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

Return id e

def Lean.Meta.mkExpectedTypeHint (e : Lean.Expr) (expectedType : Lean.Expr) : Lean.MetaM Lean.Expr

Given e s.t. inferType e is definitionally equal to expectedType, return term @id expectedType e.

def Lean.Meta.mkEq (a : Lean.Expr) (b : Lean.Expr) : Lean.MetaM Lean.Expr

Return a = b.

def Lean.Meta.mkHEq (a : Lean.Expr) (b : Lean.Expr) : Lean.MetaM Lean.Expr

Return HEq a b.

def Lean.Meta.mkEqHEq (a : Lean.Expr) (b : Lean.Expr) : Lean.MetaM Lean.Expr

If a and b have definitionally equal types, return Eq a b, otherwise return HEq a b.

def Lean.Meta.mkEqRefl (a : Lean.Expr) : Lean.MetaM Lean.Expr

Return a proof of a = a.

def Lean.Meta.mkHEqRefl (a : Lean.Expr) : Lean.MetaM Lean.Expr

Return a proof of HEq a a.

def Lean.Meta.mkAbsurd (e : Lean.Expr) (hp : Lean.Expr) (hnp : Lean.Expr) : Lean.MetaM Lean.Expr

Given hp : P and nhp : Not P returns an instance of type e.

def Lean.Meta.mkFalseElim (e : Lean.Expr) (h : Lean.Expr) : Lean.MetaM Lean.Expr

Given h : False, return an instance of type e.

def Lean.Meta.mkEqSymm (h : Lean.Expr) : Lean.MetaM Lean.Expr

Given h : a = b, returns a proof of b = a.

def Lean.Meta.mkEqTrans (h₁ : Lean.Expr) (h₂ : Lean.Expr) : Lean.MetaM Lean.Expr

Given h₁ : a = b and h₂ : b = c returns a proof of a = c.

def Lean.Meta.mkHEqSymm (h : Lean.Expr) : Lean.MetaM Lean.Expr

Given h : HEq a b, returns a proof of HEq b a.

def Lean.Meta.mkHEqTrans (h₁ : Lean.Expr) (h₂ : Lean.Expr) : Lean.MetaM Lean.Expr

Given h₁ : HEq a b, h₂ : HEq b c, returns a proof of HEq a c.

def Lean.Meta.mkEqOfHEq (h : Lean.Expr) : Lean.MetaM Lean.Expr

Given h : Eq a b, returns a proof of HEq a b.

def Lean.Meta.mkCongrArg (f : Lean.Expr) (h : Lean.Expr) : Lean.MetaM Lean.Expr

Given f : α → β and h : a = b, returns a proof of f a = f b.

def Lean.Meta.mkCongrFun (h : Lean.Expr) (a : Lean.Expr) : Lean.MetaM Lean.Expr

Given h : f = g and a : α, returns a proof of f a = g a.

def Lean.Meta.mkCongr (h₁ : Lean.Expr) (h₂ : Lean.Expr) : Lean.MetaM Lean.Expr

Given h₁ : f = g and h₂ : a = b, returns a proof of f a = g b.

def Lean.Meta.mkAppM (constName : Lake.Name) (xs : Array Lean.Expr) : Lean.MetaM Lean.Expr

Return the application constName xs. It tries to fill the implicit arguments before the last element in xs.

Remark: mkAppM `arbitrary #[α] returns @arbitrary.{u} α without synthesizing the implicit argument occurring after α. Given a x : (([Decidable p] → Bool) × Nat, mkAppM `Prod.fst #[x] returns @Prod.fst ([Decidable p] → Bool) Nat x

def Lean.Meta.mkAppM' (f : Lean.Expr) (xs : Array Lean.Expr) : Lean.MetaM Lean.Expr

Similar to mkAppM, but takes an Expr instead of a constant name.

def Lean.Meta.mkAppOptM (constName : Lake.Name) (xs : Array (Option Lean.Expr)) : Lean.MetaM Lean.Expr

Similar to mkAppM, but it allows us to specify which arguments are provided explicitly using Option type. Example: Given Pure.pure {m : Type u → Type v} [Pure m] {α : Type u} (a : α) : m α,

mkAppOptM `Pure.pure #[m, none, none, a]

returns a Pure.pure application if the instance Pure m can be synthesized, and the universe match. Note that,

mkAppM `Pure.pure #[a]

fails because the only explicit argument (a : α) is not sufficient for inferring the remaining arguments, we would need the expected type.

def Lean.Meta.mkAppOptM' (f : Lean.Expr) (xs : Array (Option Lean.Expr)) : Lean.MetaM Lean.Expr

Similar to mkAppOptM, but takes an Expr instead of a constant name

def Lean.Meta.mkEqNDRec (motive : Lean.Expr) (h1 : Lean.Expr) (h2 : Lean.Expr) : Lean.MetaM Lean.Expr

def Lean.Meta.mkEqRec (motive : Lean.Expr) (h1 : Lean.Expr) (h2 : Lean.Expr) : Lean.MetaM Lean.Expr

def Lean.Meta.mkEqMP (eqProof : Lean.Expr) (pr : Lean.Expr) : Lean.MetaM Lean.Expr

def Lean.Meta.mkEqMPR (eqProof : Lean.Expr) (pr : Lean.Expr) : Lean.MetaM Lean.Expr

def Lean.Meta.mkNoConfusion (target : Lean.Expr) (h : Lean.Expr) : Lean.MetaM Lean.Expr

def Lean.Meta.mkPure (monad : Lean.Expr) (e : Lean.Expr) : Lean.MetaM Lean.Expr

Given a monad and e : α, makes pure e.

partial def Lean.Meta.mkProjection (s : Lean.Expr) (fieldName : Lake.Name) : Lean.MetaM Lean.Expr

mkProjection s fieldName return an expression for accessing field fieldName of the structure s. Remark: fieldName may be a subfield of s.

def Lean.Meta.mkListLit (type : Lean.Expr) (xs : List Lean.Expr) : Lean.MetaM Lean.Expr

def Lean.Meta.mkArrayLit (type : Lean.Expr) (xs : List Lean.Expr) : Lean.MetaM Lean.Expr

def Lean.Meta.mkSorry (type : Lean.Expr) (synthetic : Bool) : Lean.MetaM Lean.Expr

def Lean.Meta.mkDecide (p : Lean.Expr) : Lean.MetaM Lean.Expr

Return Decidable.decide p

def Lean.Meta.mkDecideProof (p : Lean.Expr) : Lean.MetaM Lean.Expr

Return a proof for p : Prop using decide p

def Lean.Meta.mkLt (a : Lean.Expr) (b : Lean.Expr) : Lean.MetaM Lean.Expr

Return a < b

def Lean.Meta.mkLe (a : Lean.Expr) (b : Lean.Expr) : Lean.MetaM Lean.Expr

Return a <= b

def Lean.Meta.mkDefault (α : Lean.Expr) : Lean.MetaM Lean.Expr

Return Inhabited.default α

def Lean.Meta.mkOfNonempty (α : Lean.Expr) : Lean.MetaM Lean.Expr

Return @Classical.ofNonempty α _

def Lean.Meta.mkSyntheticSorry (type : Lean.Expr) : Lean.MetaM Lean.Expr

Return sorryAx type

def Lean.Meta.mkFunExt (h : Lean.Expr) : Lean.MetaM Lean.Expr

Return funext h

def Lean.Meta.mkPropExt (h : Lean.Expr) : Lean.MetaM Lean.Expr

Return propext h

def Lean.Meta.mkLetCongr (h₁ : Lean.Expr) (h₂ : Lean.Expr) : Lean.MetaM Lean.Expr

Return let_congr h₁ h₂

def Lean.Meta.mkLetValCongr (b : Lean.Expr) (h : Lean.Expr) : Lean.MetaM Lean.Expr

Return let_val_congr b h

def Lean.Meta.mkLetBodyCongr (a : Lean.Expr) (h : Lean.Expr) : Lean.MetaM Lean.Expr

Return let_body_congr a h

def Lean.Meta.mkOfEqTrue (h : Lean.Expr) : Lean.MetaM Lean.Expr

Return of_eq_true h

def Lean.Meta.mkEqTrue (h : Lean.Expr) : Lean.MetaM Lean.Expr

Return eq_true h

def Lean.Meta.mkEqFalse (h : Lean.Expr) : Lean.MetaM Lean.Expr

Return eq_false h h must have type definitionally equal to ¬ p in the current reducibility setting.

def Lean.Meta.mkEqFalse' (h : Lean.Expr) : Lean.MetaM Lean.Expr

Return eq_false' h h must have type definitionally equal to p → False in the current reducibility setting.

def Lean.Meta.mkImpCongr (h₁ : Lean.Expr) (h₂ : Lean.Expr) : Lean.MetaM Lean.Expr

def Lean.Meta.mkImpCongrCtx (h₁ : Lean.Expr) (h₂ : Lean.Expr) : Lean.MetaM Lean.Expr

def Lean.Meta.mkImpDepCongrCtx (h₁ : Lean.Expr) (h₂ : Lean.Expr) : Lean.MetaM Lean.Expr

def Lean.Meta.mkForallCongr (h : Lean.Expr) : Lean.MetaM Lean.Expr

def Lean.Meta.isMonad? (m : Lean.Expr) : Lean.MetaM (Option Lean.Expr)

Return instance for [Monad m] if there is one

def Lean.Meta.mkNumeral (type : Lean.Expr) (n : Nat) : Lean.MetaM Lean.Expr

Return (n : type), a numeric literal of type type. The method fails if we don't have an instance OfNat type n

def Lean.Meta.mkAdd (a : Lean.Expr) (b : Lean.Expr) : Lean.MetaM Lean.Expr

Return a + b using a heterogeneous +. This method assumes a and b have the same type.

def Lean.Meta.mkSub (a : Lean.Expr) (b : Lean.Expr) : Lean.MetaM Lean.Expr

Return a - b using a heterogeneous -. This method assumes a and b have the same type.

def Lean.Meta.mkMul (a : Lean.Expr) (b : Lean.Expr) : Lean.MetaM Lean.Expr

Return a * b using a heterogeneous *. This method assumes a and b have the same type.

def Lean.Meta.mkLE (a : Lean.Expr) (b : Lean.Expr) : Lean.MetaM Lean.Expr

Return a ≤ b. This method assumes a and b have the same type.

def Lean.Meta.mkLT (a : Lean.Expr) (b : Lean.Expr) : Lean.MetaM Lean.Expr

Return a < b. This method assumes a and b have the same type.

def Lean.Meta.mkIffOfEq (h : Lean.Expr) : Lean.MetaM Lean.Expr

Given h : a = b, return a proof for a ↔ b.