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 HaskLiteralsAndTyCons.
14 Require Import HaskWeakTypes.
15 Require Import HaskWeakVars.
16 Require Import HaskWeak.
17 Require Import HaskStrongTypes.
18 Require Import HaskStrong.
19 Require Import HaskCoreVars.
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 (* This can be used to turn HaskStrong's with arbitrary expression variables into HaskStrong's which use WeakExprVar's
60 * for their variables; those can subsequently be passed to the following function (strongExprToWeakExpr) *)
62 Definition reindexStrongExpr {VV}{HH}{eqVV:EqDecidable VV}{eqHH:EqDecidable HH}
63 {Γ}{Δ}{ξ}{lev}(exp:@Expr VV eqVV Γ Δ ξ lev) : { ξ' : HH -> LeveledHaskType Γ & @Expr HH eqHH Γ Δ ξ' lev }.
67 Definition updateITE {Γ:TypeEnv}{TV:Kind->Type}{κ}(tv:TV κ)(ite:InstantiatedTypeEnv TV Γ) : InstantiatedTypeEnv TV (κ::Γ)
70 Definition coercionToWeakCoercion Γ Δ κ t1 t2 ftv ite (γ:@HaskCoercion Γ Δ (@mkHaskCoercionKind Γ κ t1 t2)) : WeakCoercion :=
71 WCoUnsafe (@typeToWeakType ftv Γ κ t1 ite) (@typeToWeakType ftv Γ κ t2 ite).
73 Section strongExprToWeakExpr.
75 Context (hetmet_brak : WeakExprVar).
76 Context (hetmet_esc : WeakExprVar).
78 Fixpoint strongExprToWeakExpr {Γ}{Δ}{ξ}{τ}
79 (ftv:Fresh Kind (fun _ => WeakTypeVar))
80 (fcv:Fresh (WeakType*WeakType) (fun _ => WeakCoerVar))
81 (fev:Fresh WeakType (fun _ => WeakExprVar))
82 (exp:@Expr _ CoreVarEqDecidable Γ Δ ξ τ)
83 : InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ -> WeakExpr :=
84 match exp as E in @Expr _ _ G D X L return InstantiatedTypeEnv (fun _ => WeakTypeVar) G -> WeakExpr with
85 | EVar Γ' _ ξ' ev => fun ite => WEVar (weakExprVar ev (@typeToWeakType ftv Γ' ★ (unlev (ξ' ev)) ite))
86 | ELit _ _ _ lit _ => fun ite => WELit lit
87 | EApp Γ' _ _ _ _ _ e1 e2 => fun ite => WEApp (strongExprToWeakExpr ftv fcv fev e1 ite) (strongExprToWeakExpr ftv fcv fev e2 ite)
88 | ELam Γ' _ _ _ t _ cv e => fun ite => WELam (weakExprVar cv (typeToWeakType ftv t ite)) (strongExprToWeakExpr ftv fcv fev e ite)
89 | ELet Γ' _ _ t _ _ ev e1 e2 => fun ite => WELet (weakExprVar ev (typeToWeakType ftv t ite)) (strongExprToWeakExpr ftv fcv fev e1 ite) (strongExprToWeakExpr ftv fcv fev e2 ite)
90 | EEsc Γ' _ _ ec t _ e => fun ite => WEEsc hetmet_esc (ec _ ite) (strongExprToWeakExpr ftv fcv fev e ite) (typeToWeakType ftv t ite)
91 | EBrak Γ' _ _ ec t _ e => fun ite => WEBrak hetmet_brak (ec _ ite) (strongExprToWeakExpr ftv fcv fev e ite) (typeToWeakType ftv t ite)
92 | ENote _ _ _ _ n e => fun ite => WENote n (strongExprToWeakExpr ftv fcv fev e ite)
93 | ETyApp Γ Δ κ σ τ ξ l e => fun ite => WETyApp (strongExprToWeakExpr ftv fcv fev e ite) (typeToWeakType ftv τ ite)
94 | ELetRec _ _ _ _ _ vars elrb e => fun ite => WELetRec (exprLetRec2WeakExprLetRec ftv fcv fev elrb ite)(strongExprToWeakExpr ftv fcv fev e ite)
95 | ECast Γ Δ ξ t1 t2 γ l e => fun ite => WECast (strongExprToWeakExpr ftv fcv fev e ite)
96 (coercionToWeakCoercion _ _ _ _ _ ftv ite γ)
97 | ECoApp Γ Δ κ σ₁ σ₂ γ σ ξ l e => fun ite => WECoApp (strongExprToWeakExpr ftv fcv fev e ite)
98 (coercionToWeakCoercion _ _ _ _ _ ftv ite γ)
99 | ECase Γ Δ ξ l tc tbranches atypes e alts => fun ite =>
100 let (ev,fev') := next _ _ fev (typeToWeakType ftv (unlev (caseType tc atypes @@ l)) ite) in
103 (strongExprToWeakExpr ftv fcv fev' e ite)
104 (@typeToWeakType ftv Γ _ tbranches ite)
106 (ilist_to_list (@ilmap _ _ (fun _ => WeakType) _ (fun _ t => typeToWeakType ftv t ite) atypes))
108 (tree:Tree ??{ scb : StrongCaseBranchWithVVs _ _ tc atypes
110 (sac_Δ scb Γ atypes (weakCK'' Δ))
111 (update_ξ (weakLT'○ξ) (vec2list (vec_map
112 (fun x => ((fst x),(snd x @@ weakL' l))) (scbwv_varstypes scb))))
113 (weakLT' (tbranches@@l)) })
114 : Tree ??(WeakAltCon * list WeakTypeVar * list WeakCoerVar * list WeakExprVar * WeakExpr) :=
117 | T_Leaf (Some x) => let (scb,e) := x in
118 let (ftv',evarsite') := mfresh ftv _ ite in
120 let (evars,ite') := evarsite' in
124 map (fun vt => weakExprVar (fst vt) (typeToWeakType ftv' (snd vt) ite')) (vec2list (scbwv_varstypes scb)),
125 strongExprToWeakExpr ftv' fcv' fev' e ite'
127 | T_Branch b1 b2 => (caseBranches b1),,(caseBranches b2)
130 | ETyLam _ _ _ k _ _ e => fun ite =>
131 let (tv,ftv') := next _ _ ftv k in WETyLam tv (strongExprToWeakExpr ftv' fcv fev e (updateITE tv ite))
132 | ECoLam Γ Δ κ σ σ₁ σ₂ ξ l e => fun ite =>
133 let t1' := typeToWeakType ftv σ₁ ite in
134 let t2' := typeToWeakType ftv σ₂ ite in
135 let (cv,fcv') := next _ _ fcv (t1',t2') in WECoLam cv (strongExprToWeakExpr ftv fcv' fev e ite)
137 with exprLetRec2WeakExprLetRec {Γ}{Δ}{ξ}{τ}{vars}
138 (ftv:Fresh Kind (fun _ => WeakTypeVar))
139 (fcv:Fresh (WeakType*WeakType) (fun _ => WeakCoerVar))
140 (fev:Fresh WeakType (fun _ => WeakExprVar))
141 (elrb:@ELetRecBindings _ CoreVarEqDecidable Γ Δ ξ τ vars)
142 : InstantiatedTypeEnv (fun _ => WeakTypeVar) Γ -> Tree ??(WeakExprVar * WeakExpr) :=
143 match elrb as E in ELetRecBindings G D X L V
144 return InstantiatedTypeEnv (fun _ => WeakTypeVar) G -> Tree ??(WeakExprVar * WeakExpr) with
145 | ELR_nil _ _ _ _ => fun ite => []
146 | ELR_leaf _ _ ξ' cv v e => fun ite => [((weakExprVar v (typeToWeakType ftv (unlev (ξ' v)) ite)),(strongExprToWeakExpr ftv fcv fev e ite))]
147 | ELR_branch _ _ _ _ _ _ b1 b2 => fun ite => (exprLetRec2WeakExprLetRec ftv fcv fev b1 ite),, (exprLetRec2WeakExprLetRec ftv fcv fev b2 ite)
149 End strongExprToWeakExpr.