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.ReplaceExpr
import Lean.Util.MonadBacktrack
import Lean.Compiler.InlineAttrs
import Lean.Meta.TransparencyMode

/-!
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

/--
Configuration flags for the `MetaM` monad.
Many of them are used to control the `isDefEq` function that checks whether two terms are definitionally equal or not.
Recall that when `isDefEq` is trying to check whether
`?m@C a₁ ... aₙ` and `t` are definitionally equal (`?m@C a₁ ... aₙ =?= t`), where
`?m@C` as a shorthand for `C |- ?m : t` where `t` is the type of `?m`.
We solve it using the assignment `?m := fun a₁ ... aₙ => t` if
1) `a₁ ... aₙ` are pairwise distinct free variables that are ​*not*​ let-variables.
2) `a₁ ... aₙ` are not in `C`
3) `t` only contains free variables in `C` and/or `{a₁, ..., aₙ}`
4) For every metavariable `?m'@C'` occurring in `t`, `C'` is a subprefix of `C`
5) `?m` does not occur in `t`
-/
structure Config where
  /--
    If `foApprox` is set to true, and some `aᵢ` is not a free variable,
    then we use first-order unification
    ```
      ?m a_1 ... a_i a_{i+1} ... a_{i+k} =?= f b_1 ... b_k
    ```
    reduces to
    ```
      ?m a_1 ... a_i =?= f
      a_{i+1}        =?= b_1
      ...
      a_{i+k}        =?= b_k
    ```
  -/
  foApprox           : Bool := false
  /--
    When `ctxApprox` is set to true, we relax condition 4, by creating an
    auxiliary metavariable `?n'` with a smaller context than `?m'`.
  -/
  ctxApprox          : Bool := false
  /--
    When `quasiPatternApprox` is set to true, we ignore condition 2.
  -/
  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 exception `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 solvable
    later after it assigns `?m`. -/
  isDefEqStuckEx     : Bool := false
  /-- Enable/disable the unification hints feature. -/
  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
  /-- Enable/Disable support for offset constraints such as `?x + 1 =?= e` -/
  offsetCnstrs          : Bool := true
  /--
    Controls which definitions and theorems can be unfolded by `isDefEq` and `whnf`.
   -/
  transparency       : TransparencyMode := TransparencyMode.default
  /--
  When `trackZeta = true`, we track all free variables that have been zeta-expanded.
  That is, suppose the local context contains
  the declaration `x : t := v`, and we reduce `x` to `v`, then we insert `x` into `State.zetaFVarIds`.
  We use `trackZeta` to discover which let-declarations `let x := v; e` can be represented as `(fun x => e) v`.
  When we find these declarations we set their `nonDep` flag with `true`.
  To find these let-declarations in a given term `s`, we
  1- Reset `State.zetaFVarIds`
  2- Set `trackZeta := true`
  3- Type-check `s`.
  -/
  trackZeta          : Bool := false
  /-- Eta for structures configuration mode. -/
  etaStruct          : EtaStructMode := .all

/--
  Function parameter information cache.
-/
structure ParamInfo where
  /-- The binder annotation for the parameter. -/
  binderInfo     : BinderInfo := BinderInfo.default
  /-- `hasFwdDeps` is true if there is another parameter whose type depends on this one. -/
  hasFwdDeps     : Bool       := false
  /-- `backDeps` contains the backwards dependencies. That is, the (0-indexed) position of previous parameters that this one depends on. -/
  backDeps       : Array Nat  := #[]
  /-- `isProp` is true if the parameter is always a proposition. -/
  isProp         : Bool       := false
  /--
    `isDecInst` is true if the parameter's type is of the form `Decidable ...`.
    This information affects the generation of congruence theorems.
  -/
  isDecInst      : Bool       := false
  /--
    `higherOrderOutParam` is true if this parameter is a higher-order output parameter
    of local instance.
    Example:
    ```
    getElem :
      {cont : Type u_1} → {idx : Type u_2} → {elem : Type u_3} →
      {dom : cont → idx → Prop} → [self : GetElem cont idx elem dom] →
      (xs : cont) → (i : idx) → dom xs i → elem
    ```
    This flag is true for the parameter `dom` because it is output parameter of
    `[self : GetElem cont idx elem dom]`
   -/
  higherOrderOutParam : Bool  := false
  /--
    `dependsOnHigherOrderOutParam` is true if the type of this parameter depends on
    the higher-order output parameter of a previous local instance.
    Example:
    ```
    getElem :
      {cont : Type u_1} → {idx : Type u_2} → {elem : Type u_3} →
      {dom : cont → idx → Prop} → [self : GetElem cont idx elem dom] →
      (xs : cont) → (i : idx) → dom xs i → elem
    ```
    This flag is true for the parameter with type `dom xs i` since `dom` is an output parameter
    of the instance `[self : GetElem cont idx elem dom]`
  -/
  dependsOnHigherOrderOutParam : Bool := false
  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


/--
  Function information cache. See `ParamInfo`.
-/
structure FunInfo where
  /-- Parameter information cache. -/
  paramInfo  : Array ParamInfo := #[]
  /--
    `resultDeps` contains the function result type backwards dependencies.
    That is, the (0-indexed) position of parameters that the result type depends on.
  -/
  resultDeps : Array Nat       := #[]

/--
  Key for the function information cache.
-/
structure InfoCacheKey where
  /-- The transparency mode used to compute the `FunInfo`. -/
  transparency : TransparencyMode
  /-- The function being cached information about. It is quite often an `Expr.const`. -/
  expr         : Expr
  /--
    `nargs? = some n` if the cached information was computed assuming the function has arity `n`.
    If `nargs? = none`, then the cache information consumed the arrow type as much as possible
    using the current transparency setting.
  X-/
  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

abbrev SynthInstanceCache := PersistentHashMap (LocalInstances × Expr) (Option Expr)

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

/--
  A mapping `(s, t) ↦ isDefEq s t` per transparency level.
  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. -/
structure DefEqCache where
  reducible : PersistentHashMap (Expr × Expr) Bool := {}
  instances : PersistentHashMap (Expr × Expr) Bool := {}
  default   : PersistentHashMap (Expr × Expr) Bool := {}
  all       : PersistentHashMap (Expr × Expr) Bool := {}
  deriving Inhabited

/--
  Cache datastructures for type inference, type class resolution, whnf, and definitional equality.
-/
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`
  defEqTrans     : DefEqCache := {} -- transient cache for terms containing mvars or using nonstandard configuration options, it is frequently reset.
  defEqPerm      : DefEqCache := {} -- permanent cache for terms not containing mvars and using standard configuration options
  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
  /-- We save the `ref` at entry creation time. This is used for reporting errors back to the user. -/
  ref  : Syntax
  lhs  : Level
  rhs  : Level
  /-- Context for the surrounding `isDefEq` call when entry was created. -/
  ctx? : Option DefEqContext
  deriving Inhabited

/--
  `MetaM` monad state.
-/
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 := {}
  /-- Array of postponed universe level constraints -/
  postponed      : PersistentArray PostponedEntry := {}
  deriving Inhabited

/--
  Backtrackable state for the `MetaM` monad.
-/
structure SavedState where
  core        : Core.State
  meta        : State
  deriving Nonempty

/--
  Contextual information for the `MetaM` monad.
-/
structure Context where
  config            : Config               := {}
  /-- Local context -/
  lctx              : LocalContext         := {}
  /-- Local instances in `lctx`. -/
  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
  /--
    A predicate to control whether a constant can be unfolded or not at `whnf`.
    Note that we do not cache results at `whnf` when `canUnfold?` is not `none`. -/
  canUnfold?        : Option (Config → ConstantInfo → CoreM Bool) := none

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`.
@[always_inline]
instance : Monad MetaM := let i := inferInstanceAs (Monad MetaM); { pure := i.pure, bind := i.bind }

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

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 : MonadEnv MetaM where
  getEnv      := return (← getThe Core.State).env
  modifyEnv f := do modifyThe Core.State fun s => { s with env := f s.env, cache := {} }; modify fun s => { s with cache := {} }

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

export Core (instantiateTypeLevelParams instantiateValueLevelParams)

@[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, cache := 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⟩

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

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

@[inline] def resetDefEqPermCaches : MetaM Unit :=
  modifyDefEqPermCache fun _ => {}

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

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

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

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

/-- Return the array of postponed universe level constraints. -/
def getPostponed : MetaM (PersistentArray PostponedEntry) :=
  return (← get).postponed

/-- Set the array of postponed universe level constraints. -/
def setPostponed (postponed : PersistentArray PostponedEntry) : MetaM Unit :=
  modify fun s => { s with postponed := postponed }

/-- Modify the array of postponed universe level constraints. -/
@[inline] def modifyPostponed (f : PersistentArray PostponedEntry → PersistentArray PostponedEntry) : MetaM Unit :=
  modify fun s => { s with postponed := f s.postponed }

/--
  `useEtaStruct inductName` return `true` if we eta for structures is enabled for
  for the inductive datatype `inductName`.

  Recall we have three different settings: `.none` (never use it), `.all` (always use it), `.notClasses`
  (enabled only for structure-like inductive types that are not classes).

  The parameter `inductName` affects the result only if the current setting is `.notClasses`.
-/
def useEtaStruct (inductName : Name) : MetaM Bool := do
  match (← getConfig).etaStruct with
  | .none => return false
  | .all  => return true
  | .notClasses => return !isClass (← getEnv) inductName

/-! 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. -/

/-- Reduces an expression to its Weak Head Normal Form.
This is when the topmost expression has been fully reduced,
but may contain subexpressions which have not been reduced. -/
@[extern 6 "lean_whnf"] opaque whnf : Expr → MetaM Expr
/-- Returns the inferred type of the given expression, or fails if it is not type-correct. -/
@[extern 6 "lean_infer_type"] opaque inferType : Expr → MetaM Expr
@[extern 7 "lean_is_expr_def_eq"] opaque isExprDefEqAux : Expr → Expr → MetaM Bool
@[extern 7 "lean_is_level_def_eq"] opaque isLevelDefEqAux : Level → Level → MetaM Bool
@[extern 6 "lean_synth_pending"] protected opaque 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 ← mkFreshLMVarId
  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

/--
Create a constant with the given name and new universe metavariables.
Example: ``mkConstWithFreshMVarLevels `Monad`` returns `@Monad.{?u, ?v}`
-/
def mkConstWithFreshMVarLevels (declName : Name) : MetaM Expr := do
  let info ← getConstInfo declName
  return mkConst declName (← mkFreshLevelMVarsFor info)

/-- Return current transparency setting/mode. -/
def getTransparency : MetaM TransparencyMode :=
  return (← getConfig).transparency

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

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

/--
Return `some mvarDecl` where `mvarDecl` is `mvarId` declaration in the current metavariable context.
Return `none` if `mvarId` has no declaration in the current metavariable context.
-/
def _root_.Lean.MVarId.findDecl? (mvarId : MVarId) : MetaM (Option MetavarDecl) :=
  return (← getMCtx).findDecl? mvarId

@[deprecated MVarId.findDecl?]
def findMVarDecl? (mvarId : MVarId) : MetaM (Option MetavarDecl) :=
  mvarId.findDecl?

/--
Return `mvarId` declaration in the current metavariable context.
Throw an exception if `mvarId` is not declared in the current metavariable context.
-/
def _root_.Lean.MVarId.getDecl (mvarId : MVarId) : MetaM MetavarDecl := do
  match (← mvarId.findDecl?) with
  | some d => pure d
  | none   => throwError "unknown metavariable '?{mvarId.name}'"

@[deprecated MVarId.getDecl]
def getMVarDecl (mvarId : MVarId) : MetaM MetavarDecl := do
  mvarId.getDecl

/--
Return `mvarId` kind. Throw an exception if `mvarId` is not declared in the current metavariable context.
-/
def _root_.Lean.MVarId.getKind (mvarId : MVarId) : MetaM MetavarKind :=
  return (← mvarId.getDecl).kind

@[deprecated MVarId.getKind]
def getMVarDeclKind (mvarId : MVarId) : MetaM MetavarKind :=
  mvarId.getKind

/-- Return `true` if `e` is a synthetic (or synthetic opaque) metavariable -/
def isSyntheticMVar (e : Expr) : MetaM Bool := do
  if e.isMVar then
     return (← e.mvarId!.getKind) matches .synthetic | .syntheticOpaque
  else
     return false

/--
Set `mvarId` kind in the current metavariable context.
-/
def _root_.Lean.MVarId.setKind (mvarId : MVarId) (kind : MetavarKind) : MetaM Unit :=
  modifyMCtx fun mctx => mctx.setMVarKind mvarId kind

@[deprecated MVarId.setKind]
def setMVarKind (mvarId : MVarId) (kind : MetavarKind) : MetaM Unit :=
  mvarId.setKind kind

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

@[deprecated MVarId.setType]
def setMVarType (mvarId : MVarId) (type : Expr) : MetaM Unit := do
  mvarId.setType type

/--
Return true if the given metavariable is "read-only".
That is, its `depth` is different from the current metavariable context depth.
-/
def _root_.Lean.MVarId.isReadOnly (mvarId : MVarId) : MetaM Bool := do
  return (← mvarId.getDecl).depth != (← getMCtx).depth

@[deprecated MVarId.isReadOnly]
def isReadOnlyExprMVar (mvarId : MVarId) : MetaM Bool := do
  mvarId.isReadOnly

/--
Return true if `mvarId.isReadOnly` return true or if `mvarId` is a synthetic opaque metavariable.

Recall `isDefEq` will not assign a value to `mvarId` if `mvarId.isReadOnlyOrSyntheticOpaque`.
-/
def _root_.Lean.MVarId.isReadOnlyOrSyntheticOpaque (mvarId : MVarId) : MetaM Bool := do
  let mvarDecl ← mvarId.getDecl
  match mvarDecl.kind with
  | MetavarKind.syntheticOpaque => return !(← getConfig).assignSyntheticOpaque
  | _ => return mvarDecl.depth != (← getMCtx).depth

@[deprecated MVarId.isReadOnlyOrSyntheticOpaque]
def isReadOnlyOrSyntheticOpaqueExprMVar (mvarId : MVarId) : MetaM Bool := do
  mvarId.isReadOnlyOrSyntheticOpaque

/--
Return the level of the given universe level metavariable.
-/
def _root_.Lean.LMVarId.getLevel (mvarId : LMVarId) : MetaM Nat := do
  match (← getMCtx).findLevelDepth? mvarId with
  | some depth => return depth
  | _          => throwError "unknown universe metavariable '?{mvarId.name}'"

@[deprecated LMVarId.getLevel]
def getLevelMVarDepth (mvarId : LMVarId) : MetaM Nat :=
  mvarId.getLevel

/--
Return true if the given universe metavariable is "read-only".
That is, its `depth` is different from the current metavariable context depth.
-/
def _root_.Lean.LMVarId.isReadOnly (mvarId : LMVarId) : MetaM Bool :=
  return (← mvarId.getLevel) < (← getMCtx).levelAssignDepth

@[deprecated LMVarId.isReadOnly]
def isReadOnlyLevelMVar (mvarId : LMVarId) : MetaM Bool := do
  mvarId.isReadOnly

/--
Set the user-facing name for the given metavariable.
-/
def _root_.Lean.MVarId.setUserName (mvarId : MVarId) (newUserName : Name) : MetaM Unit :=
  modifyMCtx fun mctx => mctx.setMVarUserName mvarId newUserName

@[deprecated MVarId.setUserName]
def setMVarUserName (mvarId : MVarId) (userNameNew : Name) : MetaM Unit :=
  mvarId.setUserName userNameNew

/--
Throw an exception saying `fvarId` is not declared in the current local context.
-/
def _root_.Lean.FVarId.throwUnknown (fvarId : FVarId) : CoreM α :=
  throwError "unknown free variable '{mkFVar fvarId}'"

@[deprecated FVarId.throwUnknown]
def throwUnknownFVar (fvarId : FVarId) : MetaM α :=
  fvarId.throwUnknown

/--
Return `some decl` if `fvarId` is declared in the current local context.
-/
def _root_.Lean.FVarId.findDecl? (fvarId : FVarId) : MetaM (Option LocalDecl) :=
  return (← getLCtx).find? fvarId

@[deprecated FVarId.findDecl?]
def findLocalDecl? (fvarId : FVarId) : MetaM (Option LocalDecl) :=
  fvarId.findDecl?

/--
  Return the local declaration for the given free variable.
  Throw an exception if local declaration is not in the current local context.
-/
def _root_.Lean.FVarId.getDecl (fvarId : FVarId) : MetaM LocalDecl := do
  match (← getLCtx).find? fvarId with
  | some d => return d
  | none   => fvarId.throwUnknown

@[deprecated FVarId.getDecl]
def getLocalDecl (fvarId : FVarId) : MetaM LocalDecl := do
  fvarId.getDecl

/-- Return the type of the given free variable. -/
def _root_.Lean.FVarId.getType (fvarId : FVarId) : MetaM Expr :=
  return (← fvarId.getDecl).type

/-- Return the binder information for the given free variable. -/
def _root_.Lean.FVarId.getBinderInfo (fvarId : FVarId) : MetaM BinderInfo :=
  return (← fvarId.getDecl).binderInfo

/-- Return `some value` if the given free variable is a let-declaration, and `none` otherwise. -/
def _root_.Lean.FVarId.getValue? (fvarId : FVarId) : MetaM (Option Expr) :=
  return (← fvarId.getDecl).value?

/-- Return the user-facing name for the given free variable. -/
def _root_.Lean.FVarId.getUserName (fvarId : FVarId) : MetaM Name :=
  return (← fvarId.getDecl).userName

/-- Return `true` is the free variable is a let-variable. -/
def _root_.Lean.FVarId.isLetVar (fvarId : FVarId) : MetaM Bool :=
  return (← fvarId.getDecl).isLet

/-- Get the local declaration associated to the given `Expr` in the current local
context. Fails if the given expression is not a fvar or if no such declaration exists. -/
def getFVarLocalDecl (fvar : Expr) : MetaM LocalDecl :=
  fvar.fvarId!.getDecl

/--
Given a user-facing name for a free variable, return its declaration in the current local context.
Throw an exception if free variable is not declared.
-/
def getLocalDeclFromUserName (userName : Name) : MetaM LocalDecl := do
  match (← getLCtx).findFromUserName? userName with
  | some d => pure d
  | none   => throwError "unknown local declaration '{userName}'"

/-- Given a user-facing name for a free variable, return the free variable or throw if not declared. -/
def getFVarFromUserName (userName : Name) : MetaM Expr := do
  let d ← getLocalDeclFromUserName userName
  return Expr.fvar d.fvarId

/--
Lift a `MkBindingM` monadic action `x` to `MetaM`.
-/
@[inline] def liftMkBindingM (x : MetavarContext.MkBindingM α) : MetaM α := do
  match x { lctx := (← getLCtx), mainModule := (← getEnv).mainModule } { mctx := (← getMCtx), ngen := (← getNGen), nextMacroScope := (← getThe Core.State).nextMacroScope } with
  | .ok e sNew => do
    setMCtx sNew.mctx
    modifyThe Core.State fun s => { s with ngen := sNew.ngen, nextMacroScope := sNew.nextMacroScope }
    pure e
  | .error (.revertFailure ..) sNew => do
    setMCtx sNew.mctx
    modifyThe Core.State fun s => { s with ngen := sNew.ngen, nextMacroScope := sNew.nextMacroScope }
    throwError "failed to create binder due to failure when reverting variable dependencies"

/--
Similar to `abstracM` but consider only the first `min n xs.size` entries in `xs`

It is also similar to `Expr.abstractRange`, but handles metavariables correctly.
It uses `elimMVarDeps` to ensure `e` and the type of the free variables `xs` do not
contain a metavariable `?m` s.t. local context of `?m` contains a free variable in `xs`.
-/
def _root_.Lean.Expr.abstractRangeM (e : Expr) (n : Nat) (xs : Array Expr) : MetaM Expr :=
  liftMkBindingM <| MetavarContext.abstractRange e n xs

@[deprecated Expr.abstractRangeM]
def abstractRange (e : Expr) (n : Nat) (xs : Array Expr) : MetaM Expr :=
  e.abstractRangeM n xs

/--
Replace free (or meta) variables `xs` with loose bound variables.
Similar to `Expr.abstract`, but handles metavariables correctly.
-/
def _root_.Lean.Expr.abstractM (e : Expr) (xs : Array Expr) : MetaM Expr :=
  e.abstractRangeM xs.size xs

@[deprecated Expr.abstractM]
def abstract (e : Expr) (xs : Array Expr) : MetaM Expr :=
  e.abstractM xs

/--
Collect forward dependencies for the free variables in `toRevert`.
Recall that when reverting free variables `xs`, we must also revert their forward dependencies.
-/
def collectForwardDeps (toRevert : Array Expr) (preserveOrder : Bool) : MetaM (Array Expr) := do
  liftMkBindingM <| MetavarContext.collectForwardDeps toRevert preserveOrder

/-- Takes an array `xs` of free variables or metavariables and a term `e` that may contain those variables, and abstracts and binds them as universal quantifiers.

- if `usedOnly = true` then only variables that the expression body depends on will appear.
- if `usedLetOnly = true` same as `usedOnly` except for let-bound variables. (That is, local constants which have been assigned a value.)
 -/
def mkForallFVars (xs : Array Expr) (e : Expr) (usedOnly : Bool := false) (usedLetOnly : Bool := true) (binderInfoForMVars := BinderInfo.implicit) : MetaM Expr :=
  if xs.isEmpty then return e else liftMkBindingM <| MetavarContext.mkForall xs e usedOnly usedLetOnly binderInfoForMVars

/-- Takes an array `xs` of free variables and metavariables and a
body term `e` and creates `fun ..xs => e`, suitably
abstracting `e` and the types in `xs`. -/
def mkLambdaFVars (xs : Array Expr) (e : Expr) (usedOnly : Bool := false) (usedLetOnly : Bool := true) (binderInfoForMVars := BinderInfo.implicit) : MetaM Expr :=
  if xs.isEmpty then return e else liftMkBindingM <| MetavarContext.mkLambda xs e usedOnly usedLetOnly binderInfoForMVars

def mkLetFVars (xs : Array Expr) (e : Expr) (usedLetOnly := true) (binderInfoForMVars := BinderInfo.implicit) : MetaM Expr :=
  mkLambdaFVars xs e (usedLetOnly := usedLetOnly) (binderInfoForMVars := binderInfoForMVars)

/-- `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

/-- `withConfig f x` executes `x` using the updated configuration object obtained by applying `f`. -/
@[inline] def withConfig (f : Config → Config) : n α → n α :=
  mapMetaM <| withReader (fun ctx => { ctx with config := f ctx.config })

/--
Executes `x` tracking zeta reductions `Config.trackZeta := true`
-/
@[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 })

/-- `withDefault x` executes `x` using the default transparency setting. -/
@[inline] def withDefault (x : n α) : n α :=
  withTransparency TransparencyMode.default x

/-- `withReducible x` executes `x` using the reducible transparency setting. In this setting only definitions tagged as `[reducible]` are unfolded. -/
@[inline] def withReducible (x : n α) : n α :=
  withTransparency TransparencyMode.reducible x

/--
`withReducibleAndInstances x` executes `x` using the `.instances` transparency setting. In this setting only definitions tagged as `[reducible]`
or type class instances are unfolded.
-/
@[inline] def withReducibleAndInstances (x : n α) : n α :=
  withTransparency TransparencyMode.instances x

/--
Execute `x` ensuring the transparency setting is at least `mode`.
Recall that `.all > .default > .instances > .reducible`.
-/
@[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 `getUnfoldableConst?` at `GetConst.lean` after we define `Instances.lean`.
   This method is only used to implement `isClassQuickConst?`.
   It is very similar to `getUnfoldableConst?`, 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
    return .some constName
  else
    match (← getConstTemp? constName) with
    | some (.defnInfo ..) => return .undef -- We may be able to unfold the definition
    | _ => return .none

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

private def withNewLocalInstanceImp (className : Name) (fvar : Expr) (k : MetaM α) : MetaM α := do
  let localDecl ← getFVarLocalDecl fvar
  if localDecl.isImplementationDetail then
    k
  else
    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`. -/
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.
    - `isClassExpensive` uses `whnf` which depends (indirectly) on the set of local instances. -/
  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
      | .none   => withNewLocalInstancesImp fvars (i+1) k
      | .undef  =>
        match (← isClassExpensive? decl.type) with
        | none   => withNewLocalInstancesImp fvars (i+1) k
        | some c => withNewLocalInstance c fvar <| withNewLocalInstancesImp fvars (i+1) k
      | .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
      execute 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
      | .forallE n d b bi =>
        if fvarsSizeLtMaxFVars fvars maxFVars? then
          let d     := d.instantiateRevRange j fvars.size fvars
          let fvarId ← mkFreshFVarId
          let lctx  := lctx.mkLocalDecl fvarId n d bi
          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


  -- Helper method for isClassExpensive?
  private partial def isClassApp? (type : Expr) (instantiated := false) : MetaM (Option Name) := do
    match type.getAppFn with
    | .const c _ =>
      let env ← getEnv
      if isClass env c then
        return some c
      else
        -- Use whnf to make sure abbreviations are unfolded
        match (← whnf type).getAppFn with
        | .const c _ => if isClass env c then return some c else return none
        | _ => return none
    | .mvar .. =>
      if instantiated then return none
      isClassApp? (← instantiateMVars type) true
    | _ => return none

  private partial def isClassExpensive? (type : Expr) : MetaM (Option Name) :=
    withReducible do -- when testing whether a type is a type class, we only unfold reducible constants.
      forallTelescopeReducingAux type none fun _ type => isClassApp? type

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

end

/--
  `isClass? type` return `some ClsName` if `type` is an instance of the class `ClsName`.
  Example:
  ```
  #eval do
    let x ← mkAppM ``Inhabited #[mkConst ``Nat]
    IO.println (← isClass? x)
    -- (some Inhabited)
  ```
-/
def isClass? (type : Expr) : MetaM (Option Name) :=
  try isClassImp? type catch _ => return 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 building 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
    | _, .lam n d b bi =>
      let d := d.instantiateRevRange j fvars.size fvars
      let fvarId ← mkFreshFVarId
      let lctx := lctx.mkLocalDecl fvarId n d bi
      let fvar := mkFVar fvarId
      process consumeLet lctx (fvars.push fvar) j b
    | true, .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 `lambdaTelescope` but for lambda and let expressions. -/
def lambdaLetTelescope (e : Expr) (k : Array Expr → Expr → n α) : n α :=
  map2MetaM (fun k => lambdaTelescopeImp e true k) k

/--
  Given `e` of the form `fun ..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 lambdaTelescope (e : Expr) (k : Array Expr → Expr → n α) : n α :=
  map2MetaM (fun k => lambdaTelescopeImp e false k) k

/-- Return the parameter names for the given global declaration. -/
def getParamNames (declName : Name) : MetaM (Array Name) := do
  forallTelescopeReducing (← getConstInfo declName).type fun xs _ => do
    xs.mapM fun x => do
      let localDecl ← x.fvarId!.getDecl
      return 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
      | .forallE n d b bi =>
        let d  := d.instantiateRevRange j mvars.size mvars
        let k  := if bi.isInstImplicit then  MetavarKind.synthetic else kind
        let mvar ← mkFreshExprMVar d k n
        let mvars := mvars.push mvar
        let bis   := bis.push bi
        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)

/-- Given `e` of the form `forall ..xs, A`, this combinator will create a new
  metavariable for each `x` in `xs` and instantiate `A` with these.
  Returns a product containing
  - the new metavariables
  - the binder info for the `xs`
  - the instantiated `A`
  -/
def forallMetaTelescope (e : Expr) (kind := MetavarKind.natural) : MetaM (Array Expr × Array BinderInfo × Expr) :=
  forallMetaTelescopeReducingAux e (reducing := false) (maxMVars? := none) kind

/-- Similar to `forallMetaTelescope`, but if `e = forall ..xs, A`
it will reduce `A` to construct further mvars.  -/
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
      return (mvars, bis, type)
    if maxMVars?.isEqSome mvars.size then
      finalize ()
    else
      match type with
      | .lam _ d b bi =>
        let d     := d.instantiateRevRange j mvars.size mvars
        let mvar ← mkFreshExprMVar d
        let mvars := mvars.push mvar
        let bis   := bis.push bi
        process mvars bis j b
      | _ => finalize ()

private def withNewFVar (n : Name) (fvar fvarType : Expr) (k : Expr → MetaM α) : MetaM α := do
  if let some c ← isClass? fvarType then
    withNewLocalInstance c fvar <| k fvar
  else
    k fvar

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

/-- Create a free variable `x` with name, binderInfo and type, add it to the context and run in `k`.
Then revert the context. -/
def withLocalDecl (name : Name) (bi : BinderInfo) (type : Expr) (k : Expr → n α) (kind : LocalDeclKind := .default) : n α :=
  map1MetaM (fun k => withLocalDeclImp name bi type k kind) k

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

/-- Append an array of free variables `xs` to the local context and execute `k xs`.
declInfos takes the form of an array consisting of:
- the name of the variable
- the binder info of the variable
- a type constructor for the variable, where the array consists of all of the free variables
  defined prior to this one. This is needed because the type of the variable may depend on prior variables.
-/
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

/--
 Execute `k` using a local context where any `x` in `xs` that is tagged as
 instance implicit is treated as a regular implicit. -/
def withInstImplicitAsImplict (xs : Array Expr) (k : MetaM α) : MetaM α := do
  let newBinderInfos ← xs.filterMapM fun x => do
    let bi ← x.fvarId!.getBinderInfo
    if bi == .instImplicit then
      return some (x.fvarId!, .implicit)
    else
      return none
  withNewBinderInfos newBinderInfos k

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

/--
  Add the local declaration `<name> : <type> := <val>` to the local context and execute `k x`, where `x` is a new
  free variable corresponding to the `let`-declaration. After executing `k x`, the local context is restored.
-/
def withLetDecl (name : Name) (type : Expr) (val : Expr) (k : Expr → n α) (kind : LocalDeclKind := .default) : n α :=
  map1MetaM (fun k => withLetDeclImp name type val k kind) k

def withLocalInstancesImp (decls : List LocalDecl) (k : MetaM α) : MetaM α := do
  let mut localInsts := (← read).localInstances
  let size := localInsts.size
  for decl in decls do
    unless decl.isImplementationDetail do
      if let some className ← isClass? decl.type then
        localInsts := localInsts.push { className, fvar := decl.toExpr }
  if localInsts.size == size then
    k
  else
    withReader (fun ctx => { ctx with localInstances := localInsts }) k

/-- Register any local instance in `decls` -/
def withLocalInstances (decls : List LocalDecl) : n α → n α :=
  mapMetaM <| withLocalInstancesImp decls

private def withExistingLocalDeclsImp (decls : List LocalDecl) (k : MetaM α) : MetaM α := do
  let ctx ← read
  let lctx := decls.foldl (fun (lctx : LocalContext) decl => lctx.addDecl decl) ctx.lctx
  withReader (fun ctx => { ctx with lctx := lctx }) do
    withLocalInstancesImp decls k

/--
  `withExistingLocalDecls decls k`, adds the given local declarations to the local context,
  and then executes `k`. This method assumes declarations in `decls` have valid `FVarId`s.
  After executing `k`, the local context is restored.

  Remark: this method is used, for example, to implement the `match`-compiler.
  Each `match`-alternative commes with a local declarations (corresponding to pattern variables),
  and we use `withExistingLocalDecls` to add them to the local context before we process
  them.
-/
def withExistingLocalDecls (decls : List LocalDecl) : n α → n α :=
  mapMetaM <| withExistingLocalDeclsImp decls

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

/--
  `withNewMCtxDepth k` executes `k` with a higher metavariable context depth,
  where metavariables created outside the `withNewMCtxDepth` (with a lower depth) cannot be assigned.
  If `allowLevelAssignments` is set to true, then the level metavariable depth
  is not increased, and level metavariables from the outer scope can be
  assigned.  (This is used by TC synthesis.)
-/
def withNewMCtxDepth (k : n α) (allowLevelAssignments := false) : n α :=
  mapMetaM (withNewMCtxDepthImp allowLevelAssignments) k

private def withLocalContextImp (lctx : LocalContext) (localInsts : LocalInstances) (x : MetaM α) : MetaM α := do
  withReader (fun ctx => { ctx with lctx := lctx, localInstances := localInsts }) do
    x

/--
  `withLCtx lctx localInsts k` replaces the local context and local instances, and then executes `k`.
  The local context and instances are restored after executing `k`.
  This method assumes that the local instances in `localInsts` are in the local context `lctx`.
-/
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 ← mvarId.getDecl
  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 _root_.Lean.MVarId.withContext (mvarId : MVarId) : n α → n α :=
  mapMetaM <| withMVarContextImp mvarId

@[deprecated MVarId.withContext]
def withMVarContext (mvarId : MVarId) : n α → n α :=
  mvarId.withContext

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

/--
  `withMCtx mctx k` replaces the metavariable context and then executes `k`.
  The metavariable context is restored after executing `k`.

  This method is used to implement the type class resolution procedure. -/
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

/-- Instantiate assigned universe metavariables in `u`, and then normalize it. -/
def normalizeLevel (u : Level) : MetaM Level := do
  let u ← instantiateLevelMVars u
  pure u.normalize

/-- `whnf` with reducible transparency.-/
def whnfR (e : Expr) : MetaM Expr :=
  withTransparency TransparencyMode.reducible <| whnf e

/-- `whnf` with default transparency.-/
def whnfD (e : Expr) : MetaM Expr :=
  withTransparency TransparencyMode.default <| whnf e

/-- `whnf` with instances transparency.-/
def whnfI (e : Expr) : MetaM Expr :=
  withTransparency TransparencyMode.instances <| whnf e

/--
  Mark declaration `declName` with the attribute `[inline]`.
  This method does not check whether the given declaration is a definition.

  Recall that this attribute can only be set in the same module where `declName` has been declared.
-/
def setInlineAttribute (declName : Name) (kind := Compiler.InlineAttributeKind.inline): MetaM Unit := do
  let env ← getEnv
  match Compiler.setInlineAttribute env declName kind with
  | .ok env    => setEnv env
  | .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
    | .forallE _ _ b _ => instantiateForallAux ps (i+1) (b.instantiate1 p)
    | _                => throwError "invalid instantiateForall, too many parameters"
  else
    return 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
    | .lam _ _ b _ => instantiateLambdaAux ps (i+1) (b.instantiate1 p)
    | _            => throwError "invalid instantiateLambda, too many parameters"
  else
    return 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

/-- Pretty-print the given expression. -/
def ppExprWithInfos (e : Expr) : MetaM FormatWithInfos := do
  let ctxCore  ← readThe Core.Context
  Lean.ppExprWithInfos { env := (← getEnv), mctx := (← getMCtx), lctx := (← getLCtx), opts := (← getOptions), currNamespace := ctxCore.currNamespace, openDecls := ctxCore.openDecls } e

/-- Pretty-print the given expression. -/
def ppExpr (e : Expr) : MetaM Format := (·.fmt) <$> ppExprWithInfos 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 {_} => throwError "failed"
  orElse  := Meta.orElse

@[inline] private def orelseMergeErrorsImp (x y : MetaM α)
    (mergeRef : Syntax → Syntax → Syntax := fun r₁ _ => 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 _ => 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

/-- Return `true` if `declName` is an inductive predicate. That is, `inductive` type in `Prop`. -/
def isInductivePredicate (declName : Name) : MetaM Bool := do
  match (← getEnv).find? declName with
  | some (.inductInfo { type := type, ..}) =>
    forallTelescopeReducing type fun _ type => do
      match (← whnfD type) with
      | .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

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
    | .const _ us => if us.any p then some (e.setPPUniverses true) else none
    | .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 | .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 := 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
        withRef p.ref do
          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
    let numPostponedBegin ← getNumPostponed
    withTraceNode `Meta.isLevelDefEq.postponed
        (fun _ => return m!"processing #{numPostponedBegin} postponed is-def-eq level constraints") do
      let rec loop : MetaM Bool := do
        let numPostponed ← getNumPostponed
        if numPostponed == 0 then
          return true
        else
          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
  /-
    It is not safe to use the `isDefEq` cache between different `isDefEq` calls.
    Reason: different configuration settings, and result depends on the state of the `MetavarContext`
    We have tried in the past to track when the result was independent of the `MetavarContext` state
    but it was not effective. It is more important to cache aggressively inside of a single `isDefEq`
    call because some of the heuristics create many similar subproblems.
    See issue #1102 for an example that triggers an exponential blowup if we don't use this more
    aggressive form of caching.
  -/
  modifyDefEqTransientCache fun _ => {}
  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

/--
  Determines whether two universe level expressions are definitionally equal to each other.
-/
def isLevelDefEq (u v : Level) : MetaM Bool :=
  checkpointDefEq (mayPostpone := true) <| Meta.isLevelDefEqAux u v

/-- See `isDefEq`. -/
def isExprDefEq (t s : Expr) : MetaM Bool :=
  withReader (fun ctx => { ctx with defEqCtx? := some { lhs := t, rhs := s, lctx := ctx.lctx, localInstances := ctx.localInstances } }) do
    /-
    The following `resetDefEqPermCaches` is a workaround. Without it the test suite fails, and we probably cannot compile complex libraries such as Mathlib.
    TODO: investigate why we need this reset.
    Some conjectures:
    - It is not enough to check whether `t` and `s` do not contain metavariables. We would need to check the type
      of all local variables `t` and `s` depend on. If the local variables contain metavariables, the result of `isDefEq` may change if these
      variables are instantiated.
    - Related to the previous one: the operation
      ```lean
      _root_.Lean.MVarId.replaceLocalDeclDefEq (mvarId : MVarId) (fvarId : FVarId) (typeNew : Expr)
      ```
      is probably being misused. We are probably using it to replace a `type` with `typeNew` where these two types
      are definitionally equal IFF we can assign the metavariables in `type`.

    Possible fix: always generate new `FVarId`s when update the type of local variables.
    Drawback: this operation can be quite expensive, and we must evaluate whether it is worth doing to remove the following `reset`.

    Remark: the kernel does *not* update the type of variables in the local context.
    -/
    resetDefEqPermCaches
    checkpointDefEq (mayPostpone := true) <| Meta.isExprDefEqAux t s

/--
  Determines whether two expressions are definitionally equal to each other.

  To control how metavariables are assigned and unified, metavariables and their context have a "depth".
  Given a metavariable `?m` and a `MetavarContext` `mctx`, `?m` is not assigned if `?m.depth != mctx.depth`.
  The combinator `withNewMCtxDepth x` will bump the depth while executing `x`.
  So, `withNewMCtxDepth (isDefEq a b)` is `isDefEq` without any mvar assignment happening
  whereas `isDefEq a b` will assign any metavariables of the current depth in `a` and `b` to unify them.

  For matching (where only mvars in `b` should be assigned), we create the term inside the `withNewMCtxDepth`.
  For an example, see [Lean.Meta.Simp.tryTheoremWithExtraArgs?](https://github.com/leanprover/lean4/blob/master/src/Lean/Meta/Tactic/Simp/Rewrite.lean#L100-L106)
 -/
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

/-- Similar to `isDefEq`, but returns `false` if an exception has been thrown. -/
abbrev isDefEqGuarded (t s : Expr) : MetaM Bool :=
  isExprDefEqGuarded t s

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

/--
  Eta expand the given expression.
  Example:
  ```
  etaExpand (mkConst ``Nat.add)
  ```
  produces `fun x y => Nat.add x y`
-/
def etaExpand (e : Expr) : MetaM Expr :=
  withDefault do forallTelescopeReducing (← inferType e) fun xs _ => mkLambdaFVars xs (mkAppN e xs)

end Meta

builtin_initialize
  registerTraceClass `Meta.isLevelDefEq.postponed

export Meta (MetaM)

end Lean