-(* calculate the free WeakVar's in a WeakExpr *)
-Fixpoint getWeakExprFreeVars (me:WeakExpr) : list WeakExprVar :=
- 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 _ 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 =>
- mergeDistinctLists (getWeakExprFreeVars scrutinee) (
- ((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), 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 ??(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 ??(WeakExprVar * 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 expression variables *)
-Definition makeClosedExpression : WeakExpr -> WeakExpr :=
- 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) : 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 (weakExprVar v t) => OK t
- | WELit lit => OK (haskLiteralToCoreType lit)
- | WEApp e1 e2 => coreTypeOfWeakExpr e1 >>= fun t' =>
- match t' with
- | (TyConApp 2 tc (t1::t2::nil)) =>
- if (tyCon_eq tc ArrowTyCon)
- then OK t2
- else Error ("found non-function type "+++(weakTypeToString t')+++" in EApp")
- | _ => Error ("found non-function type "+++(weakTypeToString t')+++" in EApp")
- end
- | WETyApp e t => coreTypeOfWeakExpr e >>= fun te =>
- match te with
- | ForAllTy v ct => OK (replaceCoreVar ct v t)
- | _ => Error ("found non-forall type "+++(weakTypeToString te)+++" in ETyApp")
- end
- | WECoApp e co => coreTypeOfWeakExpr e >>= fun te =>
- match te with
- | TyConApp 2 tc ((PredTy (EqPred t1 t2))::t3::nil) =>
- if (tyCon_eq tc ArrowTyCon)
- then OK t3
- else Error ("found non-coercion type "+++(weakTypeToString te)+++" in ETyApp")
- | _ => Error ("found non-coercion type "+++(weakTypeToString te)+++" in ETyApp")
- end
- | WELam (weakExprVar ev vt) e => coreTypeOfWeakExpr e >>= fun t' => OK (TyConApp ArrowTyCon (vt::t'::nil))
- | WETyLam tv e => coreTypeOfWeakExpr e >>= fun t' => match tv with weakTypeVar tvc _ => OK (ForAllTy tvc t') end
- | WECoLam (weakCoerVar cv φ₁ φ₂) e =>
- coreTypeOfWeakExpr e >>= fun t' => OK (TyConApp ArrowTyCon ((PredTy (EqPred φ₁ φ₂))::t'::nil))
- | WELet ev ve e => coreTypeOfWeakExpr e
- | WELetRec rb e => coreTypeOfWeakExpr e
- | WENote n e => coreTypeOfWeakExpr e
- | WECast e (weakCoercion t1 t2 _) => OK t2
- | WECase scrutinee tbranches n tc type_params alts => OK tbranches
-
- (* note that we willfully ignore the type stashed in WEBrak/WEEsc here *)
- | WEBrak ec e _ => coreTypeOfWeakExpr e >>= fun t' => match ec with weakTypeVar ecc _ =>
- OK (TyConApp hetMetCodeTypeTyCon ((TyVarTy ecc)::t'::nil)) end
- | WEEsc ec e _ => coreTypeOfWeakExpr e >>= fun t' => match ec with weakTypeVar ecc _ =>
- match t' with
- | (TyConApp 2 tc ((TyVarTy ec')::t''::nil)) =>
- if (tyCon_eq tc hetMetCodeTypeTyCon)
- then if eqd_dec ecc ec' then OK t''
- else Error "level mismatch in escapification"
- else Error "ill-typed escapification"
- | _ => Error "ill-typed escapification"
- end end
- end.