Generalizable All Variables.
Require Import Preamble.
Require Import General.
-Require Import HaskGeneral.
-Require Import HaskLiterals.
-Require Import HaskCoreVars.
-Require Import HaskCoreTypes.
+Require Import Coq.Lists.List.
+Require Import HaskKinds.
+Require Import HaskLiteralsAndTyCons.
+Require Import HaskWeakVars.
+Require Import HaskWeakTypes.
+
+Inductive WeakAltCon :=
+| WeakDataAlt : CoreDataCon -> WeakAltCon
+| WeakLitAlt : HaskLiteral -> WeakAltCon
+| WeakDEFAULT : WeakAltCon.
Inductive WeakExpr :=
-| WEVar : CoreVar -> WeakExpr
-| WELit : HaskLiteral -> WeakExpr
-| WELet : CoreVar -> WeakExpr -> WeakExpr -> WeakExpr
-| WELetRec : Tree ??(CoreVar * WeakExpr) -> WeakExpr -> WeakExpr
-| WECast : WeakExpr -> CoreCoercion -> WeakExpr
-| WENote : Note -> WeakExpr -> WeakExpr
-| WEApp : WeakExpr -> WeakExpr -> WeakExpr
-| WETyApp : WeakExpr -> CoreType -> WeakExpr
-| WECoApp : WeakExpr -> CoreCoercion -> WeakExpr
-| WELam : CoreVar -> WeakExpr -> WeakExpr
-| WETyLam : CoreVar -> WeakExpr -> WeakExpr
-| WECoLam : CoreVar -> WeakExpr -> WeakExpr
-| WEBrak : CoreVar -> WeakExpr -> WeakExpr
-| WEEsc : CoreVar -> WeakExpr -> WeakExpr
-| WECase : forall (scrutinee:WeakExpr)
- (tbranches:CoreType)
- {n:nat}(tc:TyCon n)
- (type_params:vec CoreType n)
- (alts : Tree ??(AltCon*list CoreVar*WeakExpr)),
+| WEVar : WeakExprVar -> WeakExpr
+| WELit : HaskLiteral -> WeakExpr
+| WELet : WeakExprVar -> WeakExpr -> WeakExpr -> WeakExpr
+| WELetRec : Tree ??(WeakExprVar * WeakExpr) -> WeakExpr -> WeakExpr
+| WECast : WeakExpr -> WeakCoercion -> WeakExpr
+| WENote : Note -> WeakExpr -> WeakExpr
+| WEApp : WeakExpr -> WeakExpr -> WeakExpr
+| WETyApp : WeakExpr -> WeakType -> WeakExpr
+| WECoApp : WeakExpr -> WeakCoercion -> WeakExpr
+| WELam : WeakExprVar -> WeakExpr -> WeakExpr
+| WETyLam : WeakTypeVar -> WeakExpr -> WeakExpr
+| WECoLam : WeakCoerVar -> WeakExpr -> WeakExpr
+
+(* The WeakType argument in WEBrak/WEEsc is used only when going back *)
+(* from Weak to Core; it lets us dodge a possibly-failing type *)
+(* calculation. The CoreVar argument is the GlobalVar for the hetmet_brak *)
+(* or hetmet_esc identifier *)
+| WEBrak : WeakExprVar -> WeakTypeVar -> WeakExpr -> WeakType -> WeakExpr
+| WEEsc : WeakExprVar -> WeakTypeVar -> WeakExpr -> WeakType -> WeakExpr
+| WECSP : WeakExprVar -> WeakTypeVar -> WeakExpr -> WeakType -> WeakExpr
+
+| WECase : forall (vscrut:WeakExprVar)
+ (scrutinee:WeakExpr)
+ (tbranches:WeakType)
+ (tc:TyCon)
+ (type_params:list WeakType)
+ (alts : Tree ??(WeakAltCon*list WeakTypeVar*list WeakCoerVar*list WeakExprVar*WeakExpr)),
WeakExpr.
-(* calculate the free CoreVar's in a WeakExpr *)
-Fixpoint getWeakExprFreeVars (me:WeakExpr) : list CoreVar :=
- match me with
- | WELit _ => nil
- | WEVar cv => cv::nil
- | WECast e co => getWeakExprFreeVars e
- | WENote n e => getWeakExprFreeVars e
- | WETyApp e t => getWeakExprFreeVars e
- | WECoApp e co => getWeakExprFreeVars e
- | WEBrak ec e => getWeakExprFreeVars e
- | WEEsc ec e => getWeakExprFreeVars e
- | WELet cv e1 e2 => mergeDistinctLists (getWeakExprFreeVars e1) (removeFromDistinctList cv (getWeakExprFreeVars e2))
- | WEApp e1 e2 => mergeDistinctLists (getWeakExprFreeVars e1) (getWeakExprFreeVars e2)
- | WELam cv e => removeFromDistinctList cv (getWeakExprFreeVars e)
- | WETyLam cv e => removeFromDistinctList cv (getWeakExprFreeVars e)
- | WECoLam cv e => removeFromDistinctList cv (getWeakExprFreeVars e)
-
- (* the messy fixpoints below are required by Coq's termination conditions *)
- | WECase scrutinee tbranches n tc type_params alts =>
- mergeDistinctLists (getWeakExprFreeVars scrutinee) (
- ((fix getWeakExprFreeVarsAlts (alts:Tree ??(AltCon*list CoreVar*WeakExpr)) {struct alts} : list CoreVar :=
- match alts with
- | T_Leaf None => nil
- | T_Leaf (Some (DEFAULT,_,e)) => getWeakExprFreeVars e
- | T_Leaf (Some (LitAlt lit,_,e)) => getWeakExprFreeVars e
- | T_Leaf (Some (DataAlt _ _ _ _ _ dc, vars,e)) => removeFromDistinctList' vars (getWeakExprFreeVars e)
- | T_Branch b1 b2 => mergeDistinctLists (getWeakExprFreeVarsAlts b1) (getWeakExprFreeVarsAlts b2)
- end) alts))
- | WELetRec mlr e => (fix removeVarsLetRec (mlr:Tree ??(CoreVar * WeakExpr))(cvl:list CoreVar) :=
- match mlr with
- | T_Leaf None => cvl
- | T_Leaf (Some (cv,e)) => removeFromDistinctList cv cvl
- | T_Branch b1 b2 => removeVarsLetRec b1 (removeVarsLetRec b2 cvl)
- end) mlr (mergeDistinctLists (getWeakExprFreeVars e)
- ((fix getWeakExprFreeVarsLetRec (mlr:Tree ??(CoreVar * WeakExpr)) :=
- match mlr with
- | T_Leaf None => nil
- | T_Leaf (Some (cv,e)) => getWeakExprFreeVars e
- | T_Branch b1 b2 => mergeDistinctLists (getWeakExprFreeVarsLetRec b1) (getWeakExprFreeVarsLetRec b2)
- end) mlr))
- end.
-
-(* wrap lambdas around an expression until it has no free variables *)
-Definition makeClosedExpression : WeakExpr -> WeakExpr :=
- fun me => (fix closeExpression (me:WeakExpr)(cvl:list CoreVar) :=
- match cvl with
- | nil => me
- | cv::cvl' => WELam cv (closeExpression me cvl')
- end) me (getWeakExprFreeVars me).
-
-(* messy first-order capture-avoiding substitution on CoreType's *)
-Fixpoint replaceCoreVar (te:CoreType)(tv:CoreVar)(tsubst:CoreType) :=
- match te with
- | TyVarTy tv' => if eqd_dec tv tv' then tsubst else te
- | AppTy t1 t2 => AppTy (replaceCoreVar t1 tv tsubst) (replaceCoreVar t2 tv tsubst)
- | FunTy t1 t2 => FunTy (replaceCoreVar t1 tv tsubst) (replaceCoreVar t2 tv tsubst)
- | ForAllTy tv' t => if eqd_dec tv tv' then te else ForAllTy tv' (replaceCoreVar t tv tsubst)
- | PredTy (EqPred t1 t2) => PredTy (EqPred (replaceCoreVar t1 tv tsubst) (replaceCoreVar t2 tv tsubst))
- | PredTy (IParam ip ty) => PredTy (IParam ip (replaceCoreVar ty tv tsubst))
- | PredTy (ClassP _ c lt) => PredTy (ClassP c ((fix replaceCoreDistinctList (lt:list CoreType) :=
- match lt with
- | nil => nil
- | h::t => (replaceCoreVar h tv tsubst)::(replaceCoreDistinctList t)
- end) lt))
- | TyConApp _ tc lt => TyConApp tc ((fix replaceCoreDistinctList (lt:list CoreType) :=
- match lt with
- | nil => nil
- | h::t => (replaceCoreVar h tv tsubst)::(replaceCoreDistinctList t)
- end) lt)
- end.
-
-(* calculate the CoreType of a WeakExpr *)
-Fixpoint coreTypeOfWeakExpr (ce:WeakExpr) : ???CoreType :=
- match ce with
- | WEVar v => match coreVarSort v with
- | CoreExprVar t => OK t
- | CoreTypeVar _ => Error "found tyvar in expression"
- | CoreCoerVar _ => Error "found coercion variable in expression"
- end
- | WELit lit => OK (haskLiteralToCoreType lit)
- | WEApp e1 e2 => coreTypeOfWeakExpr e1 >>= fun t' =>
- match t' with
- | FunTy t1 t2 => OK t2
- | (TyConApp 2 tc (t1::t2::nil)) =>
- if (tyCon_eq tc ArrowTyCon)
- then OK t2
- else Error ("found non-function type "+++(coreTypeToString t')+++" in EApp")
- | _ => Error ("found non-function type "+++(coreTypeToString t')+++" in EApp")
- end
- | WETyApp e t => coreTypeOfWeakExpr e >>= fun te =>
- match te with
- | ForAllTy v ct => match coreVarSort v with
- | CoreExprVar _ => Error "found an expression variable inside an forall-type!"
- | CoreTypeVar _ => OK (replaceCoreVar ct v t)
- | CoreCoerVar _ => Error "found a coercion variable inside an forall-type!"
- end
- | _ => Error ("found non-forall type "+++(coreTypeToString te)+++" in ETyApp")
- end
- | WECoApp e co => coreTypeOfWeakExpr e >>= fun te =>
- match te with
- | FunTy (PredTy (EqPred t1 t2)) t3 => OK t3
- | TyConApp 2 tc ((PredTy (EqPred t1 t2))::t3::nil) =>
- if (tyCon_eq tc ArrowTyCon)
- then OK t3
- else Error ("found non-coercion type "+++(coreTypeToString te)+++" in ETyApp")
- | _ => Error ("found non-coercion type "+++(coreTypeToString te)+++" in ETyApp")
- end
- | WELam ev e => coreTypeOfWeakExpr e >>= fun t' => match coreVarSort ev with
- | CoreExprVar vt => OK (FunTy vt t')
- | CoreTypeVar _ => Error "found a type variable in a WELam!"
- | CoreCoerVar _ => Error "found a coercion variable in a WELam!"
- end
- | WETyLam tv e => coreTypeOfWeakExpr e >>= fun t' => OK (ForAllTy tv t')
- | WECoLam cv e => coreTypeOfWeakExpr e >>= fun t' => match coreVarSort cv with
- | CoreExprVar vt => Error "found an expression variable in a WECoLam!"
- | CoreTypeVar _ => Error "found a type variable in a WECoLam!"
- | CoreCoerVar (φ₁,φ₂) => OK (FunTy (PredTy (EqPred φ₁ φ₂)) t')
- end
- | WELet ev ve e => coreTypeOfWeakExpr e
- | WELetRec rb e => coreTypeOfWeakExpr e
- | WENote n e => coreTypeOfWeakExpr e
- | WECast e co => OK (snd (coreCoercionKind co))
- | WECase scrutinee tbranches n tc type_params alts => OK tbranches
- | WEBrak ec e => coreTypeOfWeakExpr e >>= fun t' => OK (TyConApp hetMetCodeTypeTyCon ((TyVarTy ec)::t'::nil))
- | WEEsc ec e => coreTypeOfWeakExpr e >>= fun t' =>
- match t' with
- | (TyConApp 2 tc ((TyVarTy ec')::t''::nil)) =>
- if (tyCon_eq tc hetMetCodeTypeTyCon)
- then if eqd_dec ec ec' then OK t''
- else Error "level mismatch in escapification"
- else Error "ill-typed escapification"
- | _ => Error "ill-typed escapification"
- end
- end.
+Definition weakTypeOfLiteral (lit:HaskLiteral) : WeakType :=
+ (WTyCon (haskLiteralToTyCon lit)).