Generalizable All Variables.
Require Import Preamble.
Require Import General.
-Require Import HaskGeneral.
-Require Import HaskLiterals.
+Require Import Coq.Lists.List.
+Require Import HaskKinds.
+Require Import HaskCoreLiterals.
Require Import HaskCoreVars.
Require Import HaskCoreTypes.
+Require Import HaskCoreTypes.
+Require Import HaskWeakVars.
+Require Import HaskWeakTypes.
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
+| 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 *)
+| WEBrak : WeakTypeVar -> WeakExpr -> WeakType -> WeakExpr
+| WEEsc : WeakTypeVar -> WeakExpr -> WeakType -> WeakExpr
+
+(* note that HaskWeak "Case" does not bind a variable; coreExprToWeakExpr adds a let-binder *)
| WECase : forall (scrutinee:WeakExpr)
- (tbranches:CoreType)
- {n:nat}(tc:TyCon n)
- (type_params:vec CoreType n)
- (alts : Tree ??(AltCon*list CoreVar*WeakExpr)),
+ (tbranches:WeakType)
+ (tc:TyCon)
+ (type_params:list WeakType)
+ (alts : Tree ??(AltCon*list WeakTypeVar*list WeakCoerVar*list WeakExprVar*WeakExpr)),
WeakExpr.
-(* calculate the free CoreVar's in a WeakExpr *)
-Fixpoint getWeakExprFreeVars (me:WeakExpr) : list CoreVar :=
+(* calculate the free WeakVar's in a WeakExpr *)
+Fixpoint getWeakExprFreeVars (me:WeakExpr) : list WeakExprVar :=
match me with
| WELit _ => nil
| WEVar cv => cv::nil
| 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
+ | 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)
+ | WELam cv e => @removeFromDistinctList _ WeakExprVarEqDecidable cv (getWeakExprFreeVars e)
+ | WETyLam cv e => getWeakExprFreeVars e
+ | WECoLam cv e => getWeakExprFreeVars e
- (* the messy fixpoints below are required by Coq's termination conditions *)
- | WECase scrutinee tbranches n tc type_params alts =>
+ (* the messy fixpoints below are required by Coq's termination conditions; trust me, I tried to get rid of them *)
+ | WECase scrutinee tbranches tc type_params alts =>
mergeDistinctLists (getWeakExprFreeVars scrutinee) (
- ((fix getWeakExprFreeVarsAlts (alts:Tree ??(AltCon*list CoreVar*WeakExpr)) {struct alts} : list CoreVar :=
+ ((fix getWeakExprFreeVarsAlts (alts:Tree ??(AltCon*list WeakTypeVar*list WeakCoerVar*list WeakExprVar*WeakExpr))
+ {struct alts} : list WeakExprVar :=
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_Leaf (Some (DEFAULT,_,_,_,e)) => getWeakExprFreeVars e
+ | T_Leaf (Some (LitAlt lit,_,_,_,e)) => getWeakExprFreeVars e
+ | T_Leaf (Some ((DataAlt dc), tvars, cvars, evars,e)) => removeFromDistinctList' evars (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) :=
+ | WELetRec mlr e => (fix removeVarsLetRec (mlr:Tree ??(WeakExprVar * WeakExpr))(cvl:list WeakExprVar) :=
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)) :=
+ ((fix getWeakExprFreeVarsLetRec (mlr:Tree ??(WeakExprVar * WeakExpr)) :=
match mlr with
| T_Leaf None => nil
| T_Leaf (Some (cv,e)) => getWeakExprFreeVars e
end) mlr))
end.
-(* wrap lambdas around an expression until it has no free variables *)
+(* wrap lambdas around an expression until it has no free expression variables *)
Definition makeClosedExpression : WeakExpr -> WeakExpr :=
- fun me => (fix closeExpression (me:WeakExpr)(cvl:list CoreVar) :=
+ fun me => (fix closeExpression (me:WeakExpr)(cvl:list WeakExprVar) :=
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.
+Definition weakTypeOfLiteral (lit:HaskLiteral) : WeakType :=
+ (WTyCon (haskLiteralToTyCon lit)).
(* calculate the CoreType of a WeakExpr *)
-Fixpoint coreTypeOfWeakExpr (ce:WeakExpr) : ???CoreType :=
+Fixpoint weakTypeOfWeakExpr (ce:WeakExpr) : ???WeakType :=
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' =>
+ | WEVar (weakExprVar v t) => OK t
+ | WELit lit => OK (weakTypeOfLiteral lit)
+ | WEApp e1 e2 => weakTypeOfWeakExpr 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")
+ | (WAppTy (WAppTy WFunTyCon t1) t2) => OK t2
+ | _ => Error ("found non-function type "+++(weakTypeToString t')+++" in EApp")
end
- | WETyApp e t => coreTypeOfWeakExpr e >>= fun te =>
+ | WETyApp e t => weakTypeOfWeakExpr 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")
+ | WForAllTy v ct => OK (replaceWeakTypeVar ct v t)
+ | _ => Error ("found non-forall type "+++(weakTypeToString te)+++" in ETyApp")
end
- | WECoApp e co => coreTypeOfWeakExpr e >>= fun te =>
+ | WECoApp e co => weakTypeOfWeakExpr 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")
+ | WCoFunTy t1 t2 t => OK t
+ | _ => Error ("found non-coercion type "+++(weakTypeToString 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' =>
+ | WELam (weakExprVar ev vt) e => weakTypeOfWeakExpr e >>= fun t' => OK (WAppTy (WAppTy WFunTyCon vt) t')
+ | WETyLam tv e => weakTypeOfWeakExpr e >>= fun t' => OK (WForAllTy tv t')
+ | WECoLam (weakCoerVar cv φ₁ φ₂) e => weakTypeOfWeakExpr e >>= fun t' => OK (WCoFunTy φ₁ φ₂ t')
+ | WELet ev ve e => weakTypeOfWeakExpr e
+ | WELetRec rb e => weakTypeOfWeakExpr e
+ | WENote n e => weakTypeOfWeakExpr e
+ | WECast e (weakCoercion t1 t2 _) => OK t2
+ | WECase scrutinee tbranches tc type_params alts => OK tbranches
+
+ (* note that we willfully ignore the type stashed in WEBrak/WEEsc here *)
+ | WEBrak ec e _ => weakTypeOfWeakExpr e >>= fun t' => OK (WCodeTy ec t')
+ | WEEsc ec e _ => weakTypeOfWeakExpr 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''
+ | (WAppTy (WAppTy WCodeTyCon (WTyVarTy ec')) t'') =>
+ 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.
projects / coq-hetmet.git / blobdiff