId) with
    | some val => isClassQuick? val
    | none     => pure LOption.none
  | Expr.app f _ _       =>
    match f.getAppFn with
    | Expr.const n .. => isClassQuickConst? n
    | Expr.lam ..     => pure LOption.undef
    | _              => pure LOption.none

def saveAndResetSynthInstanceCache : MetaM SynthInstanceCache := do
  let savedSythInstance := (← get).cache.synthInstance
  modifyCache fun c => { c with synthInstance := {} }
  pure savedSythInstance

def restoreSynthInstanceCache (cache : SynthInstanceCache) : MetaM Unit :=
  modifyCache fun c => { c with synthInstance := cache }

@[inline] private def resettingSynthInstanceCacheImpl (x : MetaM α) : MetaM α := do
  let savedSythInstance ← saveAndResetSynthInstanceCache
  try x finally restoreSynthInstanceCache savedSythInstance

/-- Reset `synthInstance` cache, execute `x`, and restore cache -/
@[inline] def resettingSynthInstanceCache : n α → n α :=
  mapMetaM resettingSynthInstanceCacheImpl

@[inline] def resettingSynthInstanceCacheWhen (b : Bool) (x : n α) : n α :=
  if b then resettingSynthInstanceCache x else x

private def withNewLocalInstanceImp (className : Name) (fvar : Expr) (k : MetaM α) : MetaM α := do
  let localDecl ← getFVarLocalDecl fvar
  /- Recall that we use `auxDecl` binderInfo when compiling recursive declarations. -/
  match localDecl.binderInfo with
  | BinderInfo.auxDecl => k
  | _ =>
    resettingSynthInstanceCache <|
      withReader
        (fun ctx => { ctx with localInstances := ctx.localInstances.push { className := className, fvar := fvar } })
        k

/-- Add entry `{ className := className, fvar := fvar }` to localInstances,
    and then execute continuation `k`.
    It resets the type class cache using `resettingSynthInstanceCache`. -/
def withNewLocalInstance (className : Name) (fvar : Expr) : n α → n α :=
  mapMetaM <| withNewLocalInstanceImp className fvar

private def fvarsSizeLtMaxFVars (fvars : Array Expr) (maxFVars? : Option Nat) : Bool :=
  match maxFVars? with
  | some maxFVars => fvars.size < maxFVars
  | none          => true

mutual
  /--
    `withNewLocalInstances isClassExpensive fvars j k` updates the vector or local instances
    using free variables `fvars[j] ... fvars.back`, and execute `k`.

    - `isClassExpensive` is defined later.
    - The type class chache is reset whenever a new local instance is found.
    - `isClassExpensive` uses `whnf` which depends (indirectly) on the set of local instances.
      Thus, each new local instance requires a new `resettingSynthInstanceCache`. -/
  private partial def withNewLocalInstancesImp
      (fvars : Array Expr) (i : Nat) (k : MetaM α) : MetaM α := do
    if h : i < fvars.size then
      let fvar := fvars.get ⟨i, h⟩
      let decl ← getFVarLocalDecl fvar
      match (← isClassQuick? decl.type) with
      | LOption.none   => withNewLocalInstancesImp fvars (i+1) k
      | LOption.undef  =>
        match (← isClassExpensive? decl.type) with
        | none   => withNewLocalInstancesImp fvars (i+1) k
        | some c => withNewLocalInstance c fvar <| withNewLocalInstancesImp fvars (i+1) k
      | LOption.some c => withNewLocalInstance c fvar <| withNewLocalInstancesImp fvars (i+1) k
    else
      k

  /--
    `forallTelescopeAuxAux lctx fvars j type`
    Remarks:
    - `lctx` is the `MetaM` local context extended with declarations for `fvars`.
    - `type` is the type we are computing the telescope for. It contains only
      dangling bound variables in the range `[j, fvars.size)`
    - if `reducing? == true` and `type` is not `forallE`, we use `whnf`.
    - when `type` is not a `forallE` nor it can't be reduced to one, we
      excute the continuation `k`.

    Here is an example that demonstrates the `reducing?`.
    Suppose we have
    ```
    abbrev StateM s a := s -> Prod a s
    ```
    Now, assume we are trying to build the telescope for
    ```
    forall (x : Nat), StateM Int Bool
    ```
    if `reducing == true`, the function executes `k #[(x : Nat) (s : Int)] Bool`.
    if `reducing == false`, the function executes `k #[(x : Nat)] (StateM Int Bool)`

    if `maxFVars?` is `some max`, then we interrupt the telescope construction
    when `fvars.size == max`
  -/
  private partial def forallTelescopeReducingAuxAux
      (reducing          : Bool) (maxFVars? : Option Nat)
      (type              : Expr)
      (k                 : Array Expr → Expr → MetaM α) : MetaM α := do
    let rec process (lctx : LocalContext) (fvars : Array Expr) (j : Nat) (type : Expr) : MetaM α := do
      match type with
      | Expr.forallE n d b c =>
        if fvarsSizeLtMaxFVars fvars maxFVars? then
          let d     := d.instantiateRevRange j fvars.size fvars
          let fvarId ← mkFreshFVarId
          let lctx  := lctx.mkLocalDecl fvarId n d c.binderInfo
          let fvar  := mkFVar fvarId
          let fvars := fvars.push fvar
          process lctx fvars j b
        else
          let type := type.instantiateRevRange j fvars.size fvars;
          withReader (fun ctx => { ctx with lctx := lctx }) do
            withNewLocalInstancesImp fvars j do
              k fvars type
      | _ =>
        let type := type.instantiateRevRange j fvars.size fvars;
        withReader (fun ctx => { ctx with lctx := lctx }) do
          withNewLocalInstancesImp fvars j do
            if reducing && fvarsSizeLtMaxFVars fvars maxFVars? then
              let newType ← whnf type
              if newType.isForall then
                process lctx fvars fvars.size newType
              else
                k fvars type
            else
              k fvars type
    process (← getLCtx) #[] 0 type

  private partial def forallTelescopeReducingAux (type : Expr) (maxFVars? : Option Nat) (k : Array Expr → Expr → MetaM α) : MetaM α := do
    match maxFVars? with
    | some 0 => k #[] type
    | _ => do
      let newType ← whnf type
      if newType.isForall then
        forallTelescopeReducingAuxAux true maxFVars? newType k
      else
        k #[] type

  private partial def isClassExpensive? : Expr → MetaM (Option Name)
    | type => withReducible <| -- when testing whether a type is a type class, we only unfold reducible constants.
      forallTelescopeReducingAux type none fun xs type => do
        let env ← getEnv
        match type.getAppFn with
        | Expr.const c _ _ => do
          if isClass env c then
            return some c
          else
            -- make sure abbreviations are unfolded
            match (← whnf type).getAppFn with
            | Expr.const c _ _ => return if isClass env c then some c else none
            | _ => return none
        | _ => return none

  private partial def isClassImp? (type : Expr) : MetaM (Option Name) := do
    match (← isClassQuick? type) with
    | LOption.none   => pure none
    | LOption.some c => pure (some c)
    | LOption.undef  => isClassExpensive? type

end

def isClass? (type : Expr) : MetaM (Option Name) :=
  try isClassImp? type catch _ => pure none

private def withNewLocalInstancesImpAux (fvars : Array Expr) (j : Nat) : n α → n α :=
  mapMetaM <| withNewLocalInstancesImp fvars j

partial def withNewLocalInstances (fvars : Array Expr) (j : Nat) : n α → n α :=
  mapMetaM <| withNewLocalInstancesImpAux fvars j

@[inline] private def forallTelescopeImp (type : Expr) (k : Array Expr → Expr → MetaM α) : MetaM α := do
  forallTelescopeReducingAuxAux (reducing := false) (maxFVars? := none) type k

/--
  Given `type` of the form `forall xs, A`, execute `k xs A`.
  This combinator will declare local declarations, create free variables for them,
  execute `k` with updated local context, and make sure the cache is restored after executing `k`. -/
def forallTelescope (type : Expr) (k : Array Expr → Expr → n α) : n α :=
  map2MetaM (fun k => forallTelescopeImp type k) k

private def forallTelescopeReducingImp (type : Expr) (k : Array Expr → Expr → MetaM α) : MetaM α :=
  forallTelescopeReducingAux type (maxFVars? := none) k

/--
  Similar to `forallTelescope`, but given `type` of the form `forall xs, A`,
  it reduces `A` and continues bulding the telescope if it is a `forall`. -/
def forallTelescopeReducing (type : Expr) (k : Array Expr → Expr → n α) : n α :=
  map2MetaM (fun k => forallTelescopeReducingImp type k) k

private def forallBoundedTelescopeImp (type : Expr) (maxFVars? : Option Nat) (k : Array Expr → Expr → MetaM α) : MetaM α :=
  forallTelescopeReducingAux type maxFVars? k

/--
  Similar to `forallTelescopeReducing`, stops constructing the telescope when
  it reaches size `maxFVars`. -/
def forallBoundedTelescope (type : Expr) (maxFVars? : Option Nat) (k : Array Expr → Expr → n α) : n α :=
  map2MetaM (fun k => forallBoundedTelescopeImp type maxFVars? k) k

private partial def lambdaTelescopeImp (e : Expr) (consumeLet : Bool) (k : Array Expr → Expr → MetaM α) : MetaM α := do
  process consumeLet (← getLCtx) #[] 0 e
where
  process (consumeLet : Bool) (lctx : LocalContext) (fvars : Array Expr) (j : Nat) (e : Expr) : MetaM α := do
    match consumeLet, e with
    | _, Expr.lam n d b c =>
      let d := d.instantiateRevRange j fvars.size fvars
      let fvarId ← mkFreshFVarId
      let lctx := lctx.mkLocalDecl fvarId n d c.binderInfo
      let fvar := mkFVar fvarId
      process consumeLet lctx (fvars.push fvar) j b
    | true, Expr.letE n t v b _ => do
      let t := t.instantiateRevRange j fvars.size fvars
      let v := v.instantiateRevRange j fvars.size fvars
      let fvarId ← mkFreshFVarId
      let lctx := lctx.mkLetDecl fvarId n t v
      let fvar := mkFVar fvarId
      process true lctx (fvars.push fvar) j b
    | _, e =>
      let e := e.instantiateRevRange j fvars.size fvars
      withReader (fun ctx => { ctx with lctx := lctx }) do
        withNewLocalInstancesImp fvars j do
          k fvars e

/-- Similar to `forallTelescope` but for lambda and let expressions. -/
def lambdaLetTelescope (type : Expr) (k : Array Expr → Expr → n α) : n α :=
  map2MetaM (fun k => lambdaTelescopeImp type true k) k

/-- Similar to `forallTelescope` but for lambda expressions. -/
def lambdaTelescope (type : Expr) (k : Array Expr → Expr → n α) : n α :=
  map2MetaM (fun k => lambdaTelescopeImp type false k) k

/-- Return the parameter names for the givel global declaration. -/
def getParamNames (declName : Name) : MetaM (Array Name) := do
  forallTelescopeReducing (← getConstInfo declName).type fun xs _ => do
    xs.mapM fun x => do
      let localDecl ← getLocalDecl x.fvarId!
      pure localDecl.userName

-- `kind` specifies the metavariable kind for metavariables not corresponding to instance implicit `[ ... ]` arguments.
private partial def forallMetaTelescopeReducingAux
    (e : Expr) (reducing : Bool) (maxMVars? : Option Nat) (kind : MetavarKind) : MetaM (Array Expr × Array BinderInfo × Expr) :=
  process #[] #[] 0 e
where
  process (mvars : Array Expr) (bis : Array BinderInfo) (j : Nat) (type : Expr) : MetaM (Array Expr × Array BinderInfo × Expr) := do
    if maxMVars?.isEqSome mvars.size then
      let type := type.instantiateRevRange j mvars.size mvars;
      return (mvars, bis, type)
    else
      match type with
      | Expr.forallE n d b c =>
        let d  := d.instantiateRevRange j mvars.size mvars
        let k  := if c.binderInfo.isInstImplicit then  MetavarKind.synthetic else kind
        let mvar ← mkFreshExprMVar d k n
        let mvars := mvars.push mvar
        let bis   := bis.push c.binderInfo
        process mvars bis j b
      | _ =>
        let type := type.instantiateRevRange j mvars.size mvars;
        if reducing then do
          let newType ← whnf type;
          if newType.isForall then
            process mvars bis mvars.size newType
          else
            return (mvars, bis, type)
        else
          return (mvars, bis, type)

/-- Similar to `forallTelescope`, but creates metavariables instead of free variables. -/
def forallMetaTelescope (e : Expr) (kind := MetavarKind.natural) : MetaM (Array Expr × Array BinderInfo × Expr) :=
  forallMetaTelescopeReducingAux e (reducing := false) (maxMVars? := none) kind

/-- Similar to `forallTelescopeReducing`, but creates metavariables instead of free variables. -/
def forallMetaTelescopeReducing (e : Expr) (maxMVars? : Option Nat := none) (kind := MetavarKind.natural) : MetaM (Array Expr × Array BinderInfo × Expr) :=
  forallMetaTelescopeReducingAux e (reducing := true) maxMVars? kind

/-- Similar to `forallMetaTelescopeReducing`, stops constructing the telescope when it reaches size `maxMVars`. -/
def forallMetaBoundedTelescope (e : Expr) (maxMVars : Nat) (kind : MetavarKind := MetavarKind.natural) : MetaM (Array Expr × Array BinderInfo × Expr) :=
  forallMetaTelescopeReducingAux e (reducing := true) (maxMVars? := some maxMVars) (kind := kind)

/-- Similar to `forallMetaTelescopeReducingAux` but for lambda expressions. -/
partial def lambdaMetaTelescope (e : Expr) (maxMVars? : Option Nat := none) : MetaM (Array Expr × Array BinderInfo × Expr) :=
  process #[] #[] 0 e
where
  process (mvars : Array Expr) (bis : Array BinderInfo) (j : Nat) (type : Expr) : MetaM (Array Expr × Array BinderInfo × Expr) := do
    let finalize : Unit → MetaM (Array Expr × Array BinderInfo × Expr) := fun _ => do
      let type := type.instantiateRevRange j mvars.size mvars
      pure (mvars, bis, type)
    if maxMVars?.isEqSome mvars.size then
      finalize ()
    else
      match type with
      | Expr.lam n d b c =>
        let d     := d.instantiateRevRange j mvars.size mvars
        let mvar ← mkFreshExprMVar d
        let mvars := mvars.push mvar
        let bis   := bis.push c.binderInfo
        process mvars bis j b
      | _ => finalize ()

private def withNewFVar (fvar fvarType : Expr) (k : Expr → MetaM α) : MetaM α := do
  match (← isClass? fvarType) with
  | none   => k fvar
  | some c => withNewLocalInstance c fvar <| k fvar

private def withLocalDeclImp (n : Name) (bi : BinderInfo) (type : Expr) (k : Expr → MetaM α) : MetaM α := do
  let fvarId ← mkFreshFVarId
  let ctx ← read
  let lctx := ctx.lctx.mkLocalDecl fvarId n type bi
  let fvar := mkFVar fvarId
  withReader (fun ctx => { ctx with lctx := lctx }) do
    withNewFVar fvar type k

def withLocalDecl (name : Name) (bi : BinderInfo) (type : Expr) (k : Expr → n α) : n α :=
  map1MetaM (fun k => withLocalDeclImp name bi type k) k

def withLocalDeclD (name : Name) (type : Expr) (k : Expr → n α) : n α :=
  withLocalDecl name BinderInfo.default type k

partial def withLocalDecls
    [Inhabited α]
    (declInfos : Array (Name × BinderInfo × (Array Expr → n Expr)))
    (k : (xs : Array Expr) → n α)
    : n α :=
  loop #[]
where
  loop [Inhabited α] (acc : Array Expr) : n α := do
    if acc.size < declInfos.size then
      let (name, bi, typeCtor) := declInfos[acc.size]
      withLocalDecl name bi (←typeCtor acc) fun x => loop (acc.push x)
    else
      k acc

def withLocalDeclsD [Inhabited α] (declInfos : Array (Name × (Array Expr → n Expr))) (k : (xs : Array Expr) → n α) : n α :=
  withLocalDecls
    (declInfos.map (fun (name, typeCtor) => (name, BinderInfo.default, typeCtor))) k

private def withNewBinderInfosImp (bs : Array (FVarId × BinderInfo)) (k : MetaM α) : MetaM α := do
  let lctx := bs.foldl (init := (← getLCtx)) fun lctx (fvarId, bi) =>
      lctx.setBinderInfo fvarId bi
  withReader (fun ctx => { ctx with lctx := lctx }) k

def withNewBinderInfos (bs : Array (FVarId × BinderInfo)) (k : n α) : n α :=
  mapMetaM (fun k => withNewBinderInfosImp bs k) k

private def withLetDeclImp (n : Name) (type : Expr) (val : Expr) (k : Expr → MetaM α) : MetaM α := do
  let fvarId ← mkFreshFVarId
  let ctx ← read
  let lctx := ctx.lctx.mkLetDecl fvarId n type val
  let fvar := mkFVar fvarId
  withReader (fun ctx => { ctx with lctx := lctx }) do
    withNewFVar fvar type k

def withLetDecl (name : Name) (type : Expr) (val : Expr) (k : Expr → n α) : n α :=
  map1MetaM (fun k => withLetDeclImp name type val k) k

private def withExistingLocalDeclsImp (decls : List LocalDecl) (k : MetaM α) : MetaM α := do
  let ctx ← read
  let numLocalInstances := ctx.localInstances.size
  let lctx := decls.foldl (fun (lctx : LocalContext) decl => lctx.addDecl decl) ctx.lctx
  withReader (fun ctx => { ctx with lctx := lctx }) do
    let newLocalInsts ← decls.foldlM
      (fun (newlocalInsts : Array LocalInstance) (decl : LocalDecl) => (do {
        match (← isClass? decl.type) with
        | none   => pure newlocalInsts
        | some c => pure <| newlocalInsts.push { className := c, fvar := decl.toExpr } } : MetaM _))
      ctx.localInstances;
    if newLocalInsts.size == numLocalInstances then
      k
    else
      resettingSynthInstanceCache <| withReader (fun ctx => { ctx with localInstances := newLocalInsts }) k

def withExistingLocalDecls (decls : List LocalDecl) : n α → n α :=
  mapMetaM <| withExistingLocalDeclsImp decls

private def withNewMCtxDepthImp (x : MetaM α) : MetaM α := do
  let saved ← get
  modify fun s => { s with mctx := s.mctx.incDepth, postponed := {} }
  try
    x
  finally
    modify fun s => { s with mctx := saved.mctx, postponed := saved.postponed }

/--
  Save cache and `MetavarContext`, bump the `MetavarContext` depth, execute `x`,
  and restore saved data. -/
def withNewMCtxDepth : n α → n α :=
  mapMetaM withNewMCtxDepthImp

private def withLocalContextImp (lctx : LocalContext) (localInsts : LocalInstances) (x : MetaM α) : MetaM α := do
  let localInstsCurr ← getLocalInstances
  withReader (fun ctx => { ctx with lctx := lctx, localInstances := localInsts }) do
    if localInsts == localInstsCurr then
      x
    else
      resettingSynthInstanceCache x

def withLCtx (lctx : LocalContext) (localInsts : LocalInstances) : n α → n α :=
  mapMetaM <| withLocalContextImp lctx localInsts

private def withMVarContextImp (mvarId : MVarId) (x : MetaM α) : MetaM α := do
  let mvarDecl ← getMVarDecl mvarId
  withLocalContextImp mvarDecl.lctx mvarDecl.localInstances x

/--
  Execute `x` using the given metavariable `LocalContext` and `LocalInstances`.
  The type class resolution cache is flushed when executing `x` if its `LocalInstances` are
  different from the current ones. -/
def withMVarContext (mvarId : MVarId) : n α → n α :=
  mapMetaM <| withMVarContextImp mvarId

private def withMCtxImp (mctx : MetavarContext) (x : MetaM α) : MetaM α := do
  let mctx' ← getMCtx
  setMCtx mctx
  try x finally setMCtx mctx'

def withMCtx (mctx : MetavarContext) : n α → n α :=
  mapMetaM <| withMCtxImp mctx

@[inline] private def approxDefEqImp (x : MetaM α) : MetaM α :=
  withConfig (fun config => { config with foApprox := true, ctxApprox := true, quasiPatternApprox := true}) x

/-- Execute `x` using approximate unification: `foApprox`, `ctxApprox` and `quasiPatternApprox`.  -/
@[inline] def approxDefEq : n α → n α :=
  mapMetaM approxDefEqImp

@[inline] private def fullApproxDefEqImp (x : MetaM α) : MetaM α :=
  withConfig (fun config => { config with foApprox := true, ctxApprox := true, quasiPatternApprox := true, constApprox := true }) x

/--
  Similar to `approxDefEq`, but uses all available approximations.
  We don't use `constApprox` by default at `approxDefEq` because it often produces undesirable solution for monadic code.
  For example, suppose we have `pure (x > 0)` which has type `?m Prop`. We also have the goal `[Pure ?m]`.
  Now, assume the expected type is `IO Bool`. Then, the unification constraint `?m Prop =?= IO Bool` could be solved
  as `?m := fun _ => IO Bool` using `constApprox`, but this spurious solution would generate a failure when we try to
  solve `[Pure (fun _ => IO Bool)]` -/
@[inline] def fullApproxDefEq : n α → n α :=
  mapMetaM fullApproxDefEqImp

def normalizeLevel (u : Level) : MetaM Level := do
  let u ← instantiateLevelMVars u
  pure u.normalize

def assignLevelMVar (mvarId : MVarId) (u : Level) : MetaM Unit := do
  modifyMCtx fun mctx => mctx.assignLevel mvarId u

def whnfR (e : Expr) : MetaM Expr :=
  withTransparency TransparencyMode.reducible <| whnf e

def whnfD (e : Expr) : MetaM Expr :=
  withTransparency TransparencyMode.default <| whnf e

def whnfI (e : Expr) : MetaM Expr :=
  withTransparency TransparencyMode.instances <| whnf e

def setInlineAttribute (declName : Name) (kind := Compiler.InlineAttributeKind.inline): MetaM Unit := do
  let env ← getEnv
  match Compiler.setInlineAttribute env declName kind with
  | Except.ok env    => setEnv env
  | Except.error msg => throwError msg

private partial def instantiateForallAux (ps : Array Expr) (i : Nat) (e : Expr) : MetaM Expr := do
  if h : i < ps.size then
    let p := ps.get ⟨i, h⟩
    match (← whnf e) with
    | Expr.forallE _ _ b _ => instantiateForallAux ps (i+1) (b.instantiate1 p)
    | _                    => throwError "invalid instantiateForall, too many parameters"
  else
    pure e

/- Given `e` of the form `forall (a_1 : A_1) ... (a_n : A_n), B[a_1, ..., a_n]` and `p_1 : A_1, ... p_n : A_n`, return `B[p_1, ..., p_n]`. -/
def instantiateForall (e : Expr) (ps : Array Expr) : MetaM Expr :=
  instantiateForallAux ps 0 e

private partial def instantiateLambdaAux (ps : Array Expr) (i : Nat) (e : Expr) : MetaM Expr := do
  if h : i < ps.size then
    let p := ps.get ⟨i, h⟩
    match (← whnf e) with
    | Expr.lam _ _ b _ => instantiateLambdaAux ps (i+1) (b.instantiate1 p)
    | _                => throwError "invalid instantiateLambda, too many parameters"
  else
    pure e

/- Given `e` of the form `fun (a_1 : A_1) ... (a_n : A_n) => t[a_1, ..., a_n]` and `p_1 : A_1, ... p_n : A_n`, return `t[p_1, ..., p_n]`.
   It uses `whnf` to reduce `e` if it is not a lambda -/
def instantiateLambda (e : Expr) (ps : Array Expr) : MetaM Expr :=
  instantiateLambdaAux ps 0 e

/-- Return true iff `e` depends on the free variable `fvarId` -/
def dependsOn (e : Expr) (fvarId : FVarId) : MetaM Bool :=
  return (← getMCtx).exprDependsOn e fvarId

/-- Return true iff `e` depends on a free variable `x` s.t. `p x` -/
def dependsOnPred (e : Expr) (p : FVarId → Bool) : MetaM Bool :=
  return (← getMCtx).findExprDependsOn e p

/-- Return true iff the local declaration `localDecl` depends on a free variable `x` s.t. `p x` -/
def localDeclDependsOnPred (localDecl : LocalDecl) (p : FVarId → Bool) : MetaM Bool := do
  return (← getMCtx).findLocalDeclDependsOn localDecl p

def ppExpr (e : Expr) : MetaM Format := do
  let ctxCore  ← readThe Core.Context
  Lean.ppExpr { env := (← getEnv), mctx := (← getMCtx), lctx := (← getLCtx), opts := (← getOptions), currNamespace := ctxCore.currNamespace, openDecls := ctxCore.openDecls  } e

@[inline] protected def orElse (x : MetaM α) (y : Unit → MetaM α) : MetaM α := do
  let s ← saveState
  try x catch _ => s.restore; y ()

instance : OrElse (MetaM α) := ⟨Meta.orElse⟩

instance : Alternative MetaM where
  failure := fun {α} => throwError "failed"
  orElse  := Meta.orElse

@[inline] private def orelseMergeErrorsImp (x y : MetaM α)
    (mergeRef : Syntax → Syntax → Syntax := fun r₁ r₂ => r₁)
    (mergeMsg : MessageData → MessageData → MessageData := fun m₁ m₂ => m₁ ++ Format.line ++ m₂) : MetaM α := do
  let env  ← getEnv
  let mctx ← getMCtx
  try
    x
  catch ex =>
    setEnv env
    setMCtx mctx
    match ex with
    | Exception.error ref₁ m₁ =>
      try
        y
      catch
        | Exception.error ref₂ m₂ => throw <| Exception.error (mergeRef ref₁ ref₂) (mergeMsg m₁ m₂)
        | ex => throw ex
    | ex => throw ex

/--
  Similar to `orelse`, but merge errors. Note that internal errors are not caught.
  The default `mergeRef` uses the `ref` (position information) for the first message.
  The default `mergeMsg` combines error messages using `Format.line ++ Format.line` as a separator. -/
@[inline] def orelseMergeErrors [MonadControlT MetaM m] [Monad m] (x y : m α)
    (mergeRef : Syntax → Syntax → Syntax := fun r₁ r₂ => r₁)
    (mergeMsg : MessageData → MessageData → MessageData := fun m₁ m₂ => m₁ ++ Format.line ++ Format.line ++ m₂) : m α := do
  controlAt MetaM fun runInBase => orelseMergeErrorsImp (runInBase x) (runInBase y) mergeRef mergeMsg

/-- Execute `x`, and apply `f` to the produced error message -/
def mapErrorImp (x : MetaM α) (f : MessageData → MessageData) : MetaM α := do
  try
    x
  catch
    | Exception.error ref msg => throw <| Exception.error ref <| f msg
    | ex => throw ex

@[inline] def mapError [MonadControlT MetaM m] [Monad m] (x : m α) (f : MessageData → MessageData) : m α :=
  controlAt MetaM fun runInBase => mapErrorImp (runInBase x) f

/--
  Sort free variables using an order `x < y` iff `x` was defined before `y`.
  If a free variable is not in the local context, we use their id. -/
def sortFVarIds (fvarIds : Array FVarId) : MetaM (Array FVarId) := do
  let lctx ← getLCtx
  return fvarIds.qsort fun fvarId₁ fvarId₂ =>
    match lctx.find? fvarId₁, lctx.find? fvarId₂ with
    | some d₁, some d₂ => d₁.index < d₂.index
    | some _,  none    => false
    | none,    some _  => true
    | none,    none    => Name.quickLt fvarId₁.name fvarId₂.name

end Methods

def isInductivePredicate (declName : Name) : MetaM Bool := do
  match (← getEnv).find? declName with
  | some (ConstantInfo.inductInfo { type := type, ..}) =>
    forallTelescopeReducing type fun _ type => do
      match (← whnfD type) with
      | Expr.sort u .. => return u == levelZero
      | _ => return false
  | _ => return false

/- -/
def isListLevelDefEqAux : List Level → List Level → MetaM Bool
  | [],    []    => return true
  | u::us, v::vs => isLevelDefEqAux u v <&&> isListLevelDefEqAux us vs
  | _,     _     => return false

private def getNumPostponed : MetaM Nat := do
  return (← getPostponed).size

def getResetPostponed : MetaM (PersistentArray PostponedEntry) := do
  let ps ← getPostponed
  setPostponed {}
  return ps

/-- Annotate any constant and sort in `e` that satisfies `p` with `pp.universes true` -/
private def exposeRelevantUniverses (e : Expr) (p : Level → Bool) : Expr :=
  e.replace fun
    | Expr.const _ us _ => if us.any p then some (e.setPPUniverses true) else none
    | Expr.sort u _     => if p u then some (e.setPPUniverses true) else none
    | _                 => none

private def mkLeveErrorMessageCore (header : String) (entry : PostponedEntry) : MetaM MessageData := do
  match entry.ctx? with
  | none =>
    return m!"{header}{indentD m!"{entry.lhs} =?= {entry.rhs}"}"
  | some ctx =>
    withLCtx ctx.lctx ctx.localInstances do
      let s   := entry.lhs.collectMVars entry.rhs.collectMVars
      /- `p u` is true if it contains a universe metavariable in `s` -/
      let p (u : Level) := u.any fun | Level.mvar m _ => s.contains m | _ => false
      let lhs := exposeRelevantUniverses (← instantiateMVars ctx.lhs) p
      let rhs := exposeRelevantUniverses (← instantiateMVars ctx.rhs) p
      try
        addMessageContext m!"{header}{indentD m!"{entry.lhs} =?= {entry.rhs}"}\nwhile trying to unify{indentD m!"{lhs} : {← inferType lhs}"}\nwith{indentD m!"{rhs} : {← inferType rhs}"}"
      catch _ =>
        addMessageContext m!"{header}{indentD m!"{entry.lhs} =?= {entry.rhs}"}\nwhile trying to unify{indentD lhs}\nwith{indentD rhs}"

def mkLevelStuckErrorMessage (entry : PostponedEntry) : MetaM MessageData := do
  mkLeveErrorMessageCore "stuck at solving universe constraint" entry

def mkLevelErrorMessage (entry : PostponedEntry) : MetaM MessageData := do
  mkLeveErrorMessageCore "failed to solve universe constraint" entry

private def processPostponedStep (exceptionOnFailure : Bool) : MetaM Bool :=
  traceCtx `Meta.isLevelDefEq.postponed.step do
    let ps ← getResetPostponed
    for p in ps do
      unless (← withReader (fun ctx => { ctx with defEqCtx? := p.ctx? }) <| isLevelDefEqAux p.lhs p.rhs) do
        if exceptionOnFailure then
          throwError (← mkLevelErrorMessage p)
        else
          return false
    return true

partial def processPostponed (mayPostpone : Bool := true) (exceptionOnFailure := false) : MetaM Bool := do
  if (← getNumPostponed) == 0 then
    return true
  else
    traceCtx `Meta.isLevelDefEq.postponed do
      let rec loop : MetaM Bool := do
        let numPostponed ← getNumPostponed
        if numPostponed == 0 then
          return true
        else
          trace[Meta.isLevelDefEq.postponed] "processing #{numPostponed} postponed is-def-eq level constraints"
          if !(← processPostponedStep exceptionOnFailure) then
            return false
          else
            let numPostponed' ← getNumPostponed
            if numPostponed' == 0 then
              return true
            else if numPostponed' < numPostponed then
              loop
            else
              trace[Meta.isLevelDefEq.postponed] "no progress solving pending is-def-eq level constraints"
              return mayPostpone
      loop

/--
  `checkpointDefEq x` executes `x` and process all postponed universe level constraints produced by `x`.
  We keep the modifications only if `processPostponed` return true and `x` returned `true`.

  If `mayPostpone == false`, all new postponed universe level constraints must be solved before returning.
  We currently try to postpone universe constraints as much as possible, even when by postponing them we
  are not sure whether `x` really succeeded or not.
-/
@[specialize] def checkpointDefEq (x : MetaM Bool) (mayPostpone : Bool := true) : MetaM Bool := do
  let s ← saveState
  let postponed ← getResetPostponed
  try
    if (← x) then
      if (← processPostponed mayPostpone) then
        let newPostponed ← getPostponed
        setPostponed (postponed ++ newPostponed)
        return true
      else
        s.restore
        return false
    else
      s.restore
      return false
  catch ex =>
    s.restore
    throw ex

def isLevelDefEq (u v : Level) : MetaM Bool :=
  traceCtx `Meta.isLevelDefEq do
    let b ← checkpointDefEq (mayPostpone := true) <| Meta.isLevelDefEqAux u v
    trace[Meta.isLevelDefEq] "{u} =?= {v} ... {if b then "success" else "failure"}"
    return b

def isExprDefEq (t s : Expr) : MetaM Bool :=
  traceCtx `Meta.isDefEq <| withReader (fun ctx => { ctx with defEqCtx? := some { lhs := t, rhs := s, lctx := ctx.lctx, localInstances := ctx.localInstances } }) do
    let b ← checkpointDefEq (mayPostpone := true) <| Meta.isExprDefEqAux t s
    trace[Meta.isDefEq] "{t} =?= {s} ... {if b then "success" else "failure"}"
    return b

abbrev isDefEq (t s : Expr) : MetaM Bool :=
  isExprDefEq t s

def isExprDefEqGuarded (a b : Expr) : MetaM Bool := do
  try isExprDefEq a b catch _ => return false

abbrev isDefEqGuarded (t s : Expr) : MetaM Bool :=
  isExprDefEqGuarded t s

def isDefEqNoConstantApprox (t s : Expr) : MetaM Bool :=
  approxDefEq <| isDefEq t s

end Meta

builtin_initialize
  registerTraceClass `Meta.isLevelDefEq.postponed

export Meta (MetaM)

end Lean