def Lean.Meta.getExpectedNumArgsAux (e : Lean.Expr) : Lean.MetaM (Nat × Bool)

Compute the number of expected arguments and whether the result type is of the form (?m ...) where ?m is an unassigned metavariable.

Equations

• Lean.Meta.getExpectedNumArgsAux e = Lean.Meta.withDefault (Lean.Meta.forallTelescopeReducing e fun (xs : Array Lean.Expr) (body : Lean.Expr) => pure (xs.size, body.getAppFn.isMVar))

def Lean.Meta.getExpectedNumArgs (e : Lean.Expr) : Lean.MetaM Nat

Equations

• Lean.Meta.getExpectedNumArgs e = do let __discr ← Lean.Meta.getExpectedNumArgsAux e match __discr with | (numArgs, snd) => pure numArgs

def Lean.Meta.synthAppInstances (tacticName : Lean.Name) (mvarId : Lean.MVarId) (mvarsNew : Array Lean.Expr) (binderInfos : Array Lean.BinderInfo) (synthAssignedInstances allowSynthFailures : Bool) : Lean.MetaM Unit

def Lean.Meta.synthAppInstances.step (tacticName : Lean.Name) (mvarId : Lean.MVarId) (allowSynthFailures : Bool) (mvars : Array Lean.Expr) : Lean.MetaM (Array Lean.Expr)

Try to synthesize instances for the metavariables mvars. Returns metavariables that still need to be synthesized. We can view the resulting array as the set of metavariables that we should try again. This is needed when applying or rewriting with functions with complex instances. For example, consider rw [@map_smul] where map_smul is

map_smul {F : Type u_1} {M : Type u_2} {N : Type u_3} {φ : M → N}
         {X : Type u_4} {Y : Type u_5}
         [SMul M X] [SMul N Y] [FunLike F X Y] [MulActionSemiHomClass F φ X Y]
         (f : F) (c : M) (x : X) : DFunLike.coe f (c • x) = φ c • DFunLike.coe f x

and MulActionSemiHomClass is defined as

class MulActionSemiHomClass (F : Type _)
   {M N : outParam (Type _)} (φ : outParam (M → N))
   (X Y : outParam (Type _)) [SMul M X] [SMul N Y] [FunLike F X Y] : Prop where

The left-hand-side of the equation does not bind N. Thus, SMul N Y cannot be synthesized until we synthesize MulActionSemiHomClass F φ X Y. Note that N is an output parameter for MulActionSemiHomClass.

Equations

• One or more equations did not get rendered due to their size.

def Lean.Meta.appendParentTag (mvarId : Lean.MVarId) (newMVars : Array Lean.Expr) (binderInfos : Array Lean.BinderInfo) : Lean.MetaM Unit

def Lean.Meta.postprocessAppMVars (tacticName : Lean.Name) (mvarId : Lean.MVarId) (newMVars : Array Lean.Expr) (binderInfos : Array Lean.BinderInfo) (synthAssignedInstances : Bool := true) (allowSynthFailures : Bool := false) : Lean.MetaM Unit

If synthAssignedInstances is true, then apply will synthesize instance implicit arguments even if they have assigned by isDefEq, and then check whether the synthesized value matches the one inferred. The congr tactic sets this flag to false.

def Lean.MVarId.apply (mvarId : Lean.MVarId) (e : Lean.Expr) (cfg : Lean.Meta.ApplyConfig := { newGoals := Lean.Meta.ApplyNewGoals.nonDependentFirst, synthAssignedInstances := true, allowSynthFailures := false, approx := true }) : Lean.MetaM (List Lean.MVarId)

Close the given goal using apply e.

@[irreducible]

def Lean.MVarId.apply.go (mvarId : Lean.MVarId) (cfg : Lean.Meta.ApplyConfig := { newGoals := Lean.Meta.ApplyNewGoals.nonDependentFirst, synthAssignedInstances := true, allowSynthFailures := false, approx := true }) (targetType eType : Lean.Expr) (rangeNumArgs : Std.Range) (i : Nat) : Lean.MetaM (Array Lean.Expr × Array Lean.BinderInfo)

def Lean.MVarId.applyConst (mvar : Lean.MVarId) (c : Lean.Name) (cfg : Lean.Meta.ApplyConfig := { newGoals := Lean.Meta.ApplyNewGoals.nonDependentFirst, synthAssignedInstances := true, allowSynthFailures := false, approx := true }) : Lean.MetaM (List Lean.MVarId)

Short-hand for applying a constant to the goal.

def Lean.MVarId.splitAndCore (mvarId : Lean.MVarId) : Lean.MetaM (List Lean.MVarId)

Equations

• One or more equations did not get rendered due to their size.

partial def Lean.MVarId.splitAndCore.go (tag : Lean.Name) (type : Lean.Expr) : StateRefT' IO.RealWorld (Array Lean.MVarId) Lean.MetaM Lean.Expr

@[reducible, inline]

abbrev Lean.MVarId.splitAnd (mvarId : Lean.MVarId) : Lean.MetaM (List Lean.MVarId)

Apply And.intro as much as possible to goal mvarId.

Equations

• mvarId.splitAnd = mvarId.splitAndCore

def Lean.MVarId.exfalso (mvarId : Lean.MVarId) : Lean.MetaM Lean.MVarId

Equations

• One or more equations did not get rendered due to their size.

def Lean.MVarId.nthConstructor (name : Lean.Name) (idx : Nat) (expected? : Option Nat := none) (goal : Lean.MVarId) : Lean.MetaM (List Lean.MVarId)

Apply the n-th constructor of the target type, checking that it is an inductive type, and that there are the expected number of constructors.

Equations

• One or more equations did not get rendered due to their size.

def Lean.MVarId.iffOfEq (mvarId : Lean.MVarId) : Lean.MetaM Lean.MVarId

Try to convert an Iff into an Eq by applying iff_of_eq. If successful, returns the new goal, and otherwise returns the original MVarId.

This may be regarded as being a special case of Lean.MVarId.liftReflToEq, specifically for Iff.

def Lean.MVarId.propext (mvarId : Lean.MVarId) : Lean.MetaM Lean.MVarId

Try to convert an Eq into an Iff by applying propext. If successful, then returns then new goal, otherwise returns the original MVarId.

def Lean.MVarId.proofIrrelHeq (mvarId : Lean.MVarId) : Lean.MetaM Bool

Try to close the goal using proof_irrel_heq. Returns whether or not it succeeds.

We need to be somewhat careful not to assign metavariables while doing this, otherwise we might specialize Sort _ to Prop.

Equations

• One or more equations did not get rendered due to their size.

def Lean.MVarId.subsingletonElim (mvarId : Lean.MVarId) : Lean.MetaM Bool

Try to close the goal using Subsingleton.elim. Returns whether or not it succeeds.

We are careful to apply Subsingleton.elim in a way that does not assign any metavariables. This is to prevent the Subsingleton Prop instance from being used as justification to specialize Sort _ to Prop.