inductive Lean.TransformStep : Type

• done (e : Lean.Expr) : Lean.TransformStep

  Return expression without visiting any subexpressions.

• visit (e : Lean.Expr) : Lean.TransformStep

  Visit expression (which should be different from current expression) instead. The new expression e is passed to pre again.

• continue (e? : Option Lean.Expr := none) : Lean.TransformStep

  Continue transformation with the given expression (defaults to current expression). For pre, this means visiting the children of the expression. For post, this is equivalent to returning done.

instance Lean.instInhabitedTransformStep : Inhabited Lean.TransformStep

Equations

• Lean.instInhabitedTransformStep = { default := Lean.TransformStep.done default }

instance Lean.instReprTransformStep : Repr Lean.TransformStep

Equations

• Lean.instReprTransformStep = { reprPrec := Lean.reprTransformStep✝ }

def Lean.Core.transform {m : Type → Type} [Monad m] [MonadLiftT Lean.CoreM m] [MonadControlT Lean.CoreM m] (input : Lean.Expr) (pre : Lean.Expr → m Lean.TransformStep := fun (x : Lean.Expr) => pure Lean.TransformStep.continue) (post : Lean.Expr → m Lean.TransformStep := fun (e : Lean.Expr) => pure (Lean.TransformStep.done e)) : m Lean.Expr

Transform the expression input using pre and post.

• First pre is invoked with the current expression and recursion is continued according to the TransformStep result. In all cases, the expression contained in the result, if any, must be definitionally equal to the current expression.
• After recursion, if any, post is invoked on the resulting expression.

The term s in both pre s and post s may contain loose bound variables. So, this method is not appropriate for if one needs to apply operations (e.g., whnf, inferType) that do not handle loose bound variables. Consider using Meta.transform to avoid loose bound variables.

This method is useful for applying transformations such as beta-reduction and delta-reduction.

Equations

• Lean.Core.transform input pre post = (Lean.Core.transform.visit pre post { } { monadLift := fun {α : Type} (x : ST IO.RealWorld α) => liftM (liftM x) } input).run

partial def Lean.Core.transform.visit {m : Type → Type} [Monad m] [MonadControlT Lean.CoreM m] (pre : Lean.Expr → m Lean.TransformStep := fun (x : Lean.Expr) => pure Lean.TransformStep.continue) (post : Lean.Expr → m Lean.TransformStep := fun (e : Lean.Expr) => pure (Lean.TransformStep.done e)) (x✝ : STWorld IO.RealWorld m) : MonadLiftT (ST IO.RealWorld) m → (e : Lean.Expr) → Lean.MonadCacheT Lean.ExprStructEq Lean.Expr m Lean.Expr

partial def Lean.Core.transform.visit.visitPost {m : Type → Type} [Monad m] [MonadControlT Lean.CoreM m] (pre : Lean.Expr → m Lean.TransformStep := fun (x : Lean.Expr) => pure Lean.TransformStep.continue) (post : Lean.Expr → m Lean.TransformStep := fun (e : Lean.Expr) => pure (Lean.TransformStep.done e)) (x✝ : STWorld IO.RealWorld m) : MonadLiftT (ST IO.RealWorld) m → (e : Lean.Expr) → Lean.MonadCacheT Lean.ExprStructEq Lean.Expr m Lean.Expr

def Lean.Core.betaReduce (e : Lean.Expr) : Lean.CoreM Lean.Expr

Equations

• Lean.Core.betaReduce e = Lean.Core.transform e fun (e : Lean.Expr) => pure (if e.isHeadBetaTarget = true then Lean.TransformStep.visit e.headBeta else Lean.TransformStep.continue)

def Lean.Meta.transform {m : Type → Type} [Monad m] [MonadLiftT Lean.MetaM m] [MonadControlT Lean.MetaM m] (input : Lean.Expr) (pre : Lean.Expr → m Lean.TransformStep := fun (x : Lean.Expr) => pure Lean.TransformStep.continue) (post : Lean.Expr → m Lean.TransformStep := fun (e : Lean.Expr) => pure (Lean.TransformStep.done e)) (usedLetOnly skipConstInApp : Bool := false) : m Lean.Expr

Similar to Core.transform, but terms provided to pre and post do not contain loose bound variables. So, it is safe to use any MetaM method at pre and post.

If skipConstInApp := true, then for an expression mkAppN (.const f) args, the subexpression .const f is not visited again. Put differently: every .const f is visited once, with its arguments if present, on its own otherwise.

Equations

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partial def Lean.Meta.transform.visit {m : Type → Type} [Monad m] [MonadLiftT Lean.MetaM m] [MonadControlT Lean.MetaM m] (pre : Lean.Expr → m Lean.TransformStep := fun (x : Lean.Expr) => pure Lean.TransformStep.continue) (post : Lean.Expr → m Lean.TransformStep := fun (e : Lean.Expr) => pure (Lean.TransformStep.done e)) (usedLetOnly skipConstInApp : Bool := false) (x✝ : STWorld IO.RealWorld m) : MonadLiftT (ST IO.RealWorld) m → (e : Lean.Expr) → Lean.MonadCacheT Lean.ExprStructEq Lean.Expr m Lean.Expr

partial def Lean.Meta.transform.visit.visitPost {m : Type → Type} [Monad m] [MonadLiftT Lean.MetaM m] [MonadControlT Lean.MetaM m] (pre : Lean.Expr → m Lean.TransformStep := fun (x : Lean.Expr) => pure Lean.TransformStep.continue) (post : Lean.Expr → m Lean.TransformStep := fun (e : Lean.Expr) => pure (Lean.TransformStep.done e)) (usedLetOnly skipConstInApp : Bool := false) (x✝ : STWorld IO.RealWorld m) : MonadLiftT (ST IO.RealWorld) m → (e : Lean.Expr) → Lean.MonadCacheT Lean.ExprStructEq Lean.Expr m Lean.Expr

partial def Lean.Meta.transform.visit.visitLambda {m : Type → Type} [Monad m] [MonadLiftT Lean.MetaM m] [MonadControlT Lean.MetaM m] (pre : Lean.Expr → m Lean.TransformStep := fun (x : Lean.Expr) => pure Lean.TransformStep.continue) (post : Lean.Expr → m Lean.TransformStep := fun (e : Lean.Expr) => pure (Lean.TransformStep.done e)) (usedLetOnly skipConstInApp : Bool := false) (x✝ : STWorld IO.RealWorld m) : MonadLiftT (ST IO.RealWorld) m → (fvars : Array Lean.Expr) → (e : Lean.Expr) → Lean.MonadCacheT Lean.ExprStructEq Lean.Expr m Lean.Expr

partial def Lean.Meta.transform.visit.visitForall {m : Type → Type} [Monad m] [MonadLiftT Lean.MetaM m] [MonadControlT Lean.MetaM m] (pre : Lean.Expr → m Lean.TransformStep := fun (x : Lean.Expr) => pure Lean.TransformStep.continue) (post : Lean.Expr → m Lean.TransformStep := fun (e : Lean.Expr) => pure (Lean.TransformStep.done e)) (usedLetOnly skipConstInApp : Bool := false) (x✝ : STWorld IO.RealWorld m) : MonadLiftT (ST IO.RealWorld) m → (fvars : Array Lean.Expr) → (e : Lean.Expr) → Lean.MonadCacheT Lean.ExprStructEq Lean.Expr m Lean.Expr

partial def Lean.Meta.transform.visit.visitLet {m : Type → Type} [Monad m] [MonadLiftT Lean.MetaM m] [MonadControlT Lean.MetaM m] (pre : Lean.Expr → m Lean.TransformStep := fun (x : Lean.Expr) => pure Lean.TransformStep.continue) (post : Lean.Expr → m Lean.TransformStep := fun (e : Lean.Expr) => pure (Lean.TransformStep.done e)) (usedLetOnly skipConstInApp : Bool := false) (x✝ : STWorld IO.RealWorld m) : MonadLiftT (ST IO.RealWorld) m → (fvars : Array Lean.Expr) → (e : Lean.Expr) → Lean.MonadCacheT Lean.ExprStructEq Lean.Expr m Lean.Expr

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

Equations

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def Lean.Meta.zetaDeltaFVars (e : Lean.Expr) (fvars : Array Lean.FVarId) : Lean.MetaM Lean.Expr

Zeta reduces only the provided fvars, beta reducing the substitutions.

Equations

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def Lean.Meta.unfoldDeclsFrom (biggerEnv : Lean.Environment) (e : Lean.Expr) : Lean.CoreM Lean.Expr

Unfold definitions and theorems in e that are not in the current environment, but are in biggerEnv.

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def Lean.Meta.eraseInaccessibleAnnotations (e : Lean.Expr) : Lean.CoreM Lean.Expr

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def Lean.Meta.erasePatternRefAnnotations (e : Lean.Expr) : Lean.CoreM Lean.Expr

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