2 % (c) The GRASP/AQUA Project, Glasgow University, 1998
4 \section[Type]{Type - public interface}
9 -- re-exports from TypeRep
10 TyThing(..), Type, PredType(..), ThetaType,
14 Kind, SimpleKind, KindVar,
15 kindFunResult, splitKindFunTys,
17 liftedTypeKindTyCon, openTypeKindTyCon, unliftedTypeKindTyCon,
18 argTypeKindTyCon, ubxTupleKindTyCon,
20 liftedTypeKind, unliftedTypeKind, openTypeKind,
21 argTypeKind, ubxTupleKind,
23 tySuperKind, coSuperKind,
25 isLiftedTypeKind, isUnliftedTypeKind, isOpenTypeKind,
26 isUbxTupleKind, isArgTypeKind, isKind, isTySuperKind,
27 isCoSuperKind, isSuperKind, isCoercionKind,
28 mkArrowKind, mkArrowKinds,
30 isSubArgTypeKind, isSubOpenTypeKind, isSubKind, defaultKind, eqKind,
33 -- Re-exports from TyCon
36 mkTyVarTy, mkTyVarTys, getTyVar, getTyVar_maybe, isTyVarTy,
38 mkAppTy, mkAppTys, splitAppTy, splitAppTys,
39 splitAppTy_maybe, repSplitAppTy_maybe,
41 mkFunTy, mkFunTys, splitFunTy, splitFunTy_maybe,
42 splitFunTys, splitFunTysN,
43 funResultTy, funArgTy, zipFunTys, isFunTy,
45 mkTyConApp, mkTyConTy,
46 tyConAppTyCon, tyConAppArgs,
47 splitTyConApp_maybe, splitTyConApp,
48 splitNewTyConApp_maybe, splitNewTyConApp,
50 repType, typePrimRep, coreView, tcView, kindView,
52 mkForAllTy, mkForAllTys, splitForAllTy_maybe, splitForAllTys,
53 applyTy, applyTys, isForAllTy, dropForAlls,
56 predTypeRep, mkPredTy, mkPredTys,
59 splitRecNewType_maybe, newTyConInstRhs,
62 isUnLiftedType, isUnboxedTupleType, isAlgType, isPrimitiveType,
63 isStrictType, isStrictPred,
66 tyVarsOfType, tyVarsOfTypes, tyVarsOfPred, tyVarsOfTheta,
67 typeKind, addFreeTyVars,
69 -- Tidying up for printing
71 tidyOpenType, tidyOpenTypes,
72 tidyTyVarBndr, tidyFreeTyVars,
73 tidyOpenTyVar, tidyOpenTyVars,
74 tidyTopType, tidyPred,
78 coreEqType, tcEqType, tcEqTypes, tcCmpType, tcCmpTypes,
79 tcEqPred, tcCmpPred, tcEqTypeX,
85 TvSubstEnv, emptyTvSubstEnv, -- Representation widely visible
86 TvSubst(..), emptyTvSubst, -- Representation visible to a few friends
87 mkTvSubst, mkOpenTvSubst, zipOpenTvSubst, zipTopTvSubst, mkTopTvSubst, notElemTvSubst,
88 getTvSubstEnv, setTvSubstEnv, getTvInScope, extendTvInScope,
89 extendTvSubst, extendTvSubstList, isInScope, composeTvSubst, zipTyEnv,
91 -- Performing substitution on types
92 substTy, substTys, substTyWith, substTheta,
93 substPred, substTyVar, substTyVarBndr, deShadowTy, lookupTyVar,
96 pprType, pprParendType, pprTyThingCategory,
97 pprPred, pprTheta, pprThetaArrow, pprClassPred, pprKind, pprParendKind
100 #include "HsVersions.h"
102 -- We import the representation and primitive functions from TypeRep.
103 -- Many things are reexported, but not the representation!
108 import Var ( Var, TyVar, tyVarKind, tyVarName,
109 setTyVarName, setTyVarKind )
113 import OccName ( tidyOccName )
114 import Name ( NamedThing(..), tidyNameOcc )
115 import Class ( Class, classTyCon )
116 import PrelNames( openTypeKindTyConKey, unliftedTypeKindTyConKey,
117 ubxTupleKindTyConKey, argTypeKindTyConKey )
118 import TyCon ( TyCon, isRecursiveTyCon, isPrimTyCon,
119 isUnboxedTupleTyCon, isUnLiftedTyCon,
120 isFunTyCon, isNewTyCon, newTyConRep, newTyConRhs,
121 isAlgTyCon, tyConArity, isSuperKindTyCon,
122 tcExpandTyCon_maybe, coreExpandTyCon_maybe,
123 tyConKind, PrimRep(..), tyConPrimRep, tyConUnique,
124 isCoercionTyCon_maybe, isCoercionTyCon
128 import StaticFlags ( opt_DictsStrict )
129 import Util ( mapAccumL, seqList, lengthIs, snocView, thenCmp, isEqual, all2 )
131 import UniqSet ( sizeUniqSet ) -- Should come via VarSet
132 import Maybe ( isJust )
136 %************************************************************************
140 %************************************************************************
142 In Core, we "look through" non-recursive newtypes and PredTypes.
145 {-# INLINE coreView #-}
146 coreView :: Type -> Maybe Type
147 -- Strips off the *top layer only* of a type to give
148 -- its underlying representation type.
149 -- Returns Nothing if there is nothing to look through.
151 -- In the case of newtypes, it returns
152 -- *either* a vanilla TyConApp (recursive newtype, or non-saturated)
153 -- *or* the newtype representation (otherwise), meaning the
154 -- type written in the RHS of the newtype decl,
155 -- which may itself be a newtype
157 -- Example: newtype R = MkR S
159 -- newtype T = MkT (T -> T)
160 -- expandNewTcApp on R gives Just S
162 -- on T gives Nothing (no expansion)
164 -- By being non-recursive and inlined, this case analysis gets efficiently
165 -- joined onto the case analysis that the caller is already doing
166 coreView (NoteTy _ ty) = Just ty
167 coreView (PredTy p) = Just (predTypeRep p)
168 coreView (TyConApp tc tys) | Just (tenv, rhs, tys') <- coreExpandTyCon_maybe tc tys
169 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
170 -- Its important to use mkAppTys, rather than (foldl AppTy),
171 -- because the function part might well return a
172 -- partially-applied type constructor; indeed, usually will!
173 coreView ty = Nothing
177 -----------------------------------------------
178 {-# INLINE tcView #-}
179 tcView :: Type -> Maybe Type
180 -- Same, but for the type checker, which just looks through synonyms
181 tcView (NoteTy _ ty) = Just ty
182 tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- tcExpandTyCon_maybe tc tys
183 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
186 -----------------------------------------------
187 {-# INLINE kindView #-}
188 kindView :: Kind -> Maybe Kind
189 -- C.f. coreView, tcView
190 -- For the moment, we don't even handle synonyms in kinds
191 kindView (NoteTy _ k) = Just k
192 kindView other = Nothing
196 %************************************************************************
198 \subsection{Constructor-specific functions}
200 %************************************************************************
203 ---------------------------------------------------------------------
207 mkTyVarTy :: TyVar -> Type
210 mkTyVarTys :: [TyVar] -> [Type]
211 mkTyVarTys = map mkTyVarTy -- a common use of mkTyVarTy
213 getTyVar :: String -> Type -> TyVar
214 getTyVar msg ty = case getTyVar_maybe ty of
216 Nothing -> panic ("getTyVar: " ++ msg)
218 isTyVarTy :: Type -> Bool
219 isTyVarTy ty = isJust (getTyVar_maybe ty)
221 getTyVar_maybe :: Type -> Maybe TyVar
222 getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty'
223 getTyVar_maybe (TyVarTy tv) = Just tv
224 getTyVar_maybe other = Nothing
229 ---------------------------------------------------------------------
232 We need to be pretty careful with AppTy to make sure we obey the
233 invariant that a TyConApp is always visibly so. mkAppTy maintains the
237 mkAppTy orig_ty1 orig_ty2
240 mk_app (NoteTy _ ty1) = mk_app ty1
241 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ [orig_ty2])
242 mk_app ty1 = AppTy orig_ty1 orig_ty2
243 -- Note that the TyConApp could be an
244 -- under-saturated type synonym. GHC allows that; e.g.
245 -- type Foo k = k a -> k a
247 -- foo :: Foo Id -> Foo Id
249 -- Here Id is partially applied in the type sig for Foo,
250 -- but once the type synonyms are expanded all is well
252 mkAppTys :: Type -> [Type] -> Type
253 mkAppTys orig_ty1 [] = orig_ty1
254 -- This check for an empty list of type arguments
255 -- avoids the needless loss of a type synonym constructor.
256 -- For example: mkAppTys Rational []
257 -- returns to (Ratio Integer), which has needlessly lost
258 -- the Rational part.
259 mkAppTys orig_ty1 orig_tys2
262 mk_app (NoteTy _ ty1) = mk_app ty1
263 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ orig_tys2)
264 -- mkTyConApp: see notes with mkAppTy
265 mk_app ty1 = foldl AppTy orig_ty1 orig_tys2
268 splitAppTy_maybe :: Type -> Maybe (Type, Type)
269 splitAppTy_maybe ty | Just ty' <- coreView ty
270 = splitAppTy_maybe ty'
271 splitAppTy_maybe ty = repSplitAppTy_maybe ty
274 repSplitAppTy_maybe :: Type -> Maybe (Type,Type)
275 -- Does the AppTy split, but assumes that any view stuff is already done
276 repSplitAppTy_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
277 repSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
278 repSplitAppTy_maybe (TyConApp tc tys) = case snocView tys of
279 Just (tys', ty') -> Just (TyConApp tc tys', ty')
281 repSplitAppTy_maybe other = Nothing
283 splitAppTy :: Type -> (Type, Type)
284 splitAppTy ty = case splitAppTy_maybe ty of
286 Nothing -> panic "splitAppTy"
289 splitAppTys :: Type -> (Type, [Type])
290 splitAppTys ty = split ty ty []
292 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
293 split orig_ty (AppTy ty arg) args = split ty ty (arg:args)
294 split orig_ty (TyConApp tc tc_args) args = (TyConApp tc [], tc_args ++ args)
295 split orig_ty (FunTy ty1 ty2) args = ASSERT( null args )
296 (TyConApp funTyCon [], [ty1,ty2])
297 split orig_ty ty args = (orig_ty, args)
302 ---------------------------------------------------------------------
307 mkFunTy :: Type -> Type -> Type
308 mkFunTy arg res = FunTy arg res
310 mkFunTys :: [Type] -> Type -> Type
311 mkFunTys tys ty = foldr FunTy ty tys
313 isFunTy :: Type -> Bool
314 isFunTy ty = isJust (splitFunTy_maybe ty)
316 splitFunTy :: Type -> (Type, Type)
317 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
318 splitFunTy (FunTy arg res) = (arg, res)
319 splitFunTy other = pprPanic "splitFunTy" (ppr other)
321 splitFunTy_maybe :: Type -> Maybe (Type, Type)
322 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
323 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
324 splitFunTy_maybe other = Nothing
326 splitFunTys :: Type -> ([Type], Type)
327 splitFunTys ty = split [] ty ty
329 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
330 split args orig_ty (FunTy arg res) = split (arg:args) res res
331 split args orig_ty ty = (reverse args, orig_ty)
333 splitFunTysN :: Int -> Type -> ([Type], Type)
334 -- Split off exactly n arg tys
335 splitFunTysN 0 ty = ([], ty)
336 splitFunTysN n ty = case splitFunTy ty of { (arg, res) ->
337 case splitFunTysN (n-1) res of { (args, res) ->
340 zipFunTys :: Outputable a => [a] -> Type -> ([(a,Type)], Type)
341 zipFunTys orig_xs orig_ty = split [] orig_xs orig_ty orig_ty
343 split acc [] nty ty = (reverse acc, nty)
345 | Just ty' <- coreView ty = split acc xs nty ty'
346 split acc (x:xs) nty (FunTy arg res) = split ((x,arg):acc) xs res res
347 split acc (x:xs) nty ty = pprPanic "zipFunTys" (ppr orig_xs <+> ppr orig_ty)
349 funResultTy :: Type -> Type
350 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
351 funResultTy (FunTy arg res) = res
352 funResultTy ty = pprPanic "funResultTy" (ppr ty)
354 funArgTy :: Type -> Type
355 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
356 funArgTy (FunTy arg res) = arg
357 funArgTy ty = pprPanic "funArgTy" (ppr ty)
361 ---------------------------------------------------------------------
364 @mkTyConApp@ is a key function, because it builds a TyConApp, FunTy or PredTy,
368 mkTyConApp :: TyCon -> [Type] -> Type
370 | isFunTyCon tycon, [ty1,ty2] <- tys
376 mkTyConTy :: TyCon -> Type
377 mkTyConTy tycon = mkTyConApp tycon []
379 -- splitTyConApp "looks through" synonyms, because they don't
380 -- mean a distinct type, but all other type-constructor applications
381 -- including functions are returned as Just ..
383 tyConAppTyCon :: Type -> TyCon
384 tyConAppTyCon ty = fst (splitTyConApp ty)
386 tyConAppArgs :: Type -> [Type]
387 tyConAppArgs ty = snd (splitTyConApp ty)
389 splitTyConApp :: Type -> (TyCon, [Type])
390 splitTyConApp ty = case splitTyConApp_maybe ty of
392 Nothing -> pprPanic "splitTyConApp" (ppr ty)
394 splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
395 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
396 splitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
397 splitTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
398 splitTyConApp_maybe other = Nothing
400 -- Sometimes we do NOT want to look throught a newtype. When case matching
401 -- on a newtype we want a convenient way to access the arguments of a newty
402 -- constructor so as to properly form a coercion.
403 splitNewTyConApp :: Type -> (TyCon, [Type])
404 splitNewTyConApp ty = case splitNewTyConApp_maybe ty of
406 Nothing -> pprPanic "splitNewTyConApp" (ppr ty)
407 splitNewTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
408 splitNewTyConApp_maybe ty | Just ty' <- tcView ty = splitNewTyConApp_maybe ty'
409 splitNewTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
410 splitNewTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
411 splitNewTyConApp_maybe other = Nothing
413 -- get instantiated newtype rhs, the arguments had better saturate
415 newTyConInstRhs :: TyCon -> [Type] -> Type
416 newTyConInstRhs tycon tys =
417 let (tvs, ty) = newTyConRhs tycon in substTyWith tvs tys ty
422 ---------------------------------------------------------------------
426 Notes on type synonyms
427 ~~~~~~~~~~~~~~~~~~~~~~
428 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
429 to return type synonyms whereever possible. Thus
434 splitFunTys (a -> Foo a) = ([a], Foo a)
437 The reason is that we then get better (shorter) type signatures in
438 interfaces. Notably this plays a role in tcTySigs in TcBinds.lhs.
443 repType looks through
447 (d) usage annotations
448 (e) all newtypes, including recursive ones
449 It's useful in the back end.
452 repType :: Type -> Type
453 -- Only applied to types of kind *; hence tycons are saturated
454 repType ty | Just ty' <- coreView ty = repType ty'
455 repType (ForAllTy _ ty) = repType ty
456 repType (TyConApp tc tys)
457 | isNewTyCon tc = -- Recursive newtypes are opaque to coreView
458 -- but we must expand them here. Sure to
459 -- be saturated because repType is only applied
460 -- to types of kind *
461 ASSERT( {- isRecursiveTyCon tc && -} tys `lengthIs` tyConArity tc )
462 repType (new_type_rep tc tys)
465 -- new_type_rep doesn't ask any questions:
466 -- it just expands newtype, whether recursive or not
467 new_type_rep new_tycon tys = ASSERT( tys `lengthIs` tyConArity new_tycon )
468 case newTyConRep new_tycon of
469 (tvs, rep_ty) -> substTyWith tvs tys rep_ty
471 -- ToDo: this could be moved to the code generator, using splitTyConApp instead
472 -- of inspecting the type directly.
473 typePrimRep :: Type -> PrimRep
474 typePrimRep ty = case repType ty of
475 TyConApp tc _ -> tyConPrimRep tc
477 AppTy _ _ -> PtrRep -- See note below
479 other -> pprPanic "typePrimRep" (ppr ty)
480 -- Types of the form 'f a' must be of kind *, not *#, so
481 -- we are guaranteed that they are represented by pointers.
482 -- The reason is that f must have kind *->*, not *->*#, because
483 -- (we claim) there is no way to constrain f's kind any other
489 ---------------------------------------------------------------------
494 mkForAllTy :: TyVar -> Type -> Type
496 = mkForAllTys [tyvar] ty
498 mkForAllTys :: [TyVar] -> Type -> Type
499 mkForAllTys tyvars ty = foldr ForAllTy ty tyvars
501 isForAllTy :: Type -> Bool
502 isForAllTy (NoteTy _ ty) = isForAllTy ty
503 isForAllTy (ForAllTy _ _) = True
504 isForAllTy other_ty = False
506 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
507 splitForAllTy_maybe ty = splitFAT_m ty
509 splitFAT_m ty | Just ty' <- coreView ty = splitFAT_m ty'
510 splitFAT_m (ForAllTy tyvar ty) = Just(tyvar, ty)
511 splitFAT_m _ = Nothing
513 splitForAllTys :: Type -> ([TyVar], Type)
514 splitForAllTys ty = split ty ty []
516 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
517 split orig_ty (ForAllTy tv ty) tvs = split ty ty (tv:tvs)
518 split orig_ty t tvs = (reverse tvs, orig_ty)
520 dropForAlls :: Type -> Type
521 dropForAlls ty = snd (splitForAllTys ty)
524 -- (mkPiType now in CoreUtils)
528 Instantiate a for-all type with one or more type arguments.
529 Used when we have a polymorphic function applied to type args:
531 Then we use (applyTys type-of-f [t1,t2]) to compute the type of
535 applyTy :: Type -> Type -> Type
536 applyTy ty arg | Just ty' <- coreView ty = applyTy ty' arg
537 applyTy (ForAllTy tv ty) arg = substTyWith [tv] [arg] ty
538 applyTy other arg = panic "applyTy"
540 applyTys :: Type -> [Type] -> Type
541 -- This function is interesting because
542 -- a) the function may have more for-alls than there are args
543 -- b) less obviously, it may have fewer for-alls
544 -- For case (b) think of
545 -- applyTys (forall a.a) [forall b.b, Int]
546 -- This really can happen, via dressing up polymorphic types with newtype
547 -- clothing. Here's an example:
548 -- newtype R = R (forall a. a->a)
549 -- foo = case undefined :: R of
552 applyTys orig_fun_ty [] = orig_fun_ty
553 applyTys orig_fun_ty arg_tys
554 | n_tvs == n_args -- The vastly common case
555 = substTyWith tvs arg_tys rho_ty
556 | n_tvs > n_args -- Too many for-alls
557 = substTyWith (take n_args tvs) arg_tys
558 (mkForAllTys (drop n_args tvs) rho_ty)
559 | otherwise -- Too many type args
560 = ASSERT2( n_tvs > 0, ppr orig_fun_ty ) -- Zero case gives infnite loop!
561 applyTys (substTyWith tvs (take n_tvs arg_tys) rho_ty)
564 (tvs, rho_ty) = splitForAllTys orig_fun_ty
566 n_args = length arg_tys
570 %************************************************************************
572 \subsection{Source types}
574 %************************************************************************
576 A "source type" is a type that is a separate type as far as the type checker is
577 concerned, but which has low-level representation as far as the back end is concerned.
579 Source types are always lifted.
581 The key function is predTypeRep which gives the representation of a source type:
584 mkPredTy :: PredType -> Type
585 mkPredTy pred = PredTy pred
587 mkPredTys :: ThetaType -> [Type]
588 mkPredTys preds = map PredTy preds
590 predTypeRep :: PredType -> Type
591 -- Convert a PredType to its "representation type";
592 -- the post-type-checking type used by all the Core passes of GHC.
593 -- Unwraps only the outermost level; for example, the result might
594 -- be a newtype application
595 predTypeRep (IParam _ ty) = ty
596 predTypeRep (ClassP clas tys) = mkTyConApp (classTyCon clas) tys
597 -- Result might be a newtype application, but the consumer will
598 -- look through that too if necessary
602 %************************************************************************
606 %************************************************************************
609 splitRecNewType_maybe :: Type -> Maybe Type
610 -- Sometimes we want to look through a recursive newtype, and that's what happens here
611 -- It only strips *one layer* off, so the caller will usually call itself recursively
612 -- Only applied to types of kind *, hence the newtype is always saturated
613 splitRecNewType_maybe ty | Just ty' <- coreView ty = splitRecNewType_maybe ty'
614 splitRecNewType_maybe (TyConApp tc tys)
616 = ASSERT( tys `lengthIs` tyConArity tc ) -- splitRecNewType_maybe only be applied
617 -- to *types* (of kind *)
618 ASSERT( isRecursiveTyCon tc ) -- Guaranteed by coreView
619 case newTyConRhs tc of
620 (tvs, rep_ty) -> ASSERT( length tvs == length tys )
621 Just (substTyWith tvs tys rep_ty)
623 splitRecNewType_maybe other = Nothing
630 %************************************************************************
632 \subsection{Kinds and free variables}
634 %************************************************************************
636 ---------------------------------------------------------------------
637 Finding the kind of a type
638 ~~~~~~~~~~~~~~~~~~~~~~~~~~
640 typeKind :: Type -> Kind
641 typeKind (TyConApp tycon tys) = ASSERT( not (isCoercionTyCon tycon) )
642 -- We should be looking for the coercion kind,
644 foldr (\_ k -> kindFunResult k) (tyConKind tycon) tys
645 typeKind (NoteTy _ ty) = typeKind ty
646 typeKind (PredTy pred) = predKind pred
647 typeKind (AppTy fun arg) = kindFunResult (typeKind fun)
648 typeKind (ForAllTy tv ty) = typeKind ty
649 typeKind (TyVarTy tyvar) = tyVarKind tyvar
650 typeKind (FunTy arg res)
651 -- Hack alert. The kind of (Int -> Int#) is liftedTypeKind (*),
652 -- not unliftedTypKind (#)
653 -- The only things that can be after a function arrow are
654 -- (a) types (of kind openTypeKind or its sub-kinds)
655 -- (b) kinds (of super-kind TY) (e.g. * -> (* -> *))
656 | isTySuperKind k = k
657 | otherwise = ASSERT( isSubOpenTypeKind k) liftedTypeKind
661 predKind :: PredType -> Kind
662 predKind (EqPred {}) = coSuperKind -- A coercion kind!
663 predKind (ClassP {}) = liftedTypeKind -- Class and implicitPredicates are
664 predKind (IParam {}) = liftedTypeKind -- always represented by lifted types
668 ---------------------------------------------------------------------
669 Free variables of a type
670 ~~~~~~~~~~~~~~~~~~~~~~~~
672 tyVarsOfType :: Type -> TyVarSet
673 -- NB: for type synonyms tyVarsOfType does *not* expand the synonym
674 tyVarsOfType (TyVarTy tv) = unitVarSet tv
675 tyVarsOfType (TyConApp tycon tys) = tyVarsOfTypes tys
676 tyVarsOfType (NoteTy (FTVNote tvs) ty2) = tvs
677 tyVarsOfType (PredTy sty) = tyVarsOfPred sty
678 tyVarsOfType (FunTy arg res) = tyVarsOfType arg `unionVarSet` tyVarsOfType res
679 tyVarsOfType (AppTy fun arg) = tyVarsOfType fun `unionVarSet` tyVarsOfType arg
680 tyVarsOfType (ForAllTy tyvar ty) = delVarSet (tyVarsOfType ty) tyvar
682 tyVarsOfTypes :: [Type] -> TyVarSet
683 tyVarsOfTypes tys = foldr (unionVarSet.tyVarsOfType) emptyVarSet tys
685 tyVarsOfPred :: PredType -> TyVarSet
686 tyVarsOfPred (IParam _ ty) = tyVarsOfType ty
687 tyVarsOfPred (ClassP _ tys) = tyVarsOfTypes tys
688 tyVarsOfPred (EqPred ty1 ty2) = tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2
690 tyVarsOfTheta :: ThetaType -> TyVarSet
691 tyVarsOfTheta = foldr (unionVarSet . tyVarsOfPred) emptyVarSet
693 -- Add a Note with the free tyvars to the top of the type
694 addFreeTyVars :: Type -> Type
695 addFreeTyVars ty@(NoteTy (FTVNote _) _) = ty
696 addFreeTyVars ty = NoteTy (FTVNote (tyVarsOfType ty)) ty
700 %************************************************************************
702 \subsection{TidyType}
704 %************************************************************************
706 tidyTy tidies up a type for printing in an error message, or in
709 It doesn't change the uniques at all, just the print names.
712 tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
713 tidyTyVarBndr (tidy_env, subst) tyvar
714 = case tidyOccName tidy_env (getOccName name) of
715 (tidy', occ') -> ((tidy', subst'), tyvar')
717 subst' = extendVarEnv subst tyvar tyvar'
718 tyvar' = setTyVarName tyvar name'
719 name' = tidyNameOcc name occ'
721 name = tyVarName tyvar
723 tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv
724 -- Add the free tyvars to the env in tidy form,
725 -- so that we can tidy the type they are free in
726 tidyFreeTyVars env tyvars = fst (tidyOpenTyVars env (varSetElems tyvars))
728 tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
729 tidyOpenTyVars env tyvars = mapAccumL tidyOpenTyVar env tyvars
731 tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
732 -- Treat a new tyvar as a binder, and give it a fresh tidy name
733 tidyOpenTyVar env@(tidy_env, subst) tyvar
734 = case lookupVarEnv subst tyvar of
735 Just tyvar' -> (env, tyvar') -- Already substituted
736 Nothing -> tidyTyVarBndr env tyvar -- Treat it as a binder
738 tidyType :: TidyEnv -> Type -> Type
739 tidyType env@(tidy_env, subst) ty
742 go (TyVarTy tv) = case lookupVarEnv subst tv of
743 Nothing -> TyVarTy tv
744 Just tv' -> TyVarTy tv'
745 go (TyConApp tycon tys) = let args = map go tys
746 in args `seqList` TyConApp tycon args
747 go (NoteTy note ty) = (NoteTy $! (go_note note)) $! (go ty)
748 go (PredTy sty) = PredTy (tidyPred env sty)
749 go (AppTy fun arg) = (AppTy $! (go fun)) $! (go arg)
750 go (FunTy fun arg) = (FunTy $! (go fun)) $! (go arg)
751 go (ForAllTy tv ty) = ForAllTy tvp $! (tidyType envp ty)
753 (envp, tvp) = tidyTyVarBndr env tv
755 go_note note@(FTVNote ftvs) = note -- No need to tidy the free tyvars
757 tidyTypes env tys = map (tidyType env) tys
759 tidyPred :: TidyEnv -> PredType -> PredType
760 tidyPred env (IParam n ty) = IParam n (tidyType env ty)
761 tidyPred env (ClassP clas tys) = ClassP clas (tidyTypes env tys)
762 tidyPred env (EqPred ty1 ty2) = EqPred (tidyType env ty1) (tidyType env ty2)
766 @tidyOpenType@ grabs the free type variables, tidies them
767 and then uses @tidyType@ to work over the type itself
770 tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
772 = (env', tidyType env' ty)
774 env' = tidyFreeTyVars env (tyVarsOfType ty)
776 tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
777 tidyOpenTypes env tys = mapAccumL tidyOpenType env tys
779 tidyTopType :: Type -> Type
780 tidyTopType ty = tidyType emptyTidyEnv ty
785 tidyKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
786 tidyKind env k = tidyOpenType env k
791 %************************************************************************
793 \subsection{Liftedness}
795 %************************************************************************
798 isUnLiftedType :: Type -> Bool
799 -- isUnLiftedType returns True for forall'd unlifted types:
800 -- x :: forall a. Int#
801 -- I found bindings like these were getting floated to the top level.
802 -- They are pretty bogus types, mind you. It would be better never to
805 isUnLiftedType ty | Just ty' <- coreView ty = isUnLiftedType ty'
806 isUnLiftedType (ForAllTy tv ty) = isUnLiftedType ty
807 isUnLiftedType (TyConApp tc _) = isUnLiftedTyCon tc
808 isUnLiftedType other = False
810 isUnboxedTupleType :: Type -> Bool
811 isUnboxedTupleType ty = case splitTyConApp_maybe ty of
812 Just (tc, ty_args) -> isUnboxedTupleTyCon tc
815 -- Should only be applied to *types*; hence the assert
816 isAlgType :: Type -> Bool
817 isAlgType ty = case splitTyConApp_maybe ty of
818 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
823 @isStrictType@ computes whether an argument (or let RHS) should
824 be computed strictly or lazily, based only on its type.
825 Works just like isUnLiftedType, except that it has a special case
826 for dictionaries. Since it takes account of ClassP, you might think
827 this function should be in TcType, but isStrictType is used by DataCon,
828 which is below TcType in the hierarchy, so it's convenient to put it here.
831 isStrictType (PredTy pred) = isStrictPred pred
832 isStrictType ty | Just ty' <- coreView ty = isStrictType ty'
833 isStrictType (ForAllTy tv ty) = isStrictType ty
834 isStrictType (TyConApp tc _) = isUnLiftedTyCon tc
835 isStrictType other = False
837 isStrictPred (ClassP clas _) = opt_DictsStrict && not (isNewTyCon (classTyCon clas))
838 isStrictPred other = False
839 -- We may be strict in dictionary types, but only if it
840 -- has more than one component.
841 -- [Being strict in a single-component dictionary risks
842 -- poking the dictionary component, which is wrong.]
846 isPrimitiveType :: Type -> Bool
847 -- Returns types that are opaque to Haskell.
848 -- Most of these are unlifted, but now that we interact with .NET, we
849 -- may have primtive (foreign-imported) types that are lifted
850 isPrimitiveType ty = case splitTyConApp_maybe ty of
851 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
857 %************************************************************************
859 \subsection{Sequencing on types
861 %************************************************************************
864 seqType :: Type -> ()
865 seqType (TyVarTy tv) = tv `seq` ()
866 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
867 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
868 seqType (NoteTy note t2) = seqNote note `seq` seqType t2
869 seqType (PredTy p) = seqPred p
870 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
871 seqType (ForAllTy tv ty) = tv `seq` seqType ty
873 seqTypes :: [Type] -> ()
875 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
877 seqNote :: TyNote -> ()
878 seqNote (FTVNote set) = sizeUniqSet set `seq` ()
880 seqPred :: PredType -> ()
881 seqPred (ClassP c tys) = c `seq` seqTypes tys
882 seqPred (IParam n ty) = n `seq` seqType ty
883 seqPred (EqPred ty1 ty2) = seqType ty1 `seq` seqType ty2
887 %************************************************************************
889 Equality for Core types
890 (We don't use instances so that we know where it happens)
892 %************************************************************************
894 Note that eqType works right even for partial applications of newtypes.
895 See Note [Newtype eta] in TyCon.lhs
898 coreEqType :: Type -> Type -> Bool
902 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
904 eq env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 == rnOccR env tv2
905 eq env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = eq (rnBndr2 env tv1 tv2) t1 t2
906 eq env (AppTy s1 t1) (AppTy s2 t2) = eq env s1 s2 && eq env t1 t2
907 eq env (FunTy s1 t1) (FunTy s2 t2) = eq env s1 s2 && eq env t1 t2
908 eq env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
909 | tc1 == tc2, all2 (eq env) tys1 tys2 = True
910 -- The lengths should be equal because
911 -- the two types have the same kind
912 -- NB: if the type constructors differ that does not
913 -- necessarily mean that the types aren't equal
914 -- (synonyms, newtypes)
915 -- Even if the type constructors are the same, but the arguments
916 -- differ, the two types could be the same (e.g. if the arg is just
917 -- ignored in the RHS). In both these cases we fall through to an
918 -- attempt to expand one side or the other.
920 -- Now deal with newtypes, synonyms, pred-tys
921 eq env t1 t2 | Just t1' <- coreView t1 = eq env t1' t2
922 | Just t2' <- coreView t2 = eq env t1 t2'
924 -- Fall through case; not equal!
929 %************************************************************************
931 Comparision for source types
932 (We don't use instances so that we know where it happens)
934 %************************************************************************
938 do *not* look through newtypes, PredTypes
941 tcEqType :: Type -> Type -> Bool
942 tcEqType t1 t2 = isEqual $ cmpType t1 t2
944 tcEqTypes :: [Type] -> [Type] -> Bool
945 tcEqTypes tys1 tys2 = isEqual $ cmpTypes tys1 tys2
947 tcCmpType :: Type -> Type -> Ordering
948 tcCmpType t1 t2 = cmpType t1 t2
950 tcCmpTypes :: [Type] -> [Type] -> Ordering
951 tcCmpTypes tys1 tys2 = cmpTypes tys1 tys2
953 tcEqPred :: PredType -> PredType -> Bool
954 tcEqPred p1 p2 = isEqual $ cmpPred p1 p2
956 tcCmpPred :: PredType -> PredType -> Ordering
957 tcCmpPred p1 p2 = cmpPred p1 p2
959 tcEqTypeX :: RnEnv2 -> Type -> Type -> Bool
960 tcEqTypeX env t1 t2 = isEqual $ cmpTypeX env t1 t2
963 Now here comes the real worker
966 cmpType :: Type -> Type -> Ordering
967 cmpType t1 t2 = cmpTypeX rn_env t1 t2
969 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
971 cmpTypes :: [Type] -> [Type] -> Ordering
972 cmpTypes ts1 ts2 = cmpTypesX rn_env ts1 ts2
974 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfTypes ts1 `unionVarSet` tyVarsOfTypes ts2))
976 cmpPred :: PredType -> PredType -> Ordering
977 cmpPred p1 p2 = cmpPredX rn_env p1 p2
979 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfPred p1 `unionVarSet` tyVarsOfPred p2))
981 cmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
982 cmpTypeX env t1 t2 | Just t1' <- tcView t1 = cmpTypeX env t1' t2
983 | Just t2' <- tcView t2 = cmpTypeX env t1 t2'
985 cmpTypeX env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 `compare` rnOccR env tv2
986 cmpTypeX env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = cmpTypeX (rnBndr2 env tv1 tv2) t1 t2
987 cmpTypeX env (AppTy s1 t1) (AppTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
988 cmpTypeX env (FunTy s1 t1) (FunTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
989 cmpTypeX env (PredTy p1) (PredTy p2) = cmpPredX env p1 p2
990 cmpTypeX env (TyConApp tc1 tys1) (TyConApp tc2 tys2) = (tc1 `compare` tc2) `thenCmp` cmpTypesX env tys1 tys2
991 cmpTypeX env t1 (NoteTy _ t2) = cmpTypeX env t1 t2
993 -- Deal with the rest: TyVarTy < AppTy < FunTy < TyConApp < ForAllTy < PredTy
994 cmpTypeX env (AppTy _ _) (TyVarTy _) = GT
996 cmpTypeX env (FunTy _ _) (TyVarTy _) = GT
997 cmpTypeX env (FunTy _ _) (AppTy _ _) = GT
999 cmpTypeX env (TyConApp _ _) (TyVarTy _) = GT
1000 cmpTypeX env (TyConApp _ _) (AppTy _ _) = GT
1001 cmpTypeX env (TyConApp _ _) (FunTy _ _) = GT
1003 cmpTypeX env (ForAllTy _ _) (TyVarTy _) = GT
1004 cmpTypeX env (ForAllTy _ _) (AppTy _ _) = GT
1005 cmpTypeX env (ForAllTy _ _) (FunTy _ _) = GT
1006 cmpTypeX env (ForAllTy _ _) (TyConApp _ _) = GT
1008 cmpTypeX env (PredTy _) t2 = GT
1010 cmpTypeX env _ _ = LT
1013 cmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
1014 cmpTypesX env [] [] = EQ
1015 cmpTypesX env (t1:tys1) (t2:tys2) = cmpTypeX env t1 t2 `thenCmp` cmpTypesX env tys1 tys2
1016 cmpTypesX env [] tys = LT
1017 cmpTypesX env ty [] = GT
1020 cmpPredX :: RnEnv2 -> PredType -> PredType -> Ordering
1021 cmpPredX env (IParam n1 ty1) (IParam n2 ty2) = (n1 `compare` n2) `thenCmp` cmpTypeX env ty1 ty2
1022 -- Compare types as well as names for implicit parameters
1023 -- This comparison is used exclusively (I think) for the
1024 -- finite map built in TcSimplify
1025 cmpPredX env (ClassP c1 tys1) (ClassP c2 tys2) = (c1 `compare` c2) `thenCmp` cmpTypesX env tys1 tys2
1026 cmpPredX env (IParam _ _) (ClassP _ _) = LT
1027 cmpPredX env (ClassP _ _) (IParam _ _) = GT
1030 PredTypes are used as a FM key in TcSimplify,
1031 so we take the easy path and make them an instance of Ord
1034 instance Eq PredType where { (==) = tcEqPred }
1035 instance Ord PredType where { compare = tcCmpPred }
1039 %************************************************************************
1043 %************************************************************************
1047 = TvSubst InScopeSet -- The in-scope type variables
1048 TvSubstEnv -- The substitution itself
1049 -- See Note [Apply Once]
1051 {- ----------------------------------------------------------
1054 We use TvSubsts to instantiate things, and we might instantiate
1058 So the substition might go [a->b, b->a]. A similar situation arises in Core
1059 when we find a beta redex like
1060 (/\ a /\ b -> e) b a
1061 Then we also end up with a substition that permutes type variables. Other
1062 variations happen to; for example [a -> (a, b)].
1064 ***************************************************
1065 *** So a TvSubst must be applied precisely once ***
1066 ***************************************************
1068 A TvSubst is not idempotent, but, unlike the non-idempotent substitution
1069 we use during unifications, it must not be repeatedly applied.
1070 -------------------------------------------------------------- -}
1073 type TvSubstEnv = TyVarEnv Type
1074 -- A TvSubstEnv is used both inside a TvSubst (with the apply-once
1075 -- invariant discussed in Note [Apply Once]), and also independently
1076 -- in the middle of matching, and unification (see Types.Unify)
1077 -- So you have to look at the context to know if it's idempotent or
1078 -- apply-once or whatever
1079 emptyTvSubstEnv :: TvSubstEnv
1080 emptyTvSubstEnv = emptyVarEnv
1082 composeTvSubst :: InScopeSet -> TvSubstEnv -> TvSubstEnv -> TvSubstEnv
1083 -- (compose env1 env2)(x) is env1(env2(x)); i.e. apply env2 then env1
1084 -- It assumes that both are idempotent
1085 -- Typically, env1 is the refinement to a base substitution env2
1086 composeTvSubst in_scope env1 env2
1087 = env1 `plusVarEnv` mapVarEnv (substTy subst1) env2
1088 -- First apply env1 to the range of env2
1089 -- Then combine the two, making sure that env1 loses if
1090 -- both bind the same variable; that's why env1 is the
1091 -- *left* argument to plusVarEnv, because the right arg wins
1093 subst1 = TvSubst in_scope env1
1095 emptyTvSubst = TvSubst emptyInScopeSet emptyVarEnv
1097 isEmptyTvSubst :: TvSubst -> Bool
1098 isEmptyTvSubst (TvSubst _ env) = isEmptyVarEnv env
1100 mkTvSubst :: InScopeSet -> TvSubstEnv -> TvSubst
1103 getTvSubstEnv :: TvSubst -> TvSubstEnv
1104 getTvSubstEnv (TvSubst _ env) = env
1106 getTvInScope :: TvSubst -> InScopeSet
1107 getTvInScope (TvSubst in_scope _) = in_scope
1109 isInScope :: Var -> TvSubst -> Bool
1110 isInScope v (TvSubst in_scope _) = v `elemInScopeSet` in_scope
1112 notElemTvSubst :: TyVar -> TvSubst -> Bool
1113 notElemTvSubst tv (TvSubst _ env) = not (tv `elemVarEnv` env)
1115 setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst
1116 setTvSubstEnv (TvSubst in_scope _) env = TvSubst in_scope env
1118 extendTvInScope :: TvSubst -> [Var] -> TvSubst
1119 extendTvInScope (TvSubst in_scope env) vars = TvSubst (extendInScopeSetList in_scope vars) env
1121 extendTvSubst :: TvSubst -> TyVar -> Type -> TvSubst
1122 extendTvSubst (TvSubst in_scope env) tv ty = TvSubst in_scope (extendVarEnv env tv ty)
1124 extendTvSubstList :: TvSubst -> [TyVar] -> [Type] -> TvSubst
1125 extendTvSubstList (TvSubst in_scope env) tvs tys
1126 = TvSubst in_scope (extendVarEnvList env (tvs `zip` tys))
1128 -- mkOpenTvSubst and zipOpenTvSubst generate the in-scope set from
1129 -- the types given; but it's just a thunk so with a bit of luck
1130 -- it'll never be evaluated
1132 mkOpenTvSubst :: TvSubstEnv -> TvSubst
1133 mkOpenTvSubst env = TvSubst (mkInScopeSet (tyVarsOfTypes (varEnvElts env))) env
1135 zipOpenTvSubst :: [TyVar] -> [Type] -> TvSubst
1136 zipOpenTvSubst tyvars tys
1138 | length tyvars /= length tys
1139 = pprTrace "zipOpenTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1142 = TvSubst (mkInScopeSet (tyVarsOfTypes tys)) (zipTyEnv tyvars tys)
1144 -- mkTopTvSubst is called when doing top-level substitutions.
1145 -- Here we expect that the free vars of the range of the
1146 -- substitution will be empty.
1147 mkTopTvSubst :: [(TyVar, Type)] -> TvSubst
1148 mkTopTvSubst prs = TvSubst emptyInScopeSet (mkVarEnv prs)
1150 zipTopTvSubst :: [TyVar] -> [Type] -> TvSubst
1151 zipTopTvSubst tyvars tys
1153 | length tyvars /= length tys
1154 = pprTrace "zipOpenTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1157 = TvSubst emptyInScopeSet (zipTyEnv tyvars tys)
1159 zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
1162 | length tyvars /= length tys
1163 = pprTrace "mkTopTvSubst" (ppr tyvars $$ ppr tys) emptyVarEnv
1166 = zip_ty_env tyvars tys emptyVarEnv
1168 -- Later substitutions in the list over-ride earlier ones,
1169 -- but there should be no loops
1170 zip_ty_env [] [] env = env
1171 zip_ty_env (tv:tvs) (ty:tys) env = zip_ty_env tvs tys (extendVarEnv env tv ty)
1172 -- There used to be a special case for when
1174 -- (a not-uncommon case) in which case the substitution was dropped.
1175 -- But the type-tidier changes the print-name of a type variable without
1176 -- changing the unique, and that led to a bug. Why? Pre-tidying, we had
1177 -- a type {Foo t}, where Foo is a one-method class. So Foo is really a newtype.
1178 -- And it happened that t was the type variable of the class. Post-tiding,
1179 -- it got turned into {Foo t2}. The ext-core printer expanded this using
1180 -- sourceTypeRep, but that said "Oh, t == t2" because they have the same unique,
1181 -- and so generated a rep type mentioning t not t2.
1183 -- Simplest fix is to nuke the "optimisation"
1184 zip_ty_env tvs tys env = pprTrace "Var/Type length mismatch: " (ppr tvs $$ ppr tys) env
1185 -- zip_ty_env _ _ env = env
1187 instance Outputable TvSubst where
1188 ppr (TvSubst ins env)
1189 = brackets $ sep[ ptext SLIT("TvSubst"),
1190 nest 2 (ptext SLIT("In scope:") <+> ppr ins),
1191 nest 2 (ptext SLIT("Env:") <+> ppr env) ]
1194 %************************************************************************
1196 Performing type substitutions
1198 %************************************************************************
1201 substTyWith :: [TyVar] -> [Type] -> Type -> Type
1202 substTyWith tvs tys = ASSERT( length tvs == length tys )
1203 substTy (zipOpenTvSubst tvs tys)
1205 substTy :: TvSubst -> Type -> Type
1206 substTy subst ty | isEmptyTvSubst subst = ty
1207 | otherwise = subst_ty subst ty
1209 substTys :: TvSubst -> [Type] -> [Type]
1210 substTys subst tys | isEmptyTvSubst subst = tys
1211 | otherwise = map (subst_ty subst) tys
1213 substTheta :: TvSubst -> ThetaType -> ThetaType
1214 substTheta subst theta
1215 | isEmptyTvSubst subst = theta
1216 | otherwise = map (substPred subst) theta
1218 substPred :: TvSubst -> PredType -> PredType
1219 substPred subst (IParam n ty) = IParam n (subst_ty subst ty)
1220 substPred subst (ClassP clas tys) = ClassP clas (map (subst_ty subst) tys)
1221 substPred subst (EqPred ty1 ty2) = EqPred (subst_ty subst ty1) (subst_ty subst ty2)
1223 deShadowTy :: TyVarSet -> Type -> Type -- Remove any nested binders mentioning tvs
1225 = subst_ty (mkTvSubst in_scope emptyTvSubstEnv) ty
1227 in_scope = mkInScopeSet tvs
1229 subst_ty :: TvSubst -> Type -> Type
1230 -- subst_ty is the main workhorse for type substitution
1232 -- Note that the in_scope set is poked only if we hit a forall
1233 -- so it may often never be fully computed
1237 go (TyVarTy tv) = substTyVar subst tv
1238 go (TyConApp tc tys) = let args = map go tys
1239 in args `seqList` TyConApp tc args
1241 go (PredTy p) = PredTy $! (substPred subst p)
1243 go (NoteTy (FTVNote _) ty2) = go ty2 -- Discard the free tyvar note
1245 go (FunTy arg res) = (FunTy $! (go arg)) $! (go res)
1246 go (AppTy fun arg) = mkAppTy (go fun) $! (go arg)
1247 -- The mkAppTy smart constructor is important
1248 -- we might be replacing (a Int), represented with App
1249 -- by [Int], represented with TyConApp
1250 go (ForAllTy tv ty) = case substTyVarBndr subst tv of
1251 (subst', tv') -> ForAllTy tv' $! (subst_ty subst' ty)
1253 substTyVar :: TvSubst -> TyVar -> Type
1254 substTyVar subst@(TvSubst in_scope env) tv
1255 = case lookupTyVar subst tv of {
1256 Nothing -> TyVarTy tv;
1257 Just ty -> ty -- See Note [Apply Once]
1260 lookupTyVar :: TvSubst -> TyVar -> Maybe Type
1261 lookupTyVar (TvSubst in_scope env) tv = lookupVarEnv env tv
1263 substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)
1264 substTyVarBndr subst@(TvSubst in_scope env) old_var
1265 = (TvSubst (in_scope `extendInScopeSet` new_var) new_env, new_var)
1268 new_env | no_change = delVarEnv env old_var
1269 | otherwise = extendVarEnv env old_var (TyVarTy new_var)
1271 no_change = new_var == old_var && not is_co_var
1272 -- no_change means that the new_var is identical in
1273 -- all respects to the old_var (same unique, same kind)
1275 -- In that case we don't need to extend the substitution
1276 -- to map old to new. But instead we must zap any
1277 -- current substitution for the variable. For example:
1278 -- (\x.e) with id_subst = [x |-> e']
1279 -- Here we must simply zap the substitution for x
1281 new_var = uniqAway in_scope subst_old_var
1282 -- The uniqAway part makes sure the new variable is not already in scope
1284 subst_old_var -- subst_old_var is old_var with the substitution applied to its kind
1285 -- It's only worth doing the substitution for coercions,
1286 -- becuase only they can have free type variables
1287 | is_co_var = setTyVarKind old_var (substTy subst kind)
1288 | otherwise = old_var
1289 kind = tyVarKind old_var
1290 is_co_var = isCoercionKind kind
1293 ----------------------------------------------------
1298 There's a little subtyping at the kind level:
1307 where * [LiftedTypeKind] means boxed type
1308 # [UnliftedTypeKind] means unboxed type
1309 (#) [UbxTupleKind] means unboxed tuple
1310 ?? [ArgTypeKind] is the lub of *,#
1311 ? [OpenTypeKind] means any type at all
1315 error :: forall a:?. String -> a
1316 (->) :: ?? -> ? -> *
1317 (\(x::t) -> ...) Here t::?? (i.e. not unboxed tuple)
1320 type KindVar = TyVar -- invariant: KindVar will always be a
1321 -- TcTyVar with details MetaTv TauTv ...
1322 -- kind var constructors and functions are in TcType
1324 type SimpleKind = Kind
1329 During kind inference, a kind variable unifies only with
1331 sk ::= * | sk1 -> sk2
1333 data T a = MkT a (T Int#)
1334 fails. We give T the kind (k -> *), and the kind variable k won't unify
1335 with # (the kind of Int#).
1339 When creating a fresh internal type variable, we give it a kind to express
1340 constraints on it. E.g. in (\x->e) we make up a fresh type variable for x,
1343 During unification we only bind an internal type variable to a type
1344 whose kind is lower in the sub-kind hierarchy than the kind of the tyvar.
1346 When unifying two internal type variables, we collect their kind constraints by
1347 finding the GLB of the two. Since the partial order is a tree, they only
1348 have a glb if one is a sub-kind of the other. In that case, we bind the
1349 less-informative one to the more informative one. Neat, eh?
1356 %************************************************************************
1358 Functions over Kinds
1360 %************************************************************************
1363 kindFunResult :: Kind -> Kind
1364 kindFunResult k = funResultTy k
1366 splitKindFunTys :: Kind -> ([Kind],Kind)
1367 splitKindFunTys k = splitFunTys k
1369 isUbxTupleKind, isOpenTypeKind, isArgTypeKind, isUnliftedTypeKind :: Kind -> Bool
1371 isOpenTypeKindCon tc = tyConUnique tc == openTypeKindTyConKey
1373 isOpenTypeKind (TyConApp tc _) = isOpenTypeKindCon tc
1374 isOpenTypeKind other = False
1376 isUbxTupleKindCon tc = tyConUnique tc == ubxTupleKindTyConKey
1378 isUbxTupleKind (TyConApp tc _) = isUbxTupleKindCon tc
1379 isUbxTupleKind other = False
1381 isArgTypeKindCon tc = tyConUnique tc == argTypeKindTyConKey
1383 isArgTypeKind (TyConApp tc _) = isArgTypeKindCon tc
1384 isArgTypeKind other = False
1386 isUnliftedTypeKindCon tc = tyConUnique tc == unliftedTypeKindTyConKey
1388 isUnliftedTypeKind (TyConApp tc _) = isUnliftedTypeKindCon tc
1389 isUnliftedTypeKind other = False
1391 isSubOpenTypeKind :: Kind -> Bool
1392 -- True of any sub-kind of OpenTypeKind (i.e. anything except arrow)
1393 isSubOpenTypeKind (FunTy k1 k2) = ASSERT2 ( isKind k1, text "isSubOpenTypeKind" <+> ppr k1 <+> text "::" <+> ppr (typeKind k1) )
1394 ASSERT2 ( isKind k2, text "isSubOpenTypeKind" <+> ppr k2 <+> text "::" <+> ppr (typeKind k2) )
1396 isSubOpenTypeKind (TyConApp kc []) = ASSERT( isKind (TyConApp kc []) ) True
1397 isSubOpenTypeKind other = ASSERT( isKind other ) False
1398 -- This is a conservative answer
1399 -- It matters in the call to isSubKind in
1400 -- checkExpectedKind.
1402 isSubArgTypeKindCon kc
1403 | isUnliftedTypeKindCon kc = True
1404 | isLiftedTypeKindCon kc = True
1405 | isArgTypeKindCon kc = True
1408 isSubArgTypeKind :: Kind -> Bool
1409 -- True of any sub-kind of ArgTypeKind
1410 isSubArgTypeKind (TyConApp kc []) = isSubArgTypeKindCon kc
1411 isSubArgTypeKind other = False
1413 isSuperKind :: Type -> Bool
1414 isSuperKind (TyConApp (skc) []) = isSuperKindTyCon skc
1415 isSuperKind other = False
1417 isKind :: Kind -> Bool
1418 isKind k = isSuperKind (typeKind k)
1422 isSubKind :: Kind -> Kind -> Bool
1423 -- (k1 `isSubKind` k2) checks that k1 <: k2
1424 isSubKind (TyConApp kc1 []) (TyConApp kc2 []) = kc1 `isSubKindCon` kc1
1425 isSubKind (FunTy a1 r1) (FunTy a2 r2) = (a2 `isSubKind` a1) && (r1 `isSubKind` r2)
1426 isSubKind k1 k2 = False
1428 eqKind :: Kind -> Kind -> Bool
1431 isSubKindCon :: TyCon -> TyCon -> Bool
1432 -- (kc1 `isSubKindCon` kc2) checks that kc1 <: kc2
1433 isSubKindCon kc1 kc2
1434 | isLiftedTypeKindCon kc1 && isLiftedTypeKindCon kc2 = True
1435 | isUnliftedTypeKindCon kc1 && isUnliftedTypeKindCon kc2 = True
1436 | isUbxTupleKindCon kc1 && isUbxTupleKindCon kc2 = True
1437 | isOpenTypeKindCon kc2 = True
1438 -- we already know kc1 is not a fun, its a TyCon
1439 | isArgTypeKindCon kc2 && isSubArgTypeKindCon kc1 = True
1442 defaultKind :: Kind -> Kind
1443 -- Used when generalising: default kind '?' and '??' to '*'
1445 -- When we generalise, we make generic type variables whose kind is
1446 -- simple (* or *->* etc). So generic type variables (other than
1447 -- built-in constants like 'error') always have simple kinds. This is important;
1450 -- We want f to get type
1451 -- f :: forall (a::*). a -> Bool
1453 -- f :: forall (a::??). a -> Bool
1454 -- because that would allow a call like (f 3#) as well as (f True),
1455 --and the calling conventions differ. This defaulting is done in TcMType.zonkTcTyVarBndr.
1457 | isSubOpenTypeKind k = liftedTypeKind
1458 | isSubArgTypeKind k = liftedTypeKind
1461 isCoercionKind :: Kind -> Bool
1462 -- All coercions are of form (ty1 :=: ty2)
1463 -- This function is here rather than in Coercion,
1464 -- because it's used by substTy
1465 isCoercionKind k | Just k' <- kindView k = isCoercionKind k'
1466 isCoercionKind (PredTy (EqPred {})) = True
1467 isCoercionKind other = False