1 (*********************************************************************************************************************************)
2 (* HaskStrongToWeak: convert HaskStrong to HaskWeak *)
3 (*********************************************************************************************************************************)
5 Generalizable All Variables.
6 Require Import Preamble.
7 Require Import General.
8 Require Import NaturalDeduction.
9 Require Import Coq.Strings.String.
10 Require Import Coq.Lists.List.
11 Require Import Coq.Init.Specif.
12 Require Import HaskKinds.
13 Require Import HaskCoreLiterals.
14 Require Import HaskCoreVars.
15 Require Import HaskWeakTypes.
16 Require Import HaskWeakVars.
17 Require Import HaskWeak.
18 Require Import HaskStrongTypes.
19 Require Import HaskStrong.
21 Fixpoint mfresh (f:Fresh Kind (fun _ => WeakTypeVar))(lk:list Kind){Γ}(ite:IList _ (fun _ => WeakTypeVar) Γ)
22 : (Fresh Kind (fun _ => WeakTypeVar)) * ((vec WeakTypeVar (length lk)) * (IList _ (fun _ => WeakTypeVar) (app lk Γ))) :=
23 match lk as LK return (Fresh Kind (fun _ => WeakTypeVar)) * ((vec WeakTypeVar (length LK)) *
24 (IList _ (fun _ => WeakTypeVar) (app LK Γ))) with
25 | nil => (f,(vec_nil,ite))
27 let (f',varsite') := mfresh f lk' ite
28 in let (vars,ite') := varsite'
29 in let (v,f'') := next _ _ f' k
30 in (f'',((v:::vars),v::::ite'))
33 Fixpoint rawHaskTypeToWeakType (f:Fresh Kind (fun _ => WeakTypeVar)){κ}(rht:RawHaskType (fun _ => WeakTypeVar) κ)
34 {struct rht} : WeakType :=
36 | TVar _ v => WTyVarTy v
37 | TCon tc => WTyCon tc
38 | TCoerc _ t1 t2 t3 => WCoFunTy (rawHaskTypeToWeakType f t1) (rawHaskTypeToWeakType f t2) (rawHaskTypeToWeakType f t3)
40 | TApp _ _ t1 t2 => WAppTy (rawHaskTypeToWeakType f t1) (rawHaskTypeToWeakType f t2)
41 | TAll k rht' => let (tv,f') := next _ _ f k in WForAllTy tv (rawHaskTypeToWeakType f' (rht' tv))
43 match (rawHaskTypeToWeakType f t1) with
44 | WTyVarTy ec => WCodeTy ec (rawHaskTypeToWeakType f t2)
45 | impossible => impossible (* TODO: find a way to convince Coq this can't happen *)
47 | TyFunApp tfc tls => WTyFunApp tfc (rawHaskTypeListToWeakType f tls)
49 with rawHaskTypeListToWeakType (f:Fresh Kind (fun _ => WeakTypeVar)){κ}(rht:RawHaskTypeList κ) :=
52 | TyFunApp_cons κ kl rht' rhtl' => (rawHaskTypeToWeakType f rht')::(rawHaskTypeListToWeakType f rhtl')
55 Definition typeToWeakType (f:Fresh Kind (fun _ => WeakTypeVar))
56 {Γ}{κ}(τ:HaskType Γ κ)(φ:InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ) : WeakType :=
57 rawHaskTypeToWeakType f (τ _ φ).
59 Variable unsafeCoerce : WeakCoercion. Extract Inlined Constant unsafeCoerce => "Coercion.unsafeCoerce".
61 Definition strongCoercionToWeakCoercion {Γ}{Δ}{ck}(τ:HaskCoercion Γ Δ ck)(φ:InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ)
62 : WeakCoercion := unsafeCoerce.
64 (* This can be used to turn HaskStrong's with arbitrary expression variables into HaskStrong's which use WeakExprVar's
65 * for their variables; those can subsequently be passed to the following function (strongExprToWeakExpr) *)
67 Definition reindexStrongExpr {VV}{HH}{eqVV:EqDecidable VV}{eqHH:EqDecidable HH}
68 {Γ}{Δ}{ξ}{lev}(exp:@Expr VV eqVV Γ Δ ξ lev) : { ξ' : HH -> LeveledHaskType Γ & @Expr HH eqHH Γ Δ ξ' lev }.
72 Definition updateITE {Γ:TypeEnv}{TV:Kind->Type}{κ}(tv:TV κ)(ite:InstantiatedTypeEnv TV Γ) : InstantiatedTypeEnv TV (κ::Γ)
75 Fixpoint strongExprToWeakExpr {Γ}{Δ}{ξ}{τ}
76 (ftv:Fresh Kind (fun _ => WeakTypeVar))
77 (fcv:Fresh (WeakType*WeakType) (fun _ => WeakCoerVar))
78 (exp:@Expr _ CoreVarEqDecidable Γ Δ ξ τ)
79 : InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ -> WeakExpr :=
80 match exp as E in @Expr _ _ G D X L return InstantiatedTypeEnv (fun _ => WeakTypeVar) G -> WeakExpr with
81 | EVar Γ' _ ξ' ev => fun ite => WEVar (weakExprVar ev (@typeToWeakType ftv Γ' ★ (unlev (ξ' ev)) ite))
82 | ELit _ _ _ lit _ => fun ite => WELit lit
83 | EApp Γ' _ _ _ _ _ e1 e2 => fun ite => WEApp (strongExprToWeakExpr ftv fcv e1 ite) (strongExprToWeakExpr ftv fcv e2 ite)
84 | ELam Γ' _ _ _ t _ cv e => fun ite => WELam (weakExprVar cv (typeToWeakType ftv t ite)) (strongExprToWeakExpr ftv fcv e ite)
85 | 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)
86 | EEsc Γ' _ _ ec t _ e => fun ite => WEEsc (ec _ ite) (strongExprToWeakExpr ftv fcv e ite) (typeToWeakType ftv t ite)
87 | EBrak Γ' _ _ ec t _ e => fun ite => WEBrak (ec _ ite) (strongExprToWeakExpr ftv fcv e ite) (typeToWeakType ftv t ite)
88 | ECast Γ Δ ξ t1 t2 γ l e => fun ite => WECast (strongExprToWeakExpr ftv fcv e ite) (strongCoercionToWeakCoercion γ ite)
89 | ENote _ _ _ _ n e => fun ite => WENote n (strongExprToWeakExpr ftv fcv e ite)
90 | ETyApp Γ Δ κ σ τ ξ l e => fun ite => WETyApp (strongExprToWeakExpr ftv fcv e ite) (typeToWeakType ftv τ ite)
91 | ELetRec _ _ _ _ _ vars elrb e =>fun ite=>WELetRec (exprLetRec2WeakExprLetRec ftv fcv elrb ite)(strongExprToWeakExpr ftv fcv e ite)
92 | ECoApp Γ Δ κ σ₁ σ₂ γ σ ξ l e => fun ite => WECoApp (strongExprToWeakExpr ftv fcv e ite) (strongCoercionToWeakCoercion γ ite)
93 | ECase Γ Δ ξ l tc tbranches atypes e alts =>
95 (strongExprToWeakExpr ftv fcv e ite)
96 (@typeToWeakType ftv Γ _ tbranches ite)
98 (ilist_to_list (@ilmap _ _ (fun _ => WeakType) _ (fun _ t => typeToWeakType ftv t ite) atypes))
100 (tree:Tree ??{ scb : StrongCaseBranchWithVVs _ _ tc atypes
102 (sac_Δ scb Γ atypes (weakCK'' Δ))
103 (update_ξ (weakLT'○ξ) (vec2list (vec_map
104 (fun x => ((fst x),(snd x @@ weakL' l))) (scbwv_varstypes scb))))
105 (weakLT' (tbranches@@l)) })
106 : Tree ??(AltCon * list WeakTypeVar * list WeakCoerVar * list WeakExprVar * WeakExpr) :=
109 | T_Leaf (Some x) => let (scb,e) := x in
110 let (ftv',evarsite') := mfresh ftv _ ite in
112 let (evars,ite') := evarsite' in
116 map (fun vt => weakExprVar (fst vt) (typeToWeakType ftv' (snd vt) ite')) (vec2list (scbwv_varstypes scb)),
117 strongExprToWeakExpr ftv' fcv' e ite'
119 | T_Branch b1 b2 => (caseBranches b1),,(caseBranches b2)
122 | ETyLam _ _ _ k _ _ e => fun ite =>
123 let (tv,ftv') := next _ _ ftv k in WETyLam tv (strongExprToWeakExpr ftv' fcv e (updateITE tv ite))
124 | ECoLam Γ Δ κ σ σ₁ σ₂ ξ l e => fun ite =>
125 let t1' := typeToWeakType ftv σ₁ ite in
126 let t2' := typeToWeakType ftv σ₂ ite in
127 let (cv,fcv') := next _ _ fcv (t1',t2') in WECoLam cv (strongExprToWeakExpr ftv fcv' e ite)
129 with exprLetRec2WeakExprLetRec {Γ}{Δ}{ξ}{τ}{vars}
130 (ftv:Fresh Kind (fun _ => WeakTypeVar))
131 (fcv:Fresh (WeakType*WeakType) (fun _ => WeakCoerVar))
132 (elrb:@ELetRecBindings _ CoreVarEqDecidable Γ Δ ξ τ vars)
133 : InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ -> Tree ??(WeakExprVar * WeakExpr) :=
134 match elrb as E in ELetRecBindings G D X L V
135 return InstantiatedTypeEnv (fun _ => WeakTypeVar) G -> Tree ??(WeakExprVar * WeakExpr) with
136 | ELR_nil _ _ _ _ => fun ite => []
137 | ELR_leaf _ _ ξ' cv v e => fun ite => [((weakExprVar v (typeToWeakType ftv (unlev (ξ' v)) ite)),(strongExprToWeakExpr ftv fcv e ite))]
138 | ELR_branch _ _ _ _ _ _ b1 b2 => fun ite => (exprLetRec2WeakExprLetRec ftv fcv b1 ite),, (exprLetRec2WeakExprLetRec ftv fcv b2 ite)