Require Import Coq.Lists.List.
Require Import Coq.Init.Specif.
Require Import HaskKinds.
-Require Import HaskCoreLiterals.
-Require Import HaskCoreVars.
+Require Import HaskLiterals.
+Require Import HaskTyCons.
Require Import HaskWeakTypes.
Require Import HaskWeakVars.
Require Import HaskWeak.
+Require Import HaskWeakToCore.
Require Import HaskStrongTypes.
Require Import HaskStrong.
-CoInductive Fresh A T :=
-{ next : forall a:A, (T a * Fresh A T)
-; split : Fresh A T * Fresh A T
-}.
+Section HaskStrongToWeak.
-Fixpoint rawHaskTypeToWeakType (f:Fresh Kind (fun _ => WeakTypeVar)){κ}(rht:RawHaskType (fun _ => WeakTypeVar) κ)
- {struct rht} : WeakType :=
-match rht with
- | TVar _ v => WTyVarTy v
- | TCon tc => WTyCon tc
- | TCoerc _ t1 t2 t3 => WCoFunTy (rawHaskTypeToWeakType f t1) (rawHaskTypeToWeakType f t2) (rawHaskTypeToWeakType f t3)
- | TArrow => WFunTyCon
- | TApp _ _ t1 t2 => WAppTy (rawHaskTypeToWeakType f t1) (rawHaskTypeToWeakType f t2)
- | TAll k rht' => let (tv,f') := next _ _ f k in WForAllTy tv (rawHaskTypeToWeakType f' (rht' tv))
- | TCode t1 t2 =>
- match (rawHaskTypeToWeakType f t1) with
- | WTyVarTy ec => WCodeTy ec (rawHaskTypeToWeakType f t2)
- | impossible => impossible (* TODO: find a way to convince Coq this can't happen *)
- end
- | TyFunApp tfc tls => WTyFunApp tfc (rawHaskTypeListToWeakType f tls)
-end
-with rawHaskTypeListToWeakType (f:Fresh Kind (fun _ => WeakTypeVar)){κ}(rht:RawHaskTypeList κ) :=
-match rht with
- | TyFunApp_nil => nil
- | TyFunApp_cons κ kl rht' rhtl' => (rawHaskTypeToWeakType f rht')::(rawHaskTypeListToWeakType f rhtl')
-end.
+ Context (hetmet_brak : WeakExprVar).
+ Context (hetmet_esc : WeakExprVar).
+
+ Context (mkWeakTypeVar_ : Unique -> Kind -> WeakTypeVar).
+ Context (mkWeakCoerVar_ : Unique -> Kind -> WeakType -> WeakType -> WeakCoerVar).
+ Context (mkWeakExprVar_ : Unique -> WeakType -> WeakExprVar).
+
+ Definition mkWeakTypeVar (k:Kind) : UniqM WeakTypeVar := bind u = getU ; return mkWeakTypeVar_ u k.
+ Definition mkWeakCoerVar (k:Kind)(t1 t2:WeakType) : UniqM WeakCoerVar := bind u = getU ; return mkWeakCoerVar_ u k t1 t2.
+ Definition mkWeakExprVar (t:WeakType) : UniqM WeakExprVar := bind u = getU ; return mkWeakExprVar_ u t.
-Definition typeToWeakType (f:Fresh Kind (fun _ => WeakTypeVar))
- {Γ}{κ}(τ:HaskType Γ κ)(φ:InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ) : WeakType :=
- rawHaskTypeToWeakType f (τ _ φ).
+ Fixpoint mfresh (lk:list Kind){Γ}(ite:IList _ (fun _ => WeakTypeVar) Γ)
+ : UniqM (((vec WeakTypeVar (length lk)) * (IList _ (fun _ => WeakTypeVar) (app lk Γ)))) :=
+ match lk as LK return UniqM ((vec WeakTypeVar (length LK)) * (IList _ (fun _ => WeakTypeVar) (app LK Γ))) with
+ | nil => return (vec_nil,ite)
+ | k::lk' => bind v = mkWeakTypeVar k
+ ; bind vars_ite' = mfresh lk' ite
+ ; return ((v:::(fst vars_ite')),v::::(snd vars_ite'))
+ end.
-Variable unsafeCoerce : WeakCoercion. Extract Inlined Constant unsafeCoerce => "Coercion.unsafeCoerce".
+ Fixpoint rawHaskTypeToWeakType {κ}(rht:RawHaskType (fun _ => WeakTypeVar) κ) {struct rht} : UniqM WeakType :=
+ match rht with
+ | TVar _ v => return WTyVarTy v
+ | TCon tc => return WTyCon tc
+ | TCoerc _ t1 t2 t3 => bind t1' = rawHaskTypeToWeakType t1
+ ; bind t2' = rawHaskTypeToWeakType t2
+ ; bind t3' = rawHaskTypeToWeakType t3
+ ; return WCoFunTy t1' t2' t3'
+ | TArrow => return WFunTyCon
+ | TApp _ _ t1 t2 => bind t1' = rawHaskTypeToWeakType t1
+ ; bind t2' = rawHaskTypeToWeakType t2
+ ; return WAppTy t1' t2'
+ | TAll k rht' => bind tv = mkWeakTypeVar k
+ ; bind t' = rawHaskTypeToWeakType (rht' tv)
+ ; return WForAllTy tv t'
+ | TCode t1 t2 => bind t1' = rawHaskTypeToWeakType t1
+ ; bind t2' = rawHaskTypeToWeakType t2
+ ; match t1' with
+ | WTyVarTy ec => return WCodeTy ec t2'
+ | _ => failM "impossible"
+ end
+ | TyFunApp tfc _ _ tls => bind tls' = rawHaskTypeListToWeakType tls
+ ; return WTyFunApp tfc tls'
+ end
+ with rawHaskTypeListToWeakType {κ}(rht:RawHaskTypeList κ) : UniqM (list WeakType) :=
+ match rht with
+ | TyFunApp_nil => return nil
+ | TyFunApp_cons κ kl rht' rhtl' => bind t = rawHaskTypeToWeakType rht'
+ ; bind tl = rawHaskTypeListToWeakType rhtl'
+ ; return t::tl
+ end.
+
+ Definition typeToWeakType {Γ}{κ}(τ:HaskType Γ κ)(φ:InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ) : UniqM WeakType :=
+ rawHaskTypeToWeakType (τ _ φ).
+
+ Definition updateITE {Γ:TypeEnv}{TV:Kind->Type}{κ}(tv:TV κ)(ite:InstantiatedTypeEnv TV Γ) : InstantiatedTypeEnv TV (κ::Γ)
+ := tv::::ite.
+
+ Definition updateITE_ {Γ:TypeEnv}{TV:Kind->Type}{κ}{n}(tv:TV κ)(ite:InstantiatedTypeEnv TV Γ)
+ : InstantiatedTypeEnv TV (list_ins n κ Γ).
+ rewrite list_ins_app.
+ rewrite <- (list_take_drop _ Γ n) in ite.
+ apply ilist_app.
+ apply ilist_chop in ite; auto.
+ apply ICons.
+ apply tv.
+ apply ilist_chop' in ite.
+ apply ite.
+ Defined.
+
+ Definition coercionToWeakCoercion Γ Δ κ t1 t2 ite (γ:@HaskCoercion Γ Δ (@mkHaskCoercionKind Γ κ t1 t2))
+ : UniqM WeakCoercion
+ := bind t1' = @typeToWeakType Γ κ t1 ite
+ ; bind t2' = @typeToWeakType Γ κ t2 ite
+ ; return WCoUnsafe t1' t2'.
+
+ Fixpoint seqM {a}(l:list (UniqM a)) : UniqM (list a) :=
+ match l with
+ | nil => return nil
+ | x::y => bind x' = x
+ ; bind y' = seqM y
+ ; return x'::y'
+ end.
+
+ Context {VV}{eqVV:EqDecidable VV}{toStringVV:ToString VV}.
+
+ Definition update_chi (χ:VV->???WeakExprVar)(vv:VV)(ev':WeakExprVar) : VV->???WeakExprVar :=
+ fun vv' =>
+ if eqd_dec vv vv'
+ then OK ev'
+ else χ vv'.
-Definition strongCoercionToWeakCoercion {Γ}{Δ}{ck}(τ:HaskCoercion Γ Δ ck)(φ:InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ)
- : WeakCoercion.
- unfold HaskCoercion in τ.
- admit.
- Defined.
+ Fixpoint update_chi' (χ:VV->???WeakExprVar)(varsexprs:list (VV * WeakExprVar)) : VV->???WeakExprVar :=
+ match varsexprs with
+ | nil => χ
+ | (vv,wev)::rest => update_chi (update_chi' χ rest) vv wev
+ end.
-(* This can be used to turn HaskStrong's with arbitrary expression variables into HaskStrong's which use WeakExprVar's
- * for their variables; those can subsequently be passed to the following function (strongExprToWeakExpr) *)
-(*
-Definition reindexStrongExpr {VV}{HH}{eqVV:EqDecidable VV}{eqHH:EqDecidable HH}
- {Γ}{Δ}{ξ}{lev}(exp:@Expr VV eqVV Γ Δ ξ lev) : { ξ' : HH -> LeveledHaskType Γ & @Expr HH eqHH Γ Δ ξ' lev }.
- Defined.
- *)
+ Fixpoint exprToWeakExpr {Γ}{Δ}{ξ}{τ}{l}(χ:VV->???WeakExprVar)(exp:@Expr _ eqVV Γ Δ ξ τ l)
+ : InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ
+ -> UniqM WeakExpr :=
+ match exp as E in @Expr _ _ G D X T L return InstantiatedTypeEnv (fun _ => WeakTypeVar) G -> UniqM WeakExpr with
+ | EVar Γ' _ ξ' ev => fun ite => match χ ev with OK v => return WEVar v | Error s => failM s end
+ | EGlobal Γ' _ ξ' g v lev => fun ite => bind tv' = mapM (ilist_to_list (ilmap (fun κ x => typeToWeakType x ite) v))
+ ; return (fold_left (fun x y => WETyApp x y) tv' (WEVar g))
+ | ELam Γ' _ _ tv _ _ cv e => fun ite => bind tv' = typeToWeakType tv ite
+ ; bind ev' = mkWeakExprVar tv'
+ ; bind e' = exprToWeakExpr (update_chi χ cv ev') e ite
+ ; return WELam ev' e'
+ | ELet Γ' _ _ t _ _ ev e1 e2 => fun ite => bind tv' = typeToWeakType t ite
+ ; bind e1' = exprToWeakExpr χ e1 ite
+ ; bind ev' = mkWeakExprVar tv'
+ ; bind e2' = exprToWeakExpr (update_chi χ ev ev') e2 ite
+ ; return WELet ev' e1' e2'
+ | ELit _ _ _ lit _ => fun ite => return WELit lit
+ | EApp Γ' _ _ _ _ _ e1 e2 => fun ite => bind e1' = exprToWeakExpr χ e1 ite
+ ; bind e2' = exprToWeakExpr χ e2 ite
+ ; return WEApp e1' e2'
+ | EEsc Γ' _ _ ec t _ e => fun ite => bind t' = typeToWeakType t ite
+ ; bind e' = exprToWeakExpr χ e ite
+ ; return WEEsc hetmet_esc (ec _ ite) e' t'
+ | EBrak Γ' _ _ ec t _ e => fun ite => bind t' = typeToWeakType t ite
+ ; bind e' = exprToWeakExpr χ e ite
+ ; return WEBrak hetmet_brak (ec _ ite) e' t'
+ | ENote _ _ _ _ _ n e => fun ite => bind e' = exprToWeakExpr χ e ite
+ ; return WENote n e'
+ | ETyApp Γ Δ κ σ τ ξ l e => fun ite => bind t' = typeToWeakType τ ite
+ ; bind e' = exprToWeakExpr χ e ite
+ ; return WETyApp e' t'
+ | ECoApp Γ Δ κ σ₁ σ₂ γ σ ξ l e => fun ite => bind e' = exprToWeakExpr χ e ite
+ ; bind c' = coercionToWeakCoercion _ _ _ _ _ ite γ
+ ; return WECoApp e' c'
+ | ECast Γ Δ ξ t1 t2 γ l e => fun ite => bind e' = exprToWeakExpr χ e ite
+ ; bind c' = coercionToWeakCoercion _ _ _ _ _ ite γ
+ ; return WECast e' c'
+ | ETyLam _ _ _ k _ _ n e => fun ite => bind tv = mkWeakTypeVar k
+ ; bind e' = exprToWeakExpr χ e (updateITE_ tv ite)
+ ; return WETyLam tv e'
+ | ECoLam Γ Δ κ σ σ₁ σ₂ ξ l e => fun ite => bind t1' = typeToWeakType σ₁ ite
+ ; bind t2' = typeToWeakType σ₂ ite
+ ; bind cv = mkWeakCoerVar κ t1' t2'
+ ; bind e' = exprToWeakExpr χ e ite
+ ; return WECoLam cv e'
+ | ECase Γ Δ ξ l tc tbranches atypes escrut alts =>
+ fun ite => bind tscrut' = typeToWeakType (caseType tc atypes) ite
+ ; bind vscrut' = mkWeakExprVar tscrut'
+ ; bind tbranches' = @typeToWeakType Γ _ tbranches ite
+ ; bind escrut' = exprToWeakExpr χ escrut ite
+ ; bind branches' =
+ ((fix caseBranches (tree:Tree ??{sac : _ & { scb : StrongCaseBranchWithVVs VV _ _ _ sac & Expr _ _ _ _ _ } })
+ : UniqM (Tree ??(WeakAltCon*list WeakTypeVar*list WeakCoerVar*list WeakExprVar*WeakExpr)) :=
+ match tree with
+ | T_Leaf None => return []
+ | T_Leaf (Some x) =>
+ let (sac,scb_e) := x in
+ let (scb,e) := scb_e in
+ let varstypes := vec2list (scbwv_varstypes scb) in
+ bind evars_ite = mfresh _ ite
+ ; bind exprvars = seqM (map (fun vt:VV * HaskType _ ★
+ => bind tleaf = typeToWeakType (snd vt) (snd evars_ite)
+ ; bind v' = mkWeakExprVar tleaf
+ ; return ((fst vt),v'))
+ varstypes)
+ ; let χ' := update_chi' χ exprvars in
+ bind e'' = exprToWeakExpr χ' e (snd evars_ite)
+ ; return [(sac_altcon sac, vec2list (fst evars_ite), nil, (map (@snd _ _) exprvars), e'')]
+ | T_Branch b1 b2 => bind b1' = caseBranches b1
+ ; bind b2' = caseBranches b2
+ ; return (b1',,b2')
+ end) alts)
+ ; bind tys = seqM (ilist_to_list (@ilmap _ _
+ (fun _ => UniqM WeakType) _ (fun _ t => typeToWeakType t ite) atypes))
+ ; return WECase vscrut' escrut' tbranches' tc tys branches'
+
+ | ELetRec _ _ _ _ _ vars disti elrb e => fun ite => bind vars' = seqM (map (fun vt:VV * HaskType _ ★
+ => bind tleaf = typeToWeakType (snd vt) ite
+ ; bind v' = mkWeakExprVar tleaf
+ ; return ((fst vt),v'))
+ (leaves vars))
+ ; let χ' := update_chi' χ vars' in
+ bind elrb' = exprLetRec2WeakExprLetRec χ' elrb ite
+ ; bind e' = exprToWeakExpr χ' e ite
+ ; return WELetRec elrb' e'
+ end
+ with exprLetRec2WeakExprLetRec {Γ}{Δ}{ξ}{τ}(χ:VV->???WeakExprVar){vars}(elrb:@ELetRecBindings _ eqVV Γ Δ ξ τ vars)
+ : InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ -> UniqM (Tree ??(WeakExprVar * WeakExpr)) :=
+ match elrb as E in ELetRecBindings G D X L V
+ return InstantiatedTypeEnv (fun _ => WeakTypeVar) G -> UniqM (Tree ??(WeakExprVar * WeakExpr)) with
+ | ELR_nil _ _ _ _ => fun ite => return []
+ | ELR_leaf _ _ ξ' cv v t e => fun ite => bind t' = typeToWeakType t ite
+ ; bind e' = exprToWeakExpr χ e ite
+ ; bind v' = match χ v with Error s => failM s | OK y => return y end
+ ; return [(v',e')]
+ | ELR_branch _ _ _ _ _ _ b1 b2 => fun ite => bind b1' = exprLetRec2WeakExprLetRec χ b1 ite
+ ; bind b2' = exprLetRec2WeakExprLetRec χ b2 ite
+ ; return b1',,b2'
+ end.
-Definition updateITE {Γ:TypeEnv}{TV:Kind->Type}{κ}(tv:TV κ)(ite:InstantiatedTypeEnv TV Γ) : InstantiatedTypeEnv TV (κ::Γ)
- := tv::::ite.
-Definition unlev {Γ}{κ}(lht:LeveledHaskType Γ κ) :=
- match lht with t@@l => t end.
+ Fixpoint strongExprToWeakExpr (us:UniqSupply){Γ}{Δ}{ξ}{τ}{l}(exp:@Expr _ eqVV Γ Δ ξ τ l)
+ (ite:InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ)
+ : ???WeakExpr :=
+ match exprToWeakExpr (fun v => Error ("unbound variable " +++ toString v)) exp ite with
+ uniqM f => f us >>= fun x => OK (snd x)
+ end.
-Fixpoint strongExprToWeakExpr {Γ}{Δ}{ξ}{τ}
- (ftv:Fresh Kind (fun _ => WeakTypeVar))
- (fcv:Fresh (WeakType*WeakType) (fun _ => WeakCoerVar))
- (exp:@Expr _ CoreVarEqDecidable Γ Δ ξ τ)
- : InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ -> WeakExpr :=
-match exp as E in @Expr _ _ G D X L return InstantiatedTypeEnv (fun _ => WeakTypeVar) G -> WeakExpr with
-| EVar Γ' _ ξ' ev => fun ite => WEVar (weakExprVar ev (@typeToWeakType ftv Γ' ★ (unlev (ξ' ev)) ite))
-| ELit _ _ _ lit _ => fun ite => WELit lit
-| EApp Γ' _ _ _ _ _ e1 e2 => fun ite => WEApp (strongExprToWeakExpr ftv fcv e1 ite) (strongExprToWeakExpr ftv fcv e2 ite)
-| ELam Γ' _ _ _ t _ cv e => fun ite => WELam (weakExprVar cv (typeToWeakType ftv t ite)) (strongExprToWeakExpr ftv fcv e ite)
-| ELet Γ' _ _ t _ _ ev e1 e2 => fun ite => WELet (weakExprVar ev (typeToWeakType ftv t ite)) (strongExprToWeakExpr ftv fcv e1 ite) (strongExprToWeakExpr ftv fcv e2 ite)
-| EEsc Γ' _ _ ec t _ e => fun ite => WEEsc (ec _ ite) (strongExprToWeakExpr ftv fcv e ite) (typeToWeakType ftv t ite)
-| EBrak Γ' _ _ ec t _ e => fun ite => WEBrak (ec _ ite) (strongExprToWeakExpr ftv fcv e ite) (typeToWeakType ftv t ite)
-| ECast Γ Δ ξ t1 t2 γ l e => fun ite => WECast (strongExprToWeakExpr ftv fcv e ite) (strongCoercionToWeakCoercion γ ite)
-| ENote _ _ _ _ n e => fun ite => WENote n (strongExprToWeakExpr ftv fcv e ite)
-| ETyApp Γ Δ κ σ τ ξ l e => fun ite => WETyApp (strongExprToWeakExpr ftv fcv e ite) (typeToWeakType ftv τ ite)
-| ELetRec _ _ _ _ _ vars elrb e =>fun ite=>WELetRec (exprLetRec2WeakExprLetRec ftv fcv elrb ite)(strongExprToWeakExpr ftv fcv e ite)
-| ECoApp Γ Δ κ σ₁ σ₂ γ σ ξ l e => fun ite => WECoApp (strongExprToWeakExpr ftv fcv e ite) (strongCoercionToWeakCoercion γ ite)
-| ECase Γ Δ ξ l tc tbranches sac atypes e alts =>
- fun ite => WECase
- (strongExprToWeakExpr ftv fcv e ite)
- (@typeToWeakType ftv Γ _ tbranches ite)
- tc
- (ilist_to_list (@ilmap _ _ (fun _ => WeakType) _ (fun _ t => typeToWeakType ftv t ite) atypes))
- ((fix caseBranches
- (tree:Tree ??{ scb : StrongCaseBranchWithVVs _ _ tc sac atypes
- & Expr (sac_Γ scb Γ)
- (sac_Δ scb Γ atypes (weakCK'' Δ))
- (update_ξ (weakLT'○ξ) (vec2list (vec_map
- (fun x => ((fst x),(snd x @@ weakL' l))) (scbwv_varstypes scb))))
- (weakLT' (tbranches@@l)) })
- : Tree ??(AltCon * list WeakTypeVar * list WeakCoerVar * list WeakExprVar * WeakExpr) :=
- match tree with
- | T_Leaf None => []
- | T_Leaf (Some x) => let (scb,e) := x in
- (*[(sac_altcon scb,
- nil, (* FIXME *)
- nil, (* FIXME *)
- (*map (fun t => typeToWeakType ftv t ite') (vec2list (sac_types scb))*)nil, (* FIXME *)
- strongExprToWeakExpr ftv fcv e (weakITE' ite))]*) []
- | T_Branch b1 b2 => (caseBranches b1),,(caseBranches b2)
- end
- ) alts)
-| ETyLam _ _ _ k _ _ e => fun ite =>
- let (tv,ftv') := next _ _ ftv k in WETyLam tv (strongExprToWeakExpr ftv' fcv e (updateITE tv ite))
-| ECoLam Γ Δ κ σ σ₁ σ₂ ξ l e => fun ite =>
- let t1' := typeToWeakType ftv σ₁ ite in
- let t2' := typeToWeakType ftv σ₂ ite in
- let (cv,fcv') := next _ _ fcv (t1',t2') in WECoLam cv (strongExprToWeakExpr ftv fcv' e ite)
-end
-with exprLetRec2WeakExprLetRec {Γ}{Δ}{ξ}{τ}{vars}
- (ftv:Fresh Kind (fun _ => WeakTypeVar))
- (fcv:Fresh (WeakType*WeakType) (fun _ => WeakCoerVar))
- (elrb:@ELetRecBindings _ CoreVarEqDecidable Γ Δ ξ τ vars)
- : InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ -> Tree ??(WeakExprVar * WeakExpr) :=
-match elrb as E in ELetRecBindings G D X L V
- return InstantiatedTypeEnv (fun _ => WeakTypeVar) G -> Tree ??(WeakExprVar * WeakExpr) with
-| ELR_nil _ _ _ _ => fun ite => []
-| ELR_leaf _ _ _ t cv v e => fun ite => [((weakExprVar v (typeToWeakType ftv t ite)),(strongExprToWeakExpr ftv fcv e ite))]
-| ELR_branch _ _ _ _ _ _ b1 b2 => fun ite => (exprLetRec2WeakExprLetRec ftv fcv b1 ite),, (exprLetRec2WeakExprLetRec ftv fcv b2 ite)
-end.
+End HaskStrongToWeak.
projects / coq-hetmet.git / blobdiff