1 (*********************************************************************************************************************************)
2 (* HaskWeak: a non-dependently-typed but Coq-friendly version of HaskCore *)
3 (*********************************************************************************************************************************)
5 Generalizable All Variables.
6 Require Import Preamble.
7 Require Import General.
8 Require Import Coq.Lists.List.
9 Require Import HaskGeneral.
10 Require Import HaskLiterals.
11 Require Import HaskCoreVars.
12 Require Import HaskCoreTypes.
13 Require Import HaskCoreTypes.
14 Require Import HaskWeakVars.
17 | WEVar : WeakExprVar -> WeakExpr
18 | WELit : HaskLiteral -> WeakExpr
19 | WELet : WeakExprVar -> WeakExpr -> WeakExpr -> WeakExpr
20 | WELetRec : Tree ??(WeakExprVar * WeakExpr) -> WeakExpr -> WeakExpr
21 | WECast : WeakExpr -> WeakCoercion -> WeakExpr
22 | WENote : Note -> WeakExpr -> WeakExpr
23 | WEApp : WeakExpr -> WeakExpr -> WeakExpr
24 | WETyApp : WeakExpr -> CoreType -> WeakExpr
25 | WECoApp : WeakExpr -> WeakCoercion -> WeakExpr
26 | WELam : WeakExprVar -> WeakExpr -> WeakExpr
27 | WETyLam : WeakTypeVar -> WeakExpr -> WeakExpr
28 | WECoLam : WeakCoerVar -> WeakExpr -> WeakExpr
29 | WEBrak : WeakTypeVar -> WeakExpr -> WeakExpr
30 | WEEsc : WeakTypeVar -> WeakExpr -> WeakExpr
31 | WECase : forall (scrutinee:WeakExpr)
34 (type_params:vec CoreType n)
35 (alts : Tree ??(AltCon*list WeakVar*WeakExpr)),
38 (* calculate the free WeakVar's in a WeakExpr *)
39 Fixpoint getWeakExprFreeVars (me:WeakExpr) : list WeakExprVar :=
43 | WECast e co => getWeakExprFreeVars e
44 | WENote n e => getWeakExprFreeVars e
45 | WETyApp e t => getWeakExprFreeVars e
46 | WECoApp e co => getWeakExprFreeVars e
47 | WEBrak ec e => getWeakExprFreeVars e
48 | WEEsc ec e => getWeakExprFreeVars e
49 | WELet cv e1 e2 => mergeDistinctLists (getWeakExprFreeVars e1) (removeFromDistinctList cv (getWeakExprFreeVars e2))
50 | WEApp e1 e2 => mergeDistinctLists (getWeakExprFreeVars e1) (getWeakExprFreeVars e2)
51 | WELam cv e => @removeFromDistinctList _ WeakExprVarEqDecidable cv (getWeakExprFreeVars e)
52 | WETyLam cv e => getWeakExprFreeVars e
53 | WECoLam cv e => getWeakExprFreeVars e
55 (* the messy fixpoints below are required by Coq's termination conditions *)
56 | WECase scrutinee tbranches n tc type_params alts =>
57 mergeDistinctLists (getWeakExprFreeVars scrutinee) (
58 ((fix getWeakExprFreeVarsAlts (alts:Tree ??(AltCon*list WeakVar*WeakExpr)) {struct alts} : list WeakExprVar :=
61 | T_Leaf (Some (DEFAULT,_,e)) => getWeakExprFreeVars e
62 | T_Leaf (Some (LitAlt lit,_,e)) => getWeakExprFreeVars e
63 | T_Leaf (Some (DataAlt _ _ _ _ _ dc, vars,e)) => removeFromDistinctList'
64 (General.filter (map (fun v => match v with
65 | WExprVar ev => Some ev
69 (getWeakExprFreeVars e)
70 | T_Branch b1 b2 => mergeDistinctLists (getWeakExprFreeVarsAlts b1) (getWeakExprFreeVarsAlts b2)
72 | WELetRec mlr e => (fix removeVarsLetRec (mlr:Tree ??(WeakExprVar * WeakExpr))(cvl:list WeakExprVar) :=
75 | T_Leaf (Some (cv,e)) => removeFromDistinctList cv cvl
76 | T_Branch b1 b2 => removeVarsLetRec b1 (removeVarsLetRec b2 cvl)
77 end) mlr (mergeDistinctLists (getWeakExprFreeVars e)
78 ((fix getWeakExprFreeVarsLetRec (mlr:Tree ??(WeakExprVar * WeakExpr)) :=
81 | T_Leaf (Some (cv,e)) => getWeakExprFreeVars e
82 | T_Branch b1 b2 => mergeDistinctLists (getWeakExprFreeVarsLetRec b1) (getWeakExprFreeVarsLetRec b2)
86 (* wrap lambdas around an expression until it has no free expression variables *)
87 Definition makeClosedExpression : WeakExpr -> WeakExpr :=
88 fun me => (fix closeExpression (me:WeakExpr)(cvl:list WeakExprVar) :=
91 | cv::cvl' => WELam cv (closeExpression me cvl')
92 end) me (getWeakExprFreeVars me).
94 (* messy first-order capture-avoiding substitution on CoreType's *)
95 Fixpoint replaceCoreVar (te:CoreType)(tv:CoreVar)(tsubst:CoreType) : CoreType :=
97 | TyVarTy tv' => if eqd_dec tv tv' then tsubst else te
98 | AppTy t1 t2 => AppTy (replaceCoreVar t1 tv tsubst) (replaceCoreVar t2 tv tsubst)
99 | FunTy t1 t2 => FunTy (replaceCoreVar t1 tv tsubst) (replaceCoreVar t2 tv tsubst)
100 | ForAllTy tv' t => if eqd_dec tv tv' then te else ForAllTy tv' (replaceCoreVar t tv tsubst)
101 | PredTy (EqPred t1 t2) => PredTy (EqPred (replaceCoreVar t1 tv tsubst) (replaceCoreVar t2 tv tsubst))
102 | PredTy (IParam ip ty) => PredTy (IParam ip (replaceCoreVar ty tv tsubst))
103 | PredTy (ClassP _ c lt) => PredTy (ClassP c ((fix replaceCoreDistinctList (lt:list CoreType) :=
106 | h::t => (replaceCoreVar h tv tsubst)::(replaceCoreDistinctList t)
108 | TyConApp _ tc lt => TyConApp tc ((fix replaceCoreDistinctList (lt:list CoreType) :=
111 | h::t => (replaceCoreVar h tv tsubst)::(replaceCoreDistinctList t)
115 (* calculate the CoreType of a WeakExpr *)
116 Fixpoint coreTypeOfWeakExpr (ce:WeakExpr) : ???CoreType :=
118 | WEVar (weakExprVar v t) => OK t
119 | WELit lit => OK (haskLiteralToCoreType lit)
120 | WEApp e1 e2 => coreTypeOfWeakExpr e1 >>= fun t' =>
122 | (TyConApp 2 tc (t1::t2::nil)) =>
123 if (tyCon_eq tc ArrowTyCon)
125 else Error ("found non-function type "+++(weakTypeToString t')+++" in EApp")
126 | _ => Error ("found non-function type "+++(weakTypeToString t')+++" in EApp")
128 | WETyApp e t => coreTypeOfWeakExpr e >>= fun te =>
130 | ForAllTy v ct => OK (replaceCoreVar ct v t)
131 | _ => Error ("found non-forall type "+++(weakTypeToString te)+++" in ETyApp")
133 | WECoApp e co => coreTypeOfWeakExpr e >>= fun te =>
135 | TyConApp 2 tc ((PredTy (EqPred t1 t2))::t3::nil) =>
136 if (tyCon_eq tc ArrowTyCon)
138 else Error ("found non-coercion type "+++(weakTypeToString te)+++" in ETyApp")
139 | _ => Error ("found non-coercion type "+++(weakTypeToString te)+++" in ETyApp")
141 | WELam (weakExprVar ev vt) e => coreTypeOfWeakExpr e >>= fun t' => OK (TyConApp ArrowTyCon (vt::t'::nil))
142 | WETyLam tv e => coreTypeOfWeakExpr e >>= fun t' => match tv with weakTypeVar tvc _ => OK (ForAllTy tvc t') end
143 | WECoLam (weakCoerVar cv φ₁ φ₂) e =>
144 coreTypeOfWeakExpr e >>= fun t' => OK (TyConApp ArrowTyCon ((PredTy (EqPred φ₁ φ₂))::t'::nil))
145 | WELet ev ve e => coreTypeOfWeakExpr e
146 | WELetRec rb e => coreTypeOfWeakExpr e
147 | WENote n e => coreTypeOfWeakExpr e
148 | WECast e (weakCoercion t1 t2 _) => OK t2
149 | WECase scrutinee tbranches n tc type_params alts => OK tbranches
150 | WEBrak ec e => coreTypeOfWeakExpr e >>= fun t' => match ec with weakTypeVar ecc _ =>
151 OK (TyConApp hetMetCodeTypeTyCon ((TyVarTy ecc)::t'::nil)) end
152 | WEEsc ec e => coreTypeOfWeakExpr e >>= fun t' => match ec with weakTypeVar ecc _ =>
154 | (TyConApp 2 tc ((TyVarTy ec')::t''::nil)) =>
155 if (tyCon_eq tc hetMetCodeTypeTyCon)
156 then if eqd_dec ecc ec' then OK t''
157 else Error "level mismatch in escapification"
158 else Error "ill-typed escapification"
159 | _ => Error "ill-typed escapification"