383 lines
16 KiB
Text
383 lines
16 KiB
Text
/-
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Copyright (c) 2019 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Leonardo de Moura
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-/
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import Lean.Structure
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import Lean.Util.Recognizers
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import Lean.Meta.SynthInstance
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import Lean.Meta.Check
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namespace Lean
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namespace Meta
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variables {m : Type → Type} [MonadLiftT MetaM m]
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private def mkIdImp (e : Expr) : MetaM Expr := do
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type ← inferType e;
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u ← getLevel type;
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pure $ mkApp2 (mkConst `id [u]) type e
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/-- Return `id e` -/
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def mkId (e : Expr) : m Expr := liftMetaM $ mkIdImp e
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private def mkExpectedTypeHint (e : Expr) (expectedType : Expr) : MetaM Expr := do
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u ← getLevel expectedType;
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pure $ mkApp2 (mkConst `id [u]) expectedType e
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/-- Given `e` s.t. `inferType e` is definitionally equal to `expectedType`, return
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term `@id expectedType e`. -/
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def mkExpectedTypeHint (e : Expr) (expectedType : Expr) : m Expr :=
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liftMetaM $ mkExpectedTypeHint e expectedType
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private def mkEqImp (a b : Expr) : MetaM Expr := do
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aType ← inferType a;
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u ← getLevel aType;
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pure $ mkApp3 (mkConst `Eq [u]) aType a b
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def mkEq (a b : Expr) : m Expr := liftMetaM $ mkEqImp a b
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private def mkHEqImp (a b : Expr) : MetaM Expr := do
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aType ← inferType a;
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bType ← inferType b;
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u ← getLevel aType;
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pure $ mkApp4 (mkConst `HEq [u]) aType a bType b
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def mkHEq (a b : Expr) : m Expr := liftMetaM $ mkHEqImp a b
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private def mkEqReflImp (a : Expr) : MetaM Expr := do
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aType ← inferType a;
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u ← getLevel aType;
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pure $ mkApp2 (mkConst `Eq.refl [u]) aType a
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def mkEqRefl (a : Expr) : m Expr := liftMetaM $ mkEqReflImp a
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private def mkHEqReflImp (a : Expr) : MetaM Expr := do
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aType ← inferType a;
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u ← getLevel aType;
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pure $ mkApp2 (mkConst `HEq.refl [u]) aType a
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def mkHEqRefl (a : Expr) : m Expr := liftMetaM $ mkHEqReflImp a
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private def infer (h : Expr) : MetaM Expr := do
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hType ← inferType h;
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whnfD hType
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private def hasTypeMsg (e type : Expr) : MessageData :=
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indentExpr e ++ Format.line ++ "has type" ++ indentExpr type
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private def throwAppBuilderException {α} (op : Name) (msg : MessageData) : MetaM α :=
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throwError ("AppBuilder for '" ++ op ++ "', " ++ msg)
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private def mkEqSymmImp (h : Expr) : MetaM Expr :=
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if h.isAppOf `Eq.refl then pure h
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else do
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hType ← infer h;
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match hType.eq? with
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| some (α, a, b) => do u ← getLevel α; pure $ mkApp4 (mkConst `Eq.symm [u]) α a b h
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| none => throwAppBuilderException `Eq.symm ("equality proof expected" ++ hasTypeMsg h hType)
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def mkEqSymm (h : Expr) : m Expr := liftMetaM $ mkEqSymmImp h
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private def mkEqTransImp (h₁ h₂ : Expr) : MetaM Expr :=
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if h₁.isAppOf `Eq.refl then pure h₂
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else if h₂.isAppOf `Eq.refl then pure h₁
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else do
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hType₁ ← infer h₁;
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hType₂ ← infer h₂;
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match hType₁.eq?, hType₂.eq? with
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| some (α, a, b), some (_, _, c) =>
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do u ← getLevel α; pure $ mkApp6 (mkConst `Eq.trans [u]) α a b c h₁ h₂
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| none, _ => throwAppBuilderException `Eq.trans ("equality proof expected" ++ hasTypeMsg h₁ hType₁)
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| _, none => throwAppBuilderException `Eq.trans ("equality proof expected" ++ hasTypeMsg h₂ hType₂)
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def mkEqTrans (h₁ h₂ : Expr) : m Expr := liftMetaM $ mkEqTransImp h₁ h₂
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private def mkHEqSymmImp (h : Expr) : MetaM Expr :=
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if h.isAppOf `HEq.refl then pure h
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else do
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hType ← infer h;
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match hType.heq? with
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| some (α, a, β, b) => do u ← getLevel α; pure $ mkApp5 (mkConst `HEq.symm [u]) α β a b h
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| none => throwAppBuilderException `HEq.symm ("heterogeneous equality proof expected" ++ hasTypeMsg h hType)
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def mkHEqSymm (h : Expr) : m Expr := liftMetaM $ mkHEqSymmImp h
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private def mkHEqTransImp (h₁ h₂ : Expr) : MetaM Expr :=
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if h₁.isAppOf `HEq.refl then pure h₂
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else if h₂.isAppOf `HEq.refl then pure h₁
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else do
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hType₁ ← infer h₁;
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hType₂ ← infer h₂;
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match hType₁.heq?, hType₂.heq? with
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| some (α, a, β, b), some (_, _, γ, c) => do
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u ← getLevel α; pure $ mkApp8 (mkConst `HEq.trans [u]) α β γ a b c h₁ h₂
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| none, _ => throwAppBuilderException `HEq.trans ("heterogeneous equality proof expected" ++ hasTypeMsg h₁ hType₁)
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| _, none => throwAppBuilderException `HEq.trans ("heterogeneous equality proof expected" ++ hasTypeMsg h₂ hType₂)
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def mkHEqTrans (h₁ h₂ : Expr) : m Expr := liftMetaM $ mkHEqTransImp h₁ h₂
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private def mkEqOfHEqImp (h : Expr) : MetaM Expr := do
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hType ← infer h;
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match hType.heq? with
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| some (α, a, β, b) => do
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unlessM (isDefEq α β) $ throwAppBuilderException `eqOfHEq
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("heterogeneous equality types are not definitionally equal" ++ indentExpr α ++ Format.line ++ "is not definitionally equal to" ++ indentExpr β);
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u ← getLevel α;
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pure $ mkApp4 (mkConst `eqOfHEq [u]) α a b h
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| _ =>
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throwAppBuilderException `HEq.trans ("heterogeneous equality proof expected" ++ indentExpr h)
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def mkEqOfHEq (h : Expr) : m Expr := liftMetaM $ mkEqOfHEqImp h
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private def mkCongrArgImp (f h : Expr) : MetaM Expr := do
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hType ← infer h;
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fType ← infer f;
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match fType.arrow?, hType.eq? with
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| some (α, β), some (_, a, b) => do
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u ← getLevel α; v ← getLevel β; pure $ mkApp6 (mkConst `congrArg [u, v]) α β a b f h
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| none, _ => throwAppBuilderException `congrArg ("non-dependent function expected" ++ hasTypeMsg f fType)
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| _, none => throwAppBuilderException `congrArg ("equality proof expected" ++ hasTypeMsg h hType)
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def mkCongrArg (f h : Expr) : m Expr := liftMetaM $ mkCongrArgImp f h
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private def mkCongrFunImp (h a : Expr) : MetaM Expr := do
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hType ← infer h;
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match hType.eq? with
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| some (ρ, f, g) => do
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ρ ← whnfD ρ;
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match ρ with
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| Expr.forallE n α β _ => do
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let β' := Lean.mkLambda n BinderInfo.default α β;
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u ← getLevel α;
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v ← getLevel (mkApp β' a);
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pure $ mkApp6 (mkConst `congrFun [u, v]) α β' f g h a
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| _ => throwAppBuilderException `congrFun ("equality proof between functions expected" ++ hasTypeMsg h hType)
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| _ => throwAppBuilderException `congrFun ("equality proof expected" ++ hasTypeMsg h hType)
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def mkCongrFun (h a : Expr) : m Expr := liftMetaM $ mkCongrFunImp h a
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private def mkCongrImp (h₁ h₂ : Expr) : MetaM Expr := do
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hType₁ ← infer h₁;
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hType₂ ← infer h₂;
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match hType₁.eq?, hType₂.eq? with
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| some (ρ, f, g), some (α, a, b) => do
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ρ ← whnfD ρ;
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match ρ.arrow? with
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| some (_, β) => do
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u ← getLevel α;
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v ← getLevel β;
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pure $ mkApp8 (mkConst `congr [u, v]) α β f g a b h₁ h₂
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| _ => throwAppBuilderException `congr ("non-dependent function expected" ++ hasTypeMsg h₁ hType₁)
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| none, _ => throwAppBuilderException `congr ("equality proof expected" ++ hasTypeMsg h₁ hType₁)
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| _, none => throwAppBuilderException `congr ("equality proof expected" ++ hasTypeMsg h₂ hType₂)
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def mkCongr (h₁ h₂ : Expr) : m Expr := liftMetaM $ mkCongrImp h₁ h₂
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private def mkAppMFinal (methodName : Name) (f : Expr) (args : Array Expr) (instMVars : Array MVarId) : MetaM Expr := do
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instMVars.forM $ fun mvarId => do {
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mvarDecl ← getMVarDecl mvarId;
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mvarVal ← synthInstance mvarDecl.type;
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assignExprMVar mvarId mvarVal
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};
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result ← instantiateMVars (mkAppN f args);
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whenM (hasAssignableMVar result) $ throwAppBuilderException methodName ("result contains metavariables" ++ indentExpr result);
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pure result
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private partial def mkAppMAux (f : Expr) (xs : Array Expr) : Nat → Array Expr → Nat → Array MVarId → Expr → MetaM Expr
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| i, args, j, instMVars, Expr.forallE n d b c => do
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let d := d.instantiateRevRange j args.size args;
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match c.binderInfo with
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| BinderInfo.implicit => do mvar ← mkFreshExprMVar d MetavarKind.natural n; mkAppMAux i (args.push mvar) j instMVars b
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| BinderInfo.instImplicit => do mvar ← mkFreshExprMVar d MetavarKind.synthetic n; mkAppMAux i (args.push mvar) j (instMVars.push mvar.mvarId!) b
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| _ =>
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if h : i < xs.size then do
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let x := xs.get ⟨i, h⟩;
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xType ← inferType x;
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condM (isDefEq d xType)
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(mkAppMAux (i+1) (args.push x) j instMVars b)
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(throwAppTypeMismatch (mkAppN f args) x)
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else
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mkAppMFinal `mkAppM f args instMVars
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| i, args, j, instMVars, type => do
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let type := type.instantiateRevRange j args.size args;
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type ← whnfD type;
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if type.isForall then
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mkAppMAux i args args.size instMVars type
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else if i == xs.size then
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mkAppMFinal `mkAppM f args instMVars
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else
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throwAppBuilderException `mkAppM ("too many explicit arguments provided to" ++ indentExpr f ++ Format.line ++ "arguments" ++ xs)
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private def mkFun (constName : Name) : MetaM (Expr × Expr) := do
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cinfo ← getConstInfo constName;
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us ← cinfo.lparams.mapM $ fun _ => mkFreshLevelMVar;
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let f := mkConst constName us;
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let fType := cinfo.instantiateTypeLevelParams us;
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pure (f, fType)
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def mkAppM (constName : Name) (xs : Array Expr) : m Expr := liftMetaM do
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traceCtx `Meta.appBuilder $ withNewMCtxDepth $ do
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(f, fType) ← mkFun constName;
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mkAppMAux f xs 0 #[] 0 #[] fType
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private partial def mkAppOptMAux (f : Expr) (xs : Array (Option Expr)) : Nat → Array Expr → Nat → Array MVarId → Expr → MetaM Expr
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| i, args, j, instMVars, Expr.forallE n d b c => do
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let d := d.instantiateRevRange j args.size args;
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if h : i < xs.size then do
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match xs.get ⟨i, h⟩ with
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| none =>
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match c.binderInfo with
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| BinderInfo.instImplicit => do mvar ← mkFreshExprMVar d MetavarKind.synthetic n; mkAppOptMAux (i+1) (args.push mvar) j (instMVars.push mvar.mvarId!) b
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| _ => do mvar ← mkFreshExprMVar d MetavarKind.natural n; mkAppOptMAux (i+1) (args.push mvar) j instMVars b
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| some x => do
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xType ← inferType x;
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condM (isDefEq d xType)
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(mkAppOptMAux (i+1) (args.push x) j instMVars b)
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(throwAppTypeMismatch (mkAppN f args) x)
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else
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mkAppMFinal `mkAppOptM f args instMVars
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| i, args, j, instMVars, type => do
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let type := type.instantiateRevRange j args.size args;
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type ← whnfD type;
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if type.isForall then
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mkAppOptMAux i args args.size instMVars type
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else if i == xs.size then
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mkAppMFinal `mkAppOptM f args instMVars
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else do
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let xs : Array Expr := xs.foldl (fun r x? => match x? with | none => r | some x => r.push x) #[];
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throwAppBuilderException `mkAppOptM ("too many arguments provided to" ++ indentExpr f ++ Format.line ++ "arguments" ++ xs)
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/--
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Similar to `mkAppM`, but it allows us to specify which arguments are provided explicitly using `Option` type.
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Example:
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Given `HasPure.pure {m : Type u → Type v} [HasPure m] {α : Type u} (a : α) : m α`,
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```
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mkAppOptM `HasPure.pure #[m, none, none, a]
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```
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returns a `HasPure.pure` application if the instance `HasPure m` can be synthesized, and the universes match.
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Note that,
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```
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mkAppM `HasPure.pure #[a]
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```
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fails because the only explicit argument `(a : α)` is not sufficient for inferring the remaining arguments,
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we would need the expected type. -/
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def mkAppOptM (constName : Name) (xs : Array (Option Expr)) : m Expr := liftMetaM do
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traceCtx `Meta.appBuilder $ withNewMCtxDepth $ do
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(f, fType) ← mkFun constName;
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mkAppOptMAux f xs 0 #[] 0 #[] fType
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private def mkEqNDRecImp (motive h1 h2 : Expr) : MetaM Expr :=
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if h2.isAppOf `Eq.refl then pure h1
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else do
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h2Type ← infer h2;
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match h2Type.eq? with
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| none => throwAppBuilderException `Eq.ndrec ("equality proof expected" ++ hasTypeMsg h2 h2Type)
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| some (α, a, b) => do
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u2 ← getLevel α;
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motiveType ← infer motive;
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match motiveType with
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| Expr.forallE _ _ (Expr.sort u1 _) _ =>
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pure $ mkAppN (mkConst `Eq.ndrec [u1, u2]) #[α, a, motive, h1, b, h2]
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| _ => throwAppBuilderException `Eq.ndrec ("invalid motive" ++ indentExpr motive)
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def mkEqNDRec (motive h1 h2 : Expr) : m Expr := liftMetaM $ mkEqNDRecImp motive h1 h2
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private def mkEqRecImp (motive h1 h2 : Expr) : MetaM Expr :=
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if h2.isAppOf `Eq.refl then pure h1
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else do
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h2Type ← infer h2;
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match h2Type.eq? with
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| none => throwAppBuilderException `Eq.rec ("equality proof expected" ++ indentExpr h2)
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| some (α, a, b) => do
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u2 ← getLevel α;
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motiveType ← infer motive;
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match motiveType with
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| Expr.forallE _ _ (Expr.forallE _ _ (Expr.sort u1 _) _) _ =>
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pure $ mkAppN (mkConst `Eq.rec [u1, u2]) #[α, a, motive, h1, b, h2]
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| _ => throwAppBuilderException `Eq.rec ("invalid motive" ++ indentExpr motive)
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def mkEqRec (motive h1 h2 : Expr) : m Expr := liftMetaM $ mkEqRecImp motive h1 h2
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def mkEqMP (eqProof pr : Expr) : m Expr :=
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mkAppM `Eq.mp #[eqProof, pr]
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def mkEqMPR (eqProof pr : Expr) : m Expr :=
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mkAppM `Eq.mpr #[eqProof, pr]
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private def mkNoConfusionImp (target : Expr) (h : Expr) : MetaM Expr := do
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type ← inferType h;
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type ← whnf type;
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match type.eq? with
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| none => throwAppBuilderException `noConfusion ("equality expected" ++ hasTypeMsg h type)
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| some (α, a, b) => do
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α ← whnf α;
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env ← getEnv;
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let f := α.getAppFn;
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matchConst env f (fun _ => throwAppBuilderException `noConfusion ("inductive type expected" ++ indentExpr α)) $ fun cinfo us =>
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match cinfo with
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| ConstantInfo.inductInfo v => do
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u ← getLevel target;
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pure $ mkAppN (mkConst (mkNameStr v.name "noConfusion") (u :: us)) (α.getAppArgs ++ #[target, a, b, h])
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| _ => throwAppBuilderException `noConfusion ("inductive type expected" ++ indentExpr α)
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def mkNoConfusion (target : Expr) (h : Expr) : m Expr := liftMetaM $ mkNoConfusionImp target h
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def mkPure (monad : Expr) (e : Expr) : m Expr :=
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mkAppOptM `HasPure.pure #[monad, none, none, e]
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/--
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`mkProjection s fieldName` return an expression for accessing field `fieldName` of the structure `s`.
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Remark: `fieldName` may be a subfield of `s`. -/
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private partial def mkProjectionImp : Expr → Name → MetaM Expr
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| s, fieldName => do
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type ← inferType s;
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type ← whnf type;
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match type.getAppFn with
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| Expr.const structName us _ => do
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env ← getEnv;
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unless (isStructureLike env structName) $ throwAppBuilderException `mkProjection ("structure expected" ++ hasTypeMsg s type);
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match getProjFnForField? env structName fieldName with
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| some projFn =>
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let params := type.getAppArgs;
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pure $ mkApp (mkAppN (mkConst projFn us) params) s
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| none => do
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let fields := getStructureFields env structName;
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r? ← fields.findSomeM? fun fieldName' =>
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match isSubobjectField? env structName fieldName' with
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| none => pure none
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| some _ => do {
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parent ← mkProjectionImp s fieldName';
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(do r ← mkProjectionImp parent fieldName; pure $ some r)
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<|>
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pure none
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};
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match r? with
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| some r => pure r
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| none => throwAppBuilderException `mkProjectionn ("invalid field name '" ++ toString fieldName ++ "' for" ++ hasTypeMsg s type)
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| _ => throwAppBuilderException `mkProjectionn ("structure expected" ++ hasTypeMsg s type)
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def mkProjection (s : Expr) (fieldName : Name) : m Expr := liftMetaM $ mkProjectionImp s fieldName
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private def mkListLitAux (nil : Expr) (cons : Expr) : List Expr → Expr
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| [] => nil
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| x::xs => mkApp (mkApp cons x) (mkListLitAux xs)
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private def mkListLitImp (type : Expr) (xs : List Expr) : MetaM Expr := do
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u ← getDecLevel type;
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let nil := mkApp (mkConst `List.nil [u]) type;
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match xs with
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| [] => pure nil
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| _ =>
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let cons := mkApp (mkConst `List.cons [u]) type;
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pure $ mkListLitAux nil cons xs
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def mkListLit (type : Expr) (xs : List Expr) : m Expr := liftMetaM $ mkListLitImp type xs
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def mkArrayLit (type : Expr) (xs : List Expr) : m Expr := liftMetaM do
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u ← getDecLevel type;
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listLit ← mkListLit type xs;
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pure (mkApp (mkApp (mkConst `List.toArray [u]) type) listLit)
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def mkSorry (type : Expr) (synthetic : Bool) : m Expr := liftMetaM do
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u ← getLevel type;
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pure $ mkApp2 (mkConst `sorryAx [u]) type (toExpr synthetic)
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/-- Return a proof for `p : Prop` using `decide p` -/
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def mkDecideProof (p : Expr) : m Expr := liftMetaM do
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decP ← mkAppM `Decidable.decide #[p];
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decEqTrue ← mkEq decP (mkConst `Bool.true);
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h ← mkEqRefl (mkConst `Bool.true);
|
||
h ← mkExpectedTypeHint h decEqTrue;
|
||
mkAppM `ofDecideEqTrue #[h]
|
||
|
||
/-- Return `a < b` -/
|
||
def mkLt (a b : Expr) : m Expr :=
|
||
mkAppM `HasLess.Less #[a, b]
|
||
|
||
/-- Return `a <= b` -/
|
||
def mkLe (a b : Expr) : m Expr :=
|
||
mkAppM `HasLessEq.LessEq #[a, b]
|
||
|
||
end Meta
|
||
end Lean
|