inductive Lean.Meta.ApplyNewGoals : Type

Controls which new mvars are turned in to goals by the apply tactic.

• nonDependentFirst mvars that don't depend on other goals appear first in the goal list.
• nonDependentOnly only mvars that don't depend on other goals are added to goal list.
• all all unassigned mvars are added to the goal list.

• nonDependentFirst: Lean.Meta.ApplyNewGoals
• nonDependentOnly: Lean.Meta.ApplyNewGoals
• all: Lean.Meta.ApplyNewGoals

structure Lean.Meta.ApplyConfig : Type

Configures the behaviour of the apply tactic.

• newGoals : Lean.Meta.ApplyNewGoals
• synthAssignedInstances : Bool

  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.

• allowSynthFailures : Bool

  If allowSynthFailures is true, then apply will return instance implicit arguments for which typeclass search failed as new goals.

• approx : Bool

  If approx := true, then we turn on isDefEq approximations. That is, we use the approxDefEq combinator.

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 : Lake.Name) (mvarId : Lean.MVarId) (newMVars : Array Lean.Expr) (binderInfos : Array Lean.BinderInfo) (synthAssignedInstances : Bool) (allowSynthFailures : Bool) : Lean.MetaM Unit

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

Equations

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def Lean.Meta.postprocessAppMVars (tacticName : Lake.Name) (mvarId : Lean.MVarId) (newMVars : Array Lean.Expr) (binderInfos : Array Lean.BinderInfo) (synthAssignedInstances : optParam Bool true) (allowSynthFailures : optParam 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.

Equations

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def Lean.MVarId.apply (mvarId : Lean.MVarId) (e : Lean.Expr) (cfg : optParam 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.

Equations

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

Equations

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@[deprecated Lean.MVarId.apply]

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

Equations

• Lean.Meta.apply mvarId e cfg = mvarId.apply e cfg

def Lean.MVarId.applyConst (mvar : Lean.MVarId) (c : Lake.Name) (cfg : optParam 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.

Equations

• mvar.applyConst c cfg = do let __do_lift ← Lean.Meta.mkConstWithFreshMVarLevels c mvar.apply __do_lift cfg

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

Equations

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partial def Lean.MVarId.splitAndCore.go (tag : Lake.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

@[deprecated Lean.MVarId.splitAnd]

def Lean.Meta.splitAnd (mvarId : Lean.MVarId) : Lean.MetaM (List Lean.MVarId)

Equations

• Lean.Meta.splitAnd mvarId = mvarId.splitAnd

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

Equations

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def Lean.MVarId.nthConstructor (name : Lake.Name) (idx : Nat) (expected? : optParam (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

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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.

Equations

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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.

Equations

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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

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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.

Equations

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