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
30 (* the CoreType argument is used only when going back from Weak to Core; it lets us dodge a possibly-failing type calculation *)
31 | WEBrak : WeakTypeVar -> WeakExpr -> CoreType -> WeakExpr
32 | WEEsc : WeakTypeVar -> WeakExpr -> CoreType -> WeakExpr
34 (* note that HaskWeak "Case" does not bind a variable; coreExprToWeakExpr adds a let-binder *)
35 | WECase : forall (scrutinee:WeakExpr)
38 (type_params:vec CoreType n)
39 (alts : Tree ??(AltCon*list WeakVar*WeakExpr)),
42 (* calculate the free WeakVar's in a WeakExpr *)
43 Fixpoint getWeakExprFreeVars (me:WeakExpr) : list WeakExprVar :=
47 | WECast e co => getWeakExprFreeVars e
48 | WENote n e => getWeakExprFreeVars e
49 | WETyApp e t => getWeakExprFreeVars e
50 | WECoApp e co => getWeakExprFreeVars e
51 | WEBrak ec e _ => getWeakExprFreeVars e
52 | WEEsc ec e _ => getWeakExprFreeVars e
53 | WELet cv e1 e2 => mergeDistinctLists (getWeakExprFreeVars e1) (removeFromDistinctList cv (getWeakExprFreeVars e2))
54 | WEApp e1 e2 => mergeDistinctLists (getWeakExprFreeVars e1) (getWeakExprFreeVars e2)
55 | WELam cv e => @removeFromDistinctList _ WeakExprVarEqDecidable cv (getWeakExprFreeVars e)
56 | WETyLam cv e => getWeakExprFreeVars e
57 | WECoLam cv e => getWeakExprFreeVars e
59 (* the messy fixpoints below are required by Coq's termination conditions *)
60 | WECase scrutinee tbranches n tc type_params alts =>
61 mergeDistinctLists (getWeakExprFreeVars scrutinee) (
62 ((fix getWeakExprFreeVarsAlts (alts:Tree ??(AltCon*list WeakVar*WeakExpr)) {struct alts} : list WeakExprVar :=
65 | T_Leaf (Some (DEFAULT,_,e)) => getWeakExprFreeVars e
66 | T_Leaf (Some (LitAlt lit,_,e)) => getWeakExprFreeVars e
67 | T_Leaf (Some (DataAlt _ _ _ _ _ dc, vars,e)) => removeFromDistinctList'
68 (General.filter (map (fun v => match v with
69 | WExprVar ev => Some ev
73 (getWeakExprFreeVars e)
74 | T_Branch b1 b2 => mergeDistinctLists (getWeakExprFreeVarsAlts b1) (getWeakExprFreeVarsAlts b2)
76 | WELetRec mlr e => (fix removeVarsLetRec (mlr:Tree ??(WeakExprVar * WeakExpr))(cvl:list WeakExprVar) :=
79 | T_Leaf (Some (cv,e)) => removeFromDistinctList cv cvl
80 | T_Branch b1 b2 => removeVarsLetRec b1 (removeVarsLetRec b2 cvl)
81 end) mlr (mergeDistinctLists (getWeakExprFreeVars e)
82 ((fix getWeakExprFreeVarsLetRec (mlr:Tree ??(WeakExprVar * WeakExpr)) :=
85 | T_Leaf (Some (cv,e)) => getWeakExprFreeVars e
86 | T_Branch b1 b2 => mergeDistinctLists (getWeakExprFreeVarsLetRec b1) (getWeakExprFreeVarsLetRec b2)
90 (* wrap lambdas around an expression until it has no free expression variables *)
91 Definition makeClosedExpression : WeakExpr -> WeakExpr :=
92 fun me => (fix closeExpression (me:WeakExpr)(cvl:list WeakExprVar) :=
95 | cv::cvl' => WELam cv (closeExpression me cvl')
96 end) me (getWeakExprFreeVars me).
98 (* messy first-order capture-avoiding substitution on CoreType's *)
99 Fixpoint replaceCoreVar (te:CoreType)(tv:CoreVar)(tsubst:CoreType) : CoreType :=
101 | TyVarTy tv' => if eqd_dec tv tv' then tsubst else te
102 | AppTy t1 t2 => AppTy (replaceCoreVar t1 tv tsubst) (replaceCoreVar t2 tv tsubst)
103 | FunTy t1 t2 => FunTy (replaceCoreVar t1 tv tsubst) (replaceCoreVar t2 tv tsubst)
104 | ForAllTy tv' t => if eqd_dec tv tv' then te else ForAllTy tv' (replaceCoreVar t tv tsubst)
105 | PredTy (EqPred t1 t2) => PredTy (EqPred (replaceCoreVar t1 tv tsubst) (replaceCoreVar t2 tv tsubst))
106 | PredTy (IParam ip ty) => PredTy (IParam ip (replaceCoreVar ty tv tsubst))
107 | PredTy (ClassP _ c lt) => PredTy (ClassP c ((fix replaceCoreDistinctList (lt:list CoreType) :=
110 | h::t => (replaceCoreVar h tv tsubst)::(replaceCoreDistinctList t)
112 | TyConApp _ tc lt => TyConApp tc ((fix replaceCoreDistinctList (lt:list CoreType) :=
115 | h::t => (replaceCoreVar h tv tsubst)::(replaceCoreDistinctList t)
119 (* calculate the CoreType of a WeakExpr *)
120 Fixpoint coreTypeOfWeakExpr (ce:WeakExpr) : ???CoreType :=
122 | WEVar (weakExprVar v t) => OK t
123 | WELit lit => OK (haskLiteralToCoreType lit)
124 | WEApp e1 e2 => coreTypeOfWeakExpr e1 >>= fun t' =>
126 | (TyConApp 2 tc (t1::t2::nil)) =>
127 if (tyCon_eq tc ArrowTyCon)
129 else Error ("found non-function type "+++(weakTypeToString t')+++" in EApp")
130 | _ => Error ("found non-function type "+++(weakTypeToString t')+++" in EApp")
132 | WETyApp e t => coreTypeOfWeakExpr e >>= fun te =>
134 | ForAllTy v ct => OK (replaceCoreVar ct v t)
135 | _ => Error ("found non-forall type "+++(weakTypeToString te)+++" in ETyApp")
137 | WECoApp e co => coreTypeOfWeakExpr e >>= fun te =>
139 | TyConApp 2 tc ((PredTy (EqPred t1 t2))::t3::nil) =>
140 if (tyCon_eq tc ArrowTyCon)
142 else Error ("found non-coercion type "+++(weakTypeToString te)+++" in ETyApp")
143 | _ => Error ("found non-coercion type "+++(weakTypeToString te)+++" in ETyApp")
145 | WELam (weakExprVar ev vt) e => coreTypeOfWeakExpr e >>= fun t' => OK (TyConApp ArrowTyCon (vt::t'::nil))
146 | WETyLam tv e => coreTypeOfWeakExpr e >>= fun t' => match tv with weakTypeVar tvc _ => OK (ForAllTy tvc t') end
147 | WECoLam (weakCoerVar cv φ₁ φ₂) e =>
148 coreTypeOfWeakExpr e >>= fun t' => OK (TyConApp ArrowTyCon ((PredTy (EqPred φ₁ φ₂))::t'::nil))
149 | WELet ev ve e => coreTypeOfWeakExpr e
150 | WELetRec rb e => coreTypeOfWeakExpr e
151 | WENote n e => coreTypeOfWeakExpr e
152 | WECast e (weakCoercion t1 t2 _) => OK t2
153 | WECase scrutinee tbranches n tc type_params alts => OK tbranches
155 (* note that we willfully ignore the type stashed in WEBrak/WEEsc here *)
156 | WEBrak ec e _ => coreTypeOfWeakExpr e >>= fun t' => match ec with weakTypeVar ecc _ =>
157 OK (TyConApp hetMetCodeTypeTyCon ((TyVarTy ecc)::t'::nil)) end
158 | WEEsc ec e _ => coreTypeOfWeakExpr e >>= fun t' => match ec with weakTypeVar ecc _ =>
160 | (TyConApp 2 tc ((TyVarTy ec')::t''::nil)) =>
161 if (tyCon_eq tc hetMetCodeTypeTyCon)
162 then if eqd_dec ecc ec' then OK t''
163 else Error "level mismatch in escapification"
164 else Error "ill-typed escapification"
165 | _ => Error "ill-typed escapification"