2 % (c) The University of Glasgow 2006
3 % (c) The GRASP/AQUA Project, Glasgow University, 1998
6 Type - public interface
10 -- re-exports from TypeRep
11 TyThing(..), Type, PredType(..), ThetaType,
15 Kind, SimpleKind, KindVar,
16 kindFunResult, splitKindFunTys, splitKindFunTysN,
18 liftedTypeKindTyCon, openTypeKindTyCon, unliftedTypeKindTyCon,
19 argTypeKindTyCon, ubxTupleKindTyCon,
21 liftedTypeKind, unliftedTypeKind, openTypeKind,
22 argTypeKind, ubxTupleKind,
24 tySuperKind, coSuperKind,
26 isLiftedTypeKind, isUnliftedTypeKind, isOpenTypeKind,
27 isUbxTupleKind, isArgTypeKind, isKind, isTySuperKind,
28 isCoSuperKind, isSuperKind, isCoercionKind, isEqPred,
29 mkArrowKind, mkArrowKinds,
31 isSubArgTypeKind, isSubOpenTypeKind, isSubKind, defaultKind, eqKind,
34 -- Re-exports from TyCon
37 mkTyVarTy, mkTyVarTys, getTyVar, getTyVar_maybe, isTyVarTy,
39 mkAppTy, mkAppTys, splitAppTy, splitAppTys,
40 splitAppTy_maybe, repSplitAppTy_maybe,
42 mkFunTy, mkFunTys, splitFunTy, splitFunTy_maybe,
43 splitFunTys, splitFunTysN,
44 funResultTy, funArgTy, zipFunTys, isFunTy,
46 mkTyConApp, mkTyConTy,
47 tyConAppTyCon, tyConAppArgs,
48 splitTyConApp_maybe, splitTyConApp,
49 splitNewTyConApp_maybe, splitNewTyConApp,
51 repType, repType', typePrimRep, coreView, tcView, kindView,
53 mkForAllTy, mkForAllTys, splitForAllTy_maybe, splitForAllTys,
54 applyTy, applyTys, isForAllTy, dropForAlls,
57 predTypeRep, mkPredTy, mkPredTys,
60 splitRecNewType_maybe, newTyConInstRhs,
63 isUnLiftedType, isUnboxedTupleType, isAlgType, isPrimitiveType,
64 isStrictType, isStrictPred,
67 tyVarsOfType, tyVarsOfTypes, tyVarsOfPred, tyVarsOfTheta,
68 typeKind, addFreeTyVars,
70 -- Tidying up for printing
72 tidyOpenType, tidyOpenTypes,
73 tidyTyVarBndr, tidyFreeTyVars,
74 tidyOpenTyVar, tidyOpenTyVars,
75 tidyTopType, tidyPred,
79 coreEqType, tcEqType, tcEqTypes, tcCmpType, tcCmpTypes,
80 tcEqPred, tcCmpPred, tcEqTypeX,
86 TvSubstEnv, emptyTvSubstEnv, -- Representation widely visible
87 TvSubst(..), emptyTvSubst, -- Representation visible to a few friends
88 mkTvSubst, mkOpenTvSubst, zipOpenTvSubst, zipTopTvSubst, mkTopTvSubst, notElemTvSubst,
89 getTvSubstEnv, setTvSubstEnv, getTvInScope, extendTvInScope,
90 extendTvSubst, extendTvSubstList, isInScope, composeTvSubst, zipTyEnv,
92 -- Performing substitution on types
93 substTy, substTys, substTyWith, substTheta,
94 substPred, substTyVar, substTyVarBndr, deShadowTy, lookupTyVar,
97 pprType, pprParendType, pprTyThingCategory, pprForAll,
98 pprPred, pprTheta, pprThetaArrow, pprClassPred, pprKind, pprParendKind
101 #include "HsVersions.h"
103 -- We import the representation and primitive functions from TypeRep.
104 -- Many things are reexported, but not the representation!
124 import Data.Maybe ( isJust )
128 %************************************************************************
132 %************************************************************************
134 In Core, we "look through" non-recursive newtypes and PredTypes.
137 {-# INLINE coreView #-}
138 coreView :: Type -> Maybe Type
139 -- Strips off the *top layer only* of a type to give
140 -- its underlying representation type.
141 -- Returns Nothing if there is nothing to look through.
143 -- In the case of newtypes, it returns
144 -- *either* a vanilla TyConApp (recursive newtype, or non-saturated)
145 -- *or* the newtype representation (otherwise), meaning the
146 -- type written in the RHS of the newtype decl,
147 -- which may itself be a newtype
149 -- Example: newtype R = MkR S
151 -- newtype T = MkT (T -> T)
152 -- expandNewTcApp on R gives Just S
154 -- on T gives Nothing (no expansion)
156 -- By being non-recursive and inlined, this case analysis gets efficiently
157 -- joined onto the case analysis that the caller is already doing
158 coreView (NoteTy _ ty) = Just ty
160 | isEqPred p = Nothing
161 | otherwise = Just (predTypeRep p)
162 coreView (TyConApp tc tys) | Just (tenv, rhs, tys') <- coreExpandTyCon_maybe tc tys
163 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
164 -- Its important to use mkAppTys, rather than (foldl AppTy),
165 -- because the function part might well return a
166 -- partially-applied type constructor; indeed, usually will!
167 coreView ty = Nothing
171 -----------------------------------------------
172 {-# INLINE tcView #-}
173 tcView :: Type -> Maybe Type
174 -- Same, but for the type checker, which just looks through synonyms
175 tcView (NoteTy _ ty) = Just ty
176 tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- tcExpandTyCon_maybe tc tys
177 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
180 -----------------------------------------------
181 {-# INLINE kindView #-}
182 kindView :: Kind -> Maybe Kind
183 -- C.f. coreView, tcView
184 -- For the moment, we don't even handle synonyms in kinds
185 kindView (NoteTy _ k) = Just k
186 kindView other = Nothing
190 %************************************************************************
192 \subsection{Constructor-specific functions}
194 %************************************************************************
197 ---------------------------------------------------------------------
201 mkTyVarTy :: TyVar -> Type
204 mkTyVarTys :: [TyVar] -> [Type]
205 mkTyVarTys = map mkTyVarTy -- a common use of mkTyVarTy
207 getTyVar :: String -> Type -> TyVar
208 getTyVar msg ty = case getTyVar_maybe ty of
210 Nothing -> panic ("getTyVar: " ++ msg)
212 isTyVarTy :: Type -> Bool
213 isTyVarTy ty = isJust (getTyVar_maybe ty)
215 getTyVar_maybe :: Type -> Maybe TyVar
216 getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty'
217 getTyVar_maybe (TyVarTy tv) = Just tv
218 getTyVar_maybe other = Nothing
223 ---------------------------------------------------------------------
226 We need to be pretty careful with AppTy to make sure we obey the
227 invariant that a TyConApp is always visibly so. mkAppTy maintains the
231 mkAppTy orig_ty1 orig_ty2
234 mk_app (NoteTy _ ty1) = mk_app ty1
235 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ [orig_ty2])
236 mk_app ty1 = AppTy orig_ty1 orig_ty2
237 -- Note that the TyConApp could be an
238 -- under-saturated type synonym. GHC allows that; e.g.
239 -- type Foo k = k a -> k a
241 -- foo :: Foo Id -> Foo Id
243 -- Here Id is partially applied in the type sig for Foo,
244 -- but once the type synonyms are expanded all is well
246 mkAppTys :: Type -> [Type] -> Type
247 mkAppTys orig_ty1 [] = orig_ty1
248 -- This check for an empty list of type arguments
249 -- avoids the needless loss of a type synonym constructor.
250 -- For example: mkAppTys Rational []
251 -- returns to (Ratio Integer), which has needlessly lost
252 -- the Rational part.
253 mkAppTys orig_ty1 orig_tys2
256 mk_app (NoteTy _ ty1) = mk_app ty1
257 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ orig_tys2)
258 -- mkTyConApp: see notes with mkAppTy
259 mk_app ty1 = foldl AppTy orig_ty1 orig_tys2
262 splitAppTy_maybe :: Type -> Maybe (Type, Type)
263 splitAppTy_maybe ty | Just ty' <- coreView ty
264 = splitAppTy_maybe ty'
265 splitAppTy_maybe ty = repSplitAppTy_maybe ty
268 repSplitAppTy_maybe :: Type -> Maybe (Type,Type)
269 -- Does the AppTy split, but assumes that any view stuff is already done
270 repSplitAppTy_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
271 repSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
272 repSplitAppTy_maybe (TyConApp tc tys) = case snocView tys of
273 Just (tys', ty') -> Just (TyConApp tc tys', ty')
275 repSplitAppTy_maybe other = Nothing
277 splitAppTy :: Type -> (Type, Type)
278 splitAppTy ty = case splitAppTy_maybe ty of
280 Nothing -> panic "splitAppTy"
283 splitAppTys :: Type -> (Type, [Type])
284 splitAppTys ty = split ty ty []
286 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
287 split orig_ty (AppTy ty arg) args = split ty ty (arg:args)
288 split orig_ty (TyConApp tc tc_args) args = (TyConApp tc [], tc_args ++ args)
289 split orig_ty (FunTy ty1 ty2) args = ASSERT( null args )
290 (TyConApp funTyCon [], [ty1,ty2])
291 split orig_ty ty args = (orig_ty, args)
296 ---------------------------------------------------------------------
301 mkFunTy :: Type -> Type -> Type
302 mkFunTy (PredTy (EqPred ty1 ty2)) res = mkForAllTy (mkWildCoVar (PredTy (EqPred ty1 ty2))) res
303 mkFunTy arg res = FunTy arg res
305 mkFunTys :: [Type] -> Type -> Type
306 mkFunTys tys ty = foldr mkFunTy ty tys
308 isFunTy :: Type -> Bool
309 isFunTy ty = isJust (splitFunTy_maybe ty)
311 splitFunTy :: Type -> (Type, Type)
312 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
313 splitFunTy (FunTy arg res) = (arg, res)
314 splitFunTy other = pprPanic "splitFunTy" (ppr other)
316 splitFunTy_maybe :: Type -> Maybe (Type, Type)
317 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
318 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
319 splitFunTy_maybe other = Nothing
321 splitFunTys :: Type -> ([Type], Type)
322 splitFunTys ty = split [] ty ty
324 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
325 split args orig_ty (FunTy arg res) = split (arg:args) res res
326 split args orig_ty ty = (reverse args, orig_ty)
328 splitFunTysN :: Int -> Type -> ([Type], Type)
329 -- Split off exactly n arg tys
330 splitFunTysN 0 ty = ([], ty)
331 splitFunTysN n ty = case splitFunTy ty of { (arg, res) ->
332 case splitFunTysN (n-1) res of { (args, res) ->
335 zipFunTys :: Outputable a => [a] -> Type -> ([(a,Type)], Type)
336 zipFunTys orig_xs orig_ty = split [] orig_xs orig_ty orig_ty
338 split acc [] nty ty = (reverse acc, nty)
340 | Just ty' <- coreView ty = split acc xs nty ty'
341 split acc (x:xs) nty (FunTy arg res) = split ((x,arg):acc) xs res res
342 split acc (x:xs) nty ty = pprPanic "zipFunTys" (ppr orig_xs <+> ppr orig_ty)
344 funResultTy :: Type -> Type
345 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
346 funResultTy (FunTy arg res) = res
347 funResultTy ty = pprPanic "funResultTy" (ppr ty)
349 funArgTy :: Type -> Type
350 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
351 funArgTy (FunTy arg res) = arg
352 funArgTy ty = pprPanic "funArgTy" (ppr ty)
356 ---------------------------------------------------------------------
359 @mkTyConApp@ is a key function, because it builds a TyConApp, FunTy or PredTy,
363 mkTyConApp :: TyCon -> [Type] -> Type
365 | isFunTyCon tycon, [ty1,ty2] <- tys
371 mkTyConTy :: TyCon -> Type
372 mkTyConTy tycon = mkTyConApp tycon []
374 -- splitTyConApp "looks through" synonyms, because they don't
375 -- mean a distinct type, but all other type-constructor applications
376 -- including functions are returned as Just ..
378 tyConAppTyCon :: Type -> TyCon
379 tyConAppTyCon ty = fst (splitTyConApp ty)
381 tyConAppArgs :: Type -> [Type]
382 tyConAppArgs ty = snd (splitTyConApp ty)
384 splitTyConApp :: Type -> (TyCon, [Type])
385 splitTyConApp ty = case splitTyConApp_maybe ty of
387 Nothing -> pprPanic "splitTyConApp" (ppr ty)
389 splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
390 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
391 splitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
392 splitTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
393 splitTyConApp_maybe other = Nothing
395 -- Sometimes we do NOT want to look throught a newtype. When case matching
396 -- on a newtype we want a convenient way to access the arguments of a newty
397 -- constructor so as to properly form a coercion.
398 splitNewTyConApp :: Type -> (TyCon, [Type])
399 splitNewTyConApp ty = case splitNewTyConApp_maybe ty of
401 Nothing -> pprPanic "splitNewTyConApp" (ppr ty)
402 splitNewTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
403 splitNewTyConApp_maybe ty | Just ty' <- tcView ty = splitNewTyConApp_maybe ty'
404 splitNewTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
405 splitNewTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
406 splitNewTyConApp_maybe other = Nothing
408 -- get instantiated newtype rhs, the arguments had better saturate
410 newTyConInstRhs :: TyCon -> [Type] -> Type
411 newTyConInstRhs tycon tys =
412 let (tvs, ty) = newTyConRhs tycon in substTyWith tvs tys ty
417 ---------------------------------------------------------------------
421 Notes on type synonyms
422 ~~~~~~~~~~~~~~~~~~~~~~
423 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
424 to return type synonyms whereever possible. Thus
429 splitFunTys (a -> Foo a) = ([a], Foo a)
432 The reason is that we then get better (shorter) type signatures in
433 interfaces. Notably this plays a role in tcTySigs in TcBinds.lhs.
438 repType looks through
442 (d) usage annotations
443 (e) all newtypes, including recursive ones, but not newtype families
444 It's useful in the back end.
447 repType :: Type -> Type
448 -- Only applied to types of kind *; hence tycons are saturated
449 repType ty | Just ty' <- coreView ty = repType ty'
450 repType (ForAllTy _ ty) = repType ty
451 repType (TyConApp tc tys)
452 | isClosedNewTyCon tc = -- Recursive newtypes are opaque to coreView
453 -- but we must expand them here. Sure to
454 -- be saturated because repType is only applied
455 -- to types of kind *
456 ASSERT( {- isRecursiveTyCon tc && -} tys `lengthIs` tyConArity tc )
457 repType (new_type_rep tc tys)
460 -- repType' aims to be a more thorough version of repType
461 -- For now it simply looks through the TyConApp args too
462 repType' ty -- | pprTrace "repType'" (ppr ty $$ ppr (go1 ty)) False = undefined
466 go (TyConApp tc tys) = mkTyConApp tc (map repType' tys)
470 -- new_type_rep doesn't ask any questions:
471 -- it just expands newtype, whether recursive or not
472 new_type_rep new_tycon tys = ASSERT( tys `lengthIs` tyConArity new_tycon )
473 case newTyConRep new_tycon of
474 (tvs, rep_ty) -> substTyWith tvs tys rep_ty
476 -- ToDo: this could be moved to the code generator, using splitTyConApp instead
477 -- of inspecting the type directly.
478 typePrimRep :: Type -> PrimRep
479 typePrimRep ty = case repType ty of
480 TyConApp tc _ -> tyConPrimRep tc
482 AppTy _ _ -> PtrRep -- See note below
484 other -> pprPanic "typePrimRep" (ppr ty)
485 -- Types of the form 'f a' must be of kind *, not *#, so
486 -- we are guaranteed that they are represented by pointers.
487 -- The reason is that f must have kind *->*, not *->*#, because
488 -- (we claim) there is no way to constrain f's kind any other
494 ---------------------------------------------------------------------
499 mkForAllTy :: TyVar -> Type -> Type
501 = mkForAllTys [tyvar] ty
503 mkForAllTys :: [TyVar] -> Type -> Type
504 mkForAllTys tyvars ty = foldr ForAllTy ty tyvars
506 isForAllTy :: Type -> Bool
507 isForAllTy (NoteTy _ ty) = isForAllTy ty
508 isForAllTy (ForAllTy _ _) = True
509 isForAllTy other_ty = False
511 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
512 splitForAllTy_maybe ty = splitFAT_m ty
514 splitFAT_m ty | Just ty' <- coreView ty = splitFAT_m ty'
515 splitFAT_m (ForAllTy tyvar ty) = Just(tyvar, ty)
516 splitFAT_m _ = Nothing
518 splitForAllTys :: Type -> ([TyVar], Type)
519 splitForAllTys ty = split ty ty []
521 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
522 split orig_ty (ForAllTy tv ty) tvs = split ty ty (tv:tvs)
523 split orig_ty t tvs = (reverse tvs, orig_ty)
525 dropForAlls :: Type -> Type
526 dropForAlls ty = snd (splitForAllTys ty)
529 -- (mkPiType now in CoreUtils)
533 Instantiate a for-all type with one or more type arguments.
534 Used when we have a polymorphic function applied to type args:
536 Then we use (applyTys type-of-f [t1,t2]) to compute the type of
540 applyTy :: Type -> Type -> Type
541 applyTy ty arg | Just ty' <- coreView ty = applyTy ty' arg
542 applyTy (ForAllTy tv ty) arg = substTyWith [tv] [arg] ty
543 applyTy other arg = panic "applyTy"
545 applyTys :: Type -> [Type] -> Type
546 -- This function is interesting because
547 -- a) the function may have more for-alls than there are args
548 -- b) less obviously, it may have fewer for-alls
549 -- For case (b) think of
550 -- applyTys (forall a.a) [forall b.b, Int]
551 -- This really can happen, via dressing up polymorphic types with newtype
552 -- clothing. Here's an example:
553 -- newtype R = R (forall a. a->a)
554 -- foo = case undefined :: R of
557 applyTys orig_fun_ty [] = orig_fun_ty
558 applyTys orig_fun_ty arg_tys
559 | n_tvs == n_args -- The vastly common case
560 = substTyWith tvs arg_tys rho_ty
561 | n_tvs > n_args -- Too many for-alls
562 = substTyWith (take n_args tvs) arg_tys
563 (mkForAllTys (drop n_args tvs) rho_ty)
564 | otherwise -- Too many type args
565 = ASSERT2( n_tvs > 0, ppr orig_fun_ty ) -- Zero case gives infnite loop!
566 applyTys (substTyWith tvs (take n_tvs arg_tys) rho_ty)
569 (tvs, rho_ty) = splitForAllTys orig_fun_ty
571 n_args = length arg_tys
575 %************************************************************************
577 \subsection{Source types}
579 %************************************************************************
581 A "source type" is a type that is a separate type as far as the type checker is
582 concerned, but which has low-level representation as far as the back end is concerned.
584 Source types are always lifted.
586 The key function is predTypeRep which gives the representation of a source type:
589 mkPredTy :: PredType -> Type
590 mkPredTy pred = PredTy pred
592 mkPredTys :: ThetaType -> [Type]
593 mkPredTys preds = map PredTy preds
595 predTypeRep :: PredType -> Type
596 -- Convert a PredType to its "representation type";
597 -- the post-type-checking type used by all the Core passes of GHC.
598 -- Unwraps only the outermost level; for example, the result might
599 -- be a newtype application
600 predTypeRep (IParam _ ty) = ty
601 predTypeRep (ClassP clas tys) = mkTyConApp (classTyCon clas) tys
602 -- Result might be a newtype application, but the consumer will
603 -- look through that too if necessary
604 predTypeRep (EqPred ty1 ty2) = pprPanic "predTypeRep" (ppr (EqPred ty1 ty2))
608 %************************************************************************
612 %************************************************************************
615 splitRecNewType_maybe :: Type -> Maybe Type
616 -- Sometimes we want to look through a recursive newtype, and that's what happens here
617 -- It only strips *one layer* off, so the caller will usually call itself recursively
618 -- Only applied to types of kind *, hence the newtype is always saturated
619 splitRecNewType_maybe ty | Just ty' <- coreView ty = splitRecNewType_maybe ty'
620 splitRecNewType_maybe (TyConApp tc tys)
621 | isClosedNewTyCon tc
622 = ASSERT( tys `lengthIs` tyConArity tc ) -- splitRecNewType_maybe only be applied
623 -- to *types* (of kind *)
624 ASSERT( isRecursiveTyCon tc ) -- Guaranteed by coreView
625 case newTyConRhs tc of
626 (tvs, rep_ty) -> ASSERT( length tvs == length tys )
627 Just (substTyWith tvs tys rep_ty)
629 splitRecNewType_maybe other = Nothing
636 %************************************************************************
638 \subsection{Kinds and free variables}
640 %************************************************************************
642 ---------------------------------------------------------------------
643 Finding the kind of a type
644 ~~~~~~~~~~~~~~~~~~~~~~~~~~
646 typeKind :: Type -> Kind
647 typeKind (TyConApp tycon tys) = ASSERT( not (isCoercionTyCon tycon) )
648 -- We should be looking for the coercion kind,
650 foldr (\_ k -> kindFunResult k) (tyConKind tycon) tys
651 typeKind (NoteTy _ ty) = typeKind ty
652 typeKind (PredTy pred) = predKind pred
653 typeKind (AppTy fun arg) = kindFunResult (typeKind fun)
654 typeKind (ForAllTy tv ty) = typeKind ty
655 typeKind (TyVarTy tyvar) = tyVarKind tyvar
656 typeKind (FunTy arg res)
657 -- Hack alert. The kind of (Int -> Int#) is liftedTypeKind (*),
658 -- not unliftedTypKind (#)
659 -- The only things that can be after a function arrow are
660 -- (a) types (of kind openTypeKind or its sub-kinds)
661 -- (b) kinds (of super-kind TY) (e.g. * -> (* -> *))
662 | isTySuperKind k = k
663 | otherwise = ASSERT( isSubOpenTypeKind k) liftedTypeKind
667 predKind :: PredType -> Kind
668 predKind (EqPred {}) = coSuperKind -- A coercion kind!
669 predKind (ClassP {}) = liftedTypeKind -- Class and implicitPredicates are
670 predKind (IParam {}) = liftedTypeKind -- always represented by lifted types
674 ---------------------------------------------------------------------
675 Free variables of a type
676 ~~~~~~~~~~~~~~~~~~~~~~~~
678 tyVarsOfType :: Type -> TyVarSet
679 -- NB: for type synonyms tyVarsOfType does *not* expand the synonym
680 tyVarsOfType (TyVarTy tv) = unitVarSet tv
681 tyVarsOfType (TyConApp tycon tys) = tyVarsOfTypes tys
682 tyVarsOfType (NoteTy (FTVNote tvs) ty2) = tvs
683 tyVarsOfType (PredTy sty) = tyVarsOfPred sty
684 tyVarsOfType (FunTy arg res) = tyVarsOfType arg `unionVarSet` tyVarsOfType res
685 tyVarsOfType (AppTy fun arg) = tyVarsOfType fun `unionVarSet` tyVarsOfType arg
686 tyVarsOfType (ForAllTy tyvar ty) = delVarSet (tyVarsOfType ty) tyvar
688 tyVarsOfTypes :: [Type] -> TyVarSet
689 tyVarsOfTypes tys = foldr (unionVarSet.tyVarsOfType) emptyVarSet tys
691 tyVarsOfPred :: PredType -> TyVarSet
692 tyVarsOfPred (IParam _ ty) = tyVarsOfType ty
693 tyVarsOfPred (ClassP _ tys) = tyVarsOfTypes tys
694 tyVarsOfPred (EqPred ty1 ty2) = tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2
696 tyVarsOfTheta :: ThetaType -> TyVarSet
697 tyVarsOfTheta = foldr (unionVarSet . tyVarsOfPred) emptyVarSet
699 -- Add a Note with the free tyvars to the top of the type
700 addFreeTyVars :: Type -> Type
701 addFreeTyVars ty@(NoteTy (FTVNote _) _) = ty
702 addFreeTyVars ty = NoteTy (FTVNote (tyVarsOfType ty)) ty
706 %************************************************************************
708 \subsection{TidyType}
710 %************************************************************************
712 tidyTy tidies up a type for printing in an error message, or in
715 It doesn't change the uniques at all, just the print names.
718 tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
719 tidyTyVarBndr (tidy_env, subst) tyvar
720 = case tidyOccName tidy_env (getOccName name) of
721 (tidy', occ') -> ((tidy', subst'), tyvar')
723 subst' = extendVarEnv subst tyvar tyvar'
724 tyvar' = setTyVarName tyvar name'
725 name' = tidyNameOcc name occ'
727 name = tyVarName tyvar
729 tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv
730 -- Add the free tyvars to the env in tidy form,
731 -- so that we can tidy the type they are free in
732 tidyFreeTyVars env tyvars = fst (tidyOpenTyVars env (varSetElems tyvars))
734 tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
735 tidyOpenTyVars env tyvars = mapAccumL tidyOpenTyVar env tyvars
737 tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
738 -- Treat a new tyvar as a binder, and give it a fresh tidy name
739 tidyOpenTyVar env@(tidy_env, subst) tyvar
740 = case lookupVarEnv subst tyvar of
741 Just tyvar' -> (env, tyvar') -- Already substituted
742 Nothing -> tidyTyVarBndr env tyvar -- Treat it as a binder
744 tidyType :: TidyEnv -> Type -> Type
745 tidyType env@(tidy_env, subst) ty
748 go (TyVarTy tv) = case lookupVarEnv subst tv of
749 Nothing -> TyVarTy tv
750 Just tv' -> TyVarTy tv'
751 go (TyConApp tycon tys) = let args = map go tys
752 in args `seqList` TyConApp tycon args
753 go (NoteTy note ty) = (NoteTy $! (go_note note)) $! (go ty)
754 go (PredTy sty) = PredTy (tidyPred env sty)
755 go (AppTy fun arg) = (AppTy $! (go fun)) $! (go arg)
756 go (FunTy fun arg) = (FunTy $! (go fun)) $! (go arg)
757 go (ForAllTy tv ty) = ForAllTy tvp $! (tidyType envp ty)
759 (envp, tvp) = tidyTyVarBndr env tv
761 go_note note@(FTVNote ftvs) = note -- No need to tidy the free tyvars
763 tidyTypes env tys = map (tidyType env) tys
765 tidyPred :: TidyEnv -> PredType -> PredType
766 tidyPred env (IParam n ty) = IParam n (tidyType env ty)
767 tidyPred env (ClassP clas tys) = ClassP clas (tidyTypes env tys)
768 tidyPred env (EqPred ty1 ty2) = EqPred (tidyType env ty1) (tidyType env ty2)
772 @tidyOpenType@ grabs the free type variables, tidies them
773 and then uses @tidyType@ to work over the type itself
776 tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
778 = (env', tidyType env' ty)
780 env' = tidyFreeTyVars env (tyVarsOfType ty)
782 tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
783 tidyOpenTypes env tys = mapAccumL tidyOpenType env tys
785 tidyTopType :: Type -> Type
786 tidyTopType ty = tidyType emptyTidyEnv ty
791 tidyKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
792 tidyKind env k = tidyOpenType env k
797 %************************************************************************
799 \subsection{Liftedness}
801 %************************************************************************
804 isUnLiftedType :: Type -> Bool
805 -- isUnLiftedType returns True for forall'd unlifted types:
806 -- x :: forall a. Int#
807 -- I found bindings like these were getting floated to the top level.
808 -- They are pretty bogus types, mind you. It would be better never to
811 isUnLiftedType ty | Just ty' <- coreView ty = isUnLiftedType ty'
812 isUnLiftedType (ForAllTy tv ty) = isUnLiftedType ty
813 isUnLiftedType (TyConApp tc _) = isUnLiftedTyCon tc
814 isUnLiftedType other = False
816 isUnboxedTupleType :: Type -> Bool
817 isUnboxedTupleType ty = case splitTyConApp_maybe ty of
818 Just (tc, ty_args) -> isUnboxedTupleTyCon tc
821 -- Should only be applied to *types*; hence the assert
822 isAlgType :: Type -> Bool
823 isAlgType ty = case splitTyConApp_maybe ty of
824 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
829 @isStrictType@ computes whether an argument (or let RHS) should
830 be computed strictly or lazily, based only on its type.
831 Works just like isUnLiftedType, except that it has a special case
832 for dictionaries. Since it takes account of ClassP, you might think
833 this function should be in TcType, but isStrictType is used by DataCon,
834 which is below TcType in the hierarchy, so it's convenient to put it here.
837 isStrictType (PredTy pred) = isStrictPred pred
838 isStrictType ty | Just ty' <- coreView ty = isStrictType ty'
839 isStrictType (ForAllTy tv ty) = isStrictType ty
840 isStrictType (TyConApp tc _) = isUnLiftedTyCon tc
841 isStrictType other = False
843 isStrictPred (ClassP clas _) = opt_DictsStrict && not (isNewTyCon (classTyCon clas))
844 isStrictPred other = False
845 -- We may be strict in dictionary types, but only if it
846 -- has more than one component.
847 -- [Being strict in a single-component dictionary risks
848 -- poking the dictionary component, which is wrong.]
852 isPrimitiveType :: Type -> Bool
853 -- Returns types that are opaque to Haskell.
854 -- Most of these are unlifted, but now that we interact with .NET, we
855 -- may have primtive (foreign-imported) types that are lifted
856 isPrimitiveType ty = case splitTyConApp_maybe ty of
857 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
863 %************************************************************************
865 \subsection{Sequencing on types
867 %************************************************************************
870 seqType :: Type -> ()
871 seqType (TyVarTy tv) = tv `seq` ()
872 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
873 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
874 seqType (NoteTy note t2) = seqNote note `seq` seqType t2
875 seqType (PredTy p) = seqPred p
876 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
877 seqType (ForAllTy tv ty) = tv `seq` seqType ty
879 seqTypes :: [Type] -> ()
881 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
883 seqNote :: TyNote -> ()
884 seqNote (FTVNote set) = sizeUniqSet set `seq` ()
886 seqPred :: PredType -> ()
887 seqPred (ClassP c tys) = c `seq` seqTypes tys
888 seqPred (IParam n ty) = n `seq` seqType ty
889 seqPred (EqPred ty1 ty2) = seqType ty1 `seq` seqType ty2
893 %************************************************************************
895 Equality for Core types
896 (We don't use instances so that we know where it happens)
898 %************************************************************************
900 Note that eqType works right even for partial applications of newtypes.
901 See Note [Newtype eta] in TyCon.lhs
904 coreEqType :: Type -> Type -> Bool
908 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
910 eq env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 == rnOccR env tv2
911 eq env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = eq (rnBndr2 env tv1 tv2) t1 t2
912 eq env (AppTy s1 t1) (AppTy s2 t2) = eq env s1 s2 && eq env t1 t2
913 eq env (FunTy s1 t1) (FunTy s2 t2) = eq env s1 s2 && eq env t1 t2
914 eq env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
915 | tc1 == tc2, all2 (eq env) tys1 tys2 = True
916 -- The lengths should be equal because
917 -- the two types have the same kind
918 -- NB: if the type constructors differ that does not
919 -- necessarily mean that the types aren't equal
920 -- (synonyms, newtypes)
921 -- Even if the type constructors are the same, but the arguments
922 -- differ, the two types could be the same (e.g. if the arg is just
923 -- ignored in the RHS). In both these cases we fall through to an
924 -- attempt to expand one side or the other.
926 -- Now deal with newtypes, synonyms, pred-tys
927 eq env t1 t2 | Just t1' <- coreView t1 = eq env t1' t2
928 | Just t2' <- coreView t2 = eq env t1 t2'
930 -- Fall through case; not equal!
935 %************************************************************************
937 Comparision for source types
938 (We don't use instances so that we know where it happens)
940 %************************************************************************
944 do *not* look through newtypes, PredTypes
947 tcEqType :: Type -> Type -> Bool
948 tcEqType t1 t2 = isEqual $ cmpType t1 t2
950 tcEqTypes :: [Type] -> [Type] -> Bool
951 tcEqTypes tys1 tys2 = isEqual $ cmpTypes tys1 tys2
953 tcCmpType :: Type -> Type -> Ordering
954 tcCmpType t1 t2 = cmpType t1 t2
956 tcCmpTypes :: [Type] -> [Type] -> Ordering
957 tcCmpTypes tys1 tys2 = cmpTypes tys1 tys2
959 tcEqPred :: PredType -> PredType -> Bool
960 tcEqPred p1 p2 = isEqual $ cmpPred p1 p2
962 tcCmpPred :: PredType -> PredType -> Ordering
963 tcCmpPred p1 p2 = cmpPred p1 p2
965 tcEqTypeX :: RnEnv2 -> Type -> Type -> Bool
966 tcEqTypeX env t1 t2 = isEqual $ cmpTypeX env t1 t2
969 Now here comes the real worker
972 cmpType :: Type -> Type -> Ordering
973 cmpType t1 t2 = cmpTypeX rn_env t1 t2
975 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
977 cmpTypes :: [Type] -> [Type] -> Ordering
978 cmpTypes ts1 ts2 = cmpTypesX rn_env ts1 ts2
980 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfTypes ts1 `unionVarSet` tyVarsOfTypes ts2))
982 cmpPred :: PredType -> PredType -> Ordering
983 cmpPred p1 p2 = cmpPredX rn_env p1 p2
985 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfPred p1 `unionVarSet` tyVarsOfPred p2))
987 cmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
988 cmpTypeX env t1 t2 | Just t1' <- tcView t1 = cmpTypeX env t1' t2
989 | Just t2' <- tcView t2 = cmpTypeX env t1 t2'
991 cmpTypeX env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 `compare` rnOccR env tv2
992 cmpTypeX env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = cmpTypeX (rnBndr2 env tv1 tv2) t1 t2
993 cmpTypeX env (AppTy s1 t1) (AppTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
994 cmpTypeX env (FunTy s1 t1) (FunTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
995 cmpTypeX env (PredTy p1) (PredTy p2) = cmpPredX env p1 p2
996 cmpTypeX env (TyConApp tc1 tys1) (TyConApp tc2 tys2) = (tc1 `compare` tc2) `thenCmp` cmpTypesX env tys1 tys2
997 cmpTypeX env t1 (NoteTy _ t2) = cmpTypeX env t1 t2
999 -- Deal with the rest: TyVarTy < AppTy < FunTy < TyConApp < ForAllTy < PredTy
1000 cmpTypeX env (AppTy _ _) (TyVarTy _) = GT
1002 cmpTypeX env (FunTy _ _) (TyVarTy _) = GT
1003 cmpTypeX env (FunTy _ _) (AppTy _ _) = GT
1005 cmpTypeX env (TyConApp _ _) (TyVarTy _) = GT
1006 cmpTypeX env (TyConApp _ _) (AppTy _ _) = GT
1007 cmpTypeX env (TyConApp _ _) (FunTy _ _) = GT
1009 cmpTypeX env (ForAllTy _ _) (TyVarTy _) = GT
1010 cmpTypeX env (ForAllTy _ _) (AppTy _ _) = GT
1011 cmpTypeX env (ForAllTy _ _) (FunTy _ _) = GT
1012 cmpTypeX env (ForAllTy _ _) (TyConApp _ _) = GT
1014 cmpTypeX env (PredTy _) t2 = GT
1016 cmpTypeX env _ _ = LT
1019 cmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
1020 cmpTypesX env [] [] = EQ
1021 cmpTypesX env (t1:tys1) (t2:tys2) = cmpTypeX env t1 t2 `thenCmp` cmpTypesX env tys1 tys2
1022 cmpTypesX env [] tys = LT
1023 cmpTypesX env ty [] = GT
1026 cmpPredX :: RnEnv2 -> PredType -> PredType -> Ordering
1027 cmpPredX env (IParam n1 ty1) (IParam n2 ty2) = (n1 `compare` n2) `thenCmp` cmpTypeX env ty1 ty2
1028 -- Compare names only for implicit parameters
1029 -- This comparison is used exclusively (I believe)
1030 -- for the Avails finite map built in TcSimplify
1031 -- If the types differ we keep them distinct so that we see
1032 -- a distinct pair to run improvement on
1033 cmpPredX env (ClassP c1 tys1) (ClassP c2 tys2) = (c1 `compare` c2) `thenCmp` (cmpTypesX env tys1 tys2)
1034 cmpPredX env (EqPred ty1 ty2) (EqPred ty1' ty2') = (cmpTypeX env ty1 ty1') `thenCmp` (cmpTypeX env ty2 ty2')
1036 -- Constructor order: IParam < ClassP < EqPred
1037 cmpPredX env (IParam {}) _ = LT
1038 cmpPredX env (ClassP {}) (IParam {}) = GT
1039 cmpPredX env (ClassP {}) (EqPred {}) = LT
1040 cmpPredX env (EqPred {}) _ = GT
1043 PredTypes are used as a FM key in TcSimplify,
1044 so we take the easy path and make them an instance of Ord
1047 instance Eq PredType where { (==) = tcEqPred }
1048 instance Ord PredType where { compare = tcCmpPred }
1052 %************************************************************************
1056 %************************************************************************
1060 = TvSubst InScopeSet -- The in-scope type variables
1061 TvSubstEnv -- The substitution itself
1062 -- See Note [Apply Once]
1063 -- and Note [Extending the TvSubstEnv]
1065 {- ----------------------------------------------------------
1069 We use TvSubsts to instantiate things, and we might instantiate
1073 So the substition might go [a->b, b->a]. A similar situation arises in Core
1074 when we find a beta redex like
1075 (/\ a /\ b -> e) b a
1076 Then we also end up with a substition that permutes type variables. Other
1077 variations happen to; for example [a -> (a, b)].
1079 ***************************************************
1080 *** So a TvSubst must be applied precisely once ***
1081 ***************************************************
1083 A TvSubst is not idempotent, but, unlike the non-idempotent substitution
1084 we use during unifications, it must not be repeatedly applied.
1086 Note [Extending the TvSubst]
1087 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1088 The following invariant should hold of a TvSubst
1090 The in-scope set is needed *only* to
1091 guide the generation of fresh uniques
1093 In particular, the *kind* of the type variables in
1094 the in-scope set is not relevant
1096 This invariant allows a short-cut when the TvSubstEnv is empty:
1097 if the TvSubstEnv is empty --- i.e. (isEmptyTvSubt subst) holds ---
1098 then (substTy subst ty) does nothing.
1100 For example, consider:
1101 (/\a. /\b:(a~Int). ...b..) Int
1102 We substitute Int for 'a'. The Unique of 'b' does not change, but
1103 nevertheless we add 'b' to the TvSubstEnv, because b's type does change
1105 This invariant has several crucial consequences:
1107 * In substTyVarBndr, we need extend the TvSubstEnv
1108 - if the unique has changed
1109 - or if the kind has changed
1111 * In substTyVar, we do not need to consult the in-scope set;
1112 the TvSubstEnv is enough
1114 * In substTy, substTheta, we can short-circuit when the TvSubstEnv is empty
1117 -------------------------------------------------------------- -}
1120 type TvSubstEnv = TyVarEnv Type
1121 -- A TvSubstEnv is used both inside a TvSubst (with the apply-once
1122 -- invariant discussed in Note [Apply Once]), and also independently
1123 -- in the middle of matching, and unification (see Types.Unify)
1124 -- So you have to look at the context to know if it's idempotent or
1125 -- apply-once or whatever
1126 emptyTvSubstEnv :: TvSubstEnv
1127 emptyTvSubstEnv = emptyVarEnv
1129 composeTvSubst :: InScopeSet -> TvSubstEnv -> TvSubstEnv -> TvSubstEnv
1130 -- (compose env1 env2)(x) is env1(env2(x)); i.e. apply env2 then env1
1131 -- It assumes that both are idempotent
1132 -- Typically, env1 is the refinement to a base substitution env2
1133 composeTvSubst in_scope env1 env2
1134 = env1 `plusVarEnv` mapVarEnv (substTy subst1) env2
1135 -- First apply env1 to the range of env2
1136 -- Then combine the two, making sure that env1 loses if
1137 -- both bind the same variable; that's why env1 is the
1138 -- *left* argument to plusVarEnv, because the right arg wins
1140 subst1 = TvSubst in_scope env1
1142 emptyTvSubst = TvSubst emptyInScopeSet emptyVarEnv
1144 isEmptyTvSubst :: TvSubst -> Bool
1145 -- See Note [Extending the TvSubstEnv]
1146 isEmptyTvSubst (TvSubst _ env) = isEmptyVarEnv env
1148 mkTvSubst :: InScopeSet -> TvSubstEnv -> TvSubst
1151 getTvSubstEnv :: TvSubst -> TvSubstEnv
1152 getTvSubstEnv (TvSubst _ env) = env
1154 getTvInScope :: TvSubst -> InScopeSet
1155 getTvInScope (TvSubst in_scope _) = in_scope
1157 isInScope :: Var -> TvSubst -> Bool
1158 isInScope v (TvSubst in_scope _) = v `elemInScopeSet` in_scope
1160 notElemTvSubst :: TyVar -> TvSubst -> Bool
1161 notElemTvSubst tv (TvSubst _ env) = not (tv `elemVarEnv` env)
1163 setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst
1164 setTvSubstEnv (TvSubst in_scope _) env = TvSubst in_scope env
1166 extendTvInScope :: TvSubst -> [Var] -> TvSubst
1167 extendTvInScope (TvSubst in_scope env) vars = TvSubst (extendInScopeSetList in_scope vars) env
1169 extendTvSubst :: TvSubst -> TyVar -> Type -> TvSubst
1170 extendTvSubst (TvSubst in_scope env) tv ty = TvSubst in_scope (extendVarEnv env tv ty)
1172 extendTvSubstList :: TvSubst -> [TyVar] -> [Type] -> TvSubst
1173 extendTvSubstList (TvSubst in_scope env) tvs tys
1174 = TvSubst in_scope (extendVarEnvList env (tvs `zip` tys))
1176 -- mkOpenTvSubst and zipOpenTvSubst generate the in-scope set from
1177 -- the types given; but it's just a thunk so with a bit of luck
1178 -- it'll never be evaluated
1180 mkOpenTvSubst :: TvSubstEnv -> TvSubst
1181 mkOpenTvSubst env = TvSubst (mkInScopeSet (tyVarsOfTypes (varEnvElts env))) env
1183 zipOpenTvSubst :: [TyVar] -> [Type] -> TvSubst
1184 zipOpenTvSubst tyvars tys
1186 | length tyvars /= length tys
1187 = pprTrace "zipOpenTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1190 = TvSubst (mkInScopeSet (tyVarsOfTypes tys)) (zipTyEnv tyvars tys)
1192 -- mkTopTvSubst is called when doing top-level substitutions.
1193 -- Here we expect that the free vars of the range of the
1194 -- substitution will be empty.
1195 mkTopTvSubst :: [(TyVar, Type)] -> TvSubst
1196 mkTopTvSubst prs = TvSubst emptyInScopeSet (mkVarEnv prs)
1198 zipTopTvSubst :: [TyVar] -> [Type] -> TvSubst
1199 zipTopTvSubst tyvars tys
1201 | length tyvars /= length tys
1202 = pprTrace "zipOpenTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1205 = TvSubst emptyInScopeSet (zipTyEnv tyvars tys)
1207 zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
1210 | length tyvars /= length tys
1211 = pprTrace "mkTopTvSubst" (ppr tyvars $$ ppr tys) emptyVarEnv
1214 = zip_ty_env tyvars tys emptyVarEnv
1216 -- Later substitutions in the list over-ride earlier ones,
1217 -- but there should be no loops
1218 zip_ty_env [] [] env = env
1219 zip_ty_env (tv:tvs) (ty:tys) env = zip_ty_env tvs tys (extendVarEnv env tv ty)
1220 -- There used to be a special case for when
1222 -- (a not-uncommon case) in which case the substitution was dropped.
1223 -- But the type-tidier changes the print-name of a type variable without
1224 -- changing the unique, and that led to a bug. Why? Pre-tidying, we had
1225 -- a type {Foo t}, where Foo is a one-method class. So Foo is really a newtype.
1226 -- And it happened that t was the type variable of the class. Post-tiding,
1227 -- it got turned into {Foo t2}. The ext-core printer expanded this using
1228 -- sourceTypeRep, but that said "Oh, t == t2" because they have the same unique,
1229 -- and so generated a rep type mentioning t not t2.
1231 -- Simplest fix is to nuke the "optimisation"
1232 zip_ty_env tvs tys env = pprTrace "Var/Type length mismatch: " (ppr tvs $$ ppr tys) env
1233 -- zip_ty_env _ _ env = env
1235 instance Outputable TvSubst where
1236 ppr (TvSubst ins env)
1237 = brackets $ sep[ ptext SLIT("TvSubst"),
1238 nest 2 (ptext SLIT("In scope:") <+> ppr ins),
1239 nest 2 (ptext SLIT("Env:") <+> ppr env) ]
1242 %************************************************************************
1244 Performing type substitutions
1246 %************************************************************************
1249 substTyWith :: [TyVar] -> [Type] -> Type -> Type
1250 substTyWith tvs tys = ASSERT( length tvs == length tys )
1251 substTy (zipOpenTvSubst tvs tys)
1253 substTy :: TvSubst -> Type -> Type
1254 substTy subst ty | isEmptyTvSubst subst = ty
1255 | otherwise = subst_ty subst ty
1257 substTys :: TvSubst -> [Type] -> [Type]
1258 substTys subst tys | isEmptyTvSubst subst = tys
1259 | otherwise = map (subst_ty subst) tys
1261 substTheta :: TvSubst -> ThetaType -> ThetaType
1262 substTheta subst theta
1263 | isEmptyTvSubst subst = theta
1264 | otherwise = map (substPred subst) theta
1266 substPred :: TvSubst -> PredType -> PredType
1267 substPred subst (IParam n ty) = IParam n (subst_ty subst ty)
1268 substPred subst (ClassP clas tys) = ClassP clas (map (subst_ty subst) tys)
1269 substPred subst (EqPred ty1 ty2) = EqPred (subst_ty subst ty1) (subst_ty subst ty2)
1271 deShadowTy :: TyVarSet -> Type -> Type -- Remove any nested binders mentioning tvs
1273 = subst_ty (mkTvSubst in_scope emptyTvSubstEnv) ty
1275 in_scope = mkInScopeSet tvs
1277 subst_ty :: TvSubst -> Type -> Type
1278 -- subst_ty is the main workhorse for type substitution
1280 -- Note that the in_scope set is poked only if we hit a forall
1281 -- so it may often never be fully computed
1285 go (TyVarTy tv) = substTyVar subst tv
1286 go (TyConApp tc tys) = let args = map go tys
1287 in args `seqList` TyConApp tc args
1289 go (PredTy p) = PredTy $! (substPred subst p)
1291 go (NoteTy (FTVNote _) ty2) = go ty2 -- Discard the free tyvar note
1293 go (FunTy arg res) = (FunTy $! (go arg)) $! (go res)
1294 go (AppTy fun arg) = mkAppTy (go fun) $! (go arg)
1295 -- The mkAppTy smart constructor is important
1296 -- we might be replacing (a Int), represented with App
1297 -- by [Int], represented with TyConApp
1298 go (ForAllTy tv ty) = case substTyVarBndr subst tv of
1299 (subst', tv') -> ForAllTy tv' $! (subst_ty subst' ty)
1301 substTyVar :: TvSubst -> TyVar -> Type
1302 substTyVar subst@(TvSubst in_scope env) tv
1303 = case lookupTyVar subst tv of {
1304 Nothing -> TyVarTy tv;
1305 Just ty -> ty -- See Note [Apply Once]
1308 lookupTyVar :: TvSubst -> TyVar -> Maybe Type
1309 -- See Note [Extending the TvSubst]
1310 lookupTyVar (TvSubst in_scope env) tv = lookupVarEnv env tv
1312 substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)
1313 substTyVarBndr subst@(TvSubst in_scope env) old_var
1314 = (TvSubst (in_scope `extendInScopeSet` new_var) new_env, new_var)
1316 is_co_var = isCoVar old_var
1318 new_env | no_change = delVarEnv env old_var
1319 | otherwise = extendVarEnv env old_var (TyVarTy new_var)
1321 no_change = new_var == old_var && not is_co_var
1322 -- no_change means that the new_var is identical in
1323 -- all respects to the old_var (same unique, same kind)
1324 -- See Note [Extending the TvSubst]
1326 -- In that case we don't need to extend the substitution
1327 -- to map old to new. But instead we must zap any
1328 -- current substitution for the variable. For example:
1329 -- (\x.e) with id_subst = [x |-> e']
1330 -- Here we must simply zap the substitution for x
1332 new_var = uniqAway in_scope subst_old_var
1333 -- The uniqAway part makes sure the new variable is not already in scope
1335 subst_old_var -- subst_old_var is old_var with the substitution applied to its kind
1336 -- It's only worth doing the substitution for coercions,
1337 -- becuase only they can have free type variables
1338 | is_co_var = setTyVarKind old_var (substTy subst (tyVarKind old_var))
1339 | otherwise = old_var
1342 ----------------------------------------------------
1347 There's a little subtyping at the kind level:
1356 where * [LiftedTypeKind] means boxed type
1357 # [UnliftedTypeKind] means unboxed type
1358 (#) [UbxTupleKind] means unboxed tuple
1359 ?? [ArgTypeKind] is the lub of *,#
1360 ? [OpenTypeKind] means any type at all
1364 error :: forall a:?. String -> a
1365 (->) :: ?? -> ? -> *
1366 (\(x::t) -> ...) Here t::?? (i.e. not unboxed tuple)
1369 type KindVar = TyVar -- invariant: KindVar will always be a
1370 -- TcTyVar with details MetaTv TauTv ...
1371 -- kind var constructors and functions are in TcType
1373 type SimpleKind = Kind
1378 During kind inference, a kind variable unifies only with
1380 sk ::= * | sk1 -> sk2
1382 data T a = MkT a (T Int#)
1383 fails. We give T the kind (k -> *), and the kind variable k won't unify
1384 with # (the kind of Int#).
1388 When creating a fresh internal type variable, we give it a kind to express
1389 constraints on it. E.g. in (\x->e) we make up a fresh type variable for x,
1392 During unification we only bind an internal type variable to a type
1393 whose kind is lower in the sub-kind hierarchy than the kind of the tyvar.
1395 When unifying two internal type variables, we collect their kind constraints by
1396 finding the GLB of the two. Since the partial order is a tree, they only
1397 have a glb if one is a sub-kind of the other. In that case, we bind the
1398 less-informative one to the more informative one. Neat, eh?
1405 %************************************************************************
1407 Functions over Kinds
1409 %************************************************************************
1412 kindFunResult :: Kind -> Kind
1413 kindFunResult k = funResultTy k
1415 splitKindFunTys :: Kind -> ([Kind],Kind)
1416 splitKindFunTys k = splitFunTys k
1418 splitKindFunTysN :: Int -> Kind -> ([Kind],Kind)
1419 splitKindFunTysN k = splitFunTysN k
1421 isUbxTupleKind, isOpenTypeKind, isArgTypeKind, isUnliftedTypeKind :: Kind -> Bool
1423 isOpenTypeKindCon tc = tyConUnique tc == openTypeKindTyConKey
1425 isOpenTypeKind (TyConApp tc _) = isOpenTypeKindCon tc
1426 isOpenTypeKind other = False
1428 isUbxTupleKindCon tc = tyConUnique tc == ubxTupleKindTyConKey
1430 isUbxTupleKind (TyConApp tc _) = isUbxTupleKindCon tc
1431 isUbxTupleKind other = False
1433 isArgTypeKindCon tc = tyConUnique tc == argTypeKindTyConKey
1435 isArgTypeKind (TyConApp tc _) = isArgTypeKindCon tc
1436 isArgTypeKind other = False
1438 isUnliftedTypeKindCon tc = tyConUnique tc == unliftedTypeKindTyConKey
1440 isUnliftedTypeKind (TyConApp tc _) = isUnliftedTypeKindCon tc
1441 isUnliftedTypeKind other = False
1443 isSubOpenTypeKind :: Kind -> Bool
1444 -- True of any sub-kind of OpenTypeKind (i.e. anything except arrow)
1445 isSubOpenTypeKind (FunTy k1 k2) = ASSERT2 ( isKind k1, text "isSubOpenTypeKind" <+> ppr k1 <+> text "::" <+> ppr (typeKind k1) )
1446 ASSERT2 ( isKind k2, text "isSubOpenTypeKind" <+> ppr k2 <+> text "::" <+> ppr (typeKind k2) )
1448 isSubOpenTypeKind (TyConApp kc []) = ASSERT( isKind (TyConApp kc []) ) True
1449 isSubOpenTypeKind other = ASSERT( isKind other ) False
1450 -- This is a conservative answer
1451 -- It matters in the call to isSubKind in
1452 -- checkExpectedKind.
1454 isSubArgTypeKindCon kc
1455 | isUnliftedTypeKindCon kc = True
1456 | isLiftedTypeKindCon kc = True
1457 | isArgTypeKindCon kc = True
1460 isSubArgTypeKind :: Kind -> Bool
1461 -- True of any sub-kind of ArgTypeKind
1462 isSubArgTypeKind (TyConApp kc []) = isSubArgTypeKindCon kc
1463 isSubArgTypeKind other = False
1465 isSuperKind :: Type -> Bool
1466 isSuperKind (TyConApp (skc) []) = isSuperKindTyCon skc
1467 isSuperKind other = False
1469 isKind :: Kind -> Bool
1470 isKind k = isSuperKind (typeKind k)
1474 isSubKind :: Kind -> Kind -> Bool
1475 -- (k1 `isSubKind` k2) checks that k1 <: k2
1476 isSubKind (TyConApp kc1 []) (TyConApp kc2 []) = kc1 `isSubKindCon` kc2
1477 isSubKind (FunTy a1 r1) (FunTy a2 r2) = (a2 `isSubKind` a1) && (r1 `isSubKind` r2)
1478 isSubKind (PredTy (EqPred ty1 ty2)) (PredTy (EqPred ty1' ty2'))
1479 = ty1 `tcEqType` ty1' && ty2 `tcEqType` ty2'
1480 isSubKind k1 k2 = False
1482 eqKind :: Kind -> Kind -> Bool
1485 isSubKindCon :: TyCon -> TyCon -> Bool
1486 -- (kc1 `isSubKindCon` kc2) checks that kc1 <: kc2
1487 isSubKindCon kc1 kc2
1488 | isLiftedTypeKindCon kc1 && isLiftedTypeKindCon kc2 = True
1489 | isUnliftedTypeKindCon kc1 && isUnliftedTypeKindCon kc2 = True
1490 | isUbxTupleKindCon kc1 && isUbxTupleKindCon kc2 = True
1491 | isOpenTypeKindCon kc2 = True
1492 -- we already know kc1 is not a fun, its a TyCon
1493 | isArgTypeKindCon kc2 && isSubArgTypeKindCon kc1 = True
1496 defaultKind :: Kind -> Kind
1497 -- Used when generalising: default kind '?' and '??' to '*'
1499 -- When we generalise, we make generic type variables whose kind is
1500 -- simple (* or *->* etc). So generic type variables (other than
1501 -- built-in constants like 'error') always have simple kinds. This is important;
1504 -- We want f to get type
1505 -- f :: forall (a::*). a -> Bool
1507 -- f :: forall (a::??). a -> Bool
1508 -- because that would allow a call like (f 3#) as well as (f True),
1509 --and the calling conventions differ. This defaulting is done in TcMType.zonkTcTyVarBndr.
1511 | isSubOpenTypeKind k = liftedTypeKind
1512 | isSubArgTypeKind k = liftedTypeKind
1515 isEqPred :: PredType -> Bool
1516 isEqPred (EqPred _ _) = True
1517 isEqPred other = False