def Lean.Expr.instantiateBetaRevRange (e : Lean.Expr) (start : Nat) (stop : Nat) (args : Array Lean.Expr) : Lean.Expr

Auxiliary function for instantiating the loose bound variables in e with args[start:stop]. This function is similar to instantiateRevRange, but it applies beta-reduction when we instantiate a bound variable with a lambda expression. Example: Given the term #0 a, and start := 0, stop := 1, args := #[fun x => x] the result is a instead of (fun x => x) a. This reduction is useful when we are inferring the type of eliminator-like applications. For example, given (n m : Nat) (f : Nat → Nat) (h : m = n), the type of Eq.subst (motive := fun x => f m = f x) h rfl is motive n which is (fun (x : Nat) => f m = f x) n This function reduces the new application to f m = f n

We use it to implement inferAppType

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partial def Lean.Expr.instantiateBetaRevRange.visit (start : Nat) (stop : Nat) (args : Array Lean.Expr) (e : Lean.Expr) (offset : Nat) : Lean.MonadStateCacheT (Lean.ExprStructEq × Nat) Lean.Expr Id Lean.Expr

def Lean.Meta.throwFunctionExpected {α : Type} (f : Lean.Expr) : Lean.MetaM α

Equations

• Lean.Meta.throwFunctionExpected f = Lean.throwError (Lean.toMessageData "function expected" ++ Lean.toMessageData (Lean.indentExpr f) ++ Lean.toMessageData "")

def Lean.Meta.throwIncorrectNumberOfLevels {α : Type} (constName : Lake.Name) (us : List Lean.Level) : Lean.MetaM α

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def Lean.Meta.throwTypeExcepted {α : Type} (type : Lean.Expr) : Lean.MetaM α

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• Lean.Meta.throwTypeExcepted type = Lean.throwError (Lean.toMessageData "type expected" ++ Lean.toMessageData (Lean.indentExpr type) ++ Lean.toMessageData "")

def Lean.Meta.getLevel (type : Lean.Expr) : Lean.MetaM Lean.Level

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def Lean.Meta.throwUnknownMVar {α : Type} (mvarId : Lean.MVarId) : Lean.MetaM α

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• Lean.Meta.throwUnknownMVar mvarId = Lean.throwError (Lean.toMessageData "unknown metavariable '?" ++ Lean.toMessageData mvarId.name ++ Lean.toMessageData "'")

@[export lean_infer_type]

def Lean.Meta.inferTypeImp (e : Lean.Expr) : Lean.MetaM Lean.Expr

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• Lean.Meta.inferTypeImp e = Lean.withIncRecDepth (Lean.Meta.withTransparency Lean.Meta.TransparencyMode.default (Lean.Meta.inferTypeImp.infer e))

def Lean.Meta.inferTypeImp.infer (e : Lean.Expr) : Lean.MetaM Lean.Expr

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• Lean.Meta.inferTypeImp.infer (Lean.Expr.const c []) = Lean.Meta.inferConstType c []
• Lean.Meta.inferTypeImp.infer (Lean.Expr.const c us) = Lean.Meta.checkInferTypeCache (Lean.Expr.const c us) (Lean.Meta.inferConstType c us)
• Lean.Meta.inferTypeImp.infer (Lean.Expr.proj n i s) = Lean.Meta.checkInferTypeCache (Lean.Expr.proj n i s) (Lean.Meta.inferProjType n i s)
• Lean.Meta.inferTypeImp.infer (f.app arg) = Lean.Meta.checkInferTypeCache (f.app arg) (Lean.Meta.inferAppType f.getAppFn (f.app arg).getAppArgs)
• Lean.Meta.inferTypeImp.infer (Lean.Expr.mvar mvarId) = Lean.Meta.inferMVarType mvarId
• Lean.Meta.inferTypeImp.infer (Lean.Expr.fvar fvarId) = Lean.Meta.inferFVarType fvarId
• Lean.Meta.inferTypeImp.infer (Lean.Expr.bvar bidx) = Lean.throwError (Lean.toMessageData "unexpected bound variable " ++ Lean.toMessageData (Lean.mkBVar bidx) ++ Lean.toMessageData "")
• Lean.Meta.inferTypeImp.infer (Lean.Expr.mdata data e_2) = Lean.Meta.inferTypeImp.infer e_2
• Lean.Meta.inferTypeImp.infer (Lean.Expr.lit v) = pure v.type
• Lean.Meta.inferTypeImp.infer (Lean.Expr.sort lvl) = pure (Lean.mkSort (Lean.mkLevelSucc lvl))

partial def Lean.Meta.isPropQuick : Lean.Expr → Lean.MetaM Lean.LBool

isPropQuick e is an "approximate" predicate which returns LBool.true if e is a proposition.

def Lean.Meta.isProp (e : Lean.Expr) : Lean.MetaM Bool

isProp e returns true if e is a proposition.

If e contains metavariables, it may not be possible to decide whether is a proposition or not. We return false in this case. We considered using LBool and retuning LBool.undef, but we have no applications for it.

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partial def Lean.Meta.isProofQuick : Lean.Expr → Lean.MetaM Lean.LBool

isProofQuick e is an "approximate" predicate which returns LBool.true if e is a proof.

def Lean.Meta.isProof (e : Lean.Expr) : Lean.MetaM Bool

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partial def Lean.Meta.isTypeQuick : Lean.Expr → Lean.MetaM Lean.LBool

isTypeQuick e is an "approximate" predicate which returns LBool.true if e is a type.

def Lean.Meta.isType (e : Lean.Expr) : Lean.MetaM Bool

Return true iff the type of e is a Sort _.

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def Lean.Meta.typeFormerTypeLevelQuick : Lean.Expr → Option Lean.Level

Equations

• Lean.Meta.typeFormerTypeLevelQuick (Lean.Expr.forallE binderName binderType b binderInfo) = Lean.Meta.typeFormerTypeLevelQuick b
• Lean.Meta.typeFormerTypeLevelQuick (Lean.Expr.sort l) = some l
• Lean.Meta.typeFormerTypeLevelQuick x = none

def Lean.Meta.typeFormerTypeLevel (type : Lean.Expr) : Lean.MetaM (Option Lean.Level)

Return u iff type is Sort u or As → Sort u.

Equations

• Lean.Meta.typeFormerTypeLevel type = match Lean.Meta.typeFormerTypeLevelQuick type with | some l => pure (some l) | none => Lean.Meta.savingCache (Lean.Meta.typeFormerTypeLevel.go type #[])

partial def Lean.Meta.typeFormerTypeLevel.go (type : Lean.Expr) (xs : Array Lean.Expr) : Lean.MetaM (Option Lean.Level)

def Lean.Meta.isTypeFormerType (type : Lean.Expr) : Lean.MetaM Bool

Return true iff type is Sort _ or As → Sort _.

Equations

• Lean.Meta.isTypeFormerType type = do let __do_lift ← Lean.Meta.typeFormerTypeLevel type pure __do_lift.isSome

def Lean.Meta.isPropFormerType (type : Lean.Expr) : Lean.MetaM Bool

Return true iff type is Prop or As → Prop.

Equations

• Lean.Meta.isPropFormerType type = do let __do_lift ← Lean.Meta.typeFormerTypeLevel type pure (__do_lift == some Lean.Level.zero)

def Lean.Meta.isTypeFormer (e : Lean.Expr) : Lean.MetaM Bool

Return true iff e : Sort _ or e : (forall As, Sort _). Remark: it subsumes isType

Equations

• Lean.Meta.isTypeFormer e = do let __do_lift ← Lean.Meta.inferType e Lean.Meta.isTypeFormerType __do_lift