2 % (c) The University of Glasgow 2006
3 % (c) The GRASP/AQUA Project, Glasgow University, 1998
6 Type - public interface
9 {-# OPTIONS -fno-warn-incomplete-patterns #-}
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
16 -- | Main functions for manipulating types and type-related things
18 -- Note some of this is just re-exports from TyCon..
20 -- * Main data types representing Types
21 -- $type_classification
23 -- $representation_types
24 TyThing(..), Type, PredType(..), ThetaType,
26 -- ** Constructing and deconstructing types
27 mkTyVarTy, mkTyVarTys, getTyVar, getTyVar_maybe,
29 mkAppTy, mkAppTys, splitAppTy, splitAppTys,
30 splitAppTy_maybe, repSplitAppTy_maybe,
32 mkFunTy, mkFunTys, splitFunTy, splitFunTy_maybe,
33 splitFunTys, splitFunTysN,
34 funResultTy, funArgTy, zipFunTys,
36 mkTyConApp, mkTyConTy,
37 tyConAppTyCon, tyConAppArgs,
38 splitTyConApp_maybe, splitTyConApp,
40 mkForAllTy, mkForAllTys, splitForAllTy_maybe, splitForAllTys,
41 applyTy, applyTys, applyTysD, isForAllTy, dropForAlls,
44 newTyConInstRhs, carefullySplitNewType_maybe,
47 tyFamInsts, predFamInsts,
50 mkPredTy, mkPredTys, mkFamilyTyConApp,
52 -- ** Common type constructors
55 -- ** Predicates on types
58 -- (Lifting and boxity)
59 isUnLiftedType, isUnboxedTupleType, isAlgType, isClosedAlgType,
60 isPrimitiveType, isStrictType, isStrictPred,
62 -- * Main data types representing Kinds
64 Kind, SimpleKind, KindVar,
66 -- ** Deconstructing Kinds
67 kindFunResult, splitKindFunTys, splitKindFunTysN,
69 -- ** Common Kinds and SuperKinds
70 liftedTypeKind, unliftedTypeKind, openTypeKind,
71 argTypeKind, ubxTupleKind,
73 tySuperKind, coSuperKind,
75 -- ** Common Kind type constructors
76 liftedTypeKindTyCon, openTypeKindTyCon, unliftedTypeKindTyCon,
77 argTypeKindTyCon, ubxTupleKindTyCon,
79 -- ** Predicates on Kinds
80 isLiftedTypeKind, isUnliftedTypeKind, isOpenTypeKind,
81 isUbxTupleKind, isArgTypeKind, isKind, isTySuperKind,
82 isCoSuperKind, isSuperKind, isCoercionKind, isEqPred,
83 mkArrowKind, mkArrowKinds,
85 isSubArgTypeKind, isSubOpenTypeKind, isSubKind, defaultKind, eqKind,
88 -- * Type free variables
89 tyVarsOfType, tyVarsOfTypes, tyVarsOfPred, tyVarsOfTheta,
92 -- * Tidying type related things up for printing
94 tidyOpenType, tidyOpenTypes,
95 tidyTyVarBndr, tidyFreeTyVars,
96 tidyOpenTyVar, tidyOpenTyVars,
97 tidyTopType, tidyPred,
101 coreEqType, tcEqType, tcEqTypes, tcCmpType, tcCmpTypes,
102 tcEqPred, tcEqPredX, tcCmpPred, tcEqTypeX, tcPartOfType, tcPartOfPred,
104 -- * Forcing evaluation of types
107 -- * Other views onto Types
108 coreView, tcView, kindView,
112 -- * Type representation for the code generator
115 typePrimRep, predTypeRep,
117 -- * Main type substitution data types
118 TvSubstEnv, -- Representation widely visible
119 TvSubst(..), -- Representation visible to a few friends
121 -- ** Manipulating type substitutions
122 emptyTvSubstEnv, emptyTvSubst,
124 mkTvSubst, mkOpenTvSubst, zipOpenTvSubst, zipTopTvSubst, mkTopTvSubst, notElemTvSubst,
125 getTvSubstEnv, setTvSubstEnv, getTvInScope, extendTvInScope,
126 extendTvSubst, extendTvSubstList, isInScope, composeTvSubst, zipTyEnv,
129 -- ** Performing substitution on types
130 substTy, substTys, substTyWith, substTysWith, substTheta,
131 substPred, substTyVar, substTyVars, substTyVarBndr, deShadowTy, lookupTyVar,
134 pprType, pprParendType, pprTypeApp, pprTyThingCategory, pprTyThing, pprForAll,
135 pprPred, pprTheta, pprThetaArrow, pprClassPred, pprKind, pprParendKind,
140 #include "HsVersions.h"
142 -- We import the representation and primitive functions from TypeRep.
143 -- Many things are reexported, but not the representation!
164 import Data.Maybe ( isJust )
168 -- $type_classification
169 -- #type_classification#
173 -- [Unboxed] Iff its representation is other than a pointer
174 -- Unboxed types are also unlifted.
176 -- [Lifted] Iff it has bottom as an element.
177 -- Closures always have lifted types: i.e. any
178 -- let-bound identifier in Core must have a lifted
179 -- type. Operationally, a lifted object is one that
181 -- Only lifted types may be unified with a type variable.
183 -- [Algebraic] Iff it is a type with one or more constructors, whether
184 -- declared with @data@ or @newtype@.
185 -- An algebraic type is one that can be deconstructed
186 -- with a case expression. This is /not/ the same as
187 -- lifted types, because we also include unboxed
188 -- tuples in this classification.
190 -- [Data] Iff it is a type declared with @data@, or a boxed tuple.
192 -- [Primitive] Iff it is a built-in type that can't be expressed in Haskell.
194 -- Currently, all primitive types are unlifted, but that's not necessarily
195 -- the case: for example, @Int@ could be primitive.
197 -- Some primitive types are unboxed, such as @Int#@, whereas some are boxed
198 -- but unlifted (such as @ByteArray#@). The only primitive types that we
199 -- classify as algebraic are the unboxed tuples.
201 -- Some examples of type classifications that may make this a bit clearer are:
204 -- Type primitive boxed lifted algebraic
205 -- -----------------------------------------------------------------------------
207 -- ByteArray# Yes Yes No No
208 -- (\# a, b \#) Yes No No Yes
209 -- ( a, b ) No Yes Yes Yes
210 -- [a] No Yes Yes Yes
213 -- $representation_types
214 -- A /source type/ is a type that is a separate type as far as the type checker is
215 -- concerned, but which has a more low-level representation as far as Core-to-Core
216 -- passes and the rest of the back end is concerned. Notably, 'PredTy's are removed
217 -- from the representation type while they do exist in the source types.
219 -- You don't normally have to worry about this, as the utility functions in
220 -- this module will automatically convert a source into a representation type
221 -- if they are spotted, to the best of it's abilities. If you don't want this
222 -- to happen, use the equivalent functions from the "TcType" module.
225 %************************************************************************
229 %************************************************************************
232 {-# INLINE coreView #-}
233 coreView :: Type -> Maybe Type
234 -- ^ In Core, we \"look through\" non-recursive newtypes and 'PredTypes': this
235 -- function tries to obtain a different view of the supplied type given this
237 -- Strips off the /top layer only/ of a type to give
238 -- its underlying representation type.
239 -- Returns Nothing if there is nothing to look through.
241 -- In the case of @newtype@s, it returns one of:
243 -- 1) A vanilla 'TyConApp' (recursive newtype, or non-saturated)
245 -- 2) The newtype representation (otherwise), meaning the
246 -- type written in the RHS of the newtype declaration,
247 -- which may itself be a newtype
249 -- For example, with:
251 -- > newtype R = MkR S
252 -- > newtype S = MkS T
253 -- > newtype T = MkT (T -> T)
255 -- 'expandNewTcApp' on:
257 -- * @R@ gives @Just S@
258 -- * @S@ gives @Just T@
259 -- * @T@ gives @Nothing@ (no expansion)
261 -- By being non-recursive and inlined, this case analysis gets efficiently
262 -- joined onto the case analysis that the caller is already doing
264 | isEqPred p = Nothing
265 | otherwise = Just (predTypeRep p)
266 coreView (TyConApp tc tys) | Just (tenv, rhs, tys') <- coreExpandTyCon_maybe tc tys
267 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
268 -- Its important to use mkAppTys, rather than (foldl AppTy),
269 -- because the function part might well return a
270 -- partially-applied type constructor; indeed, usually will!
275 -----------------------------------------------
276 {-# INLINE tcView #-}
277 tcView :: Type -> Maybe Type
278 -- ^ Similar to 'coreView', but for the type checker, which just looks through synonyms
279 tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- tcExpandTyCon_maybe tc tys
280 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
283 -----------------------------------------------
284 {-# INLINE kindView #-}
285 kindView :: Kind -> Maybe Kind
286 -- ^ Similar to 'coreView' or 'tcView', but works on 'Kind's
288 -- For the moment, we don't even handle synonyms in kinds
293 %************************************************************************
295 \subsection{Constructor-specific functions}
297 %************************************************************************
300 ---------------------------------------------------------------------
304 mkTyVarTy :: TyVar -> Type
307 mkTyVarTys :: [TyVar] -> [Type]
308 mkTyVarTys = map mkTyVarTy -- a common use of mkTyVarTy
310 -- | Attempts to obtain the type variable underlying a 'Type', and panics with the
311 -- given message if this is not a type variable type. See also 'getTyVar_maybe'
312 getTyVar :: String -> Type -> TyVar
313 getTyVar msg ty = case getTyVar_maybe ty of
315 Nothing -> panic ("getTyVar: " ++ msg)
317 isTyVarTy :: Type -> Bool
318 isTyVarTy ty = isJust (getTyVar_maybe ty)
320 -- | Attempts to obtain the type variable underlying a 'Type'
321 getTyVar_maybe :: Type -> Maybe TyVar
322 getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty'
323 getTyVar_maybe (TyVarTy tv) = Just tv
324 getTyVar_maybe _ = Nothing
329 ---------------------------------------------------------------------
332 We need to be pretty careful with AppTy to make sure we obey the
333 invariant that a TyConApp is always visibly so. mkAppTy maintains the
337 -- | Applies a type to another, as in e.g. @k a@
338 mkAppTy :: Type -> Type -> Type
339 mkAppTy orig_ty1 orig_ty2
342 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ [orig_ty2])
343 mk_app _ = AppTy orig_ty1 orig_ty2
344 -- Note that the TyConApp could be an
345 -- under-saturated type synonym. GHC allows that; e.g.
346 -- type Foo k = k a -> k a
348 -- foo :: Foo Id -> Foo Id
350 -- Here Id is partially applied in the type sig for Foo,
351 -- but once the type synonyms are expanded all is well
353 mkAppTys :: Type -> [Type] -> Type
354 mkAppTys orig_ty1 [] = orig_ty1
355 -- This check for an empty list of type arguments
356 -- avoids the needless loss of a type synonym constructor.
357 -- For example: mkAppTys Rational []
358 -- returns to (Ratio Integer), which has needlessly lost
359 -- the Rational part.
360 mkAppTys orig_ty1 orig_tys2
363 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ orig_tys2)
364 -- mkTyConApp: see notes with mkAppTy
365 mk_app _ = foldl AppTy orig_ty1 orig_tys2
368 splitAppTy_maybe :: Type -> Maybe (Type, Type)
369 -- ^ Attempt to take a type application apart, whether it is a
370 -- function, type constructor, or plain type application. Note
371 -- that type family applications are NEVER unsaturated by this!
372 splitAppTy_maybe ty | Just ty' <- coreView ty
373 = splitAppTy_maybe ty'
374 splitAppTy_maybe ty = repSplitAppTy_maybe ty
377 repSplitAppTy_maybe :: Type -> Maybe (Type,Type)
378 -- ^ Does the AppTy split as in 'splitAppTy_maybe', but assumes that
379 -- any Core view stuff is already done
380 repSplitAppTy_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
381 repSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
382 repSplitAppTy_maybe (TyConApp tc tys)
383 | not (isOpenSynTyCon tc) || length tys > tyConArity tc
384 = case snocView tys of -- never create unsaturated type family apps
385 Just (tys', ty') -> Just (TyConApp tc tys', ty')
387 repSplitAppTy_maybe _other = Nothing
389 splitAppTy :: Type -> (Type, Type)
390 -- ^ Attempts to take a type application apart, as in 'splitAppTy_maybe',
391 -- and panics if this is not possible
392 splitAppTy ty = case splitAppTy_maybe ty of
394 Nothing -> panic "splitAppTy"
397 splitAppTys :: Type -> (Type, [Type])
398 -- ^ Recursively splits a type as far as is possible, leaving a residual
399 -- type being applied to and the type arguments applied to it. Never fails,
400 -- even if that means returning an empty list of type applications.
401 splitAppTys ty = split ty ty []
403 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
404 split _ (AppTy ty arg) args = split ty ty (arg:args)
405 split _ (TyConApp tc tc_args) args
406 = let -- keep type families saturated
407 n | isOpenSynTyCon tc = tyConArity tc
409 (tc_args1, tc_args2) = splitAt n tc_args
411 (TyConApp tc tc_args1, tc_args2 ++ args)
412 split _ (FunTy ty1 ty2) args = ASSERT( null args )
413 (TyConApp funTyCon [], [ty1,ty2])
414 split orig_ty _ args = (orig_ty, args)
419 ---------------------------------------------------------------------
424 mkFunTy :: Type -> Type -> Type
425 -- ^ Creates a function type from the given argument and result type
426 mkFunTy (PredTy (EqPred ty1 ty2)) res = mkForAllTy (mkWildCoVar (PredTy (EqPred ty1 ty2))) res
427 mkFunTy arg res = FunTy arg res
429 mkFunTys :: [Type] -> Type -> Type
430 mkFunTys tys ty = foldr mkFunTy ty tys
432 isFunTy :: Type -> Bool
433 isFunTy ty = isJust (splitFunTy_maybe ty)
435 splitFunTy :: Type -> (Type, Type)
436 -- ^ Attempts to extract the argument and result types from a type, and
437 -- panics if that is not possible. See also 'splitFunTy_maybe'
438 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
439 splitFunTy (FunTy arg res) = (arg, res)
440 splitFunTy other = pprPanic "splitFunTy" (ppr other)
442 splitFunTy_maybe :: Type -> Maybe (Type, Type)
443 -- ^ Attempts to extract the argument and result types from a type
444 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
445 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
446 splitFunTy_maybe _ = Nothing
448 splitFunTys :: Type -> ([Type], Type)
449 splitFunTys ty = split [] ty ty
451 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
452 split args _ (FunTy arg res) = split (arg:args) res res
453 split args orig_ty _ = (reverse args, orig_ty)
455 splitFunTysN :: Int -> Type -> ([Type], Type)
456 -- ^ Split off exactly the given number argument types, and panics if that is not possible
457 splitFunTysN 0 ty = ([], ty)
458 splitFunTysN n ty = case splitFunTy ty of { (arg, res) ->
459 case splitFunTysN (n-1) res of { (args, res) ->
462 -- | Splits off argument types from the given type and associating
463 -- them with the things in the input list from left to right. The
464 -- final result type is returned, along with the resulting pairs of
465 -- objects and types, albeit with the list of pairs in reverse order.
466 -- Panics if there are not enough argument types for the input list.
467 zipFunTys :: Outputable a => [a] -> Type -> ([(a, Type)], Type)
468 zipFunTys orig_xs orig_ty = split [] orig_xs orig_ty orig_ty
470 split acc [] nty _ = (reverse acc, nty)
472 | Just ty' <- coreView ty = split acc xs nty ty'
473 split acc (x:xs) _ (FunTy arg res) = split ((x,arg):acc) xs res res
474 split _ _ _ _ = pprPanic "zipFunTys" (ppr orig_xs <+> ppr orig_ty)
476 funResultTy :: Type -> Type
477 -- ^ Extract the function result type and panic if that is not possible
478 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
479 funResultTy (FunTy _arg res) = res
480 funResultTy ty = pprPanic "funResultTy" (ppr ty)
482 funArgTy :: Type -> Type
483 -- ^ Extract the function argument type and panic if that is not possible
484 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
485 funArgTy (FunTy arg _res) = arg
486 funArgTy ty = pprPanic "funArgTy" (ppr ty)
489 ---------------------------------------------------------------------
494 -- | A key function: builds a 'TyConApp' or 'FunTy' as apppropriate to its arguments.
495 -- Applies its arguments to the constructor from left to right
496 mkTyConApp :: TyCon -> [Type] -> Type
498 | isFunTyCon tycon, [ty1,ty2] <- tys
504 -- | Create the plain type constructor type which has been applied to no type arguments at all.
505 mkTyConTy :: TyCon -> Type
506 mkTyConTy tycon = mkTyConApp tycon []
508 -- splitTyConApp "looks through" synonyms, because they don't
509 -- mean a distinct type, but all other type-constructor applications
510 -- including functions are returned as Just ..
512 -- | The same as @fst . splitTyConApp@
513 tyConAppTyCon :: Type -> TyCon
514 tyConAppTyCon ty = fst (splitTyConApp ty)
516 -- | The same as @snd . splitTyConApp@
517 tyConAppArgs :: Type -> [Type]
518 tyConAppArgs ty = snd (splitTyConApp ty)
520 -- | Attempts to tease a type apart into a type constructor and the application
521 -- of a number of arguments to that constructor. Panics if that is not possible.
522 -- See also 'splitTyConApp_maybe'
523 splitTyConApp :: Type -> (TyCon, [Type])
524 splitTyConApp ty = case splitTyConApp_maybe ty of
526 Nothing -> pprPanic "splitTyConApp" (ppr ty)
528 -- | Attempts to tease a type apart into a type constructor and the application
529 -- of a number of arguments to that constructor
530 splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
531 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
532 splitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
533 splitTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
534 splitTyConApp_maybe _ = Nothing
536 newTyConInstRhs :: TyCon -> [Type] -> Type
537 -- ^ Unwrap one 'layer' of newtype on a type constructor and its arguments, using an
538 -- eta-reduced version of the @newtype@ if possible
539 newTyConInstRhs tycon tys
540 = ASSERT2( equalLength tvs tys1, ppr tycon $$ ppr tys $$ ppr tvs )
541 mkAppTys (substTyWith tvs tys1 ty) tys2
543 (tvs, ty) = newTyConEtadRhs tycon
544 (tys1, tys2) = splitAtList tvs tys
548 ---------------------------------------------------------------------
552 Notes on type synonyms
553 ~~~~~~~~~~~~~~~~~~~~~~
554 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
555 to return type synonyms whereever possible. Thus
560 splitFunTys (a -> Foo a) = ([a], Foo a)
563 The reason is that we then get better (shorter) type signatures in
564 interfaces. Notably this plays a role in tcTySigs in TcBinds.lhs.
567 Note [Expanding newtypes]
568 ~~~~~~~~~~~~~~~~~~~~~~~~~
569 When expanding a type to expose a data-type constructor, we need to be
570 careful about newtypes, lest we fall into an infinite loop. Here are
573 newtype Id x = MkId x
574 newtype Fix f = MkFix (f (Fix f))
575 newtype T = MkT (T -> T)
578 --------------------------
580 Fix Maybe Maybe (Fix Maybe)
584 Notice that we can expand T, even though it's recursive.
585 And we can expand Id (Id Int), even though the Id shows up
586 twice at the outer level.
588 So, when expanding, we keep track of when we've seen a recursive
589 newtype at outermost level; and bale out if we see it again.
601 -- 4. All newtypes, including recursive ones, but not newtype families
603 -- It's useful in the back end of the compiler.
604 repType :: Type -> Type
605 -- Only applied to types of kind *; hence tycons are saturated
609 go :: [TyCon] -> Type -> Type
610 go rec_nts ty | Just ty' <- coreView ty -- Expand synonyms
613 go rec_nts (ForAllTy _ ty) -- Look through foralls
616 go rec_nts (TyConApp tc tys) -- Expand newtypes
617 | Just (rec_nts', ty') <- carefullySplitNewType_maybe rec_nts tc tys
623 carefullySplitNewType_maybe :: [TyCon] -> TyCon -> [Type] -> Maybe ([TyCon],Type)
624 -- Return the representation of a newtype, unless
625 -- we've seen it already: see Note [Expanding newtypes]
626 carefullySplitNewType_maybe rec_nts tc tys
628 , not (tc `elem` rec_nts) = Just (rec_nts', newTyConInstRhs tc tys)
629 | otherwise = Nothing
631 rec_nts' | isRecursiveTyCon tc = tc:rec_nts
632 | otherwise = rec_nts
635 -- ToDo: this could be moved to the code generator, using splitTyConApp instead
636 -- of inspecting the type directly.
638 -- | Discovers the primitive representation of a more abstract 'Type'
639 typePrimRep :: Type -> PrimRep
640 typePrimRep ty = case repType ty of
641 TyConApp tc _ -> tyConPrimRep tc
643 AppTy _ _ -> PtrRep -- See note below
645 _ -> pprPanic "typePrimRep" (ppr ty)
646 -- Types of the form 'f a' must be of kind *, not *#, so
647 -- we are guaranteed that they are represented by pointers.
648 -- The reason is that f must have kind *->*, not *->*#, because
649 -- (we claim) there is no way to constrain f's kind any other
654 ---------------------------------------------------------------------
659 mkForAllTy :: TyVar -> Type -> Type
661 = mkForAllTys [tyvar] ty
663 -- | Wraps foralls over the type using the provided 'TyVar's from left to right
664 mkForAllTys :: [TyVar] -> Type -> Type
665 mkForAllTys tyvars ty = foldr ForAllTy ty tyvars
667 isForAllTy :: Type -> Bool
668 isForAllTy (ForAllTy _ _) = True
671 -- | Attempts to take a forall type apart, returning the bound type variable
672 -- and the remainder of the type
673 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
674 splitForAllTy_maybe ty = splitFAT_m ty
676 splitFAT_m ty | Just ty' <- coreView ty = splitFAT_m ty'
677 splitFAT_m (ForAllTy tyvar ty) = Just(tyvar, ty)
678 splitFAT_m _ = Nothing
680 -- | Attempts to take a forall type apart, returning all the immediate such bound
681 -- type variables and the remainder of the type. Always suceeds, even if that means
682 -- returning an empty list of 'TyVar's
683 splitForAllTys :: Type -> ([TyVar], Type)
684 splitForAllTys ty = split ty ty []
686 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
687 split _ (ForAllTy tv ty) tvs = split ty ty (tv:tvs)
688 split orig_ty _ tvs = (reverse tvs, orig_ty)
690 -- | Equivalent to @snd . splitForAllTys@
691 dropForAlls :: Type -> Type
692 dropForAlls ty = snd (splitForAllTys ty)
695 -- (mkPiType now in CoreUtils)
701 -- | Instantiate a forall type with one or more type arguments.
702 -- Used when we have a polymorphic function applied to type args:
706 -- We use @applyTys type-of-f [t1,t2]@ to compute the type of the expression.
707 -- Panics if no application is possible.
708 applyTy :: Type -> Type -> Type
709 applyTy ty arg | Just ty' <- coreView ty = applyTy ty' arg
710 applyTy (ForAllTy tv ty) arg = substTyWith [tv] [arg] ty
711 applyTy _ _ = panic "applyTy"
713 applyTys :: Type -> [Type] -> Type
714 -- ^ This function is interesting because:
716 -- 1. The function may have more for-alls than there are args
718 -- 2. Less obviously, it may have fewer for-alls
720 -- For case 2. think of:
722 -- > applyTys (forall a.a) [forall b.b, Int]
724 -- This really can happen, via dressing up polymorphic types with newtype
725 -- clothing. Here's an example:
727 -- > newtype R = R (forall a. a->a)
728 -- > foo = case undefined :: R of
731 applyTys ty args = applyTysD empty ty args
733 applyTysD :: SDoc -> Type -> [Type] -> Type -- Debug version
734 applyTysD _ orig_fun_ty [] = orig_fun_ty
735 applyTysD doc orig_fun_ty arg_tys
736 | n_tvs == n_args -- The vastly common case
737 = substTyWith tvs arg_tys rho_ty
738 | n_tvs > n_args -- Too many for-alls
739 = substTyWith (take n_args tvs) arg_tys
740 (mkForAllTys (drop n_args tvs) rho_ty)
741 | otherwise -- Too many type args
742 = ASSERT2( n_tvs > 0, doc $$ ppr orig_fun_ty ) -- Zero case gives infnite loop!
743 applyTysD doc (substTyWith tvs (take n_tvs arg_tys) rho_ty)
746 (tvs, rho_ty) = splitForAllTys orig_fun_ty
748 n_args = length arg_tys
752 %************************************************************************
754 \subsection{Source types}
756 %************************************************************************
758 Source types are always lifted.
760 The key function is predTypeRep which gives the representation of a source type:
763 mkPredTy :: PredType -> Type
764 mkPredTy pred = PredTy pred
766 mkPredTys :: ThetaType -> [Type]
767 mkPredTys preds = map PredTy preds
769 predTypeRep :: PredType -> Type
770 -- ^ Convert a 'PredType' to its representation type. However, it unwraps
771 -- only the outermost level; for example, the result might be a newtype application
772 predTypeRep (IParam _ ty) = ty
773 predTypeRep (ClassP clas tys) = mkTyConApp (classTyCon clas) tys
774 -- Result might be a newtype application, but the consumer will
775 -- look through that too if necessary
776 predTypeRep (EqPred ty1 ty2) = pprPanic "predTypeRep" (ppr (EqPred ty1 ty2))
778 mkFamilyTyConApp :: TyCon -> [Type] -> Type
779 -- ^ Given a family instance TyCon and its arg types, return the
780 -- corresponding family type. E.g:
783 -- > data instance T (Maybe b) = MkT b
785 -- Where the instance tycon is :RTL, so:
787 -- > mkFamilyTyConApp :RTL Int = T (Maybe Int)
788 mkFamilyTyConApp tc tys
789 | Just (fam_tc, fam_tys) <- tyConFamInst_maybe tc
790 , let fam_subst = zipTopTvSubst (tyConTyVars tc) tys
791 = mkTyConApp fam_tc (substTys fam_subst fam_tys)
795 -- | Pretty prints a 'TyCon', using the family instance in case of a
796 -- representation tycon. For example:
798 -- > data T [a] = ...
800 -- In that case we want to print @T [a]@, where @T@ is the family 'TyCon'
801 pprSourceTyCon :: TyCon -> SDoc
803 | Just (fam_tc, tys) <- tyConFamInst_maybe tycon
804 = ppr $ fam_tc `TyConApp` tys -- can't be FunTyCon
810 %************************************************************************
812 \subsection{Kinds and free variables}
814 %************************************************************************
816 ---------------------------------------------------------------------
817 Finding the kind of a type
818 ~~~~~~~~~~~~~~~~~~~~~~~~~~
820 typeKind :: Type -> Kind
821 typeKind (TyConApp tycon tys) = ASSERT( not (isCoercionTyCon tycon) )
822 -- We should be looking for the coercion kind,
824 foldr (\_ k -> kindFunResult k) (tyConKind tycon) tys
825 typeKind (PredTy pred) = predKind pred
826 typeKind (AppTy fun _) = kindFunResult (typeKind fun)
827 typeKind (ForAllTy _ ty) = typeKind ty
828 typeKind (TyVarTy tyvar) = tyVarKind tyvar
829 typeKind (FunTy _arg res)
830 -- Hack alert. The kind of (Int -> Int#) is liftedTypeKind (*),
831 -- not unliftedTypKind (#)
832 -- The only things that can be after a function arrow are
833 -- (a) types (of kind openTypeKind or its sub-kinds)
834 -- (b) kinds (of super-kind TY) (e.g. * -> (* -> *))
835 | isTySuperKind k = k
836 | otherwise = ASSERT( isSubOpenTypeKind k) liftedTypeKind
840 predKind :: PredType -> Kind
841 predKind (EqPred {}) = coSuperKind -- A coercion kind!
842 predKind (ClassP {}) = liftedTypeKind -- Class and implicitPredicates are
843 predKind (IParam {}) = liftedTypeKind -- always represented by lifted types
847 ---------------------------------------------------------------------
848 Free variables of a type
849 ~~~~~~~~~~~~~~~~~~~~~~~~
851 tyVarsOfType :: Type -> TyVarSet
852 -- ^ NB: for type synonyms tyVarsOfType does /not/ expand the synonym
853 tyVarsOfType (TyVarTy tv) = unitVarSet tv
854 tyVarsOfType (TyConApp _ tys) = tyVarsOfTypes tys
855 tyVarsOfType (PredTy sty) = tyVarsOfPred sty
856 tyVarsOfType (FunTy arg res) = tyVarsOfType arg `unionVarSet` tyVarsOfType res
857 tyVarsOfType (AppTy fun arg) = tyVarsOfType fun `unionVarSet` tyVarsOfType arg
858 tyVarsOfType (ForAllTy tyvar ty) = delVarSet (tyVarsOfType ty) tyvar
860 tyVarsOfTypes :: [Type] -> TyVarSet
861 tyVarsOfTypes tys = foldr (unionVarSet.tyVarsOfType) emptyVarSet tys
863 tyVarsOfPred :: PredType -> TyVarSet
864 tyVarsOfPred (IParam _ ty) = tyVarsOfType ty
865 tyVarsOfPred (ClassP _ tys) = tyVarsOfTypes tys
866 tyVarsOfPred (EqPred ty1 ty2) = tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2
868 tyVarsOfTheta :: ThetaType -> TyVarSet
869 tyVarsOfTheta = foldr (unionVarSet . tyVarsOfPred) emptyVarSet
873 %************************************************************************
875 \subsection{Type families}
877 %************************************************************************
880 -- | Finds type family instances occuring in a type after expanding synonyms.
881 tyFamInsts :: Type -> [(TyCon, [Type])]
883 | Just exp_ty <- tcView ty = tyFamInsts exp_ty
884 tyFamInsts (TyVarTy _) = []
885 tyFamInsts (TyConApp tc tys)
886 | isOpenSynTyCon tc = [(tc, tys)]
887 | otherwise = concat (map tyFamInsts tys)
888 tyFamInsts (FunTy ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
889 tyFamInsts (AppTy ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
890 tyFamInsts (ForAllTy _ ty) = tyFamInsts ty
891 tyFamInsts (PredTy pty) = predFamInsts pty
893 -- | Finds type family instances occuring in a predicate type after expanding
895 predFamInsts :: PredType -> [(TyCon, [Type])]
896 predFamInsts (ClassP _cla tys) = concat (map tyFamInsts tys)
897 predFamInsts (IParam _ ty) = tyFamInsts ty
898 predFamInsts (EqPred ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
902 %************************************************************************
904 \subsection{TidyType}
906 %************************************************************************
909 -- | This tidies up a type for printing in an error message, or in
910 -- an interface file.
912 -- It doesn't change the uniques at all, just the print names.
913 tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
914 tidyTyVarBndr env@(tidy_env, subst) tyvar
915 = case tidyOccName tidy_env (getOccName name) of
916 (tidy', occ') -> ((tidy', subst'), tyvar'')
918 subst' = extendVarEnv subst tyvar tyvar''
919 tyvar' = setTyVarName tyvar name'
920 name' = tidyNameOcc name occ'
921 -- Don't forget to tidy the kind for coercions!
922 tyvar'' | isCoVar tyvar = setTyVarKind tyvar' kind'
924 kind' = tidyType env (tyVarKind tyvar)
926 name = tyVarName tyvar
928 tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv
929 -- ^ Add the free 'TyVar's to the env in tidy form,
930 -- so that we can tidy the type they are free in
931 tidyFreeTyVars env tyvars = fst (tidyOpenTyVars env (varSetElems tyvars))
933 tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
934 tidyOpenTyVars env tyvars = mapAccumL tidyOpenTyVar env tyvars
936 tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
937 -- ^ Treat a new 'TyVar' as a binder, and give it a fresh tidy name
938 -- using the environment if one has not already been allocated. See
939 -- also 'tidyTyVarBndr'
940 tidyOpenTyVar env@(_, subst) tyvar
941 = case lookupVarEnv subst tyvar of
942 Just tyvar' -> (env, tyvar') -- Already substituted
943 Nothing -> tidyTyVarBndr env tyvar -- Treat it as a binder
945 tidyType :: TidyEnv -> Type -> Type
946 tidyType env@(_, subst) ty
949 go (TyVarTy tv) = case lookupVarEnv subst tv of
950 Nothing -> TyVarTy tv
951 Just tv' -> TyVarTy tv'
952 go (TyConApp tycon tys) = let args = map go tys
953 in args `seqList` TyConApp tycon args
954 go (PredTy sty) = PredTy (tidyPred env sty)
955 go (AppTy fun arg) = (AppTy $! (go fun)) $! (go arg)
956 go (FunTy fun arg) = (FunTy $! (go fun)) $! (go arg)
957 go (ForAllTy tv ty) = ForAllTy tvp $! (tidyType envp ty)
959 (envp, tvp) = tidyTyVarBndr env tv
961 tidyTypes :: TidyEnv -> [Type] -> [Type]
962 tidyTypes env tys = map (tidyType env) tys
964 tidyPred :: TidyEnv -> PredType -> PredType
965 tidyPred env (IParam n ty) = IParam n (tidyType env ty)
966 tidyPred env (ClassP clas tys) = ClassP clas (tidyTypes env tys)
967 tidyPred env (EqPred ty1 ty2) = EqPred (tidyType env ty1) (tidyType env ty2)
972 -- | Grabs the free type variables, tidies them
973 -- and then uses 'tidyType' to work over the type itself
974 tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
976 = (env', tidyType env' ty)
978 env' = tidyFreeTyVars env (tyVarsOfType ty)
980 tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
981 tidyOpenTypes env tys = mapAccumL tidyOpenType env tys
983 -- | Calls 'tidyType' on a top-level type (i.e. with an empty tidying environment)
984 tidyTopType :: Type -> Type
985 tidyTopType ty = tidyType emptyTidyEnv ty
990 tidyKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
991 tidyKind env k = tidyOpenType env k
996 %************************************************************************
998 \subsection{Liftedness}
1000 %************************************************************************
1003 -- | See "Type#type_classification" for what an unlifted type is
1004 isUnLiftedType :: Type -> Bool
1005 -- isUnLiftedType returns True for forall'd unlifted types:
1006 -- x :: forall a. Int#
1007 -- I found bindings like these were getting floated to the top level.
1008 -- They are pretty bogus types, mind you. It would be better never to
1011 isUnLiftedType ty | Just ty' <- coreView ty = isUnLiftedType ty'
1012 isUnLiftedType (ForAllTy _ ty) = isUnLiftedType ty
1013 isUnLiftedType (TyConApp tc _) = isUnLiftedTyCon tc
1014 isUnLiftedType _ = False
1016 isUnboxedTupleType :: Type -> Bool
1017 isUnboxedTupleType ty = case splitTyConApp_maybe ty of
1018 Just (tc, _ty_args) -> isUnboxedTupleTyCon tc
1021 -- | See "Type#type_classification" for what an algebraic type is.
1022 -- Should only be applied to /types/, as opposed to e.g. partially
1023 -- saturated type constructors
1024 isAlgType :: Type -> Bool
1026 = case splitTyConApp_maybe ty of
1027 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
1031 -- | See "Type#type_classification" for what an algebraic type is.
1032 -- Should only be applied to /types/, as opposed to e.g. partially
1033 -- saturated type constructors. Closed type constructors are those
1034 -- with a fixed right hand side, as opposed to e.g. associated types
1035 isClosedAlgType :: Type -> Bool
1037 = case splitTyConApp_maybe ty of
1038 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
1039 isAlgTyCon tc && not (isOpenTyCon tc)
1044 -- | Computes whether an argument (or let right hand side) should
1045 -- be computed strictly or lazily, based only on its type.
1046 -- Works just like 'isUnLiftedType', except that it has a special case
1047 -- for dictionaries (i.e. does not work purely on representation types)
1049 -- Since it takes account of class 'PredType's, you might think
1050 -- this function should be in 'TcType', but 'isStrictType' is used by 'DataCon',
1051 -- which is below 'TcType' in the hierarchy, so it's convenient to put it here.
1052 isStrictType :: Type -> Bool
1053 isStrictType (PredTy pred) = isStrictPred pred
1054 isStrictType ty | Just ty' <- coreView ty = isStrictType ty'
1055 isStrictType (ForAllTy _ ty) = isStrictType ty
1056 isStrictType (TyConApp tc _) = isUnLiftedTyCon tc
1057 isStrictType _ = False
1059 -- | We may be strict in dictionary types, but only if it
1060 -- has more than one component.
1062 -- (Being strict in a single-component dictionary risks
1063 -- poking the dictionary component, which is wrong.)
1064 isStrictPred :: PredType -> Bool
1065 isStrictPred (ClassP clas _) = opt_DictsStrict && not (isNewTyCon (classTyCon clas))
1066 isStrictPred _ = False
1070 isPrimitiveType :: Type -> Bool
1071 -- ^ Returns true of types that are opaque to Haskell.
1072 -- Most of these are unlifted, but now that we interact with .NET, we
1073 -- may have primtive (foreign-imported) types that are lifted
1074 isPrimitiveType ty = case splitTyConApp_maybe ty of
1075 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
1081 %************************************************************************
1083 \subsection{Sequencing on types}
1085 %************************************************************************
1088 seqType :: Type -> ()
1089 seqType (TyVarTy tv) = tv `seq` ()
1090 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
1091 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
1092 seqType (PredTy p) = seqPred p
1093 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
1094 seqType (ForAllTy tv ty) = tv `seq` seqType ty
1096 seqTypes :: [Type] -> ()
1098 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
1100 seqPred :: PredType -> ()
1101 seqPred (ClassP c tys) = c `seq` seqTypes tys
1102 seqPred (IParam n ty) = n `seq` seqType ty
1103 seqPred (EqPred ty1 ty2) = seqType ty1 `seq` seqType ty2
1107 %************************************************************************
1109 Equality for Core types
1110 (We don't use instances so that we know where it happens)
1112 %************************************************************************
1114 Note that eqType works right even for partial applications of newtypes.
1115 See Note [Newtype eta] in TyCon.lhs
1118 -- | Type equality test for Core types (i.e. ignores predicate-types, synonyms etc.)
1119 coreEqType :: Type -> Type -> Bool
1123 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
1125 eq env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 == rnOccR env tv2
1126 eq env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = eq (rnBndr2 env tv1 tv2) t1 t2
1127 eq env (AppTy s1 t1) (AppTy s2 t2) = eq env s1 s2 && eq env t1 t2
1128 eq env (FunTy s1 t1) (FunTy s2 t2) = eq env s1 s2 && eq env t1 t2
1129 eq env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
1130 | tc1 == tc2, all2 (eq env) tys1 tys2 = True
1131 -- The lengths should be equal because
1132 -- the two types have the same kind
1133 -- NB: if the type constructors differ that does not
1134 -- necessarily mean that the types aren't equal
1135 -- (synonyms, newtypes)
1136 -- Even if the type constructors are the same, but the arguments
1137 -- differ, the two types could be the same (e.g. if the arg is just
1138 -- ignored in the RHS). In both these cases we fall through to an
1139 -- attempt to expand one side or the other.
1141 -- Now deal with newtypes, synonyms, pred-tys
1142 eq env t1 t2 | Just t1' <- coreView t1 = eq env t1' t2
1143 | Just t2' <- coreView t2 = eq env t1 t2'
1145 -- Fall through case; not equal!
1150 %************************************************************************
1152 Comparision for source types
1153 (We don't use instances so that we know where it happens)
1155 %************************************************************************
1158 tcEqType :: Type -> Type -> Bool
1159 -- ^ Type equality on source types. Does not look through @newtypes@ or
1160 -- 'PredType's, but it does look through type synonyms.
1161 tcEqType t1 t2 = isEqual $ cmpType t1 t2
1163 tcEqTypes :: [Type] -> [Type] -> Bool
1164 tcEqTypes tys1 tys2 = isEqual $ cmpTypes tys1 tys2
1166 tcCmpType :: Type -> Type -> Ordering
1167 -- ^ Type ordering on source types. Does not look through @newtypes@ or
1168 -- 'PredType's, but it does look through type synonyms.
1169 tcCmpType t1 t2 = cmpType t1 t2
1171 tcCmpTypes :: [Type] -> [Type] -> Ordering
1172 tcCmpTypes tys1 tys2 = cmpTypes tys1 tys2
1174 tcEqPred :: PredType -> PredType -> Bool
1175 tcEqPred p1 p2 = isEqual $ cmpPred p1 p2
1177 tcEqPredX :: RnEnv2 -> PredType -> PredType -> Bool
1178 tcEqPredX env p1 p2 = isEqual $ cmpPredX env p1 p2
1180 tcCmpPred :: PredType -> PredType -> Ordering
1181 tcCmpPred p1 p2 = cmpPred p1 p2
1183 tcEqTypeX :: RnEnv2 -> Type -> Type -> Bool
1184 tcEqTypeX env t1 t2 = isEqual $ cmpTypeX env t1 t2
1188 -- | Checks whether the second argument is a subterm of the first. (We don't care
1189 -- about binders, as we are only interested in syntactic subterms.)
1190 tcPartOfType :: Type -> Type -> Bool
1192 | tcEqType t1 t2 = True
1194 | Just t2' <- tcView t2 = tcPartOfType t1 t2'
1195 tcPartOfType _ (TyVarTy _) = False
1196 tcPartOfType t1 (ForAllTy _ t2) = tcPartOfType t1 t2
1197 tcPartOfType t1 (AppTy s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1198 tcPartOfType t1 (FunTy s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1199 tcPartOfType t1 (PredTy p2) = tcPartOfPred t1 p2
1200 tcPartOfType t1 (TyConApp _ ts) = any (tcPartOfType t1) ts
1202 tcPartOfPred :: Type -> PredType -> Bool
1203 tcPartOfPred t1 (IParam _ t2) = tcPartOfType t1 t2
1204 tcPartOfPred t1 (ClassP _ ts) = any (tcPartOfType t1) ts
1205 tcPartOfPred t1 (EqPred s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1208 Now here comes the real worker
1211 cmpType :: Type -> Type -> Ordering
1212 cmpType t1 t2 = cmpTypeX rn_env t1 t2
1214 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
1216 cmpTypes :: [Type] -> [Type] -> Ordering
1217 cmpTypes ts1 ts2 = cmpTypesX rn_env ts1 ts2
1219 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfTypes ts1 `unionVarSet` tyVarsOfTypes ts2))
1221 cmpPred :: PredType -> PredType -> Ordering
1222 cmpPred p1 p2 = cmpPredX rn_env p1 p2
1224 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfPred p1 `unionVarSet` tyVarsOfPred p2))
1226 cmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
1227 cmpTypeX env t1 t2 | Just t1' <- tcView t1 = cmpTypeX env t1' t2
1228 | Just t2' <- tcView t2 = cmpTypeX env t1 t2'
1230 cmpTypeX env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 `compare` rnOccR env tv2
1231 cmpTypeX env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = cmpTypeX (rnBndr2 env tv1 tv2) t1 t2
1232 cmpTypeX env (AppTy s1 t1) (AppTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1233 cmpTypeX env (FunTy s1 t1) (FunTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1234 cmpTypeX env (PredTy p1) (PredTy p2) = cmpPredX env p1 p2
1235 cmpTypeX env (TyConApp tc1 tys1) (TyConApp tc2 tys2) = (tc1 `compare` tc2) `thenCmp` cmpTypesX env tys1 tys2
1237 -- Deal with the rest: TyVarTy < AppTy < FunTy < TyConApp < ForAllTy < PredTy
1238 cmpTypeX _ (AppTy _ _) (TyVarTy _) = GT
1240 cmpTypeX _ (FunTy _ _) (TyVarTy _) = GT
1241 cmpTypeX _ (FunTy _ _) (AppTy _ _) = GT
1243 cmpTypeX _ (TyConApp _ _) (TyVarTy _) = GT
1244 cmpTypeX _ (TyConApp _ _) (AppTy _ _) = GT
1245 cmpTypeX _ (TyConApp _ _) (FunTy _ _) = GT
1247 cmpTypeX _ (ForAllTy _ _) (TyVarTy _) = GT
1248 cmpTypeX _ (ForAllTy _ _) (AppTy _ _) = GT
1249 cmpTypeX _ (ForAllTy _ _) (FunTy _ _) = GT
1250 cmpTypeX _ (ForAllTy _ _) (TyConApp _ _) = GT
1252 cmpTypeX _ (PredTy _) _ = GT
1257 cmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
1258 cmpTypesX _ [] [] = EQ
1259 cmpTypesX env (t1:tys1) (t2:tys2) = cmpTypeX env t1 t2 `thenCmp` cmpTypesX env tys1 tys2
1260 cmpTypesX _ [] _ = LT
1261 cmpTypesX _ _ [] = GT
1264 cmpPredX :: RnEnv2 -> PredType -> PredType -> Ordering
1265 cmpPredX env (IParam n1 ty1) (IParam n2 ty2) = (n1 `compare` n2) `thenCmp` cmpTypeX env ty1 ty2
1266 -- Compare names only for implicit parameters
1267 -- This comparison is used exclusively (I believe)
1268 -- for the Avails finite map built in TcSimplify
1269 -- If the types differ we keep them distinct so that we see
1270 -- a distinct pair to run improvement on
1271 cmpPredX env (ClassP c1 tys1) (ClassP c2 tys2) = (c1 `compare` c2) `thenCmp` (cmpTypesX env tys1 tys2)
1272 cmpPredX env (EqPred ty1 ty2) (EqPred ty1' ty2') = (cmpTypeX env ty1 ty1') `thenCmp` (cmpTypeX env ty2 ty2')
1274 -- Constructor order: IParam < ClassP < EqPred
1275 cmpPredX _ (IParam {}) _ = LT
1276 cmpPredX _ (ClassP {}) (IParam {}) = GT
1277 cmpPredX _ (ClassP {}) (EqPred {}) = LT
1278 cmpPredX _ (EqPred {}) _ = GT
1281 PredTypes are used as a FM key in TcSimplify,
1282 so we take the easy path and make them an instance of Ord
1285 instance Eq PredType where { (==) = tcEqPred }
1286 instance Ord PredType where { compare = tcCmpPred }
1290 %************************************************************************
1294 %************************************************************************
1297 -- | Type substitution
1299 -- #tvsubst_invariant#
1300 -- The following invariants must hold of a 'TvSubst':
1302 -- 1. The in-scope set is needed /only/ to
1303 -- guide the generation of fresh uniques
1305 -- 2. In particular, the /kind/ of the type variables in
1306 -- the in-scope set is not relevant
1308 -- 3. The substition is only applied ONCE! This is because
1309 -- in general such application will not reached a fixed point.
1311 = TvSubst InScopeSet -- The in-scope type variables
1312 TvSubstEnv -- The substitution itself
1313 -- See Note [Apply Once]
1314 -- and Note [Extending the TvSubstEnv]
1316 {- ----------------------------------------------------------
1320 We use TvSubsts to instantiate things, and we might instantiate
1324 So the substition might go [a->b, b->a]. A similar situation arises in Core
1325 when we find a beta redex like
1326 (/\ a /\ b -> e) b a
1327 Then we also end up with a substition that permutes type variables. Other
1328 variations happen to; for example [a -> (a, b)].
1330 ***************************************************
1331 *** So a TvSubst must be applied precisely once ***
1332 ***************************************************
1334 A TvSubst is not idempotent, but, unlike the non-idempotent substitution
1335 we use during unifications, it must not be repeatedly applied.
1337 Note [Extending the TvSubst]
1338 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1339 See #tvsubst_invariant# for the invariants that must hold.
1341 This invariant allows a short-cut when the TvSubstEnv is empty:
1342 if the TvSubstEnv is empty --- i.e. (isEmptyTvSubt subst) holds ---
1343 then (substTy subst ty) does nothing.
1345 For example, consider:
1346 (/\a. /\b:(a~Int). ...b..) Int
1347 We substitute Int for 'a'. The Unique of 'b' does not change, but
1348 nevertheless we add 'b' to the TvSubstEnv, because b's type does change
1350 This invariant has several crucial consequences:
1352 * In substTyVarBndr, we need extend the TvSubstEnv
1353 - if the unique has changed
1354 - or if the kind has changed
1356 * In substTyVar, we do not need to consult the in-scope set;
1357 the TvSubstEnv is enough
1359 * In substTy, substTheta, we can short-circuit when the TvSubstEnv is empty
1362 -------------------------------------------------------------- -}
1364 -- | A substitition of 'Type's for 'TyVar's
1365 type TvSubstEnv = TyVarEnv Type
1366 -- A TvSubstEnv is used both inside a TvSubst (with the apply-once
1367 -- invariant discussed in Note [Apply Once]), and also independently
1368 -- in the middle of matching, and unification (see Types.Unify)
1369 -- So you have to look at the context to know if it's idempotent or
1370 -- apply-once or whatever
1372 emptyTvSubstEnv :: TvSubstEnv
1373 emptyTvSubstEnv = emptyVarEnv
1375 composeTvSubst :: InScopeSet -> TvSubstEnv -> TvSubstEnv -> TvSubstEnv
1376 -- ^ @(compose env1 env2)(x)@ is @env1(env2(x))@; i.e. apply @env2@ then @env1@.
1377 -- It assumes that both are idempotent.
1378 -- Typically, @env1@ is the refinement to a base substitution @env2@
1379 composeTvSubst in_scope env1 env2
1380 = env1 `plusVarEnv` mapVarEnv (substTy subst1) env2
1381 -- First apply env1 to the range of env2
1382 -- Then combine the two, making sure that env1 loses if
1383 -- both bind the same variable; that's why env1 is the
1384 -- *left* argument to plusVarEnv, because the right arg wins
1386 subst1 = TvSubst in_scope env1
1388 emptyTvSubst :: TvSubst
1389 emptyTvSubst = TvSubst emptyInScopeSet emptyVarEnv
1391 isEmptyTvSubst :: TvSubst -> Bool
1392 -- See Note [Extending the TvSubstEnv]
1393 isEmptyTvSubst (TvSubst _ env) = isEmptyVarEnv env
1395 mkTvSubst :: InScopeSet -> TvSubstEnv -> TvSubst
1398 getTvSubstEnv :: TvSubst -> TvSubstEnv
1399 getTvSubstEnv (TvSubst _ env) = env
1401 getTvInScope :: TvSubst -> InScopeSet
1402 getTvInScope (TvSubst in_scope _) = in_scope
1404 isInScope :: Var -> TvSubst -> Bool
1405 isInScope v (TvSubst in_scope _) = v `elemInScopeSet` in_scope
1407 notElemTvSubst :: TyVar -> TvSubst -> Bool
1408 notElemTvSubst tv (TvSubst _ env) = not (tv `elemVarEnv` env)
1410 setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst
1411 setTvSubstEnv (TvSubst in_scope _) env = TvSubst in_scope env
1413 extendTvInScope :: TvSubst -> [Var] -> TvSubst
1414 extendTvInScope (TvSubst in_scope env) vars = TvSubst (extendInScopeSetList in_scope vars) env
1416 extendTvSubst :: TvSubst -> TyVar -> Type -> TvSubst
1417 extendTvSubst (TvSubst in_scope env) tv ty = TvSubst in_scope (extendVarEnv env tv ty)
1419 extendTvSubstList :: TvSubst -> [TyVar] -> [Type] -> TvSubst
1420 extendTvSubstList (TvSubst in_scope env) tvs tys
1421 = TvSubst in_scope (extendVarEnvList env (tvs `zip` tys))
1423 -- mkOpenTvSubst and zipOpenTvSubst generate the in-scope set from
1424 -- the types given; but it's just a thunk so with a bit of luck
1425 -- it'll never be evaluated
1427 -- Note [Generating the in-scope set for a substitution]
1428 -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1429 -- If we want to substitute [a -> ty1, b -> ty2] I used to
1430 -- think it was enough to generate an in-scope set that includes
1431 -- fv(ty1,ty2). But that's not enough; we really should also take the
1432 -- free vars of the type we are substituting into! Example:
1433 -- (forall b. (a,b,x)) [a -> List b]
1434 -- Then if we use the in-scope set {b}, there is a danger we will rename
1435 -- the forall'd variable to 'x' by mistake, getting this:
1436 -- (forall x. (List b, x, x)
1437 -- Urk! This means looking at all the calls to mkOpenTvSubst....
1440 -- | Generates the in-scope set for the 'TvSubst' from the types in the incoming
1441 -- environment, hence "open"
1442 mkOpenTvSubst :: TvSubstEnv -> TvSubst
1443 mkOpenTvSubst env = TvSubst (mkInScopeSet (tyVarsOfTypes (varEnvElts env))) env
1445 -- | Generates the in-scope set for the 'TvSubst' from the types in the incoming
1446 -- environment, hence "open"
1447 zipOpenTvSubst :: [TyVar] -> [Type] -> TvSubst
1448 zipOpenTvSubst tyvars tys
1449 | debugIsOn && (length tyvars /= length tys)
1450 = pprTrace "zipOpenTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1452 = TvSubst (mkInScopeSet (tyVarsOfTypes tys)) (zipTyEnv tyvars tys)
1454 -- | Called when doing top-level substitutions. Here we expect that the
1455 -- free vars of the range of the substitution will be empty.
1456 mkTopTvSubst :: [(TyVar, Type)] -> TvSubst
1457 mkTopTvSubst prs = TvSubst emptyInScopeSet (mkVarEnv prs)
1459 zipTopTvSubst :: [TyVar] -> [Type] -> TvSubst
1460 zipTopTvSubst tyvars tys
1461 | debugIsOn && (length tyvars /= length tys)
1462 = pprTrace "zipTopTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1464 = TvSubst emptyInScopeSet (zipTyEnv tyvars tys)
1466 zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
1468 | debugIsOn && (length tyvars /= length tys)
1469 = pprTrace "mkTopTvSubst" (ppr tyvars $$ ppr tys) emptyVarEnv
1471 = zip_ty_env tyvars tys emptyVarEnv
1473 -- Later substitutions in the list over-ride earlier ones,
1474 -- but there should be no loops
1475 zip_ty_env :: [TyVar] -> [Type] -> TvSubstEnv -> TvSubstEnv
1476 zip_ty_env [] [] env = env
1477 zip_ty_env (tv:tvs) (ty:tys) env = zip_ty_env tvs tys (extendVarEnv env tv ty)
1478 -- There used to be a special case for when
1480 -- (a not-uncommon case) in which case the substitution was dropped.
1481 -- But the type-tidier changes the print-name of a type variable without
1482 -- changing the unique, and that led to a bug. Why? Pre-tidying, we had
1483 -- a type {Foo t}, where Foo is a one-method class. So Foo is really a newtype.
1484 -- And it happened that t was the type variable of the class. Post-tiding,
1485 -- it got turned into {Foo t2}. The ext-core printer expanded this using
1486 -- sourceTypeRep, but that said "Oh, t == t2" because they have the same unique,
1487 -- and so generated a rep type mentioning t not t2.
1489 -- Simplest fix is to nuke the "optimisation"
1490 zip_ty_env tvs tys env = pprTrace "Var/Type length mismatch: " (ppr tvs $$ ppr tys) env
1491 -- zip_ty_env _ _ env = env
1493 instance Outputable TvSubst where
1494 ppr (TvSubst ins env)
1495 = brackets $ sep[ ptext (sLit "TvSubst"),
1496 nest 2 (ptext (sLit "In scope:") <+> ppr ins),
1497 nest 2 (ptext (sLit "Env:") <+> ppr env) ]
1500 %************************************************************************
1502 Performing type substitutions
1504 %************************************************************************
1507 -- | Type substitution making use of an 'TvSubst' that
1508 -- is assumed to be open, see 'zipOpenTvSubst'
1509 substTyWith :: [TyVar] -> [Type] -> Type -> Type
1510 substTyWith tvs tys = ASSERT( length tvs == length tys )
1511 substTy (zipOpenTvSubst tvs tys)
1513 -- | Type substitution making use of an 'TvSubst' that
1514 -- is assumed to be open, see 'zipOpenTvSubst'
1515 substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type]
1516 substTysWith tvs tys = ASSERT( length tvs == length tys )
1517 substTys (zipOpenTvSubst tvs tys)
1519 -- | Substitute within a 'Type'
1520 substTy :: TvSubst -> Type -> Type
1521 substTy subst ty | isEmptyTvSubst subst = ty
1522 | otherwise = subst_ty subst ty
1524 -- | Substitute within several 'Type's
1525 substTys :: TvSubst -> [Type] -> [Type]
1526 substTys subst tys | isEmptyTvSubst subst = tys
1527 | otherwise = map (subst_ty subst) tys
1529 -- | Substitute within a 'ThetaType'
1530 substTheta :: TvSubst -> ThetaType -> ThetaType
1531 substTheta subst theta
1532 | isEmptyTvSubst subst = theta
1533 | otherwise = map (substPred subst) theta
1535 -- | Substitute within a 'PredType'
1536 substPred :: TvSubst -> PredType -> PredType
1537 substPred subst (IParam n ty) = IParam n (subst_ty subst ty)
1538 substPred subst (ClassP clas tys) = ClassP clas (map (subst_ty subst) tys)
1539 substPred subst (EqPred ty1 ty2) = EqPred (subst_ty subst ty1) (subst_ty subst ty2)
1541 -- | Remove any nested binders mentioning the 'TyVar's in the 'TyVarSet'
1542 deShadowTy :: TyVarSet -> Type -> Type
1544 = subst_ty (mkTvSubst in_scope emptyTvSubstEnv) ty
1546 in_scope = mkInScopeSet tvs
1548 subst_ty :: TvSubst -> Type -> Type
1549 -- subst_ty is the main workhorse for type substitution
1551 -- Note that the in_scope set is poked only if we hit a forall
1552 -- so it may often never be fully computed
1556 go (TyVarTy tv) = substTyVar subst tv
1557 go (TyConApp tc tys) = let args = map go tys
1558 in args `seqList` TyConApp tc args
1560 go (PredTy p) = PredTy $! (substPred subst p)
1562 go (FunTy arg res) = (FunTy $! (go arg)) $! (go res)
1563 go (AppTy fun arg) = mkAppTy (go fun) $! (go arg)
1564 -- The mkAppTy smart constructor is important
1565 -- we might be replacing (a Int), represented with App
1566 -- by [Int], represented with TyConApp
1567 go (ForAllTy tv ty) = case substTyVarBndr subst tv of
1569 ForAllTy tv' $! (subst_ty subst' ty)
1571 substTyVar :: TvSubst -> TyVar -> Type
1572 substTyVar subst@(TvSubst _ _) tv
1573 = case lookupTyVar subst tv of {
1574 Nothing -> TyVarTy tv;
1575 Just ty -> ty -- See Note [Apply Once]
1578 substTyVars :: TvSubst -> [TyVar] -> [Type]
1579 substTyVars subst tvs = map (substTyVar subst) tvs
1581 lookupTyVar :: TvSubst -> TyVar -> Maybe Type
1582 -- See Note [Extending the TvSubst]
1583 lookupTyVar (TvSubst _ env) tv = lookupVarEnv env tv
1585 substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)
1586 substTyVarBndr subst@(TvSubst in_scope env) old_var
1587 = (TvSubst (in_scope `extendInScopeSet` new_var) new_env, new_var)
1589 is_co_var = isCoVar old_var
1591 new_env | no_change = delVarEnv env old_var
1592 | otherwise = extendVarEnv env old_var (TyVarTy new_var)
1594 no_change = new_var == old_var && not is_co_var
1595 -- no_change means that the new_var is identical in
1596 -- all respects to the old_var (same unique, same kind)
1597 -- See Note [Extending the TvSubst]
1599 -- In that case we don't need to extend the substitution
1600 -- to map old to new. But instead we must zap any
1601 -- current substitution for the variable. For example:
1602 -- (\x.e) with id_subst = [x |-> e']
1603 -- Here we must simply zap the substitution for x
1605 new_var = uniqAway in_scope subst_old_var
1606 -- The uniqAway part makes sure the new variable is not already in scope
1608 subst_old_var -- subst_old_var is old_var with the substitution applied to its kind
1609 -- It's only worth doing the substitution for coercions,
1610 -- becuase only they can have free type variables
1611 | is_co_var = setTyVarKind old_var (substTy subst (tyVarKind old_var))
1612 | otherwise = old_var
1615 ----------------------------------------------------
1624 -- There's a little subtyping at the kind level:
1634 -- Where: \* [LiftedTypeKind] means boxed type
1635 -- \# [UnliftedTypeKind] means unboxed type
1636 -- (\#) [UbxTupleKind] means unboxed tuple
1637 -- ?? [ArgTypeKind] is the lub of {\*, \#}
1638 -- ? [OpenTypeKind] means any type at all
1643 -- > error :: forall a:?. String -> a
1644 -- > (->) :: ?? -> ? -> \*
1645 -- > (\\(x::t) -> ...)
1647 -- Where in the last example @t :: ??@ (i.e. is not an unboxed tuple)
1649 type KindVar = TyVar -- invariant: KindVar will always be a
1650 -- TcTyVar with details MetaTv TauTv ...
1651 -- kind var constructors and functions are in TcType
1653 type SimpleKind = Kind
1658 During kind inference, a kind variable unifies only with
1660 sk ::= * | sk1 -> sk2
1662 data T a = MkT a (T Int#)
1663 fails. We give T the kind (k -> *), and the kind variable k won't unify
1664 with # (the kind of Int#).
1668 When creating a fresh internal type variable, we give it a kind to express
1669 constraints on it. E.g. in (\x->e) we make up a fresh type variable for x,
1672 During unification we only bind an internal type variable to a type
1673 whose kind is lower in the sub-kind hierarchy than the kind of the tyvar.
1675 When unifying two internal type variables, we collect their kind constraints by
1676 finding the GLB of the two. Since the partial order is a tree, they only
1677 have a glb if one is a sub-kind of the other. In that case, we bind the
1678 less-informative one to the more informative one. Neat, eh?
1685 %************************************************************************
1687 Functions over Kinds
1689 %************************************************************************
1692 -- | Essentially 'funResultTy' on kinds
1693 kindFunResult :: Kind -> Kind
1694 kindFunResult k = funResultTy k
1696 -- | Essentially 'splitFunTys' on kinds
1697 splitKindFunTys :: Kind -> ([Kind],Kind)
1698 splitKindFunTys k = splitFunTys k
1700 -- | Essentially 'splitFunTysN' on kinds
1701 splitKindFunTysN :: Int -> Kind -> ([Kind],Kind)
1702 splitKindFunTysN k = splitFunTysN k
1704 -- | See "Type#kind_subtyping" for details of the distinction between these 'Kind's
1705 isUbxTupleKind, isOpenTypeKind, isArgTypeKind, isUnliftedTypeKind :: Kind -> Bool
1706 isOpenTypeKindCon, isUbxTupleKindCon, isArgTypeKindCon,
1707 isUnliftedTypeKindCon, isSubArgTypeKindCon :: TyCon -> Bool
1709 isOpenTypeKindCon tc = tyConUnique tc == openTypeKindTyConKey
1711 isOpenTypeKind (TyConApp tc _) = isOpenTypeKindCon tc
1712 isOpenTypeKind _ = False
1714 isUbxTupleKindCon tc = tyConUnique tc == ubxTupleKindTyConKey
1716 isUbxTupleKind (TyConApp tc _) = isUbxTupleKindCon tc
1717 isUbxTupleKind _ = False
1719 isArgTypeKindCon tc = tyConUnique tc == argTypeKindTyConKey
1721 isArgTypeKind (TyConApp tc _) = isArgTypeKindCon tc
1722 isArgTypeKind _ = False
1724 isUnliftedTypeKindCon tc = tyConUnique tc == unliftedTypeKindTyConKey
1726 isUnliftedTypeKind (TyConApp tc _) = isUnliftedTypeKindCon tc
1727 isUnliftedTypeKind _ = False
1729 isSubOpenTypeKind :: Kind -> Bool
1730 -- ^ True of any sub-kind of OpenTypeKind (i.e. anything except arrow)
1731 isSubOpenTypeKind (FunTy k1 k2) = ASSERT2 ( isKind k1, text "isSubOpenTypeKind" <+> ppr k1 <+> text "::" <+> ppr (typeKind k1) )
1732 ASSERT2 ( isKind k2, text "isSubOpenTypeKind" <+> ppr k2 <+> text "::" <+> ppr (typeKind k2) )
1734 isSubOpenTypeKind (TyConApp kc []) = ASSERT( isKind (TyConApp kc []) ) True
1735 isSubOpenTypeKind other = ASSERT( isKind other ) False
1736 -- This is a conservative answer
1737 -- It matters in the call to isSubKind in
1738 -- checkExpectedKind.
1740 isSubArgTypeKindCon kc
1741 | isUnliftedTypeKindCon kc = True
1742 | isLiftedTypeKindCon kc = True
1743 | isArgTypeKindCon kc = True
1746 isSubArgTypeKind :: Kind -> Bool
1747 -- ^ True of any sub-kind of ArgTypeKind
1748 isSubArgTypeKind (TyConApp kc []) = isSubArgTypeKindCon kc
1749 isSubArgTypeKind _ = False
1751 -- | Is this a super-kind (i.e. a type-of-kinds)?
1752 isSuperKind :: Type -> Bool
1753 isSuperKind (TyConApp (skc) []) = isSuperKindTyCon skc
1754 isSuperKind _ = False
1756 -- | Is this a kind (i.e. a type-of-types)?
1757 isKind :: Kind -> Bool
1758 isKind k = isSuperKind (typeKind k)
1760 isSubKind :: Kind -> Kind -> Bool
1761 -- ^ @k1 \`isSubKind\` k2@ checks that @k1@ <: @k2@
1762 isSubKind (TyConApp kc1 []) (TyConApp kc2 []) = kc1 `isSubKindCon` kc2
1763 isSubKind (FunTy a1 r1) (FunTy a2 r2) = (a2 `isSubKind` a1) && (r1 `isSubKind` r2)
1764 isSubKind (PredTy (EqPred ty1 ty2)) (PredTy (EqPred ty1' ty2'))
1765 = ty1 `tcEqType` ty1' && ty2 `tcEqType` ty2'
1766 isSubKind _ _ = False
1768 eqKind :: Kind -> Kind -> Bool
1771 isSubKindCon :: TyCon -> TyCon -> Bool
1772 -- ^ @kc1 \`isSubKindCon\` kc2@ checks that @kc1@ <: @kc2@
1773 isSubKindCon kc1 kc2
1774 | isLiftedTypeKindCon kc1 && isLiftedTypeKindCon kc2 = True
1775 | isUnliftedTypeKindCon kc1 && isUnliftedTypeKindCon kc2 = True
1776 | isUbxTupleKindCon kc1 && isUbxTupleKindCon kc2 = True
1777 | isOpenTypeKindCon kc2 = True
1778 -- we already know kc1 is not a fun, its a TyCon
1779 | isArgTypeKindCon kc2 && isSubArgTypeKindCon kc1 = True
1782 defaultKind :: Kind -> Kind
1783 -- ^ Used when generalising: default kind ? and ?? to *. See "Type#kind_subtyping" for more
1784 -- information on what that means
1786 -- When we generalise, we make generic type variables whose kind is
1787 -- simple (* or *->* etc). So generic type variables (other than
1788 -- built-in constants like 'error') always have simple kinds. This is important;
1791 -- We want f to get type
1792 -- f :: forall (a::*). a -> Bool
1794 -- f :: forall (a::??). a -> Bool
1795 -- because that would allow a call like (f 3#) as well as (f True),
1796 --and the calling conventions differ. This defaulting is done in TcMType.zonkTcTyVarBndr.
1798 | isSubOpenTypeKind k = liftedTypeKind
1799 | isSubArgTypeKind k = liftedTypeKind
1802 isEqPred :: PredType -> Bool
1803 isEqPred (EqPred _ _) = True