433 lines
18 KiB
Text
433 lines
18 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.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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let type ← inferType e
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let 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 :=
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liftMetaM $ mkIdImp e
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def mkIdRhsImp (e : Expr) : MetaM Expr := do
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let type ← inferType e
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let u ← getLevel type
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pure $ mkApp2 (mkConst `idRhs [u]) type e
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/-- Return `idRhs e` -/
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def mkIdRhs (e : Expr) : m Expr :=
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liftMetaM $ mkIdRhsImp e
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private def mkExpectedTypeHintImp (e : Expr) (expectedType : Expr) : MetaM Expr := do
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let 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 $ mkExpectedTypeHintImp e expectedType
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private def mkEqImp (a b : Expr) : MetaM Expr := do
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let aType ← inferType a
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let 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 :=
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liftMetaM $ mkEqImp a b
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private def mkHEqImp (a b : Expr) : MetaM Expr := do
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let aType ← inferType a
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let bType ← inferType b
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let 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 :=
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liftMetaM $ mkHEqImp a b
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private def mkEqReflImp (a : Expr) : MetaM Expr := do
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let aType ← inferType a
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let 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 :=
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liftMetaM $ mkEqReflImp a
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private def mkHEqReflImp (a : Expr) : MetaM Expr := do
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let aType ← inferType a
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let 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 :=
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liftMetaM $ mkHEqReflImp a
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private def infer (h : Expr) : MetaM Expr := do
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let hType ← inferType h
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whnfD hType
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private def hasTypeMsg (e type : Expr) : MessageData :=
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m!"{indentExpr e}\nhas 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
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pure h
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else do
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let hType ← infer h
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match hType.eq? with
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| some (α, a, b) => do let 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 :=
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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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let hType₁ ← infer h₁
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let 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 let 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 :=
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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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let hType ← infer h
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match hType.heq? with
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| some (α, a, β, b) => do let 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 :=
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liftMetaM $ mkHEqSymmImp h
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private def mkHEqTransImp (h₁ h₂ : Expr) : MetaM Expr := do
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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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let hType₁ ← infer h₁
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let 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) =>
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let 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 :=
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liftMetaM $ mkHEqTransImp h₁ h₂
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private def mkEqOfHEqImp (h : Expr) : MetaM Expr := do
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let hType ← infer h
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match hType.heq? with
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| some (α, a, β, b) =>
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unless (← isDefEq α β) do
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throwAppBuilderException `eqOfHEq m!"heterogeneous equality types are not definitionally equal{indentExpr α}\nis not definitionally equal to{indentExpr β}"
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let 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 m!"heterogeneous equality proof expected{indentExpr h}"
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def mkEqOfHEq (h : Expr) : m Expr :=
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liftMetaM $ mkEqOfHEqImp h
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private def mkCongrArgImp (f h : Expr) : MetaM Expr := do
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let hType ← infer h
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let fType ← infer f
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match fType.arrow?, hType.eq? with
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| some (α, β), some (_, a, b) =>
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let u ← getLevel α; let 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 :=
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liftMetaM $ mkCongrArgImp f h
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private def mkCongrFunImp (h a : Expr) : MetaM Expr := do
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let hType ← infer h
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match hType.eq? with
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| some (ρ, f, g) => do
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let 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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let u ← getLevel α
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let 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 :=
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liftMetaM $ mkCongrFunImp h a
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private def mkCongrImp (h₁ h₂ : Expr) : MetaM Expr := do
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let hType₁ ← infer h₁
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let 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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let ρ ← whnfD ρ
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match ρ.arrow? with
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| some (_, β) => do
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let u ← getLevel α
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let 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 :=
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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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let mvarDecl ← getMVarDecl mvarId
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let mvarVal ← synthInstance mvarDecl.type
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assignExprMVar mvarId mvarVal
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let result ← instantiateMVars (mkAppN f args)
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if (← hasAssignableMVar result) then throwAppBuilderException methodName ("result contains metavariables" ++ indentExpr result)
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pure result
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private partial def mkAppMArgs (f : Expr) (fType : Expr) (xs : Array Expr) : MetaM Expr :=
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let rec loop (type : Expr) (i : Nat) (j : Nat) (args : Array Expr) (instMVars : Array MVarId) : MetaM Expr := do
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if i >= xs.size then
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mkAppMFinal `mkAppM f args instMVars
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else match type with
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| Expr.forallE n d b c =>
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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 =>
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let mvar ← mkFreshExprMVar d MetavarKind.natural n
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loop b i j (args.push mvar) instMVars
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| BinderInfo.instImplicit =>
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let mvar ← mkFreshExprMVar d MetavarKind.synthetic n
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loop b i j (args.push mvar) (instMVars.push mvar.mvarId!)
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| _ =>
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let x := xs[i]
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let xType ← inferType x
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if (← isDefEq d xType) then
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loop b (i+1) j (args.push x) instMVars
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else
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throwAppTypeMismatch (mkAppN f args) x
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| type =>
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let type := type.instantiateRevRange j args.size args
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let type ← whnfD type
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if type.isForall then
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loop type i args.size args instMVars
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else
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throwAppBuilderException `mkAppM m!"too many explicit arguments provided to{indentExpr f}\narguments{indentD xs}"
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loop fType 0 0 #[] #[]
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private def mkFun (constName : Name) : MetaM (Expr × Expr) := do
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let cinfo ← getConstInfo constName
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let 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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/--
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Return the application `constName xs`.
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It tries to fill the implicit arguments before the last element in `xs`.
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Remark:
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``mkAppM `arbitrary #[α]`` returns `@arbitrary.{u} α` without synthesizing
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the implicit argument occurring after `α`.
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Given a `x : (([Decidable p] → Bool) × Nat`, ``mkAppM `Prod.fst #[x]`` returns `@Prod.fst ([Decidable p] → Bool) Nat x`
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-/
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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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let (f, fType) ← mkFun constName
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let r ← mkAppMArgs f fType xs
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trace[Meta.appBuilder]! "constName: {constName}, xs: {xs}, result: {r}"
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pure r
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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
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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
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let mvar ← mkFreshExprMVar d MetavarKind.synthetic n
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mkAppOptMAux f xs (i+1) (args.push mvar) j (instMVars.push mvar.mvarId!) b
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| _ => do
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let mvar ← mkFreshExprMVar d MetavarKind.natural n
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mkAppOptMAux f xs (i+1) (args.push mvar) j instMVars b
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| some x =>
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let xType ← inferType x
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if (← isDefEq d xType) then
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mkAppOptMAux f xs (i+1) (args.push x) j instMVars b
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else
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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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let type ← whnfD type
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if type.isForall then
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mkAppOptMAux f xs 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 `Pure.pure {m : Type u → Type v} [Pure m] {α : Type u} (a : α) : m α`,
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```
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mkAppOptM `Pure.pure #[m, none, none, a]
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```
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returns a `Pure.pure` application if the instance `Pure m` can be synthesized, and the universes match.
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Note that,
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```
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mkAppM `Pure.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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let (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 := do
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if h2.isAppOf `Eq.refl then pure h1
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else
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let 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) =>
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let u2 ← getLevel α
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let 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 :=
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liftMetaM $ mkEqNDRecImp motive h1 h2
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private def mkEqRecImp (motive h1 h2 : Expr) : MetaM Expr := do
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if h2.isAppOf `Eq.refl then pure h1
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else
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let 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) =>
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let u2 ← getLevel α
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let 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 :=
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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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let type ← inferType h
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let 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) =>
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let α ← whnf α
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matchConstInduct α.getAppFn (fun _ => throwAppBuilderException `noConfusion ("inductive type expected" ++ indentExpr α)) fun v us => do
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let u ← getLevel target
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pure $ mkAppN (mkConst (Name.mkStr v.name "noConfusion") (u :: us)) (α.getAppArgs ++ #[target, a, b, h])
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def mkNoConfusion (target : Expr) (h : Expr) : m Expr :=
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liftMetaM $ mkNoConfusionImp target h
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def mkPure (monad : Expr) (e : Expr) : m Expr :=
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mkAppOptM `Pure.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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let type ← inferType s
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let type ← whnf type
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match type.getAppFn with
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| Expr.const structName us _ =>
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let env ← getEnv
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unless isStructureLike env structName do 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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let r? ← fields.findSomeM? fun fieldName' => do
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match isSubobjectField? env structName fieldName' with
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| none => pure none
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| some _ =>
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let parent ← mkProjectionImp s fieldName'
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(do let r ← mkProjectionImp parent fieldName; pure $ some r)
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<|>
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pure none
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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 :=
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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 nil cons xs)
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private def mkListLitImp (type : Expr) (xs : List Expr) : MetaM Expr := do
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let u ← getDecLevel type
|
||
let nil := mkApp (mkConst `List.nil [u]) type
|
||
match xs with
|
||
| [] => pure nil
|
||
| _ =>
|
||
let cons := mkApp (mkConst `List.cons [u]) type
|
||
pure $ mkListLitAux nil cons xs
|
||
def mkListLit (type : Expr) (xs : List Expr) : m Expr :=
|
||
liftMetaM $ mkListLitImp type xs
|
||
|
||
def mkArrayLit (type : Expr) (xs : List Expr) : m Expr := liftMetaM do
|
||
let u ← getDecLevel type
|
||
let listLit ← mkListLit type xs
|
||
pure (mkApp (mkApp (mkConst `List.toArray [u]) type) listLit)
|
||
|
||
def mkSorry (type : Expr) (synthetic : Bool) : m Expr := liftMetaM do
|
||
let u ← getLevel type
|
||
pure $ mkApp2 (mkConst `sorryAx [u]) type (toExpr synthetic)
|
||
|
||
/-- Return `Decidable.decide p` -/
|
||
def mkDecide (p : Expr) : m Expr :=
|
||
mkAppOptM `Decidable.decide #[p, none]
|
||
|
||
/-- Return a proof for `p : Prop` using `decide p` -/
|
||
def mkDecideProof (p : Expr) : m Expr := liftMetaM do
|
||
let decP ← mkDecide p
|
||
let decEqTrue ← mkEq decP (mkConst `Bool.true)
|
||
let h ← mkEqRefl (mkConst `Bool.true)
|
||
let 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]
|
||
|
||
/-- Return `arbitrary α` -/
|
||
def mkArbitrary (α : Expr) : m Expr :=
|
||
mkAppOptM `arbitrary #[α, none]
|
||
|
||
builtin_initialize registerTraceClass `Meta.appBuilder
|
||
|
||
end Lean.Meta
|