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,
39 splitNewTyConApp_maybe, splitNewTyConApp,
41 mkForAllTy, mkForAllTys, splitForAllTy_maybe, splitForAllTys,
42 applyTy, applyTys, isForAllTy, dropForAlls,
51 mkPredTy, mkPredTys, mkFamilyTyConApp,
53 -- ** Common type constructors
56 -- ** Predicates on types
59 -- (Lifting and boxity)
60 isUnLiftedType, isUnboxedTupleType, isAlgType, isClosedAlgType,
61 isPrimitiveType, isStrictType, isStrictPred,
63 -- * Main data types representing Kinds
65 Kind, SimpleKind, KindVar,
67 -- ** Deconstructing Kinds
68 kindFunResult, splitKindFunTys, splitKindFunTysN,
70 -- ** Common Kinds and SuperKinds
71 liftedTypeKind, unliftedTypeKind, openTypeKind,
72 argTypeKind, ubxTupleKind,
74 tySuperKind, coSuperKind,
76 -- ** Common Kind type constructors
77 liftedTypeKindTyCon, openTypeKindTyCon, unliftedTypeKindTyCon,
78 argTypeKindTyCon, ubxTupleKindTyCon,
80 -- ** Predicates on Kinds
81 isLiftedTypeKind, isUnliftedTypeKind, isOpenTypeKind,
82 isUbxTupleKind, isArgTypeKind, isKind, isTySuperKind,
83 isCoSuperKind, isSuperKind, isCoercionKind, isEqPred,
84 mkArrowKind, mkArrowKinds,
86 isSubArgTypeKind, isSubOpenTypeKind, isSubKind, defaultKind, eqKind,
89 -- * Type free variables
90 tyVarsOfType, tyVarsOfTypes, tyVarsOfPred, tyVarsOfTheta,
93 -- * Tidying type related things up for printing
95 tidyOpenType, tidyOpenTypes,
96 tidyTyVarBndr, tidyFreeTyVars,
97 tidyOpenTyVar, tidyOpenTyVars,
98 tidyTopType, tidyPred,
102 coreEqType, tcEqType, tcEqTypes, tcCmpType, tcCmpTypes,
103 tcEqPred, tcEqPredX, tcCmpPred, tcEqTypeX, tcPartOfType, tcPartOfPred,
105 -- * Forcing evaluation of types
108 -- * Other views onto Types
109 coreView, tcView, kindView,
113 -- * Type representation for the code generator
116 typePrimRep, predTypeRep,
118 -- * Main type substitution data types
119 TvSubstEnv, -- Representation widely visible
120 TvSubst(..), -- Representation visible to a few friends
122 -- ** Manipulating type substitutions
123 emptyTvSubstEnv, emptyTvSubst,
125 mkTvSubst, mkOpenTvSubst, zipOpenTvSubst, zipTopTvSubst, mkTopTvSubst, notElemTvSubst,
126 getTvSubstEnv, setTvSubstEnv, getTvInScope, extendTvInScope,
127 extendTvSubst, extendTvSubstList, isInScope, composeTvSubst, zipTyEnv,
130 -- ** Performing substitution on types
131 substTy, substTys, substTyWith, substTheta,
132 substPred, substTyVar, substTyVars, substTyVarBndr, deShadowTy, lookupTyVar,
135 pprType, pprParendType, pprTypeApp, pprTyThingCategory, pprTyThing, pprForAll,
136 pprPred, pprTheta, pprThetaArrow, pprClassPred, pprKind, pprParendKind,
141 #include "HsVersions.h"
143 -- We import the representation and primitive functions from TypeRep.
144 -- Many things are reexported, but not the representation!
165 import Data.Maybe ( isJust )
169 -- $type_classification
170 -- #type_classification#
174 -- [Unboxed] Iff its representation is other than a pointer
175 -- Unboxed types are also unlifted.
177 -- [Lifted] Iff it has bottom as an element.
178 -- Closures always have lifted types: i.e. any
179 -- let-bound identifier in Core must have a lifted
180 -- type. Operationally, a lifted object is one that
182 -- Only lifted types may be unified with a type variable.
184 -- [Algebraic] Iff it is a type with one or more constructors, whether
185 -- declared with @data@ or @newtype@.
186 -- An algebraic type is one that can be deconstructed
187 -- with a case expression. This is /not/ the same as
188 -- lifted types, because we also include unboxed
189 -- tuples in this classification.
191 -- [Data] Iff it is a type declared with @data@, or a boxed tuple.
193 -- [Primitive] Iff it is a built-in type that can't be expressed in Haskell.
195 -- Currently, all primitive types are unlifted, but that's not necessarily
196 -- the case: for example, @Int@ could be primitive.
198 -- Some primitive types are unboxed, such as @Int#@, whereas some are boxed
199 -- but unlifted (such as @ByteArray#@). The only primitive types that we
200 -- classify as algebraic are the unboxed tuples.
202 -- Some examples of type classifications that may make this a bit clearer are:
205 -- Type primitive boxed lifted algebraic
206 -- -----------------------------------------------------------------------------
208 -- ByteArray# Yes Yes No No
209 -- (\# a, b \#) Yes No No Yes
210 -- ( a, b ) No Yes Yes Yes
211 -- [a] No Yes Yes Yes
214 -- $representation_types
215 -- A /source type/ is a type that is a separate type as far as the type checker is
216 -- concerned, but which has a more low-level representation as far as Core-to-Core
217 -- passes and the rest of the back end is concerned. Notably, 'PredTy's are removed
218 -- from the representation type while they do exist in the source types.
220 -- You don't normally have to worry about this, as the utility functions in
221 -- this module will automatically convert a source into a representation type
222 -- if they are spotted, to the best of it's abilities. If you don't want this
223 -- to happen, use the equivalent functions from the "TcType" module.
226 %************************************************************************
230 %************************************************************************
233 {-# INLINE coreView #-}
234 coreView :: Type -> Maybe Type
235 -- ^ In Core, we \"look through\" non-recursive newtypes and 'PredTypes': this
236 -- function tries to obtain a different view of the supplied type given this
238 -- Strips off the /top layer only/ of a type to give
239 -- its underlying representation type.
240 -- Returns Nothing if there is nothing to look through.
242 -- In the case of @newtype@s, it returns one of:
244 -- 1) A vanilla 'TyConApp' (recursive newtype, or non-saturated)
246 -- 2) The newtype representation (otherwise), meaning the
247 -- type written in the RHS of the newtype declaration,
248 -- which may itself be a newtype
250 -- For example, with:
252 -- > newtype R = MkR S
253 -- > newtype S = MkS T
254 -- > newtype T = MkT (T -> T)
256 -- 'expandNewTcApp' on:
258 -- * @R@ gives @Just S@
259 -- * @S@ gives @Just T@
260 -- * @T@ gives @Nothing@ (no expansion)
262 -- By being non-recursive and inlined, this case analysis gets efficiently
263 -- joined onto the case analysis that the caller is already doing
265 | isEqPred p = Nothing
266 | otherwise = Just (predTypeRep p)
267 coreView (TyConApp tc tys) | Just (tenv, rhs, tys') <- coreExpandTyCon_maybe tc tys
268 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
269 -- Its important to use mkAppTys, rather than (foldl AppTy),
270 -- because the function part might well return a
271 -- partially-applied type constructor; indeed, usually will!
276 -----------------------------------------------
277 {-# INLINE tcView #-}
278 tcView :: Type -> Maybe Type
279 -- ^ Similar to 'coreView', but for the type checker, which just looks through synonyms
280 tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- tcExpandTyCon_maybe tc tys
281 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
284 -----------------------------------------------
285 {-# INLINE kindView #-}
286 kindView :: Kind -> Maybe Kind
287 -- ^ Similar to 'coreView' or 'tcView', but works on 'Kind's
289 -- For the moment, we don't even handle synonyms in kinds
294 %************************************************************************
296 \subsection{Constructor-specific functions}
298 %************************************************************************
301 ---------------------------------------------------------------------
305 mkTyVarTy :: TyVar -> Type
308 mkTyVarTys :: [TyVar] -> [Type]
309 mkTyVarTys = map mkTyVarTy -- a common use of mkTyVarTy
311 -- | Attempts to obtain the type variable underlying a 'Type', and panics with the
312 -- given message if this is not a type variable type. See also 'getTyVar_maybe'
313 getTyVar :: String -> Type -> TyVar
314 getTyVar msg ty = case getTyVar_maybe ty of
316 Nothing -> panic ("getTyVar: " ++ msg)
318 isTyVarTy :: Type -> Bool
319 isTyVarTy ty = isJust (getTyVar_maybe ty)
321 -- | Attempts to obtain the type variable underlying a 'Type'
322 getTyVar_maybe :: Type -> Maybe TyVar
323 getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty'
324 getTyVar_maybe (TyVarTy tv) = Just tv
325 getTyVar_maybe _ = Nothing
330 ---------------------------------------------------------------------
333 We need to be pretty careful with AppTy to make sure we obey the
334 invariant that a TyConApp is always visibly so. mkAppTy maintains the
338 -- | Applies a type to another, as in e.g. @k a@
339 mkAppTy :: Type -> Type -> Type
340 mkAppTy orig_ty1 orig_ty2
343 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ [orig_ty2])
344 mk_app _ = AppTy orig_ty1 orig_ty2
345 -- Note that the TyConApp could be an
346 -- under-saturated type synonym. GHC allows that; e.g.
347 -- type Foo k = k a -> k a
349 -- foo :: Foo Id -> Foo Id
351 -- Here Id is partially applied in the type sig for Foo,
352 -- but once the type synonyms are expanded all is well
354 mkAppTys :: Type -> [Type] -> Type
355 mkAppTys orig_ty1 [] = orig_ty1
356 -- This check for an empty list of type arguments
357 -- avoids the needless loss of a type synonym constructor.
358 -- For example: mkAppTys Rational []
359 -- returns to (Ratio Integer), which has needlessly lost
360 -- the Rational part.
361 mkAppTys orig_ty1 orig_tys2
364 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ orig_tys2)
365 -- mkTyConApp: see notes with mkAppTy
366 mk_app _ = foldl AppTy orig_ty1 orig_tys2
369 splitAppTy_maybe :: Type -> Maybe (Type, Type)
370 -- ^ Attempt to take a type application apart, whether it is a
371 -- function, type constructor, or plain type application. Note
372 -- that type family applications are NEVER unsaturated by this!
373 splitAppTy_maybe ty | Just ty' <- coreView ty
374 = splitAppTy_maybe ty'
375 splitAppTy_maybe ty = repSplitAppTy_maybe ty
378 repSplitAppTy_maybe :: Type -> Maybe (Type,Type)
379 -- ^ Does the AppTy split as in 'splitAppTy_maybe', but assumes that
380 -- any Core view stuff is already done
381 repSplitAppTy_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
382 repSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
383 repSplitAppTy_maybe (TyConApp tc tys)
384 | not (isOpenSynTyCon tc) || length tys > tyConArity tc
385 = case snocView tys of -- never create unsaturated type family apps
386 Just (tys', ty') -> Just (TyConApp tc tys', ty')
388 repSplitAppTy_maybe _other = Nothing
390 splitAppTy :: Type -> (Type, Type)
391 -- ^ Attempts to take a type application apart, as in 'splitAppTy_maybe',
392 -- and panics if this is not possible
393 splitAppTy ty = case splitAppTy_maybe ty of
395 Nothing -> panic "splitAppTy"
398 splitAppTys :: Type -> (Type, [Type])
399 -- ^ Recursively splits a type as far as is possible, leaving a residual
400 -- type being applied to and the type arguments applied to it. Never fails,
401 -- even if that means returning an empty list of type applications.
402 splitAppTys ty = split ty ty []
404 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
405 split _ (AppTy ty arg) args = split ty ty (arg:args)
406 split _ (TyConApp tc tc_args) args
407 = let -- keep type families saturated
408 n | isOpenSynTyCon tc = tyConArity tc
410 (tc_args1, tc_args2) = splitAt n tc_args
412 (TyConApp tc tc_args1, tc_args2 ++ args)
413 split _ (FunTy ty1 ty2) args = ASSERT( null args )
414 (TyConApp funTyCon [], [ty1,ty2])
415 split orig_ty _ args = (orig_ty, args)
420 ---------------------------------------------------------------------
425 mkFunTy :: Type -> Type -> Type
426 -- ^ Creates a function type from the given argument and result type
427 mkFunTy (PredTy (EqPred ty1 ty2)) res = mkForAllTy (mkWildCoVar (PredTy (EqPred ty1 ty2))) res
428 mkFunTy arg res = FunTy arg res
430 mkFunTys :: [Type] -> Type -> Type
431 mkFunTys tys ty = foldr mkFunTy ty tys
433 isFunTy :: Type -> Bool
434 isFunTy ty = isJust (splitFunTy_maybe ty)
436 splitFunTy :: Type -> (Type, Type)
437 -- ^ Attempts to extract the argument and result types from a type, and
438 -- panics if that is not possible. See also 'splitFunTy_maybe'
439 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
440 splitFunTy (FunTy arg res) = (arg, res)
441 splitFunTy other = pprPanic "splitFunTy" (ppr other)
443 splitFunTy_maybe :: Type -> Maybe (Type, Type)
444 -- ^ Attempts to extract the argument and result types from a type
445 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
446 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
447 splitFunTy_maybe _ = Nothing
449 splitFunTys :: Type -> ([Type], Type)
450 splitFunTys ty = split [] ty ty
452 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
453 split args _ (FunTy arg res) = split (arg:args) res res
454 split args orig_ty _ = (reverse args, orig_ty)
456 splitFunTysN :: Int -> Type -> ([Type], Type)
457 -- ^ Split off exactly the given number argument types, and panics if that is not possible
458 splitFunTysN 0 ty = ([], ty)
459 splitFunTysN n ty = case splitFunTy ty of { (arg, res) ->
460 case splitFunTysN (n-1) res of { (args, res) ->
463 -- | Splits off argument types from the given type and associating
464 -- them with the things in the input list from left to right. The
465 -- final result type is returned, along with the resulting pairs of
466 -- objects and types, albeit with the list of pairs in reverse order.
467 -- Panics if there are not enough argument types for the input list.
468 zipFunTys :: Outputable a => [a] -> Type -> ([(a, Type)], Type)
469 zipFunTys orig_xs orig_ty = split [] orig_xs orig_ty orig_ty
471 split acc [] nty _ = (reverse acc, nty)
473 | Just ty' <- coreView ty = split acc xs nty ty'
474 split acc (x:xs) _ (FunTy arg res) = split ((x,arg):acc) xs res res
475 split _ _ _ _ = pprPanic "zipFunTys" (ppr orig_xs <+> ppr orig_ty)
477 funResultTy :: Type -> Type
478 -- ^ Extract the function result type and panic if that is not possible
479 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
480 funResultTy (FunTy _arg res) = res
481 funResultTy ty = pprPanic "funResultTy" (ppr ty)
483 funArgTy :: Type -> Type
484 -- ^ Extract the function argument type and panic if that is not possible
485 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
486 funArgTy (FunTy arg _res) = arg
487 funArgTy ty = pprPanic "funArgTy" (ppr ty)
490 ---------------------------------------------------------------------
495 -- | A key function: builds a 'TyConApp' or 'FunTy' as apppropriate to its arguments.
496 -- Applies its arguments to the constructor from left to right
497 mkTyConApp :: TyCon -> [Type] -> Type
499 | isFunTyCon tycon, [ty1,ty2] <- tys
505 -- | Create the plain type constructor type which has been applied to no type arguments at all.
506 mkTyConTy :: TyCon -> Type
507 mkTyConTy tycon = mkTyConApp tycon []
509 -- splitTyConApp "looks through" synonyms, because they don't
510 -- mean a distinct type, but all other type-constructor applications
511 -- including functions are returned as Just ..
513 -- | The same as @fst . splitTyConApp@
514 tyConAppTyCon :: Type -> TyCon
515 tyConAppTyCon ty = fst (splitTyConApp ty)
517 -- | The same as @snd . splitTyConApp@
518 tyConAppArgs :: Type -> [Type]
519 tyConAppArgs ty = snd (splitTyConApp ty)
521 -- | Attempts to tease a type apart into a type constructor and the application
522 -- of a number of arguments to that constructor. Panics if that is not possible.
523 -- See also 'splitTyConApp_maybe'
524 splitTyConApp :: Type -> (TyCon, [Type])
525 splitTyConApp ty = case splitTyConApp_maybe ty of
527 Nothing -> pprPanic "splitTyConApp" (ppr ty)
529 -- | Attempts to tease a type apart into a type constructor and the application
530 -- of a number of arguments to that constructor
531 splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
532 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
533 splitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
534 splitTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
535 splitTyConApp_maybe _ = Nothing
537 -- | Sometimes we do NOT want to look through a @newtype@. When case matching
538 -- on a newtype we want a convenient way to access the arguments of a @newtype@
539 -- constructor so as to properly form a coercion, and so we use 'splitNewTyConApp'
540 -- instead of 'splitTyConApp_maybe'
541 splitNewTyConApp :: Type -> (TyCon, [Type])
542 splitNewTyConApp ty = case splitNewTyConApp_maybe ty of
544 Nothing -> pprPanic "splitNewTyConApp" (ppr ty)
545 splitNewTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
546 splitNewTyConApp_maybe ty | Just ty' <- tcView ty = splitNewTyConApp_maybe ty'
547 splitNewTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
548 splitNewTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
549 splitNewTyConApp_maybe _ = Nothing
551 newTyConInstRhs :: TyCon -> [Type] -> Type
552 -- ^ Unwrap one 'layer' of newtype on a type constructor and it's arguments, using an
553 -- eta-reduced version of the @newtype@ if possible
554 newTyConInstRhs tycon tys
555 = ASSERT2( equalLength tvs tys1, ppr tycon $$ ppr tys $$ ppr tvs )
556 mkAppTys (substTyWith tvs tys1 ty) tys2
558 (tvs, ty) = newTyConEtadRhs tycon
559 (tys1, tys2) = splitAtList tvs tys
563 ---------------------------------------------------------------------
567 Notes on type synonyms
568 ~~~~~~~~~~~~~~~~~~~~~~
569 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
570 to return type synonyms whereever possible. Thus
575 splitFunTys (a -> Foo a) = ([a], Foo a)
578 The reason is that we then get better (shorter) type signatures in
579 interfaces. Notably this plays a role in tcTySigs in TcBinds.lhs.
582 Note [Expanding newtypes]
583 ~~~~~~~~~~~~~~~~~~~~~~~~~
584 When expanding a type to expose a data-type constructor, we need to be
585 careful about newtypes, lest we fall into an infinite loop. Here are
588 newtype Id x = MkId x
589 newtype Fix f = MkFix (f (Fix f))
590 newtype T = MkT (T -> T)
593 --------------------------
595 Fix Maybe Maybe (Fix Maybe)
599 Notice that we can expand T, even though it's recursive.
600 And we can expand Id (Id Int), even though the Id shows up
601 twice at the outer level.
603 So, when expanding, we keep track of when we've seen a recursive
604 newtype at outermost level; and bale out if we see it again.
619 -- 4. Usage annotations
621 -- 5. All newtypes, including recursive ones, but not newtype families
623 -- It's useful in the back end of the compiler.
624 repType :: Type -> Type
625 -- Only applied to types of kind *; hence tycons are saturated
629 go :: [TyCon] -> Type -> Type
630 go rec_nts ty | Just ty' <- coreView ty -- Expand synonyms
633 go rec_nts (ForAllTy _ ty) -- Look through foralls
636 go rec_nts ty@(TyConApp tc tys) -- Expand newtypes
637 | Just _co_con <- newTyConCo_maybe tc -- See Note [Expanding newtypes]
638 = if tc `elem` rec_nts -- in Type.lhs
640 else go rec_nts' nt_rhs
642 nt_rhs = newTyConInstRhs tc tys
643 rec_nts' | isRecursiveTyCon tc = tc:rec_nts
644 | otherwise = rec_nts
649 -- ToDo: this could be moved to the code generator, using splitTyConApp instead
650 -- of inspecting the type directly.
652 -- | Discovers the primitive representation of a more abstract 'Type'
653 typePrimRep :: Type -> PrimRep
654 typePrimRep ty = case repType ty of
655 TyConApp tc _ -> tyConPrimRep tc
657 AppTy _ _ -> PtrRep -- See note below
659 _ -> pprPanic "typePrimRep" (ppr ty)
660 -- Types of the form 'f a' must be of kind *, not *#, so
661 -- we are guaranteed that they are represented by pointers.
662 -- The reason is that f must have kind *->*, not *->*#, because
663 -- (we claim) there is no way to constrain f's kind any other
668 ---------------------------------------------------------------------
673 mkForAllTy :: TyVar -> Type -> Type
675 = mkForAllTys [tyvar] ty
677 -- | Wraps foralls over the type using the provided 'TyVar's from left to right
678 mkForAllTys :: [TyVar] -> Type -> Type
679 mkForAllTys tyvars ty = foldr ForAllTy ty tyvars
681 isForAllTy :: Type -> Bool
682 isForAllTy (ForAllTy _ _) = True
685 -- | Attempts to take a forall type apart, returning the bound type variable
686 -- and the remainder of the type
687 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
688 splitForAllTy_maybe ty = splitFAT_m ty
690 splitFAT_m ty | Just ty' <- coreView ty = splitFAT_m ty'
691 splitFAT_m (ForAllTy tyvar ty) = Just(tyvar, ty)
692 splitFAT_m _ = Nothing
694 -- | Attempts to take a forall type apart, returning all the immediate such bound
695 -- type variables and the remainder of the type. Always suceeds, even if that means
696 -- returning an empty list of 'TyVar's
697 splitForAllTys :: Type -> ([TyVar], Type)
698 splitForAllTys ty = split ty ty []
700 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
701 split _ (ForAllTy tv ty) tvs = split ty ty (tv:tvs)
702 split orig_ty _ tvs = (reverse tvs, orig_ty)
704 -- | Equivalent to @snd . splitForAllTys@
705 dropForAlls :: Type -> Type
706 dropForAlls ty = snd (splitForAllTys ty)
709 -- (mkPiType now in CoreUtils)
715 -- | Instantiate a forall type with one or more type arguments.
716 -- Used when we have a polymorphic function applied to type args:
720 -- We use @applyTys type-of-f [t1,t2]@ to compute the type of the expression.
721 -- Panics if no application is possible.
722 applyTy :: Type -> Type -> Type
723 applyTy ty arg | Just ty' <- coreView ty = applyTy ty' arg
724 applyTy (ForAllTy tv ty) arg = substTyWith [tv] [arg] ty
725 applyTy _ _ = panic "applyTy"
727 applyTys :: Type -> [Type] -> Type
728 -- ^ This function is interesting because:
730 -- 1. The function may have more for-alls than there are args
732 -- 2. Less obviously, it may have fewer for-alls
734 -- For case 2. think of:
736 -- > applyTys (forall a.a) [forall b.b, Int]
738 -- This really can happen, via dressing up polymorphic types with newtype
739 -- clothing. Here's an example:
741 -- > newtype R = R (forall a. a->a)
742 -- > foo = case undefined :: R of
745 applyTys orig_fun_ty [] = orig_fun_ty
746 applyTys orig_fun_ty arg_tys
747 | n_tvs == n_args -- The vastly common case
748 = substTyWith tvs arg_tys rho_ty
749 | n_tvs > n_args -- Too many for-alls
750 = substTyWith (take n_args tvs) arg_tys
751 (mkForAllTys (drop n_args tvs) rho_ty)
752 | otherwise -- Too many type args
753 = ASSERT2( n_tvs > 0, ppr orig_fun_ty ) -- Zero case gives infnite loop!
754 applyTys (substTyWith tvs (take n_tvs arg_tys) rho_ty)
757 (tvs, rho_ty) = splitForAllTys orig_fun_ty
759 n_args = length arg_tys
763 %************************************************************************
765 \subsection{Source types}
767 %************************************************************************
769 Source types are always lifted.
771 The key function is predTypeRep which gives the representation of a source type:
774 mkPredTy :: PredType -> Type
775 mkPredTy pred = PredTy pred
777 mkPredTys :: ThetaType -> [Type]
778 mkPredTys preds = map PredTy preds
780 predTypeRep :: PredType -> Type
781 -- ^ Convert a 'PredType' to its representation type. However, it unwraps
782 -- only the outermost level; for example, the result might be a newtype application
783 predTypeRep (IParam _ ty) = ty
784 predTypeRep (ClassP clas tys) = mkTyConApp (classTyCon clas) tys
785 -- Result might be a newtype application, but the consumer will
786 -- look through that too if necessary
787 predTypeRep (EqPred ty1 ty2) = pprPanic "predTypeRep" (ppr (EqPred ty1 ty2))
789 mkFamilyTyConApp :: TyCon -> [Type] -> Type
790 -- ^ Given a family instance TyCon and its arg types, return the
791 -- corresponding family type. E.g:
794 -- > data instance T (Maybe b) = MkT b
796 -- Where the instance tycon is :RTL, so:
798 -- > mkFamilyTyConApp :RTL Int = T (Maybe Int)
799 mkFamilyTyConApp tc tys
800 | Just (fam_tc, fam_tys) <- tyConFamInst_maybe tc
801 , let fam_subst = zipTopTvSubst (tyConTyVars tc) tys
802 = mkTyConApp fam_tc (substTys fam_subst fam_tys)
806 -- | Pretty prints a 'TyCon', using the family instance in case of a
807 -- representation tycon. For example:
809 -- > data T [a] = ...
811 -- In that case we want to print @T [a]@, where @T@ is the family 'TyCon'
812 pprSourceTyCon :: TyCon -> SDoc
814 | Just (fam_tc, tys) <- tyConFamInst_maybe tycon
815 = ppr $ fam_tc `TyConApp` tys -- can't be FunTyCon
821 %************************************************************************
823 \subsection{Kinds and free variables}
825 %************************************************************************
827 ---------------------------------------------------------------------
828 Finding the kind of a type
829 ~~~~~~~~~~~~~~~~~~~~~~~~~~
831 typeKind :: Type -> Kind
832 typeKind (TyConApp tycon tys) = ASSERT( not (isCoercionTyCon tycon) )
833 -- We should be looking for the coercion kind,
835 foldr (\_ k -> kindFunResult k) (tyConKind tycon) tys
836 typeKind (PredTy pred) = predKind pred
837 typeKind (AppTy fun _) = kindFunResult (typeKind fun)
838 typeKind (ForAllTy _ ty) = typeKind ty
839 typeKind (TyVarTy tyvar) = tyVarKind tyvar
840 typeKind (FunTy _arg res)
841 -- Hack alert. The kind of (Int -> Int#) is liftedTypeKind (*),
842 -- not unliftedTypKind (#)
843 -- The only things that can be after a function arrow are
844 -- (a) types (of kind openTypeKind or its sub-kinds)
845 -- (b) kinds (of super-kind TY) (e.g. * -> (* -> *))
846 | isTySuperKind k = k
847 | otherwise = ASSERT( isSubOpenTypeKind k) liftedTypeKind
851 predKind :: PredType -> Kind
852 predKind (EqPred {}) = coSuperKind -- A coercion kind!
853 predKind (ClassP {}) = liftedTypeKind -- Class and implicitPredicates are
854 predKind (IParam {}) = liftedTypeKind -- always represented by lifted types
858 ---------------------------------------------------------------------
859 Free variables of a type
860 ~~~~~~~~~~~~~~~~~~~~~~~~
862 tyVarsOfType :: Type -> TyVarSet
863 -- ^ NB: for type synonyms tyVarsOfType does /not/ expand the synonym
864 tyVarsOfType (TyVarTy tv) = unitVarSet tv
865 tyVarsOfType (TyConApp _ tys) = tyVarsOfTypes tys
866 tyVarsOfType (PredTy sty) = tyVarsOfPred sty
867 tyVarsOfType (FunTy arg res) = tyVarsOfType arg `unionVarSet` tyVarsOfType res
868 tyVarsOfType (AppTy fun arg) = tyVarsOfType fun `unionVarSet` tyVarsOfType arg
869 tyVarsOfType (ForAllTy tyvar ty) = delVarSet (tyVarsOfType ty) tyvar
871 tyVarsOfTypes :: [Type] -> TyVarSet
872 tyVarsOfTypes tys = foldr (unionVarSet.tyVarsOfType) emptyVarSet tys
874 tyVarsOfPred :: PredType -> TyVarSet
875 tyVarsOfPred (IParam _ ty) = tyVarsOfType ty
876 tyVarsOfPred (ClassP _ tys) = tyVarsOfTypes tys
877 tyVarsOfPred (EqPred ty1 ty2) = tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2
879 tyVarsOfTheta :: ThetaType -> TyVarSet
880 tyVarsOfTheta = foldr (unionVarSet . tyVarsOfPred) emptyVarSet
884 %************************************************************************
886 \subsection{Type families}
888 %************************************************************************
891 -- | Finds type family instances occuring in a type after expanding synonyms.
892 tyFamInsts :: Type -> [(TyCon, [Type])]
894 | Just exp_ty <- tcView ty = tyFamInsts exp_ty
895 tyFamInsts (TyVarTy _) = []
896 tyFamInsts (TyConApp tc tys)
897 | isOpenSynTyCon tc = [(tc, tys)]
898 | otherwise = concat (map tyFamInsts tys)
899 tyFamInsts (FunTy ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
900 tyFamInsts (AppTy ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
901 tyFamInsts (ForAllTy _ ty) = tyFamInsts ty
905 %************************************************************************
907 \subsection{TidyType}
909 %************************************************************************
912 -- | This tidies up a type for printing in an error message, or in
913 -- an interface file.
915 -- It doesn't change the uniques at all, just the print names.
916 tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
917 tidyTyVarBndr env@(tidy_env, subst) tyvar
918 = case tidyOccName tidy_env (getOccName name) of
919 (tidy', occ') -> ((tidy', subst'), tyvar'')
921 subst' = extendVarEnv subst tyvar tyvar''
922 tyvar' = setTyVarName tyvar name'
923 name' = tidyNameOcc name occ'
924 -- Don't forget to tidy the kind for coercions!
925 tyvar'' | isCoVar tyvar = setTyVarKind tyvar' kind'
927 kind' = tidyType env (tyVarKind tyvar)
929 name = tyVarName tyvar
931 tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv
932 -- ^ Add the free 'TyVar's to the env in tidy form,
933 -- so that we can tidy the type they are free in
934 tidyFreeTyVars env tyvars = fst (tidyOpenTyVars env (varSetElems tyvars))
936 tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
937 tidyOpenTyVars env tyvars = mapAccumL tidyOpenTyVar env tyvars
939 tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
940 -- ^ Treat a new 'TyVar' as a binder, and give it a fresh tidy name
941 -- using the environment if one has not already been allocated. See
942 -- also 'tidyTyVarBndr'
943 tidyOpenTyVar env@(_, subst) tyvar
944 = case lookupVarEnv subst tyvar of
945 Just tyvar' -> (env, tyvar') -- Already substituted
946 Nothing -> tidyTyVarBndr env tyvar -- Treat it as a binder
948 tidyType :: TidyEnv -> Type -> Type
949 tidyType env@(_, subst) ty
952 go (TyVarTy tv) = case lookupVarEnv subst tv of
953 Nothing -> TyVarTy tv
954 Just tv' -> TyVarTy tv'
955 go (TyConApp tycon tys) = let args = map go tys
956 in args `seqList` TyConApp tycon args
957 go (PredTy sty) = PredTy (tidyPred env sty)
958 go (AppTy fun arg) = (AppTy $! (go fun)) $! (go arg)
959 go (FunTy fun arg) = (FunTy $! (go fun)) $! (go arg)
960 go (ForAllTy tv ty) = ForAllTy tvp $! (tidyType envp ty)
962 (envp, tvp) = tidyTyVarBndr env tv
964 tidyTypes :: TidyEnv -> [Type] -> [Type]
965 tidyTypes env tys = map (tidyType env) tys
967 tidyPred :: TidyEnv -> PredType -> PredType
968 tidyPred env (IParam n ty) = IParam n (tidyType env ty)
969 tidyPred env (ClassP clas tys) = ClassP clas (tidyTypes env tys)
970 tidyPred env (EqPred ty1 ty2) = EqPred (tidyType env ty1) (tidyType env ty2)
975 -- | Grabs the free type variables, tidies them
976 -- and then uses 'tidyType' to work over the type itself
977 tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
979 = (env', tidyType env' ty)
981 env' = tidyFreeTyVars env (tyVarsOfType ty)
983 tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
984 tidyOpenTypes env tys = mapAccumL tidyOpenType env tys
986 -- | Calls 'tidyType' on a top-level type (i.e. with an empty tidying environment)
987 tidyTopType :: Type -> Type
988 tidyTopType ty = tidyType emptyTidyEnv ty
993 tidyKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
994 tidyKind env k = tidyOpenType env k
999 %************************************************************************
1001 \subsection{Liftedness}
1003 %************************************************************************
1006 -- | See "Type#type_classification" for what an unlifted type is
1007 isUnLiftedType :: Type -> Bool
1008 -- isUnLiftedType returns True for forall'd unlifted types:
1009 -- x :: forall a. Int#
1010 -- I found bindings like these were getting floated to the top level.
1011 -- They are pretty bogus types, mind you. It would be better never to
1014 isUnLiftedType ty | Just ty' <- coreView ty = isUnLiftedType ty'
1015 isUnLiftedType (ForAllTy _ ty) = isUnLiftedType ty
1016 isUnLiftedType (TyConApp tc _) = isUnLiftedTyCon tc
1017 isUnLiftedType _ = False
1019 isUnboxedTupleType :: Type -> Bool
1020 isUnboxedTupleType ty = case splitTyConApp_maybe ty of
1021 Just (tc, _ty_args) -> isUnboxedTupleTyCon tc
1024 -- | See "Type#type_classification" for what an algebraic type is.
1025 -- Should only be applied to /types/, as opposed to e.g. partially
1026 -- saturated type constructors
1027 isAlgType :: Type -> Bool
1029 = case splitTyConApp_maybe ty of
1030 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
1034 -- | See "Type#type_classification" for what an algebraic type is.
1035 -- Should only be applied to /types/, as opposed to e.g. partially
1036 -- saturated type constructors. Closed type constructors are those
1037 -- with a fixed right hand side, as opposed to e.g. associated types
1038 isClosedAlgType :: Type -> Bool
1040 = case splitTyConApp_maybe ty of
1041 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
1042 isAlgTyCon tc && not (isOpenTyCon tc)
1047 -- | Computes whether an argument (or let right hand side) should
1048 -- be computed strictly or lazily, based only on its type.
1049 -- Works just like 'isUnLiftedType', except that it has a special case
1050 -- for dictionaries (i.e. does not work purely on representation types)
1052 -- Since it takes account of class 'PredType's, you might think
1053 -- this function should be in 'TcType', but 'isStrictType' is used by 'DataCon',
1054 -- which is below 'TcType' in the hierarchy, so it's convenient to put it here.
1055 isStrictType :: Type -> Bool
1056 isStrictType (PredTy pred) = isStrictPred pred
1057 isStrictType ty | Just ty' <- coreView ty = isStrictType ty'
1058 isStrictType (ForAllTy _ ty) = isStrictType ty
1059 isStrictType (TyConApp tc _) = isUnLiftedTyCon tc
1060 isStrictType _ = False
1062 -- | We may be strict in dictionary types, but only if it
1063 -- has more than one component.
1065 -- (Being strict in a single-component dictionary risks
1066 -- poking the dictionary component, which is wrong.)
1067 isStrictPred :: PredType -> Bool
1068 isStrictPred (ClassP clas _) = opt_DictsStrict && not (isNewTyCon (classTyCon clas))
1069 isStrictPred _ = False
1073 isPrimitiveType :: Type -> Bool
1074 -- ^ Returns true of types that are opaque to Haskell.
1075 -- Most of these are unlifted, but now that we interact with .NET, we
1076 -- may have primtive (foreign-imported) types that are lifted
1077 isPrimitiveType ty = case splitTyConApp_maybe ty of
1078 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
1084 %************************************************************************
1086 \subsection{Sequencing on types}
1088 %************************************************************************
1091 seqType :: Type -> ()
1092 seqType (TyVarTy tv) = tv `seq` ()
1093 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
1094 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
1095 seqType (PredTy p) = seqPred p
1096 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
1097 seqType (ForAllTy tv ty) = tv `seq` seqType ty
1099 seqTypes :: [Type] -> ()
1101 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
1103 seqPred :: PredType -> ()
1104 seqPred (ClassP c tys) = c `seq` seqTypes tys
1105 seqPred (IParam n ty) = n `seq` seqType ty
1106 seqPred (EqPred ty1 ty2) = seqType ty1 `seq` seqType ty2
1110 %************************************************************************
1112 Equality for Core types
1113 (We don't use instances so that we know where it happens)
1115 %************************************************************************
1117 Note that eqType works right even for partial applications of newtypes.
1118 See Note [Newtype eta] in TyCon.lhs
1121 -- | Type equality test for Core types (i.e. ignores predicate-types, synonyms etc.)
1122 coreEqType :: Type -> Type -> Bool
1126 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
1128 eq env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 == rnOccR env tv2
1129 eq env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = eq (rnBndr2 env tv1 tv2) t1 t2
1130 eq env (AppTy s1 t1) (AppTy s2 t2) = eq env s1 s2 && eq env t1 t2
1131 eq env (FunTy s1 t1) (FunTy s2 t2) = eq env s1 s2 && eq env t1 t2
1132 eq env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
1133 | tc1 == tc2, all2 (eq env) tys1 tys2 = True
1134 -- The lengths should be equal because
1135 -- the two types have the same kind
1136 -- NB: if the type constructors differ that does not
1137 -- necessarily mean that the types aren't equal
1138 -- (synonyms, newtypes)
1139 -- Even if the type constructors are the same, but the arguments
1140 -- differ, the two types could be the same (e.g. if the arg is just
1141 -- ignored in the RHS). In both these cases we fall through to an
1142 -- attempt to expand one side or the other.
1144 -- Now deal with newtypes, synonyms, pred-tys
1145 eq env t1 t2 | Just t1' <- coreView t1 = eq env t1' t2
1146 | Just t2' <- coreView t2 = eq env t1 t2'
1148 -- Fall through case; not equal!
1153 %************************************************************************
1155 Comparision for source types
1156 (We don't use instances so that we know where it happens)
1158 %************************************************************************
1161 tcEqType :: Type -> Type -> Bool
1162 -- ^ Type equality on source types. Does not look through @newtypes@ or 'PredType's
1163 tcEqType t1 t2 = isEqual $ cmpType t1 t2
1165 tcEqTypes :: [Type] -> [Type] -> Bool
1166 tcEqTypes tys1 tys2 = isEqual $ cmpTypes tys1 tys2
1168 tcCmpType :: Type -> Type -> Ordering
1169 -- ^ Type ordering on source types. Does not look through @newtypes@ or 'PredType's
1170 tcCmpType t1 t2 = cmpType t1 t2
1172 tcCmpTypes :: [Type] -> [Type] -> Ordering
1173 tcCmpTypes tys1 tys2 = cmpTypes tys1 tys2
1175 tcEqPred :: PredType -> PredType -> Bool
1176 tcEqPred p1 p2 = isEqual $ cmpPred p1 p2
1178 tcEqPredX :: RnEnv2 -> PredType -> PredType -> Bool
1179 tcEqPredX env p1 p2 = isEqual $ cmpPredX env p1 p2
1181 tcCmpPred :: PredType -> PredType -> Ordering
1182 tcCmpPred p1 p2 = cmpPred p1 p2
1184 tcEqTypeX :: RnEnv2 -> Type -> Type -> Bool
1185 tcEqTypeX env t1 t2 = isEqual $ cmpTypeX env t1 t2
1189 -- | Checks whether the second argument is a subterm of the first. (We don't care
1190 -- about binders, as we are only interested in syntactic subterms.)
1191 tcPartOfType :: Type -> Type -> Bool
1193 | tcEqType t1 t2 = True
1195 | Just t2' <- tcView t2 = tcPartOfType t1 t2'
1196 tcPartOfType _ (TyVarTy _) = False
1197 tcPartOfType t1 (ForAllTy _ t2) = tcPartOfType t1 t2
1198 tcPartOfType t1 (AppTy s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1199 tcPartOfType t1 (FunTy s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1200 tcPartOfType t1 (PredTy p2) = tcPartOfPred t1 p2
1201 tcPartOfType t1 (TyConApp _ ts) = any (tcPartOfType t1) ts
1203 tcPartOfPred :: Type -> PredType -> Bool
1204 tcPartOfPred t1 (IParam _ t2) = tcPartOfType t1 t2
1205 tcPartOfPred t1 (ClassP _ ts) = any (tcPartOfType t1) ts
1206 tcPartOfPred t1 (EqPred s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1209 Now here comes the real worker
1212 cmpType :: Type -> Type -> Ordering
1213 cmpType t1 t2 = cmpTypeX rn_env t1 t2
1215 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
1217 cmpTypes :: [Type] -> [Type] -> Ordering
1218 cmpTypes ts1 ts2 = cmpTypesX rn_env ts1 ts2
1220 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfTypes ts1 `unionVarSet` tyVarsOfTypes ts2))
1222 cmpPred :: PredType -> PredType -> Ordering
1223 cmpPred p1 p2 = cmpPredX rn_env p1 p2
1225 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfPred p1 `unionVarSet` tyVarsOfPred p2))
1227 cmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
1228 cmpTypeX env t1 t2 | Just t1' <- tcView t1 = cmpTypeX env t1' t2
1229 | Just t2' <- tcView t2 = cmpTypeX env t1 t2'
1231 cmpTypeX env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 `compare` rnOccR env tv2
1232 cmpTypeX env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = cmpTypeX (rnBndr2 env tv1 tv2) t1 t2
1233 cmpTypeX env (AppTy s1 t1) (AppTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1234 cmpTypeX env (FunTy s1 t1) (FunTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1235 cmpTypeX env (PredTy p1) (PredTy p2) = cmpPredX env p1 p2
1236 cmpTypeX env (TyConApp tc1 tys1) (TyConApp tc2 tys2) = (tc1 `compare` tc2) `thenCmp` cmpTypesX env tys1 tys2
1238 -- Deal with the rest: TyVarTy < AppTy < FunTy < TyConApp < ForAllTy < PredTy
1239 cmpTypeX _ (AppTy _ _) (TyVarTy _) = GT
1241 cmpTypeX _ (FunTy _ _) (TyVarTy _) = GT
1242 cmpTypeX _ (FunTy _ _) (AppTy _ _) = GT
1244 cmpTypeX _ (TyConApp _ _) (TyVarTy _) = GT
1245 cmpTypeX _ (TyConApp _ _) (AppTy _ _) = GT
1246 cmpTypeX _ (TyConApp _ _) (FunTy _ _) = GT
1248 cmpTypeX _ (ForAllTy _ _) (TyVarTy _) = GT
1249 cmpTypeX _ (ForAllTy _ _) (AppTy _ _) = GT
1250 cmpTypeX _ (ForAllTy _ _) (FunTy _ _) = GT
1251 cmpTypeX _ (ForAllTy _ _) (TyConApp _ _) = GT
1253 cmpTypeX _ (PredTy _) _ = GT
1258 cmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
1259 cmpTypesX _ [] [] = EQ
1260 cmpTypesX env (t1:tys1) (t2:tys2) = cmpTypeX env t1 t2 `thenCmp` cmpTypesX env tys1 tys2
1261 cmpTypesX _ [] _ = LT
1262 cmpTypesX _ _ [] = GT
1265 cmpPredX :: RnEnv2 -> PredType -> PredType -> Ordering
1266 cmpPredX env (IParam n1 ty1) (IParam n2 ty2) = (n1 `compare` n2) `thenCmp` cmpTypeX env ty1 ty2
1267 -- Compare names only for implicit parameters
1268 -- This comparison is used exclusively (I believe)
1269 -- for the Avails finite map built in TcSimplify
1270 -- If the types differ we keep them distinct so that we see
1271 -- a distinct pair to run improvement on
1272 cmpPredX env (ClassP c1 tys1) (ClassP c2 tys2) = (c1 `compare` c2) `thenCmp` (cmpTypesX env tys1 tys2)
1273 cmpPredX env (EqPred ty1 ty2) (EqPred ty1' ty2') = (cmpTypeX env ty1 ty1') `thenCmp` (cmpTypeX env ty2 ty2')
1275 -- Constructor order: IParam < ClassP < EqPred
1276 cmpPredX _ (IParam {}) _ = LT
1277 cmpPredX _ (ClassP {}) (IParam {}) = GT
1278 cmpPredX _ (ClassP {}) (EqPred {}) = LT
1279 cmpPredX _ (EqPred {}) _ = GT
1282 PredTypes are used as a FM key in TcSimplify,
1283 so we take the easy path and make them an instance of Ord
1286 instance Eq PredType where { (==) = tcEqPred }
1287 instance Ord PredType where { compare = tcCmpPred }
1291 %************************************************************************
1295 %************************************************************************
1298 -- | Type substitution
1300 -- #tvsubst_invariant#
1301 -- The following invariants must hold of a 'TvSubst':
1303 -- 1. The in-scope set is needed /only/ to
1304 -- guide the generation of fresh uniques
1306 -- 2. In particular, the /kind/ of the type variables in
1307 -- the in-scope set is not relevant
1309 -- 3. The substition is only applied ONCE! This is because
1310 -- in general such application will not reached a fixed point.
1312 = TvSubst InScopeSet -- The in-scope type variables
1313 TvSubstEnv -- The substitution itself
1314 -- See Note [Apply Once]
1315 -- and Note [Extending the TvSubstEnv]
1317 {- ----------------------------------------------------------
1321 We use TvSubsts to instantiate things, and we might instantiate
1325 So the substition might go [a->b, b->a]. A similar situation arises in Core
1326 when we find a beta redex like
1327 (/\ a /\ b -> e) b a
1328 Then we also end up with a substition that permutes type variables. Other
1329 variations happen to; for example [a -> (a, b)].
1331 ***************************************************
1332 *** So a TvSubst must be applied precisely once ***
1333 ***************************************************
1335 A TvSubst is not idempotent, but, unlike the non-idempotent substitution
1336 we use during unifications, it must not be repeatedly applied.
1338 Note [Extending the TvSubst]
1339 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1340 See #tvsubst_invariant# for the invariants that must hold.
1342 This invariant allows a short-cut when the TvSubstEnv is empty:
1343 if the TvSubstEnv is empty --- i.e. (isEmptyTvSubt subst) holds ---
1344 then (substTy subst ty) does nothing.
1346 For example, consider:
1347 (/\a. /\b:(a~Int). ...b..) Int
1348 We substitute Int for 'a'. The Unique of 'b' does not change, but
1349 nevertheless we add 'b' to the TvSubstEnv, because b's type does change
1351 This invariant has several crucial consequences:
1353 * In substTyVarBndr, we need extend the TvSubstEnv
1354 - if the unique has changed
1355 - or if the kind has changed
1357 * In substTyVar, we do not need to consult the in-scope set;
1358 the TvSubstEnv is enough
1360 * In substTy, substTheta, we can short-circuit when the TvSubstEnv is empty
1363 -------------------------------------------------------------- -}
1365 -- | A substitition of 'Type's for 'TyVar's
1366 type TvSubstEnv = TyVarEnv Type
1367 -- A TvSubstEnv is used both inside a TvSubst (with the apply-once
1368 -- invariant discussed in Note [Apply Once]), and also independently
1369 -- in the middle of matching, and unification (see Types.Unify)
1370 -- So you have to look at the context to know if it's idempotent or
1371 -- apply-once or whatever
1373 emptyTvSubstEnv :: TvSubstEnv
1374 emptyTvSubstEnv = emptyVarEnv
1376 composeTvSubst :: InScopeSet -> TvSubstEnv -> TvSubstEnv -> TvSubstEnv
1377 -- ^ @(compose env1 env2)(x)@ is @env1(env2(x))@; i.e. apply @env2@ then @env1@.
1378 -- It assumes that both are idempotent.
1379 -- Typically, @env1@ is the refinement to a base substitution @env2@
1380 composeTvSubst in_scope env1 env2
1381 = env1 `plusVarEnv` mapVarEnv (substTy subst1) env2
1382 -- First apply env1 to the range of env2
1383 -- Then combine the two, making sure that env1 loses if
1384 -- both bind the same variable; that's why env1 is the
1385 -- *left* argument to plusVarEnv, because the right arg wins
1387 subst1 = TvSubst in_scope env1
1389 emptyTvSubst :: TvSubst
1390 emptyTvSubst = TvSubst emptyInScopeSet emptyVarEnv
1392 isEmptyTvSubst :: TvSubst -> Bool
1393 -- See Note [Extending the TvSubstEnv]
1394 isEmptyTvSubst (TvSubst _ env) = isEmptyVarEnv env
1396 mkTvSubst :: InScopeSet -> TvSubstEnv -> TvSubst
1399 getTvSubstEnv :: TvSubst -> TvSubstEnv
1400 getTvSubstEnv (TvSubst _ env) = env
1402 getTvInScope :: TvSubst -> InScopeSet
1403 getTvInScope (TvSubst in_scope _) = in_scope
1405 isInScope :: Var -> TvSubst -> Bool
1406 isInScope v (TvSubst in_scope _) = v `elemInScopeSet` in_scope
1408 notElemTvSubst :: TyVar -> TvSubst -> Bool
1409 notElemTvSubst tv (TvSubst _ env) = not (tv `elemVarEnv` env)
1411 setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst
1412 setTvSubstEnv (TvSubst in_scope _) env = TvSubst in_scope env
1414 extendTvInScope :: TvSubst -> [Var] -> TvSubst
1415 extendTvInScope (TvSubst in_scope env) vars = TvSubst (extendInScopeSetList in_scope vars) env
1417 extendTvSubst :: TvSubst -> TyVar -> Type -> TvSubst
1418 extendTvSubst (TvSubst in_scope env) tv ty = TvSubst in_scope (extendVarEnv env tv ty)
1420 extendTvSubstList :: TvSubst -> [TyVar] -> [Type] -> TvSubst
1421 extendTvSubstList (TvSubst in_scope env) tvs tys
1422 = TvSubst in_scope (extendVarEnvList env (tvs `zip` tys))
1424 -- mkOpenTvSubst and zipOpenTvSubst generate the in-scope set from
1425 -- the types given; but it's just a thunk so with a bit of luck
1426 -- it'll never be evaluated
1428 -- Note [Generating the in-scope set for a substitution]
1429 -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1430 -- If we want to substitute [a -> ty1, b -> ty2] I used to
1431 -- think it was enough to generate an in-scope set that includes
1432 -- fv(ty1,ty2). But that's not enough; we really should also take the
1433 -- free vars of the type we are substituting into! Example:
1434 -- (forall b. (a,b,x)) [a -> List b]
1435 -- Then if we use the in-scope set {b}, there is a danger we will rename
1436 -- the forall'd variable to 'x' by mistake, getting this:
1437 -- (forall x. (List b, x, x)
1438 -- Urk! This means looking at all the calls to mkOpenTvSubst....
1441 -- | Generates the in-scope set for the 'TvSubst' from the types in the incoming
1442 -- environment, hence "open"
1443 mkOpenTvSubst :: TvSubstEnv -> TvSubst
1444 mkOpenTvSubst env = TvSubst (mkInScopeSet (tyVarsOfTypes (varEnvElts env))) env
1446 -- | Generates the in-scope set for the 'TvSubst' from the types in the incoming
1447 -- environment, hence "open"
1448 zipOpenTvSubst :: [TyVar] -> [Type] -> TvSubst
1449 zipOpenTvSubst tyvars tys
1450 | debugIsOn && (length tyvars /= length tys)
1451 = pprTrace "zipOpenTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1453 = TvSubst (mkInScopeSet (tyVarsOfTypes tys)) (zipTyEnv tyvars tys)
1455 -- | Called when doing top-level substitutions. Here we expect that the
1456 -- free vars of the range of the substitution will be empty.
1457 mkTopTvSubst :: [(TyVar, Type)] -> TvSubst
1458 mkTopTvSubst prs = TvSubst emptyInScopeSet (mkVarEnv prs)
1460 zipTopTvSubst :: [TyVar] -> [Type] -> TvSubst
1461 zipTopTvSubst tyvars tys
1462 | debugIsOn && (length tyvars /= length tys)
1463 = pprTrace "zipTopTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1465 = TvSubst emptyInScopeSet (zipTyEnv tyvars tys)
1467 zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
1469 | debugIsOn && (length tyvars /= length tys)
1470 = pprTrace "mkTopTvSubst" (ppr tyvars $$ ppr tys) emptyVarEnv
1472 = zip_ty_env tyvars tys emptyVarEnv
1474 -- Later substitutions in the list over-ride earlier ones,
1475 -- but there should be no loops
1476 zip_ty_env :: [TyVar] -> [Type] -> TvSubstEnv -> TvSubstEnv
1477 zip_ty_env [] [] env = env
1478 zip_ty_env (tv:tvs) (ty:tys) env = zip_ty_env tvs tys (extendVarEnv env tv ty)
1479 -- There used to be a special case for when
1481 -- (a not-uncommon case) in which case the substitution was dropped.
1482 -- But the type-tidier changes the print-name of a type variable without
1483 -- changing the unique, and that led to a bug. Why? Pre-tidying, we had
1484 -- a type {Foo t}, where Foo is a one-method class. So Foo is really a newtype.
1485 -- And it happened that t was the type variable of the class. Post-tiding,
1486 -- it got turned into {Foo t2}. The ext-core printer expanded this using
1487 -- sourceTypeRep, but that said "Oh, t == t2" because they have the same unique,
1488 -- and so generated a rep type mentioning t not t2.
1490 -- Simplest fix is to nuke the "optimisation"
1491 zip_ty_env tvs tys env = pprTrace "Var/Type length mismatch: " (ppr tvs $$ ppr tys) env
1492 -- zip_ty_env _ _ env = env
1494 instance Outputable TvSubst where
1495 ppr (TvSubst ins env)
1496 = brackets $ sep[ ptext (sLit "TvSubst"),
1497 nest 2 (ptext (sLit "In scope:") <+> ppr ins),
1498 nest 2 (ptext (sLit "Env:") <+> ppr env) ]
1501 %************************************************************************
1503 Performing type substitutions
1505 %************************************************************************
1508 -- | Type substitution making use of an 'TvSubst' that
1509 -- is assumed to be open, see 'zipOpenTvSubst'
1510 substTyWith :: [TyVar] -> [Type] -> Type -> Type
1511 substTyWith tvs tys = ASSERT( length tvs == length tys )
1512 substTy (zipOpenTvSubst tvs tys)
1514 -- | Substitute within a 'Type'
1515 substTy :: TvSubst -> Type -> Type
1516 substTy subst ty | isEmptyTvSubst subst = ty
1517 | otherwise = subst_ty subst ty
1519 -- | Substitute within several 'Type's
1520 substTys :: TvSubst -> [Type] -> [Type]
1521 substTys subst tys | isEmptyTvSubst subst = tys
1522 | otherwise = map (subst_ty subst) tys
1524 -- | Substitute within a 'ThetaType'
1525 substTheta :: TvSubst -> ThetaType -> ThetaType
1526 substTheta subst theta
1527 | isEmptyTvSubst subst = theta
1528 | otherwise = map (substPred subst) theta
1530 -- | Substitute within a 'PredType'
1531 substPred :: TvSubst -> PredType -> PredType
1532 substPred subst (IParam n ty) = IParam n (subst_ty subst ty)
1533 substPred subst (ClassP clas tys) = ClassP clas (map (subst_ty subst) tys)
1534 substPred subst (EqPred ty1 ty2) = EqPred (subst_ty subst ty1) (subst_ty subst ty2)
1536 -- | Remove any nested binders mentioning the 'TyVar's in the 'TyVarSet'
1537 deShadowTy :: TyVarSet -> Type -> Type
1539 = subst_ty (mkTvSubst in_scope emptyTvSubstEnv) ty
1541 in_scope = mkInScopeSet tvs
1543 subst_ty :: TvSubst -> Type -> Type
1544 -- subst_ty is the main workhorse for type substitution
1546 -- Note that the in_scope set is poked only if we hit a forall
1547 -- so it may often never be fully computed
1551 go (TyVarTy tv) = substTyVar subst tv
1552 go (TyConApp tc tys) = let args = map go tys
1553 in args `seqList` TyConApp tc args
1555 go (PredTy p) = PredTy $! (substPred subst p)
1557 go (FunTy arg res) = (FunTy $! (go arg)) $! (go res)
1558 go (AppTy fun arg) = mkAppTy (go fun) $! (go arg)
1559 -- The mkAppTy smart constructor is important
1560 -- we might be replacing (a Int), represented with App
1561 -- by [Int], represented with TyConApp
1562 go (ForAllTy tv ty) = case substTyVarBndr subst tv of
1564 ForAllTy tv' $! (subst_ty subst' ty)
1566 substTyVar :: TvSubst -> TyVar -> Type
1567 substTyVar subst@(TvSubst _ _) tv
1568 = case lookupTyVar subst tv of {
1569 Nothing -> TyVarTy tv;
1570 Just ty -> ty -- See Note [Apply Once]
1573 substTyVars :: TvSubst -> [TyVar] -> [Type]
1574 substTyVars subst tvs = map (substTyVar subst) tvs
1576 lookupTyVar :: TvSubst -> TyVar -> Maybe Type
1577 -- See Note [Extending the TvSubst]
1578 lookupTyVar (TvSubst _ env) tv = lookupVarEnv env tv
1580 substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)
1581 substTyVarBndr subst@(TvSubst in_scope env) old_var
1582 = (TvSubst (in_scope `extendInScopeSet` new_var) new_env, new_var)
1584 is_co_var = isCoVar old_var
1586 new_env | no_change = delVarEnv env old_var
1587 | otherwise = extendVarEnv env old_var (TyVarTy new_var)
1589 no_change = new_var == old_var && not is_co_var
1590 -- no_change means that the new_var is identical in
1591 -- all respects to the old_var (same unique, same kind)
1592 -- See Note [Extending the TvSubst]
1594 -- In that case we don't need to extend the substitution
1595 -- to map old to new. But instead we must zap any
1596 -- current substitution for the variable. For example:
1597 -- (\x.e) with id_subst = [x |-> e']
1598 -- Here we must simply zap the substitution for x
1600 new_var = uniqAway in_scope subst_old_var
1601 -- The uniqAway part makes sure the new variable is not already in scope
1603 subst_old_var -- subst_old_var is old_var with the substitution applied to its kind
1604 -- It's only worth doing the substitution for coercions,
1605 -- becuase only they can have free type variables
1606 | is_co_var = setTyVarKind old_var (substTy subst (tyVarKind old_var))
1607 | otherwise = old_var
1610 ----------------------------------------------------
1619 -- There's a little subtyping at the kind level:
1629 -- Where: \* [LiftedTypeKind] means boxed type
1630 -- \# [UnliftedTypeKind] means unboxed type
1631 -- (\#) [UbxTupleKind] means unboxed tuple
1632 -- ?? [ArgTypeKind] is the lub of {\*, \#}
1633 -- ? [OpenTypeKind] means any type at all
1638 -- > error :: forall a:?. String -> a
1639 -- > (->) :: ?? -> ? -> \*
1640 -- > (\\(x::t) -> ...)
1642 -- Where in the last example @t :: ??@ (i.e. is not an unboxed tuple)
1644 type KindVar = TyVar -- invariant: KindVar will always be a
1645 -- TcTyVar with details MetaTv TauTv ...
1646 -- kind var constructors and functions are in TcType
1648 type SimpleKind = Kind
1653 During kind inference, a kind variable unifies only with
1655 sk ::= * | sk1 -> sk2
1657 data T a = MkT a (T Int#)
1658 fails. We give T the kind (k -> *), and the kind variable k won't unify
1659 with # (the kind of Int#).
1663 When creating a fresh internal type variable, we give it a kind to express
1664 constraints on it. E.g. in (\x->e) we make up a fresh type variable for x,
1667 During unification we only bind an internal type variable to a type
1668 whose kind is lower in the sub-kind hierarchy than the kind of the tyvar.
1670 When unifying two internal type variables, we collect their kind constraints by
1671 finding the GLB of the two. Since the partial order is a tree, they only
1672 have a glb if one is a sub-kind of the other. In that case, we bind the
1673 less-informative one to the more informative one. Neat, eh?
1680 %************************************************************************
1682 Functions over Kinds
1684 %************************************************************************
1687 -- | Essentially 'funResultTy' on kinds
1688 kindFunResult :: Kind -> Kind
1689 kindFunResult k = funResultTy k
1691 -- | Essentially 'splitFunTys' on kinds
1692 splitKindFunTys :: Kind -> ([Kind],Kind)
1693 splitKindFunTys k = splitFunTys k
1695 -- | Essentially 'splitFunTysN' on kinds
1696 splitKindFunTysN :: Int -> Kind -> ([Kind],Kind)
1697 splitKindFunTysN k = splitFunTysN k
1699 -- | See "Type#kind_subtyping" for details of the distinction between these 'Kind's
1700 isUbxTupleKind, isOpenTypeKind, isArgTypeKind, isUnliftedTypeKind :: Kind -> Bool
1701 isOpenTypeKindCon, isUbxTupleKindCon, isArgTypeKindCon,
1702 isUnliftedTypeKindCon, isSubArgTypeKindCon :: TyCon -> Bool
1704 isOpenTypeKindCon tc = tyConUnique tc == openTypeKindTyConKey
1706 isOpenTypeKind (TyConApp tc _) = isOpenTypeKindCon tc
1707 isOpenTypeKind _ = False
1709 isUbxTupleKindCon tc = tyConUnique tc == ubxTupleKindTyConKey
1711 isUbxTupleKind (TyConApp tc _) = isUbxTupleKindCon tc
1712 isUbxTupleKind _ = False
1714 isArgTypeKindCon tc = tyConUnique tc == argTypeKindTyConKey
1716 isArgTypeKind (TyConApp tc _) = isArgTypeKindCon tc
1717 isArgTypeKind _ = False
1719 isUnliftedTypeKindCon tc = tyConUnique tc == unliftedTypeKindTyConKey
1721 isUnliftedTypeKind (TyConApp tc _) = isUnliftedTypeKindCon tc
1722 isUnliftedTypeKind _ = False
1724 isSubOpenTypeKind :: Kind -> Bool
1725 -- ^ True of any sub-kind of OpenTypeKind (i.e. anything except arrow)
1726 isSubOpenTypeKind (FunTy k1 k2) = ASSERT2 ( isKind k1, text "isSubOpenTypeKind" <+> ppr k1 <+> text "::" <+> ppr (typeKind k1) )
1727 ASSERT2 ( isKind k2, text "isSubOpenTypeKind" <+> ppr k2 <+> text "::" <+> ppr (typeKind k2) )
1729 isSubOpenTypeKind (TyConApp kc []) = ASSERT( isKind (TyConApp kc []) ) True
1730 isSubOpenTypeKind other = ASSERT( isKind other ) False
1731 -- This is a conservative answer
1732 -- It matters in the call to isSubKind in
1733 -- checkExpectedKind.
1735 isSubArgTypeKindCon kc
1736 | isUnliftedTypeKindCon kc = True
1737 | isLiftedTypeKindCon kc = True
1738 | isArgTypeKindCon kc = True
1741 isSubArgTypeKind :: Kind -> Bool
1742 -- ^ True of any sub-kind of ArgTypeKind
1743 isSubArgTypeKind (TyConApp kc []) = isSubArgTypeKindCon kc
1744 isSubArgTypeKind _ = False
1746 -- | Is this a super-kind (i.e. a type-of-kinds)?
1747 isSuperKind :: Type -> Bool
1748 isSuperKind (TyConApp (skc) []) = isSuperKindTyCon skc
1749 isSuperKind _ = False
1751 -- | Is this a kind (i.e. a type-of-types)?
1752 isKind :: Kind -> Bool
1753 isKind k = isSuperKind (typeKind k)
1755 isSubKind :: Kind -> Kind -> Bool
1756 -- ^ @k1 \`isSubKind\` k2@ checks that @k1@ <: @k2@
1757 isSubKind (TyConApp kc1 []) (TyConApp kc2 []) = kc1 `isSubKindCon` kc2
1758 isSubKind (FunTy a1 r1) (FunTy a2 r2) = (a2 `isSubKind` a1) && (r1 `isSubKind` r2)
1759 isSubKind (PredTy (EqPred ty1 ty2)) (PredTy (EqPred ty1' ty2'))
1760 = ty1 `tcEqType` ty1' && ty2 `tcEqType` ty2'
1761 isSubKind _ _ = False
1763 eqKind :: Kind -> Kind -> Bool
1766 isSubKindCon :: TyCon -> TyCon -> Bool
1767 -- ^ @kc1 \`isSubKindCon\` kc2@ checks that @kc1@ <: @kc2@
1768 isSubKindCon kc1 kc2
1769 | isLiftedTypeKindCon kc1 && isLiftedTypeKindCon kc2 = True
1770 | isUnliftedTypeKindCon kc1 && isUnliftedTypeKindCon kc2 = True
1771 | isUbxTupleKindCon kc1 && isUbxTupleKindCon kc2 = True
1772 | isOpenTypeKindCon kc2 = True
1773 -- we already know kc1 is not a fun, its a TyCon
1774 | isArgTypeKindCon kc2 && isSubArgTypeKindCon kc1 = True
1777 defaultKind :: Kind -> Kind
1778 -- ^ Used when generalising: default kind ? and ?? to *. See "Type#kind_subtyping" for more
1779 -- information on what that means
1781 -- When we generalise, we make generic type variables whose kind is
1782 -- simple (* or *->* etc). So generic type variables (other than
1783 -- built-in constants like 'error') always have simple kinds. This is important;
1786 -- We want f to get type
1787 -- f :: forall (a::*). a -> Bool
1789 -- f :: forall (a::??). a -> Bool
1790 -- because that would allow a call like (f 3#) as well as (f True),
1791 --and the calling conventions differ. This defaulting is done in TcMType.zonkTcTyVarBndr.
1793 | isSubOpenTypeKind k = liftedTypeKind
1794 | isSubArgTypeKind k = liftedTypeKind
1797 isEqPred :: PredType -> Bool
1798 isEqPred (EqPred _ _) = True