X-Git-Url: http://git.megacz.com/?p=coq-hetmet.git;a=blobdiff_plain;f=src%2FHaskWeak.v;h=31accd29a2e1dae3d03187191b76d13d94833e74;hp=b4503303eec5344655a7aacf1197705a1e6a33a1;hb=bcb16a7fa1ff772f12807c4587609fd756b7762e;hpb=112daf37524662d6d2267d3f7e50ff3522683b8f diff --git a/src/HaskWeak.v b/src/HaskWeak.v index b450330..31accd2 100644 --- a/src/HaskWeak.v +++ b/src/HaskWeak.v @@ -5,35 +5,45 @@ 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 @@ -41,32 +51,33 @@ Fixpoint getWeakExprFreeVars (me:WeakExpr) : list CoreVar := | 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 @@ -74,95 +85,53 @@ Fixpoint getWeakExprFreeVars (me:WeakExpr) : list CoreVar := 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.