2 % (c) The University of Glasgow 2006
3 % (c) The GRASP/AQUA Project, Glasgow University, 1998
6 Type - public interface
10 -- The above warning supression flag is a temporary kludge.
11 -- While working on this module you are encouraged to remove it and fix
12 -- any warnings in the module. See
13 -- http://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#Warnings
17 -- re-exports from TypeRep
18 TyThing(..), Type, PredType(..), ThetaType,
22 Kind, SimpleKind, KindVar,
23 kindFunResult, splitKindFunTys, splitKindFunTysN,
25 liftedTypeKindTyCon, openTypeKindTyCon, unliftedTypeKindTyCon,
26 argTypeKindTyCon, ubxTupleKindTyCon,
28 liftedTypeKind, unliftedTypeKind, openTypeKind,
29 argTypeKind, ubxTupleKind,
31 tySuperKind, coSuperKind,
33 isLiftedTypeKind, isUnliftedTypeKind, isOpenTypeKind,
34 isUbxTupleKind, isArgTypeKind, isKind, isTySuperKind,
35 isCoSuperKind, isSuperKind, isCoercionKind, isEqPred,
36 mkArrowKind, mkArrowKinds,
38 isSubArgTypeKind, isSubOpenTypeKind, isSubKind, defaultKind, eqKind,
41 -- Re-exports from TyCon
44 mkTyVarTy, mkTyVarTys, getTyVar, getTyVar_maybe, isTyVarTy,
46 mkAppTy, mkAppTys, splitAppTy, splitAppTys,
47 splitAppTy_maybe, repSplitAppTy_maybe,
49 mkFunTy, mkFunTys, splitFunTy, splitFunTy_maybe,
50 splitFunTys, splitFunTysN,
51 funResultTy, funArgTy, zipFunTys, isFunTy,
53 mkTyConApp, mkTyConTy,
54 tyConAppTyCon, tyConAppArgs,
55 splitTyConApp_maybe, splitTyConApp,
56 splitNewTyConApp_maybe, splitNewTyConApp,
58 repType, typePrimRep, coreView, tcView, kindView, rttiView,
60 mkForAllTy, mkForAllTys, splitForAllTy_maybe, splitForAllTys,
61 applyTy, applyTys, isForAllTy, dropForAlls,
64 predTypeRep, mkPredTy, mkPredTys, pprSourceTyCon, mkFamilyTyConApp,
70 isUnLiftedType, isUnboxedTupleType, isAlgType, isClosedAlgType,
71 isPrimitiveType, isStrictType, isStrictPred,
74 tyVarsOfType, tyVarsOfTypes, tyVarsOfPred, tyVarsOfTheta,
75 typeKind, addFreeTyVars,
80 -- Tidying up for printing
82 tidyOpenType, tidyOpenTypes,
83 tidyTyVarBndr, tidyFreeTyVars,
84 tidyOpenTyVar, tidyOpenTyVars,
85 tidyTopType, tidyPred,
89 coreEqType, tcEqType, tcEqTypes, tcCmpType, tcCmpTypes,
90 tcEqPred, tcCmpPred, tcEqTypeX, tcPartOfType, tcPartOfPred,
96 TvSubstEnv, emptyTvSubstEnv, -- Representation widely visible
97 TvSubst(..), emptyTvSubst, -- Representation visible to a few friends
98 mkTvSubst, mkOpenTvSubst, zipOpenTvSubst, zipTopTvSubst, mkTopTvSubst, notElemTvSubst,
99 getTvSubstEnv, setTvSubstEnv, getTvInScope, extendTvInScope,
100 extendTvSubst, extendTvSubstList, isInScope, composeTvSubst, zipTyEnv,
103 -- Performing substitution on types
104 substTy, substTys, substTyWith, substTheta,
105 substPred, substTyVar, substTyVars, substTyVarBndr, deShadowTy, lookupTyVar,
108 pprType, pprParendType, pprTypeApp, pprTyThingCategory, pprTyThing, pprForAll,
109 pprPred, pprTheta, pprThetaArrow, pprClassPred, pprKind, pprParendKind
112 #include "HsVersions.h"
114 -- We import the representation and primitive functions from TypeRep.
115 -- Many things are reexported, but not the representation!
136 import Data.Maybe ( isJust )
140 %************************************************************************
144 %************************************************************************
146 In Core, we "look through" non-recursive newtypes and PredTypes.
149 {-# INLINE coreView #-}
150 coreView :: Type -> Maybe Type
151 -- Strips off the *top layer only* of a type to give
152 -- its underlying representation type.
153 -- Returns Nothing if there is nothing to look through.
155 -- In the case of newtypes, it returns
156 -- *either* a vanilla TyConApp (recursive newtype, or non-saturated)
157 -- *or* the newtype representation (otherwise), meaning the
158 -- type written in the RHS of the newtype decl,
159 -- which may itself be a newtype
161 -- Example: newtype R = MkR S
163 -- newtype T = MkT (T -> T)
164 -- expandNewTcApp on R gives Just S
166 -- on T gives Nothing (no expansion)
168 -- By being non-recursive and inlined, this case analysis gets efficiently
169 -- joined onto the case analysis that the caller is already doing
170 coreView (NoteTy _ ty) = Just ty
172 | isEqPred p = Nothing
173 | otherwise = Just (predTypeRep p)
174 coreView (TyConApp tc tys) | Just (tenv, rhs, tys') <- coreExpandTyCon_maybe tc tys
175 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
176 -- Its important to use mkAppTys, rather than (foldl AppTy),
177 -- because the function part might well return a
178 -- partially-applied type constructor; indeed, usually will!
179 coreView ty = Nothing
183 -----------------------------------------------
184 {-# INLINE tcView #-}
185 tcView :: Type -> Maybe Type
186 -- Same, but for the type checker, which just looks through synonyms
187 tcView (NoteTy _ ty) = Just ty
188 tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- tcExpandTyCon_maybe tc tys
189 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
192 -----------------------------------------------
193 rttiView :: Type -> Type
194 -- Same, but for the RTTI system, which cannot deal with predicates nor polymorphism
195 rttiView (ForAllTy _ ty) = rttiView ty
196 rttiView (NoteTy _ ty) = rttiView ty
197 rttiView (FunTy PredTy{} ty) = rttiView ty
198 rttiView (FunTy NoteTy{} ty) = rttiView ty
199 rttiView ty@TyConApp{} | Just ty' <- coreView ty
201 rttiView (TyConApp tc tys) = mkTyConApp tc (map rttiView tys)
204 -----------------------------------------------
205 {-# INLINE kindView #-}
206 kindView :: Kind -> Maybe Kind
207 -- C.f. coreView, tcView
208 -- For the moment, we don't even handle synonyms in kinds
209 kindView (NoteTy _ k) = Just k
210 kindView other = Nothing
214 %************************************************************************
216 \subsection{Constructor-specific functions}
218 %************************************************************************
221 ---------------------------------------------------------------------
225 mkTyVarTy :: TyVar -> Type
228 mkTyVarTys :: [TyVar] -> [Type]
229 mkTyVarTys = map mkTyVarTy -- a common use of mkTyVarTy
231 getTyVar :: String -> Type -> TyVar
232 getTyVar msg ty = case getTyVar_maybe ty of
234 Nothing -> panic ("getTyVar: " ++ msg)
236 isTyVarTy :: Type -> Bool
237 isTyVarTy ty = isJust (getTyVar_maybe ty)
239 getTyVar_maybe :: Type -> Maybe TyVar
240 getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty'
241 getTyVar_maybe (TyVarTy tv) = Just tv
242 getTyVar_maybe other = Nothing
247 ---------------------------------------------------------------------
250 We need to be pretty careful with AppTy to make sure we obey the
251 invariant that a TyConApp is always visibly so. mkAppTy maintains the
255 mkAppTy orig_ty1 orig_ty2
258 mk_app (NoteTy _ ty1) = mk_app ty1
259 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ [orig_ty2])
260 mk_app ty1 = AppTy orig_ty1 orig_ty2
261 -- Note that the TyConApp could be an
262 -- under-saturated type synonym. GHC allows that; e.g.
263 -- type Foo k = k a -> k a
265 -- foo :: Foo Id -> Foo Id
267 -- Here Id is partially applied in the type sig for Foo,
268 -- but once the type synonyms are expanded all is well
270 mkAppTys :: Type -> [Type] -> Type
271 mkAppTys orig_ty1 [] = orig_ty1
272 -- This check for an empty list of type arguments
273 -- avoids the needless loss of a type synonym constructor.
274 -- For example: mkAppTys Rational []
275 -- returns to (Ratio Integer), which has needlessly lost
276 -- the Rational part.
277 mkAppTys orig_ty1 orig_tys2
280 mk_app (NoteTy _ ty1) = mk_app ty1
281 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ orig_tys2)
282 -- mkTyConApp: see notes with mkAppTy
283 mk_app ty1 = foldl AppTy orig_ty1 orig_tys2
286 splitAppTy_maybe :: Type -> Maybe (Type, Type)
287 splitAppTy_maybe ty | Just ty' <- coreView ty
288 = splitAppTy_maybe ty'
289 splitAppTy_maybe ty = repSplitAppTy_maybe ty
292 repSplitAppTy_maybe :: Type -> Maybe (Type,Type)
293 -- Does the AppTy split, but assumes that any view stuff is already done
294 repSplitAppTy_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
295 repSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
296 repSplitAppTy_maybe (TyConApp tc tys)
297 | not (isOpenSynTyCon tc) || length tys > tyConArity tc
298 = case snocView tys of -- never create unsaturated type family apps
299 Just (tys', ty') -> Just (TyConApp tc tys', ty')
301 repSplitAppTy_maybe _other = Nothing
303 splitAppTy :: Type -> (Type, Type)
304 splitAppTy ty = case splitAppTy_maybe ty of
306 Nothing -> panic "splitAppTy"
309 splitAppTys :: Type -> (Type, [Type])
310 splitAppTys ty = split ty ty []
312 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
313 split orig_ty (AppTy ty arg) args = split ty ty (arg:args)
314 split orig_ty (TyConApp tc tc_args) args
315 = let -- keep type families saturated
316 n | isOpenSynTyCon tc = tyConArity tc
318 (tc_args1, tc_args2) = splitAt n tc_args
320 (TyConApp tc tc_args1, tc_args2 ++ args)
321 split orig_ty (FunTy ty1 ty2) args = ASSERT( null args )
322 (TyConApp funTyCon [], [ty1,ty2])
323 split orig_ty ty args = (orig_ty, args)
328 ---------------------------------------------------------------------
333 mkFunTy :: Type -> Type -> Type
334 mkFunTy (PredTy (EqPred ty1 ty2)) res = mkForAllTy (mkWildCoVar (PredTy (EqPred ty1 ty2))) res
335 mkFunTy arg res = FunTy arg res
337 mkFunTys :: [Type] -> Type -> Type
338 mkFunTys tys ty = foldr mkFunTy ty tys
340 isFunTy :: Type -> Bool
341 isFunTy ty = isJust (splitFunTy_maybe ty)
343 splitFunTy :: Type -> (Type, Type)
344 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
345 splitFunTy (FunTy arg res) = (arg, res)
346 splitFunTy other = pprPanic "splitFunTy" (ppr other)
348 splitFunTy_maybe :: Type -> Maybe (Type, Type)
349 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
350 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
351 splitFunTy_maybe other = Nothing
353 splitFunTys :: Type -> ([Type], Type)
354 splitFunTys ty = split [] ty ty
356 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
357 split args orig_ty (FunTy arg res) = split (arg:args) res res
358 split args orig_ty ty = (reverse args, orig_ty)
360 splitFunTysN :: Int -> Type -> ([Type], Type)
361 -- Split off exactly n arg tys
362 splitFunTysN 0 ty = ([], ty)
363 splitFunTysN n ty = case splitFunTy ty of { (arg, res) ->
364 case splitFunTysN (n-1) res of { (args, res) ->
367 zipFunTys :: Outputable a => [a] -> Type -> ([(a,Type)], Type)
368 zipFunTys orig_xs orig_ty = split [] orig_xs orig_ty orig_ty
370 split acc [] nty ty = (reverse acc, nty)
372 | Just ty' <- coreView ty = split acc xs nty ty'
373 split acc (x:xs) nty (FunTy arg res) = split ((x,arg):acc) xs res res
374 split acc (x:xs) nty ty = pprPanic "zipFunTys" (ppr orig_xs <+> ppr orig_ty)
376 funResultTy :: Type -> Type
377 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
378 funResultTy (FunTy arg res) = res
379 funResultTy ty = pprPanic "funResultTy" (ppr ty)
381 funArgTy :: Type -> Type
382 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
383 funArgTy (FunTy arg res) = arg
384 funArgTy ty = pprPanic "funArgTy" (ppr ty)
388 ---------------------------------------------------------------------
391 @mkTyConApp@ is a key function, because it builds a TyConApp, FunTy or PredTy,
395 mkTyConApp :: TyCon -> [Type] -> Type
397 | isFunTyCon tycon, [ty1,ty2] <- tys
403 mkTyConTy :: TyCon -> Type
404 mkTyConTy tycon = mkTyConApp tycon []
406 -- splitTyConApp "looks through" synonyms, because they don't
407 -- mean a distinct type, but all other type-constructor applications
408 -- including functions are returned as Just ..
410 tyConAppTyCon :: Type -> TyCon
411 tyConAppTyCon ty = fst (splitTyConApp ty)
413 tyConAppArgs :: Type -> [Type]
414 tyConAppArgs ty = snd (splitTyConApp ty)
416 splitTyConApp :: Type -> (TyCon, [Type])
417 splitTyConApp ty = case splitTyConApp_maybe ty of
419 Nothing -> pprPanic "splitTyConApp" (ppr ty)
421 splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
422 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
423 splitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
424 splitTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
425 splitTyConApp_maybe other = Nothing
427 -- Sometimes we do NOT want to look throught a newtype. When case matching
428 -- on a newtype we want a convenient way to access the arguments of a newty
429 -- constructor so as to properly form a coercion.
430 splitNewTyConApp :: Type -> (TyCon, [Type])
431 splitNewTyConApp ty = case splitNewTyConApp_maybe ty of
433 Nothing -> pprPanic "splitNewTyConApp" (ppr ty)
434 splitNewTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
435 splitNewTyConApp_maybe ty | Just ty' <- tcView ty = splitNewTyConApp_maybe ty'
436 splitNewTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
437 splitNewTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
438 splitNewTyConApp_maybe other = Nothing
440 newTyConInstRhs :: TyCon -> [Type] -> Type
441 -- Unwrap one 'layer' of newtype
442 -- Use the eta'd version if possible
443 newTyConInstRhs tycon tys
444 = ASSERT2( equalLength tvs tys1, ppr tycon $$ ppr tys $$ ppr tvs )
445 mkAppTys (substTyWith tvs tys1 ty) tys2
447 (tvs, ty) = newTyConEtadRhs tycon
448 (tys1, tys2) = splitAtList tvs tys
452 ---------------------------------------------------------------------
456 Notes on type synonyms
457 ~~~~~~~~~~~~~~~~~~~~~~
458 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
459 to return type synonyms whereever possible. Thus
464 splitFunTys (a -> Foo a) = ([a], Foo a)
467 The reason is that we then get better (shorter) type signatures in
468 interfaces. Notably this plays a role in tcTySigs in TcBinds.lhs.
473 repType looks through
477 (d) usage annotations
478 (e) all newtypes, including recursive ones, but not newtype families
479 It's useful in the back end.
482 repType :: Type -> Type
483 -- Only applied to types of kind *; hence tycons are saturated
484 repType ty | Just ty' <- coreView ty = repType ty'
485 repType (ForAllTy _ ty) = repType ty
486 repType (TyConApp tc tys)
488 , (tvs, rep_ty) <- newTyConRep tc
489 = -- Recursive newtypes are opaque to coreView
490 -- but we must expand them here. Sure to
491 -- be saturated because repType is only applied
492 -- to types of kind *
493 ASSERT( tys `lengthIs` tyConArity tc )
494 repType (substTyWith tvs tys rep_ty)
498 -- ToDo: this could be moved to the code generator, using splitTyConApp instead
499 -- of inspecting the type directly.
500 typePrimRep :: Type -> PrimRep
501 typePrimRep ty = case repType ty of
502 TyConApp tc _ -> tyConPrimRep tc
504 AppTy _ _ -> PtrRep -- See note below
506 other -> pprPanic "typePrimRep" (ppr ty)
507 -- Types of the form 'f a' must be of kind *, not *#, so
508 -- we are guaranteed that they are represented by pointers.
509 -- The reason is that f must have kind *->*, not *->*#, because
510 -- (we claim) there is no way to constrain f's kind any other
515 ---------------------------------------------------------------------
520 mkForAllTy :: TyVar -> Type -> Type
522 = mkForAllTys [tyvar] ty
524 mkForAllTys :: [TyVar] -> Type -> Type
525 mkForAllTys tyvars ty = foldr ForAllTy ty tyvars
527 isForAllTy :: Type -> Bool
528 isForAllTy (NoteTy _ ty) = isForAllTy ty
529 isForAllTy (ForAllTy _ _) = True
530 isForAllTy other_ty = False
532 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
533 splitForAllTy_maybe ty = splitFAT_m ty
535 splitFAT_m ty | Just ty' <- coreView ty = splitFAT_m ty'
536 splitFAT_m (ForAllTy tyvar ty) = Just(tyvar, ty)
537 splitFAT_m _ = Nothing
539 splitForAllTys :: Type -> ([TyVar], Type)
540 splitForAllTys ty = split ty ty []
542 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
543 split orig_ty (ForAllTy tv ty) tvs = split ty ty (tv:tvs)
544 split orig_ty t tvs = (reverse tvs, orig_ty)
546 dropForAlls :: Type -> Type
547 dropForAlls ty = snd (splitForAllTys ty)
550 -- (mkPiType now in CoreUtils)
554 Instantiate a for-all type with one or more type arguments.
555 Used when we have a polymorphic function applied to type args:
557 Then we use (applyTys type-of-f [t1,t2]) to compute the type of
561 applyTy :: Type -> Type -> Type
562 applyTy ty arg | Just ty' <- coreView ty = applyTy ty' arg
563 applyTy (ForAllTy tv ty) arg = substTyWith [tv] [arg] ty
564 applyTy other arg = panic "applyTy"
566 applyTys :: Type -> [Type] -> Type
567 -- This function is interesting because
568 -- a) the function may have more for-alls than there are args
569 -- b) less obviously, it may have fewer for-alls
570 -- For case (b) think of
571 -- applyTys (forall a.a) [forall b.b, Int]
572 -- This really can happen, via dressing up polymorphic types with newtype
573 -- clothing. Here's an example:
574 -- newtype R = R (forall a. a->a)
575 -- foo = case undefined :: R of
578 applyTys orig_fun_ty [] = orig_fun_ty
579 applyTys orig_fun_ty arg_tys
580 | n_tvs == n_args -- The vastly common case
581 = substTyWith tvs arg_tys rho_ty
582 | n_tvs > n_args -- Too many for-alls
583 = substTyWith (take n_args tvs) arg_tys
584 (mkForAllTys (drop n_args tvs) rho_ty)
585 | otherwise -- Too many type args
586 = ASSERT2( n_tvs > 0, ppr orig_fun_ty ) -- Zero case gives infnite loop!
587 applyTys (substTyWith tvs (take n_tvs arg_tys) rho_ty)
590 (tvs, rho_ty) = splitForAllTys orig_fun_ty
592 n_args = length arg_tys
596 %************************************************************************
598 \subsection{Source types}
600 %************************************************************************
602 A "source type" is a type that is a separate type as far as the type checker is
603 concerned, but which has low-level representation as far as the back end is concerned.
605 Source types are always lifted.
607 The key function is predTypeRep which gives the representation of a source type:
610 mkPredTy :: PredType -> Type
611 mkPredTy pred = PredTy pred
613 mkPredTys :: ThetaType -> [Type]
614 mkPredTys preds = map PredTy preds
616 predTypeRep :: PredType -> Type
617 -- Convert a PredType to its "representation type";
618 -- the post-type-checking type used by all the Core passes of GHC.
619 -- Unwraps only the outermost level; for example, the result might
620 -- be a newtype application
621 predTypeRep (IParam _ ty) = ty
622 predTypeRep (ClassP clas tys) = mkTyConApp (classTyCon clas) tys
623 -- Result might be a newtype application, but the consumer will
624 -- look through that too if necessary
625 predTypeRep (EqPred ty1 ty2) = pprPanic "predTypeRep" (ppr (EqPred ty1 ty2))
627 mkFamilyTyConApp :: TyCon -> [Type] -> Type
628 -- Given a family instance TyCon and its arg types, return the
629 -- corresponding family type. E.g.
631 -- data instance T (Maybe b) = MkT b -- Instance tycon :RTL
633 -- mkFamilyTyConApp :RTL Int = T (Maybe Int)
634 mkFamilyTyConApp tc tys
635 | Just (fam_tc, fam_tys) <- tyConFamInst_maybe tc
636 , let fam_subst = zipTopTvSubst (tyConTyVars tc) tys
637 = mkTyConApp fam_tc (substTys fam_subst fam_tys)
641 -- Pretty prints a tycon, using the family instance in case of a
642 -- representation tycon. For example
643 -- e.g. data T [a] = ...
644 -- In that case we want to print `T [a]', where T is the family TyCon
646 | Just (fam_tc, tys) <- tyConFamInst_maybe tycon
647 = ppr $ fam_tc `TyConApp` tys -- can't be FunTyCon
653 %************************************************************************
655 \subsection{Kinds and free variables}
657 %************************************************************************
659 ---------------------------------------------------------------------
660 Finding the kind of a type
661 ~~~~~~~~~~~~~~~~~~~~~~~~~~
663 typeKind :: Type -> Kind
664 typeKind (TyConApp tycon tys) = ASSERT( not (isCoercionTyCon tycon) )
665 -- We should be looking for the coercion kind,
667 foldr (\_ k -> kindFunResult k) (tyConKind tycon) tys
668 typeKind (NoteTy _ ty) = typeKind ty
669 typeKind (PredTy pred) = predKind pred
670 typeKind (AppTy fun arg) = kindFunResult (typeKind fun)
671 typeKind (ForAllTy tv ty) = typeKind ty
672 typeKind (TyVarTy tyvar) = tyVarKind tyvar
673 typeKind (FunTy arg res)
674 -- Hack alert. The kind of (Int -> Int#) is liftedTypeKind (*),
675 -- not unliftedTypKind (#)
676 -- The only things that can be after a function arrow are
677 -- (a) types (of kind openTypeKind or its sub-kinds)
678 -- (b) kinds (of super-kind TY) (e.g. * -> (* -> *))
679 | isTySuperKind k = k
680 | otherwise = ASSERT( isSubOpenTypeKind k) liftedTypeKind
684 predKind :: PredType -> Kind
685 predKind (EqPred {}) = coSuperKind -- A coercion kind!
686 predKind (ClassP {}) = liftedTypeKind -- Class and implicitPredicates are
687 predKind (IParam {}) = liftedTypeKind -- always represented by lifted types
691 ---------------------------------------------------------------------
692 Free variables of a type
693 ~~~~~~~~~~~~~~~~~~~~~~~~
695 tyVarsOfType :: Type -> TyVarSet
696 -- NB: for type synonyms tyVarsOfType does *not* expand the synonym
697 tyVarsOfType (TyVarTy tv) = unitVarSet tv
698 tyVarsOfType (TyConApp tycon tys) = tyVarsOfTypes tys
699 tyVarsOfType (NoteTy (FTVNote tvs) ty2) = tvs
700 tyVarsOfType (PredTy sty) = tyVarsOfPred sty
701 tyVarsOfType (FunTy arg res) = tyVarsOfType arg `unionVarSet` tyVarsOfType res
702 tyVarsOfType (AppTy fun arg) = tyVarsOfType fun `unionVarSet` tyVarsOfType arg
703 tyVarsOfType (ForAllTy tyvar ty) = delVarSet (tyVarsOfType ty) tyvar
705 tyVarsOfTypes :: [Type] -> TyVarSet
706 tyVarsOfTypes tys = foldr (unionVarSet.tyVarsOfType) emptyVarSet tys
708 tyVarsOfPred :: PredType -> TyVarSet
709 tyVarsOfPred (IParam _ ty) = tyVarsOfType ty
710 tyVarsOfPred (ClassP _ tys) = tyVarsOfTypes tys
711 tyVarsOfPred (EqPred ty1 ty2) = tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2
713 tyVarsOfTheta :: ThetaType -> TyVarSet
714 tyVarsOfTheta = foldr (unionVarSet . tyVarsOfPred) emptyVarSet
716 -- Add a Note with the free tyvars to the top of the type
717 addFreeTyVars :: Type -> Type
718 addFreeTyVars ty@(NoteTy (FTVNote _) _) = ty
719 addFreeTyVars ty = NoteTy (FTVNote (tyVarsOfType ty)) ty
723 %************************************************************************
725 \subsection{Type families}
727 %************************************************************************
729 Type family instances occuring in a type after expanding synonyms.
732 tyFamInsts :: Type -> [(TyCon, [Type])]
734 | Just exp_ty <- tcView ty = tyFamInsts exp_ty
735 tyFamInsts (TyVarTy _) = []
736 tyFamInsts (TyConApp tc tys)
737 | isOpenSynTyCon tc = [(tc, tys)]
738 | otherwise = concat (map tyFamInsts tys)
739 tyFamInsts (FunTy ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
740 tyFamInsts (AppTy ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
741 tyFamInsts (ForAllTy _ ty) = tyFamInsts ty
745 %************************************************************************
747 \subsection{TidyType}
749 %************************************************************************
751 tidyTy tidies up a type for printing in an error message, or in
754 It doesn't change the uniques at all, just the print names.
757 tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
758 tidyTyVarBndr env@(tidy_env, subst) tyvar
759 = case tidyOccName tidy_env (getOccName name) of
760 (tidy', occ') -> ((tidy', subst'), tyvar'')
762 subst' = extendVarEnv subst tyvar tyvar''
763 tyvar' = setTyVarName tyvar name'
764 name' = tidyNameOcc name occ'
765 -- Don't forget to tidy the kind for coercions!
766 tyvar'' | isCoVar tyvar = setTyVarKind tyvar' kind'
768 kind' = tidyType env (tyVarKind tyvar)
770 name = tyVarName tyvar
772 tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv
773 -- Add the free tyvars to the env in tidy form,
774 -- so that we can tidy the type they are free in
775 tidyFreeTyVars env tyvars = fst (tidyOpenTyVars env (varSetElems tyvars))
777 tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
778 tidyOpenTyVars env tyvars = mapAccumL tidyOpenTyVar env tyvars
780 tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
781 -- Treat a new tyvar as a binder, and give it a fresh tidy name
782 tidyOpenTyVar env@(tidy_env, subst) tyvar
783 = case lookupVarEnv subst tyvar of
784 Just tyvar' -> (env, tyvar') -- Already substituted
785 Nothing -> tidyTyVarBndr env tyvar -- Treat it as a binder
787 tidyType :: TidyEnv -> Type -> Type
788 tidyType env@(tidy_env, subst) ty
791 go (TyVarTy tv) = case lookupVarEnv subst tv of
792 Nothing -> TyVarTy tv
793 Just tv' -> TyVarTy tv'
794 go (TyConApp tycon tys) = let args = map go tys
795 in args `seqList` TyConApp tycon args
796 go (NoteTy note ty) = (NoteTy $! (go_note note)) $! (go ty)
797 go (PredTy sty) = PredTy (tidyPred env sty)
798 go (AppTy fun arg) = (AppTy $! (go fun)) $! (go arg)
799 go (FunTy fun arg) = (FunTy $! (go fun)) $! (go arg)
800 go (ForAllTy tv ty) = ForAllTy tvp $! (tidyType envp ty)
802 (envp, tvp) = tidyTyVarBndr env tv
804 go_note note@(FTVNote ftvs) = note -- No need to tidy the free tyvars
806 tidyTypes env tys = map (tidyType env) tys
808 tidyPred :: TidyEnv -> PredType -> PredType
809 tidyPred env (IParam n ty) = IParam n (tidyType env ty)
810 tidyPred env (ClassP clas tys) = ClassP clas (tidyTypes env tys)
811 tidyPred env (EqPred ty1 ty2) = EqPred (tidyType env ty1) (tidyType env ty2)
815 @tidyOpenType@ grabs the free type variables, tidies them
816 and then uses @tidyType@ to work over the type itself
819 tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
821 = (env', tidyType env' ty)
823 env' = tidyFreeTyVars env (tyVarsOfType ty)
825 tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
826 tidyOpenTypes env tys = mapAccumL tidyOpenType env tys
828 tidyTopType :: Type -> Type
829 tidyTopType ty = tidyType emptyTidyEnv ty
834 tidyKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
835 tidyKind env k = tidyOpenType env k
840 %************************************************************************
842 \subsection{Liftedness}
844 %************************************************************************
847 isUnLiftedType :: Type -> Bool
848 -- isUnLiftedType returns True for forall'd unlifted types:
849 -- x :: forall a. Int#
850 -- I found bindings like these were getting floated to the top level.
851 -- They are pretty bogus types, mind you. It would be better never to
854 isUnLiftedType ty | Just ty' <- coreView ty = isUnLiftedType ty'
855 isUnLiftedType (ForAllTy tv ty) = isUnLiftedType ty
856 isUnLiftedType (TyConApp tc _) = isUnLiftedTyCon tc
857 isUnLiftedType other = False
859 isUnboxedTupleType :: Type -> Bool
860 isUnboxedTupleType ty = case splitTyConApp_maybe ty of
861 Just (tc, ty_args) -> isUnboxedTupleTyCon tc
864 -- Should only be applied to *types*; hence the assert
865 isAlgType :: Type -> Bool
867 = case splitTyConApp_maybe ty of
868 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
872 -- Should only be applied to *types*; hence the assert
873 isClosedAlgType :: Type -> Bool
875 = case splitTyConApp_maybe ty of
876 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
877 isAlgTyCon tc && not (isOpenTyCon tc)
881 @isStrictType@ computes whether an argument (or let RHS) should
882 be computed strictly or lazily, based only on its type.
883 Works just like isUnLiftedType, except that it has a special case
884 for dictionaries. Since it takes account of ClassP, you might think
885 this function should be in TcType, but isStrictType is used by DataCon,
886 which is below TcType in the hierarchy, so it's convenient to put it here.
889 isStrictType (PredTy pred) = isStrictPred pred
890 isStrictType ty | Just ty' <- coreView ty = isStrictType ty'
891 isStrictType (ForAllTy tv ty) = isStrictType ty
892 isStrictType (TyConApp tc _) = isUnLiftedTyCon tc
893 isStrictType other = False
895 isStrictPred (ClassP clas _) = opt_DictsStrict && not (isNewTyCon (classTyCon clas))
896 isStrictPred other = False
897 -- We may be strict in dictionary types, but only if it
898 -- has more than one component.
899 -- [Being strict in a single-component dictionary risks
900 -- poking the dictionary component, which is wrong.]
904 isPrimitiveType :: Type -> Bool
905 -- Returns types that are opaque to Haskell.
906 -- Most of these are unlifted, but now that we interact with .NET, we
907 -- may have primtive (foreign-imported) types that are lifted
908 isPrimitiveType ty = case splitTyConApp_maybe ty of
909 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
915 %************************************************************************
917 \subsection{Sequencing on types
919 %************************************************************************
922 seqType :: Type -> ()
923 seqType (TyVarTy tv) = tv `seq` ()
924 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
925 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
926 seqType (NoteTy note t2) = seqNote note `seq` seqType t2
927 seqType (PredTy p) = seqPred p
928 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
929 seqType (ForAllTy tv ty) = tv `seq` seqType ty
931 seqTypes :: [Type] -> ()
933 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
935 seqNote :: TyNote -> ()
936 seqNote (FTVNote set) = sizeUniqSet set `seq` ()
938 seqPred :: PredType -> ()
939 seqPred (ClassP c tys) = c `seq` seqTypes tys
940 seqPred (IParam n ty) = n `seq` seqType ty
941 seqPred (EqPred ty1 ty2) = seqType ty1 `seq` seqType ty2
945 %************************************************************************
947 Equality for Core types
948 (We don't use instances so that we know where it happens)
950 %************************************************************************
952 Note that eqType works right even for partial applications of newtypes.
953 See Note [Newtype eta] in TyCon.lhs
956 coreEqType :: Type -> Type -> Bool
960 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
962 eq env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 == rnOccR env tv2
963 eq env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = eq (rnBndr2 env tv1 tv2) t1 t2
964 eq env (AppTy s1 t1) (AppTy s2 t2) = eq env s1 s2 && eq env t1 t2
965 eq env (FunTy s1 t1) (FunTy s2 t2) = eq env s1 s2 && eq env t1 t2
966 eq env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
967 | tc1 == tc2, all2 (eq env) tys1 tys2 = True
968 -- The lengths should be equal because
969 -- the two types have the same kind
970 -- NB: if the type constructors differ that does not
971 -- necessarily mean that the types aren't equal
972 -- (synonyms, newtypes)
973 -- Even if the type constructors are the same, but the arguments
974 -- differ, the two types could be the same (e.g. if the arg is just
975 -- ignored in the RHS). In both these cases we fall through to an
976 -- attempt to expand one side or the other.
978 -- Now deal with newtypes, synonyms, pred-tys
979 eq env t1 t2 | Just t1' <- coreView t1 = eq env t1' t2
980 | Just t2' <- coreView t2 = eq env t1 t2'
982 -- Fall through case; not equal!
987 %************************************************************************
989 Comparision for source types
990 (We don't use instances so that we know where it happens)
992 %************************************************************************
996 do *not* look through newtypes, PredTypes
999 tcEqType :: Type -> Type -> Bool
1000 tcEqType t1 t2 = isEqual $ cmpType t1 t2
1002 tcEqTypes :: [Type] -> [Type] -> Bool
1003 tcEqTypes tys1 tys2 = isEqual $ cmpTypes tys1 tys2
1005 tcCmpType :: Type -> Type -> Ordering
1006 tcCmpType t1 t2 = cmpType t1 t2
1008 tcCmpTypes :: [Type] -> [Type] -> Ordering
1009 tcCmpTypes tys1 tys2 = cmpTypes tys1 tys2
1011 tcEqPred :: PredType -> PredType -> Bool
1012 tcEqPred p1 p2 = isEqual $ cmpPred p1 p2
1014 tcCmpPred :: PredType -> PredType -> Ordering
1015 tcCmpPred p1 p2 = cmpPred p1 p2
1017 tcEqTypeX :: RnEnv2 -> Type -> Type -> Bool
1018 tcEqTypeX env t1 t2 = isEqual $ cmpTypeX env t1 t2
1021 Checks whether the second argument is a subterm of the first. (We don't care
1022 about binders, as we are only interested in syntactic subterms.)
1025 tcPartOfType :: Type -> Type -> Bool
1027 | tcEqType t1 t2 = True
1029 | Just t2' <- tcView t2 = tcPartOfType t1 t2'
1030 tcPartOfType _ (TyVarTy _) = False
1031 tcPartOfType t1 (ForAllTy _ t2) = tcPartOfType t1 t2
1032 tcPartOfType t1 (AppTy s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1033 tcPartOfType t1 (FunTy s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1034 tcPartOfType t1 (PredTy p2) = tcPartOfPred t1 p2
1035 tcPartOfType t1 (TyConApp _ ts) = any (tcPartOfType t1) ts
1036 tcPartOfType t1 (NoteTy _ t2) = tcPartOfType t1 t2
1038 tcPartOfPred :: Type -> PredType -> Bool
1039 tcPartOfPred t1 (IParam _ t2) = tcPartOfType t1 t2
1040 tcPartOfPred t1 (ClassP _ ts) = any (tcPartOfType t1) ts
1041 tcPartOfPred t1 (EqPred s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1044 Now here comes the real worker
1047 cmpType :: Type -> Type -> Ordering
1048 cmpType t1 t2 = cmpTypeX rn_env t1 t2
1050 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
1052 cmpTypes :: [Type] -> [Type] -> Ordering
1053 cmpTypes ts1 ts2 = cmpTypesX rn_env ts1 ts2
1055 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfTypes ts1 `unionVarSet` tyVarsOfTypes ts2))
1057 cmpPred :: PredType -> PredType -> Ordering
1058 cmpPred p1 p2 = cmpPredX rn_env p1 p2
1060 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfPred p1 `unionVarSet` tyVarsOfPred p2))
1062 cmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
1063 cmpTypeX env t1 t2 | Just t1' <- tcView t1 = cmpTypeX env t1' t2
1064 | Just t2' <- tcView t2 = cmpTypeX env t1 t2'
1066 cmpTypeX env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 `compare` rnOccR env tv2
1067 cmpTypeX env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = cmpTypeX (rnBndr2 env tv1 tv2) t1 t2
1068 cmpTypeX env (AppTy s1 t1) (AppTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1069 cmpTypeX env (FunTy s1 t1) (FunTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1070 cmpTypeX env (PredTy p1) (PredTy p2) = cmpPredX env p1 p2
1071 cmpTypeX env (TyConApp tc1 tys1) (TyConApp tc2 tys2) = (tc1 `compare` tc2) `thenCmp` cmpTypesX env tys1 tys2
1072 cmpTypeX env t1 (NoteTy _ t2) = cmpTypeX env t1 t2
1074 -- Deal with the rest: TyVarTy < AppTy < FunTy < TyConApp < ForAllTy < PredTy
1075 cmpTypeX env (AppTy _ _) (TyVarTy _) = GT
1077 cmpTypeX env (FunTy _ _) (TyVarTy _) = GT
1078 cmpTypeX env (FunTy _ _) (AppTy _ _) = GT
1080 cmpTypeX env (TyConApp _ _) (TyVarTy _) = GT
1081 cmpTypeX env (TyConApp _ _) (AppTy _ _) = GT
1082 cmpTypeX env (TyConApp _ _) (FunTy _ _) = GT
1084 cmpTypeX env (ForAllTy _ _) (TyVarTy _) = GT
1085 cmpTypeX env (ForAllTy _ _) (AppTy _ _) = GT
1086 cmpTypeX env (ForAllTy _ _) (FunTy _ _) = GT
1087 cmpTypeX env (ForAllTy _ _) (TyConApp _ _) = GT
1089 cmpTypeX env (PredTy _) t2 = GT
1091 cmpTypeX env _ _ = LT
1094 cmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
1095 cmpTypesX env [] [] = EQ
1096 cmpTypesX env (t1:tys1) (t2:tys2) = cmpTypeX env t1 t2 `thenCmp` cmpTypesX env tys1 tys2
1097 cmpTypesX env [] tys = LT
1098 cmpTypesX env ty [] = GT
1101 cmpPredX :: RnEnv2 -> PredType -> PredType -> Ordering
1102 cmpPredX env (IParam n1 ty1) (IParam n2 ty2) = (n1 `compare` n2) `thenCmp` cmpTypeX env ty1 ty2
1103 -- Compare names only for implicit parameters
1104 -- This comparison is used exclusively (I believe)
1105 -- for the Avails finite map built in TcSimplify
1106 -- If the types differ we keep them distinct so that we see
1107 -- a distinct pair to run improvement on
1108 cmpPredX env (ClassP c1 tys1) (ClassP c2 tys2) = (c1 `compare` c2) `thenCmp` (cmpTypesX env tys1 tys2)
1109 cmpPredX env (EqPred ty1 ty2) (EqPred ty1' ty2') = (cmpTypeX env ty1 ty1') `thenCmp` (cmpTypeX env ty2 ty2')
1111 -- Constructor order: IParam < ClassP < EqPred
1112 cmpPredX env (IParam {}) _ = LT
1113 cmpPredX env (ClassP {}) (IParam {}) = GT
1114 cmpPredX env (ClassP {}) (EqPred {}) = LT
1115 cmpPredX env (EqPred {}) _ = GT
1118 PredTypes are used as a FM key in TcSimplify,
1119 so we take the easy path and make them an instance of Ord
1122 instance Eq PredType where { (==) = tcEqPred }
1123 instance Ord PredType where { compare = tcCmpPred }
1127 %************************************************************************
1131 %************************************************************************
1135 = TvSubst InScopeSet -- The in-scope type variables
1136 TvSubstEnv -- The substitution itself
1137 -- See Note [Apply Once]
1138 -- and Note [Extending the TvSubstEnv]
1140 {- ----------------------------------------------------------
1144 We use TvSubsts to instantiate things, and we might instantiate
1148 So the substition might go [a->b, b->a]. A similar situation arises in Core
1149 when we find a beta redex like
1150 (/\ a /\ b -> e) b a
1151 Then we also end up with a substition that permutes type variables. Other
1152 variations happen to; for example [a -> (a, b)].
1154 ***************************************************
1155 *** So a TvSubst must be applied precisely once ***
1156 ***************************************************
1158 A TvSubst is not idempotent, but, unlike the non-idempotent substitution
1159 we use during unifications, it must not be repeatedly applied.
1161 Note [Extending the TvSubst]
1162 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1163 The following invariant should hold of a TvSubst
1165 The in-scope set is needed *only* to
1166 guide the generation of fresh uniques
1168 In particular, the *kind* of the type variables in
1169 the in-scope set is not relevant
1171 This invariant allows a short-cut when the TvSubstEnv is empty:
1172 if the TvSubstEnv is empty --- i.e. (isEmptyTvSubt subst) holds ---
1173 then (substTy subst ty) does nothing.
1175 For example, consider:
1176 (/\a. /\b:(a~Int). ...b..) Int
1177 We substitute Int for 'a'. The Unique of 'b' does not change, but
1178 nevertheless we add 'b' to the TvSubstEnv, because b's type does change
1180 This invariant has several crucial consequences:
1182 * In substTyVarBndr, we need extend the TvSubstEnv
1183 - if the unique has changed
1184 - or if the kind has changed
1186 * In substTyVar, we do not need to consult the in-scope set;
1187 the TvSubstEnv is enough
1189 * In substTy, substTheta, we can short-circuit when the TvSubstEnv is empty
1192 -------------------------------------------------------------- -}
1195 type TvSubstEnv = TyVarEnv Type
1196 -- A TvSubstEnv is used both inside a TvSubst (with the apply-once
1197 -- invariant discussed in Note [Apply Once]), and also independently
1198 -- in the middle of matching, and unification (see Types.Unify)
1199 -- So you have to look at the context to know if it's idempotent or
1200 -- apply-once or whatever
1201 emptyTvSubstEnv :: TvSubstEnv
1202 emptyTvSubstEnv = emptyVarEnv
1204 composeTvSubst :: InScopeSet -> TvSubstEnv -> TvSubstEnv -> TvSubstEnv
1205 -- (compose env1 env2)(x) is env1(env2(x)); i.e. apply env2 then env1
1206 -- It assumes that both are idempotent
1207 -- Typically, env1 is the refinement to a base substitution env2
1208 composeTvSubst in_scope env1 env2
1209 = env1 `plusVarEnv` mapVarEnv (substTy subst1) env2
1210 -- First apply env1 to the range of env2
1211 -- Then combine the two, making sure that env1 loses if
1212 -- both bind the same variable; that's why env1 is the
1213 -- *left* argument to plusVarEnv, because the right arg wins
1215 subst1 = TvSubst in_scope env1
1217 emptyTvSubst = TvSubst emptyInScopeSet emptyVarEnv
1219 isEmptyTvSubst :: TvSubst -> Bool
1220 -- See Note [Extending the TvSubstEnv]
1221 isEmptyTvSubst (TvSubst _ env) = isEmptyVarEnv env
1223 mkTvSubst :: InScopeSet -> TvSubstEnv -> TvSubst
1226 getTvSubstEnv :: TvSubst -> TvSubstEnv
1227 getTvSubstEnv (TvSubst _ env) = env
1229 getTvInScope :: TvSubst -> InScopeSet
1230 getTvInScope (TvSubst in_scope _) = in_scope
1232 isInScope :: Var -> TvSubst -> Bool
1233 isInScope v (TvSubst in_scope _) = v `elemInScopeSet` in_scope
1235 notElemTvSubst :: TyVar -> TvSubst -> Bool
1236 notElemTvSubst tv (TvSubst _ env) = not (tv `elemVarEnv` env)
1238 setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst
1239 setTvSubstEnv (TvSubst in_scope _) env = TvSubst in_scope env
1241 extendTvInScope :: TvSubst -> [Var] -> TvSubst
1242 extendTvInScope (TvSubst in_scope env) vars = TvSubst (extendInScopeSetList in_scope vars) env
1244 extendTvSubst :: TvSubst -> TyVar -> Type -> TvSubst
1245 extendTvSubst (TvSubst in_scope env) tv ty = TvSubst in_scope (extendVarEnv env tv ty)
1247 extendTvSubstList :: TvSubst -> [TyVar] -> [Type] -> TvSubst
1248 extendTvSubstList (TvSubst in_scope env) tvs tys
1249 = TvSubst in_scope (extendVarEnvList env (tvs `zip` tys))
1251 -- mkOpenTvSubst and zipOpenTvSubst generate the in-scope set from
1252 -- the types given; but it's just a thunk so with a bit of luck
1253 -- it'll never be evaluated
1255 mkOpenTvSubst :: TvSubstEnv -> TvSubst
1256 mkOpenTvSubst env = TvSubst (mkInScopeSet (tyVarsOfTypes (varEnvElts env))) env
1258 zipOpenTvSubst :: [TyVar] -> [Type] -> TvSubst
1259 zipOpenTvSubst tyvars tys
1261 | length tyvars /= length tys
1262 = pprTrace "zipOpenTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1265 = TvSubst (mkInScopeSet (tyVarsOfTypes tys)) (zipTyEnv tyvars tys)
1267 -- mkTopTvSubst is called when doing top-level substitutions.
1268 -- Here we expect that the free vars of the range of the
1269 -- substitution will be empty.
1270 mkTopTvSubst :: [(TyVar, Type)] -> TvSubst
1271 mkTopTvSubst prs = TvSubst emptyInScopeSet (mkVarEnv prs)
1273 zipTopTvSubst :: [TyVar] -> [Type] -> TvSubst
1274 zipTopTvSubst tyvars tys
1276 | length tyvars /= length tys
1277 = pprTrace "zipTopTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1280 = TvSubst emptyInScopeSet (zipTyEnv tyvars tys)
1282 zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
1285 | length tyvars /= length tys
1286 = pprTrace "mkTopTvSubst" (ppr tyvars $$ ppr tys) emptyVarEnv
1289 = zip_ty_env tyvars tys emptyVarEnv
1291 -- Later substitutions in the list over-ride earlier ones,
1292 -- but there should be no loops
1293 zip_ty_env [] [] env = env
1294 zip_ty_env (tv:tvs) (ty:tys) env = zip_ty_env tvs tys (extendVarEnv env tv ty)
1295 -- There used to be a special case for when
1297 -- (a not-uncommon case) in which case the substitution was dropped.
1298 -- But the type-tidier changes the print-name of a type variable without
1299 -- changing the unique, and that led to a bug. Why? Pre-tidying, we had
1300 -- a type {Foo t}, where Foo is a one-method class. So Foo is really a newtype.
1301 -- And it happened that t was the type variable of the class. Post-tiding,
1302 -- it got turned into {Foo t2}. The ext-core printer expanded this using
1303 -- sourceTypeRep, but that said "Oh, t == t2" because they have the same unique,
1304 -- and so generated a rep type mentioning t not t2.
1306 -- Simplest fix is to nuke the "optimisation"
1307 zip_ty_env tvs tys env = pprTrace "Var/Type length mismatch: " (ppr tvs $$ ppr tys) env
1308 -- zip_ty_env _ _ env = env
1310 instance Outputable TvSubst where
1311 ppr (TvSubst ins env)
1312 = brackets $ sep[ ptext SLIT("TvSubst"),
1313 nest 2 (ptext SLIT("In scope:") <+> ppr ins),
1314 nest 2 (ptext SLIT("Env:") <+> ppr env) ]
1317 %************************************************************************
1319 Performing type substitutions
1321 %************************************************************************
1324 substTyWith :: [TyVar] -> [Type] -> Type -> Type
1325 substTyWith tvs tys = ASSERT( length tvs == length tys )
1326 substTy (zipOpenTvSubst tvs tys)
1328 substTy :: TvSubst -> Type -> Type
1329 substTy subst ty | isEmptyTvSubst subst = ty
1330 | otherwise = subst_ty subst ty
1332 substTys :: TvSubst -> [Type] -> [Type]
1333 substTys subst tys | isEmptyTvSubst subst = tys
1334 | otherwise = map (subst_ty subst) tys
1336 substTheta :: TvSubst -> ThetaType -> ThetaType
1337 substTheta subst theta
1338 | isEmptyTvSubst subst = theta
1339 | otherwise = map (substPred subst) theta
1341 substPred :: TvSubst -> PredType -> PredType
1342 substPred subst (IParam n ty) = IParam n (subst_ty subst ty)
1343 substPred subst (ClassP clas tys) = ClassP clas (map (subst_ty subst) tys)
1344 substPred subst (EqPred ty1 ty2) = EqPred (subst_ty subst ty1) (subst_ty subst ty2)
1346 deShadowTy :: TyVarSet -> Type -> Type -- Remove any nested binders mentioning tvs
1348 = subst_ty (mkTvSubst in_scope emptyTvSubstEnv) ty
1350 in_scope = mkInScopeSet tvs
1352 subst_ty :: TvSubst -> Type -> Type
1353 -- subst_ty is the main workhorse for type substitution
1355 -- Note that the in_scope set is poked only if we hit a forall
1356 -- so it may often never be fully computed
1360 go (TyVarTy tv) = substTyVar subst tv
1361 go (TyConApp tc tys) = let args = map go tys
1362 in args `seqList` TyConApp tc args
1364 go (PredTy p) = PredTy $! (substPred subst p)
1366 go (NoteTy (FTVNote _) ty2) = go ty2 -- Discard the free tyvar note
1368 go (FunTy arg res) = (FunTy $! (go arg)) $! (go res)
1369 go (AppTy fun arg) = mkAppTy (go fun) $! (go arg)
1370 -- The mkAppTy smart constructor is important
1371 -- we might be replacing (a Int), represented with App
1372 -- by [Int], represented with TyConApp
1373 go (ForAllTy tv ty) = case substTyVarBndr subst tv of
1374 (subst', tv') -> ForAllTy tv' $! (subst_ty subst' ty)
1376 substTyVar :: TvSubst -> TyVar -> Type
1377 substTyVar subst@(TvSubst in_scope env) tv
1378 = case lookupTyVar subst tv of {
1379 Nothing -> TyVarTy tv;
1380 Just ty -> ty -- See Note [Apply Once]
1383 substTyVars :: TvSubst -> [TyVar] -> [Type]
1384 substTyVars subst tvs = map (substTyVar subst) tvs
1386 lookupTyVar :: TvSubst -> TyVar -> Maybe Type
1387 -- See Note [Extending the TvSubst]
1388 lookupTyVar (TvSubst in_scope env) tv = lookupVarEnv env tv
1390 substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)
1391 substTyVarBndr subst@(TvSubst in_scope env) old_var
1392 = (TvSubst (in_scope `extendInScopeSet` new_var) new_env, new_var)
1394 is_co_var = isCoVar old_var
1396 new_env | no_change = delVarEnv env old_var
1397 | otherwise = extendVarEnv env old_var (TyVarTy new_var)
1399 no_change = new_var == old_var && not is_co_var
1400 -- no_change means that the new_var is identical in
1401 -- all respects to the old_var (same unique, same kind)
1402 -- See Note [Extending the TvSubst]
1404 -- In that case we don't need to extend the substitution
1405 -- to map old to new. But instead we must zap any
1406 -- current substitution for the variable. For example:
1407 -- (\x.e) with id_subst = [x |-> e']
1408 -- Here we must simply zap the substitution for x
1410 new_var = uniqAway in_scope subst_old_var
1411 -- The uniqAway part makes sure the new variable is not already in scope
1413 subst_old_var -- subst_old_var is old_var with the substitution applied to its kind
1414 -- It's only worth doing the substitution for coercions,
1415 -- becuase only they can have free type variables
1416 | is_co_var = setTyVarKind old_var (substTy subst (tyVarKind old_var))
1417 | otherwise = old_var
1420 ----------------------------------------------------
1425 There's a little subtyping at the kind level:
1434 where * [LiftedTypeKind] means boxed type
1435 # [UnliftedTypeKind] means unboxed type
1436 (#) [UbxTupleKind] means unboxed tuple
1437 ?? [ArgTypeKind] is the lub of *,#
1438 ? [OpenTypeKind] means any type at all
1442 error :: forall a:?. String -> a
1443 (->) :: ?? -> ? -> *
1444 (\(x::t) -> ...) Here t::?? (i.e. not unboxed tuple)
1447 type KindVar = TyVar -- invariant: KindVar will always be a
1448 -- TcTyVar with details MetaTv TauTv ...
1449 -- kind var constructors and functions are in TcType
1451 type SimpleKind = Kind
1456 During kind inference, a kind variable unifies only with
1458 sk ::= * | sk1 -> sk2
1460 data T a = MkT a (T Int#)
1461 fails. We give T the kind (k -> *), and the kind variable k won't unify
1462 with # (the kind of Int#).
1466 When creating a fresh internal type variable, we give it a kind to express
1467 constraints on it. E.g. in (\x->e) we make up a fresh type variable for x,
1470 During unification we only bind an internal type variable to a type
1471 whose kind is lower in the sub-kind hierarchy than the kind of the tyvar.
1473 When unifying two internal type variables, we collect their kind constraints by
1474 finding the GLB of the two. Since the partial order is a tree, they only
1475 have a glb if one is a sub-kind of the other. In that case, we bind the
1476 less-informative one to the more informative one. Neat, eh?
1483 %************************************************************************
1485 Functions over Kinds
1487 %************************************************************************
1490 kindFunResult :: Kind -> Kind
1491 kindFunResult k = funResultTy k
1493 splitKindFunTys :: Kind -> ([Kind],Kind)
1494 splitKindFunTys k = splitFunTys k
1496 splitKindFunTysN :: Int -> Kind -> ([Kind],Kind)
1497 splitKindFunTysN k = splitFunTysN k
1499 isUbxTupleKind, isOpenTypeKind, isArgTypeKind, isUnliftedTypeKind :: Kind -> Bool
1501 isOpenTypeKindCon tc = tyConUnique tc == openTypeKindTyConKey
1503 isOpenTypeKind (TyConApp tc _) = isOpenTypeKindCon tc
1504 isOpenTypeKind other = False
1506 isUbxTupleKindCon tc = tyConUnique tc == ubxTupleKindTyConKey
1508 isUbxTupleKind (TyConApp tc _) = isUbxTupleKindCon tc
1509 isUbxTupleKind other = False
1511 isArgTypeKindCon tc = tyConUnique tc == argTypeKindTyConKey
1513 isArgTypeKind (TyConApp tc _) = isArgTypeKindCon tc
1514 isArgTypeKind other = False
1516 isUnliftedTypeKindCon tc = tyConUnique tc == unliftedTypeKindTyConKey
1518 isUnliftedTypeKind (TyConApp tc _) = isUnliftedTypeKindCon tc
1519 isUnliftedTypeKind other = False
1521 isSubOpenTypeKind :: Kind -> Bool
1522 -- True of any sub-kind of OpenTypeKind (i.e. anything except arrow)
1523 isSubOpenTypeKind (FunTy k1 k2) = ASSERT2 ( isKind k1, text "isSubOpenTypeKind" <+> ppr k1 <+> text "::" <+> ppr (typeKind k1) )
1524 ASSERT2 ( isKind k2, text "isSubOpenTypeKind" <+> ppr k2 <+> text "::" <+> ppr (typeKind k2) )
1526 isSubOpenTypeKind (TyConApp kc []) = ASSERT( isKind (TyConApp kc []) ) True
1527 isSubOpenTypeKind other = ASSERT( isKind other ) False
1528 -- This is a conservative answer
1529 -- It matters in the call to isSubKind in
1530 -- checkExpectedKind.
1532 isSubArgTypeKindCon kc
1533 | isUnliftedTypeKindCon kc = True
1534 | isLiftedTypeKindCon kc = True
1535 | isArgTypeKindCon kc = True
1538 isSubArgTypeKind :: Kind -> Bool
1539 -- True of any sub-kind of ArgTypeKind
1540 isSubArgTypeKind (TyConApp kc []) = isSubArgTypeKindCon kc
1541 isSubArgTypeKind other = False
1543 isSuperKind :: Type -> Bool
1544 isSuperKind (TyConApp (skc) []) = isSuperKindTyCon skc
1545 isSuperKind other = False
1547 isKind :: Kind -> Bool
1548 isKind k = isSuperKind (typeKind k)
1550 isSubKind :: Kind -> Kind -> Bool
1551 -- (k1 `isSubKind` k2) checks that k1 <: k2
1552 isSubKind (TyConApp kc1 []) (TyConApp kc2 []) = kc1 `isSubKindCon` kc2
1553 isSubKind (FunTy a1 r1) (FunTy a2 r2) = (a2 `isSubKind` a1) && (r1 `isSubKind` r2)
1554 isSubKind (PredTy (EqPred ty1 ty2)) (PredTy (EqPred ty1' ty2'))
1555 = ty1 `tcEqType` ty1' && ty2 `tcEqType` ty2'
1556 isSubKind k1 k2 = False
1558 eqKind :: Kind -> Kind -> Bool
1561 isSubKindCon :: TyCon -> TyCon -> Bool
1562 -- (kc1 `isSubKindCon` kc2) checks that kc1 <: kc2
1563 isSubKindCon kc1 kc2
1564 | isLiftedTypeKindCon kc1 && isLiftedTypeKindCon kc2 = True
1565 | isUnliftedTypeKindCon kc1 && isUnliftedTypeKindCon kc2 = True
1566 | isUbxTupleKindCon kc1 && isUbxTupleKindCon kc2 = True
1567 | isOpenTypeKindCon kc2 = True
1568 -- we already know kc1 is not a fun, its a TyCon
1569 | isArgTypeKindCon kc2 && isSubArgTypeKindCon kc1 = True
1572 defaultKind :: Kind -> Kind
1573 -- Used when generalising: default kind '?' and '??' to '*'
1575 -- When we generalise, we make generic type variables whose kind is
1576 -- simple (* or *->* etc). So generic type variables (other than
1577 -- built-in constants like 'error') always have simple kinds. This is important;
1580 -- We want f to get type
1581 -- f :: forall (a::*). a -> Bool
1583 -- f :: forall (a::??). a -> Bool
1584 -- because that would allow a call like (f 3#) as well as (f True),
1585 --and the calling conventions differ. This defaulting is done in TcMType.zonkTcTyVarBndr.
1587 | isSubOpenTypeKind k = liftedTypeKind
1588 | isSubArgTypeKind k = liftedTypeKind
1591 isEqPred :: PredType -> Bool
1592 isEqPred (EqPred _ _) = True
1593 isEqPred other = False