Use mkCastTy in subst_ty.
[ghc.git] / compiler / types / Type.hs
1 -- (c) The University of Glasgow 2006
2 -- (c) The GRASP/AQUA Project, Glasgow University, 1998
3 --
4 -- Type - public interface
5
6 {-# LANGUAGE CPP, FlexibleContexts #-}
7 {-# OPTIONS_GHC -fno-warn-orphans #-}
8
9 -- | Main functions for manipulating types and type-related things
10 module Type (
11 -- Note some of this is just re-exports from TyCon..
12
13 -- * Main data types representing Types
14 -- $type_classification
15
16 -- $representation_types
17 TyThing(..), Type, ArgFlag(..), KindOrType, PredType, ThetaType,
18 Var, TyVar, isTyVar, TyCoVar, TyBinder, TyVarBinder,
19
20 -- ** Constructing and deconstructing types
21 mkTyVarTy, mkTyVarTys, getTyVar, getTyVar_maybe, repGetTyVar_maybe,
22 getCastedTyVar_maybe, tyVarKind,
23
24 mkAppTy, mkAppTys, splitAppTy, splitAppTys, repSplitAppTys,
25 splitAppTy_maybe, repSplitAppTy_maybe, tcRepSplitAppTy_maybe,
26
27 mkFunTy, mkFunTys, splitFunTy, splitFunTy_maybe,
28 splitFunTys, funResultTy, funArgTy,
29
30 mkTyConApp, mkTyConTy,
31 tyConAppTyCon_maybe, tyConAppTyConPicky_maybe,
32 tyConAppArgs_maybe, tyConAppTyCon, tyConAppArgs,
33 splitTyConApp_maybe, splitTyConApp, tyConAppArgN, nextRole,
34 tcRepSplitTyConApp_maybe, tcSplitTyConApp_maybe,
35 splitListTyConApp_maybe,
36 repSplitTyConApp_maybe,
37
38 mkForAllTy, mkForAllTys, mkInvForAllTys, mkSpecForAllTys,
39 mkVisForAllTys, mkInvForAllTy,
40 splitForAllTys, splitForAllTyVarBndrs,
41 splitForAllTy_maybe, splitForAllTy,
42 splitPiTy_maybe, splitPiTy, splitPiTys,
43 mkPiTy, mkPiTys, mkTyConBindersPreferAnon,
44 mkLamType, mkLamTypes,
45 piResultTy, piResultTys,
46 applyTysX, dropForAlls,
47
48 mkNumLitTy, isNumLitTy,
49 mkStrLitTy, isStrLitTy,
50
51 getRuntimeRep_maybe, getRuntimeRepFromKind_maybe,
52
53 mkCastTy, mkCoercionTy, splitCastTy_maybe,
54
55 userTypeError_maybe, pprUserTypeErrorTy,
56
57 coAxNthLHS,
58 stripCoercionTy, splitCoercionType_maybe,
59
60 splitPiTysInvisible, filterOutInvisibleTypes,
61 filterOutInvisibleTyVars, partitionInvisibles,
62 synTyConResKind,
63
64 modifyJoinResTy, setJoinResTy,
65
66 -- Analyzing types
67 TyCoMapper(..), mapType, mapCoercion,
68
69 -- (Newtypes)
70 newTyConInstRhs,
71
72 -- Pred types
73 mkFamilyTyConApp,
74 isDictLikeTy,
75 mkPrimEqPred, mkReprPrimEqPred, mkPrimEqPredRole,
76 equalityTyCon,
77 mkHeteroPrimEqPred, mkHeteroReprPrimEqPred,
78 mkClassPred,
79 isClassPred, isEqPred, isNomEqPred,
80 isIPPred, isIPPred_maybe, isIPTyCon, isIPClass,
81 isCTupleClass,
82
83 -- Deconstructing predicate types
84 PredTree(..), EqRel(..), eqRelRole, classifyPredType,
85 getClassPredTys, getClassPredTys_maybe,
86 getEqPredTys, getEqPredTys_maybe, getEqPredRole,
87 predTypeEqRel,
88
89 -- ** Binders
90 sameVis,
91 mkTyVarBinder, mkTyVarBinders,
92 mkAnonBinder,
93 isAnonTyBinder, isNamedTyBinder,
94 binderVar, binderVars, binderKind, binderArgFlag,
95 tyBinderType,
96 binderRelevantType_maybe, caseBinder,
97 isVisibleArgFlag, isInvisibleArgFlag, isVisibleBinder, isInvisibleBinder,
98 tyConBindersTyBinders,
99 mkTyBinderTyConBinder,
100
101 -- ** Common type constructors
102 funTyCon,
103
104 -- ** Predicates on types
105 isTyVarTy, isFunTy, isDictTy, isPredTy, isCoercionTy,
106 isCoercionTy_maybe, isCoercionType, isForAllTy,
107 isPiTy, isTauTy, isFamFreeTy,
108
109 isValidJoinPointType,
110
111 -- (Lifting and boxity)
112 isLiftedType_maybe, isUnliftedType, isUnboxedTupleType, isUnboxedSumType,
113 isAlgType, isClosedAlgType, isDataFamilyAppType,
114 isPrimitiveType, isStrictType,
115 isRuntimeRepTy, isRuntimeRepVar, isRuntimeRepKindedTy,
116 dropRuntimeRepArgs,
117 getRuntimeRep, getRuntimeRepFromKind,
118
119 -- * Main data types representing Kinds
120 Kind,
121
122 -- ** Finding the kind of a type
123 typeKind, isTypeLevPoly, resultIsLevPoly,
124
125 -- ** Common Kind
126 liftedTypeKind,
127
128 -- * Type free variables
129 tyCoFVsOfType, tyCoFVsBndr,
130 tyCoVarsOfType, tyCoVarsOfTypes,
131 tyCoVarsOfTypeDSet,
132 coVarsOfType,
133 coVarsOfTypes, closeOverKinds, closeOverKindsList,
134 noFreeVarsOfType,
135 splitVisVarsOfType, splitVisVarsOfTypes,
136 expandTypeSynonyms,
137 typeSize,
138
139 -- * Well-scoped lists of variables
140 dVarSetElemsWellScoped, toposortTyVars, tyCoVarsOfTypeWellScoped,
141 tyCoVarsOfTypesWellScoped,
142
143 -- * Type comparison
144 eqType, eqTypeX, eqTypes, nonDetCmpType, nonDetCmpTypes, nonDetCmpTypeX,
145 nonDetCmpTypesX, nonDetCmpTc,
146 eqVarBndrs,
147
148 -- * Forcing evaluation of types
149 seqType, seqTypes,
150
151 -- * Other views onto Types
152 coreView, tcView,
153
154 tyConsOfType,
155
156 -- * Main type substitution data types
157 TvSubstEnv, -- Representation widely visible
158 TCvSubst(..), -- Representation visible to a few friends
159
160 -- ** Manipulating type substitutions
161 emptyTvSubstEnv, emptyTCvSubst, mkEmptyTCvSubst,
162
163 mkTCvSubst, zipTvSubst, mkTvSubstPrs,
164 notElemTCvSubst,
165 getTvSubstEnv, setTvSubstEnv,
166 zapTCvSubst, getTCvInScope, getTCvSubstRangeFVs,
167 extendTCvInScope, extendTCvInScopeList, extendTCvInScopeSet,
168 extendTCvSubst, extendCvSubst,
169 extendTvSubst, extendTvSubstBinder,
170 extendTvSubstList, extendTvSubstAndInScope,
171 extendTvSubstWithClone,
172 isInScope, composeTCvSubstEnv, composeTCvSubst, zipTyEnv, zipCoEnv,
173 isEmptyTCvSubst, unionTCvSubst,
174
175 -- ** Performing substitution on types and kinds
176 substTy, substTys, substTyWith, substTysWith, substTheta,
177 substTyAddInScope,
178 substTyUnchecked, substTysUnchecked, substThetaUnchecked,
179 substTyWithUnchecked,
180 substCoUnchecked, substCoWithUnchecked,
181 substTyVarBndr, substTyVar, substTyVars,
182 cloneTyVarBndr, cloneTyVarBndrs, lookupTyVar,
183
184 -- * Pretty-printing
185 pprType, pprParendType, pprTypeApp, pprTyThingCategory, pprShortTyThing,
186 pprTvBndr, pprTvBndrs, pprForAll, pprUserForAll,
187 pprSigmaType, ppSuggestExplicitKinds,
188 pprTheta, pprThetaArrowTy, pprClassPred,
189 pprKind, pprParendKind, pprSourceTyCon,
190 TyPrec(..), maybeParen,
191 pprTyVar, pprTyVars, pprPrefixApp, pprArrowChain,
192
193 -- * Tidying type related things up for printing
194 tidyType, tidyTypes,
195 tidyOpenType, tidyOpenTypes,
196 tidyOpenKind,
197 tidyTyCoVarBndr, tidyTyCoVarBndrs, tidyFreeTyCoVars,
198 tidyOpenTyCoVar, tidyOpenTyCoVars,
199 tidyTyVarOcc,
200 tidyTopType,
201 tidyKind,
202 tidyTyVarBinder, tidyTyVarBinders
203 ) where
204
205 #include "HsVersions.h"
206
207 import BasicTypes
208
209 -- We import the representation and primitive functions from TyCoRep.
210 -- Many things are reexported, but not the representation!
211
212 import Kind
213 import TyCoRep
214
215 -- friends:
216 import Var
217 import VarEnv
218 import VarSet
219 import UniqSet
220
221 import Class
222 import TyCon
223 import TysPrim
224 import {-# SOURCE #-} TysWiredIn ( listTyCon, typeNatKind
225 , typeSymbolKind, liftedTypeKind )
226 import PrelNames
227 import CoAxiom
228 import {-# SOURCE #-} Coercion
229
230 -- others
231 import Util
232 import Outputable
233 import FastString
234 import Pair
235 import ListSetOps
236 import Digraph
237 import Unique ( nonDetCmpUnique )
238 import SrcLoc ( SrcSpan )
239 import OccName ( OccName )
240 import Name ( mkInternalName )
241
242 import Maybes ( orElse )
243 import Data.Maybe ( isJust, mapMaybe )
244 import Control.Monad ( guard )
245 import Control.Arrow ( first, second )
246
247 -- $type_classification
248 -- #type_classification#
249 --
250 -- Types are one of:
251 --
252 -- [Unboxed] Iff its representation is other than a pointer
253 -- Unboxed types are also unlifted.
254 --
255 -- [Lifted] Iff it has bottom as an element.
256 -- Closures always have lifted types: i.e. any
257 -- let-bound identifier in Core must have a lifted
258 -- type. Operationally, a lifted object is one that
259 -- can be entered.
260 -- Only lifted types may be unified with a type variable.
261 --
262 -- [Algebraic] Iff it is a type with one or more constructors, whether
263 -- declared with @data@ or @newtype@.
264 -- An algebraic type is one that can be deconstructed
265 -- with a case expression. This is /not/ the same as
266 -- lifted types, because we also include unboxed
267 -- tuples in this classification.
268 --
269 -- [Data] Iff it is a type declared with @data@, or a boxed tuple.
270 --
271 -- [Primitive] Iff it is a built-in type that can't be expressed in Haskell.
272 --
273 -- Currently, all primitive types are unlifted, but that's not necessarily
274 -- the case: for example, @Int@ could be primitive.
275 --
276 -- Some primitive types are unboxed, such as @Int#@, whereas some are boxed
277 -- but unlifted (such as @ByteArray#@). The only primitive types that we
278 -- classify as algebraic are the unboxed tuples.
279 --
280 -- Some examples of type classifications that may make this a bit clearer are:
281 --
282 -- @
283 -- Type primitive boxed lifted algebraic
284 -- -----------------------------------------------------------------------------
285 -- Int# Yes No No No
286 -- ByteArray# Yes Yes No No
287 -- (\# a, b \#) Yes No No Yes
288 -- (\# a | b \#) Yes No No Yes
289 -- ( a, b ) No Yes Yes Yes
290 -- [a] No Yes Yes Yes
291 -- @
292
293 -- $representation_types
294 -- A /source type/ is a type that is a separate type as far as the type checker is
295 -- concerned, but which has a more low-level representation as far as Core-to-Core
296 -- passes and the rest of the back end is concerned.
297 --
298 -- You don't normally have to worry about this, as the utility functions in
299 -- this module will automatically convert a source into a representation type
300 -- if they are spotted, to the best of it's abilities. If you don't want this
301 -- to happen, use the equivalent functions from the "TcType" module.
302
303 {-
304 ************************************************************************
305 * *
306 Type representation
307 * *
308 ************************************************************************
309
310 Note [coreView vs tcView]
311 ~~~~~~~~~~~~~~~~~~~~~~~~~
312 So far as the typechecker is concerned, 'Constraint' and 'TYPE LiftedRep' are distinct kinds.
313
314 But in Core these two are treated as identical.
315
316 We implement this by making 'coreView' convert 'Constraint' to 'TYPE LiftedRep' on the fly.
317 The function tcView (used in the type checker) does not do this.
318
319 See also Trac #11715, which tracks removing this inconsistency.
320
321 -}
322
323 {-# INLINE coreView #-}
324 coreView :: Type -> Maybe Type
325 -- ^ This function Strips off the /top layer only/ of a type synonym
326 -- application (if any) its underlying representation type.
327 -- Returns Nothing if there is nothing to look through.
328 -- This function considers 'Constraint' to be a synonym of @TYPE LiftedRep@.
329 --
330 -- By being non-recursive and inlined, this case analysis gets efficiently
331 -- joined onto the case analysis that the caller is already doing
332 coreView (TyConApp tc tys) | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc tys
333 = Just (mkAppTys (substTy (mkTvSubstPrs tenv) rhs) tys')
334 -- The free vars of 'rhs' should all be bound by 'tenv', so it's
335 -- ok to use 'substTy' here.
336 -- See also Note [The substitution invariant] in TyCoRep.
337 -- Its important to use mkAppTys, rather than (foldl AppTy),
338 -- because the function part might well return a
339 -- partially-applied type constructor; indeed, usually will!
340 coreView (TyConApp tc [])
341 | isStarKindSynonymTyCon tc
342 = Just liftedTypeKind
343
344 coreView _ = Nothing
345
346 -- | Gives the typechecker view of a type. This unwraps synonyms but
347 -- leaves 'Constraint' alone. c.f. coreView, which turns Constraint into
348 -- TYPE LiftedRep. Returns Nothing if no unwrapping happens.
349 -- See also Note [coreView vs tcView] in Type.
350 {-# INLINE tcView #-}
351 tcView :: Type -> Maybe Type
352 tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc tys
353 = Just (mkAppTys (substTy (mkTvSubstPrs tenv) rhs) tys')
354 -- The free vars of 'rhs' should all be bound by 'tenv', so it's
355 -- ok to use 'substTy' here.
356 -- See also Note [The substitution invariant] in TyCoRep.
357 -- Its important to use mkAppTys, rather than (foldl AppTy),
358 -- because the function part might well return a
359 -- partially-applied type constructor; indeed, usually will!
360 tcView _ = Nothing
361
362 -----------------------------------------------
363 expandTypeSynonyms :: Type -> Type
364 -- ^ Expand out all type synonyms. Actually, it'd suffice to expand out
365 -- just the ones that discard type variables (e.g. type Funny a = Int)
366 -- But we don't know which those are currently, so we just expand all.
367 --
368 -- 'expandTypeSynonyms' only expands out type synonyms mentioned in the type,
369 -- not in the kinds of any TyCon or TyVar mentioned in the type.
370 --
371 -- Keep this synchronized with 'synonymTyConsOfType'
372 expandTypeSynonyms ty
373 = go (mkEmptyTCvSubst in_scope) ty
374 where
375 in_scope = mkInScopeSet (tyCoVarsOfType ty)
376
377 go subst (TyConApp tc tys)
378 | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc expanded_tys
379 = let subst' = mkTvSubst in_scope (mkVarEnv tenv)
380 -- Make a fresh substitution; rhs has nothing to
381 -- do with anything that has happened so far
382 -- NB: if you make changes here, be sure to build an
383 -- /idempotent/ substitution, even in the nested case
384 -- type T a b = a -> b
385 -- type S x y = T y x
386 -- (Trac #11665)
387 in mkAppTys (go subst' rhs) tys'
388 | otherwise
389 = TyConApp tc expanded_tys
390 where
391 expanded_tys = (map (go subst) tys)
392
393 go _ (LitTy l) = LitTy l
394 go subst (TyVarTy tv) = substTyVar subst tv
395 go subst (AppTy t1 t2) = mkAppTy (go subst t1) (go subst t2)
396 go subst (FunTy arg res)
397 = mkFunTy (go subst arg) (go subst res)
398 go subst (ForAllTy (TvBndr tv vis) t)
399 = let (subst', tv') = substTyVarBndrCallback go subst tv in
400 ForAllTy (TvBndr tv' vis) (go subst' t)
401 go subst (CastTy ty co) = mkCastTy (go subst ty) (go_co subst co)
402 go subst (CoercionTy co) = mkCoercionTy (go_co subst co)
403
404 go_co subst (Refl r ty)
405 = mkReflCo r (go subst ty)
406 -- NB: coercions are always expanded upon creation
407 go_co subst (TyConAppCo r tc args)
408 = mkTyConAppCo r tc (map (go_co subst) args)
409 go_co subst (AppCo co arg)
410 = mkAppCo (go_co subst co) (go_co subst arg)
411 go_co subst (ForAllCo tv kind_co co)
412 = let (subst', tv', kind_co') = go_cobndr subst tv kind_co in
413 mkForAllCo tv' kind_co' (go_co subst' co)
414 go_co subst (FunCo r co1 co2)
415 = mkFunCo r (go_co subst co1) (go_co subst co2)
416 go_co subst (CoVarCo cv)
417 = substCoVar subst cv
418 go_co subst (AxiomInstCo ax ind args)
419 = mkAxiomInstCo ax ind (map (go_co subst) args)
420 go_co subst (UnivCo p r t1 t2)
421 = mkUnivCo (go_prov subst p) r (go subst t1) (go subst t2)
422 go_co subst (SymCo co)
423 = mkSymCo (go_co subst co)
424 go_co subst (TransCo co1 co2)
425 = mkTransCo (go_co subst co1) (go_co subst co2)
426 go_co subst (NthCo n co)
427 = mkNthCo n (go_co subst co)
428 go_co subst (LRCo lr co)
429 = mkLRCo lr (go_co subst co)
430 go_co subst (InstCo co arg)
431 = mkInstCo (go_co subst co) (go_co subst arg)
432 go_co subst (CoherenceCo co1 co2)
433 = mkCoherenceCo (go_co subst co1) (go_co subst co2)
434 go_co subst (KindCo co)
435 = mkKindCo (go_co subst co)
436 go_co subst (SubCo co)
437 = mkSubCo (go_co subst co)
438 go_co subst (AxiomRuleCo ax cs) = AxiomRuleCo ax (map (go_co subst) cs)
439
440 go_prov _ UnsafeCoerceProv = UnsafeCoerceProv
441 go_prov subst (PhantomProv co) = PhantomProv (go_co subst co)
442 go_prov subst (ProofIrrelProv co) = ProofIrrelProv (go_co subst co)
443 go_prov _ p@(PluginProv _) = p
444 go_prov _ (HoleProv h) = pprPanic "expandTypeSynonyms hit a hole" (ppr h)
445
446 -- the "False" and "const" are to accommodate the type of
447 -- substForAllCoBndrCallback, which is general enough to
448 -- handle coercion optimization (which sometimes swaps the
449 -- order of a coercion)
450 go_cobndr subst = substForAllCoBndrCallback False (go_co subst) subst
451
452 {-
453 ************************************************************************
454 * *
455 Analyzing types
456 * *
457 ************************************************************************
458
459 These functions do a map-like operation over types, performing some operation
460 on all variables and binding sites. Primarily used for zonking.
461
462 Note [Efficiency for mapCoercion ForAllCo case]
463 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
464 As noted in Note [Forall coercions] in TyCoRep, a ForAllCo is a bit redundant.
465 It stores a TyVar and a Coercion, where the kind of the TyVar always matches
466 the left-hand kind of the coercion. This is convenient lots of the time, but
467 not when mapping a function over a coercion.
468
469 The problem is that tcm_tybinder will affect the TyVar's kind and
470 mapCoercion will affect the Coercion, and we hope that the results will be
471 the same. Even if they are the same (which should generally happen with
472 correct algorithms), then there is an efficiency issue. In particular,
473 this problem seems to make what should be a linear algorithm into a potentially
474 exponential one. But it's only going to be bad in the case where there's
475 lots of foralls in the kinds of other foralls. Like this:
476
477 forall a : (forall b : (forall c : ...). ...). ...
478
479 This construction seems unlikely. So we'll do the inefficient, easy way
480 for now.
481
482 Note [Specialising mappers]
483 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
484 These INLINABLE pragmas are indispensable. mapType/mapCoercion are used
485 to implement zonking, and it's vital that they get specialised to the TcM
486 monad. This specialisation happens automatically (that is, without a
487 SPECIALISE pragma) as long as the definitions are INLINABLE. For example,
488 this one change made a 20% allocation difference in perf/compiler/T5030.
489
490 -}
491
492 -- | This describes how a "map" operation over a type/coercion should behave
493 data TyCoMapper env m
494 = TyCoMapper
495 { tcm_smart :: Bool -- ^ Should the new type be created with smart
496 -- constructors?
497 , tcm_tyvar :: env -> TyVar -> m Type
498 , tcm_covar :: env -> CoVar -> m Coercion
499 , tcm_hole :: env -> CoercionHole -> Role
500 -> Type -> Type -> m Coercion
501 -- ^ What to do with coercion holes. See Note [Coercion holes] in
502 -- TyCoRep.
503
504 , tcm_tybinder :: env -> TyVar -> ArgFlag -> m (env, TyVar)
505 -- ^ The returned env is used in the extended scope
506 }
507
508 {-# INLINABLE mapType #-} -- See Note [Specialising mappers]
509 mapType :: Monad m => TyCoMapper env m -> env -> Type -> m Type
510 mapType mapper@(TyCoMapper { tcm_smart = smart, tcm_tyvar = tyvar
511 , tcm_tybinder = tybinder })
512 env ty
513 = go ty
514 where
515 go (TyVarTy tv) = tyvar env tv
516 go (AppTy t1 t2) = mkappty <$> go t1 <*> go t2
517 go t@(TyConApp _ []) = return t -- avoid allocation in this exceedingly
518 -- common case (mostly, for *)
519 go (TyConApp tc tys) = mktyconapp tc <$> mapM go tys
520 go (FunTy arg res) = FunTy <$> go arg <*> go res
521 go (ForAllTy (TvBndr tv vis) inner)
522 = do { (env', tv') <- tybinder env tv vis
523 ; inner' <- mapType mapper env' inner
524 ; return $ ForAllTy (TvBndr tv' vis) inner' }
525 go ty@(LitTy {}) = return ty
526 go (CastTy ty co) = mkcastty <$> go ty <*> mapCoercion mapper env co
527 go (CoercionTy co) = CoercionTy <$> mapCoercion mapper env co
528
529 (mktyconapp, mkappty, mkcastty)
530 | smart = (mkTyConApp, mkAppTy, mkCastTy)
531 | otherwise = (TyConApp, AppTy, CastTy)
532
533 {-# INLINABLE mapCoercion #-} -- See Note [Specialising mappers]
534 mapCoercion :: Monad m
535 => TyCoMapper env m -> env -> Coercion -> m Coercion
536 mapCoercion mapper@(TyCoMapper { tcm_smart = smart, tcm_covar = covar
537 , tcm_hole = cohole, tcm_tybinder = tybinder })
538 env co
539 = go co
540 where
541 go (Refl r ty) = Refl r <$> mapType mapper env ty
542 go (TyConAppCo r tc args)
543 = mktyconappco r tc <$> mapM go args
544 go (AppCo c1 c2) = mkappco <$> go c1 <*> go c2
545 go (ForAllCo tv kind_co co)
546 = do { kind_co' <- go kind_co
547 ; (env', tv') <- tybinder env tv Inferred
548 ; co' <- mapCoercion mapper env' co
549 ; return $ mkforallco tv' kind_co' co' }
550 -- See Note [Efficiency for mapCoercion ForAllCo case]
551 go (FunCo r c1 c2) = mkFunCo r <$> go c1 <*> go c2
552 go (CoVarCo cv) = covar env cv
553 go (AxiomInstCo ax i args)
554 = mkaxiominstco ax i <$> mapM go args
555 go (UnivCo (HoleProv hole) r t1 t2)
556 = cohole env hole r t1 t2
557 go (UnivCo p r t1 t2)
558 = mkunivco <$> go_prov p <*> pure r
559 <*> mapType mapper env t1 <*> mapType mapper env t2
560 go (SymCo co) = mksymco <$> go co
561 go (TransCo c1 c2) = mktransco <$> go c1 <*> go c2
562 go (AxiomRuleCo r cos) = AxiomRuleCo r <$> mapM go cos
563 go (NthCo i co) = mknthco i <$> go co
564 go (LRCo lr co) = mklrco lr <$> go co
565 go (InstCo co arg) = mkinstco <$> go co <*> go arg
566 go (CoherenceCo c1 c2) = mkcoherenceco <$> go c1 <*> go c2
567 go (KindCo co) = mkkindco <$> go co
568 go (SubCo co) = mksubco <$> go co
569
570 go_prov UnsafeCoerceProv = return UnsafeCoerceProv
571 go_prov (PhantomProv co) = PhantomProv <$> go co
572 go_prov (ProofIrrelProv co) = ProofIrrelProv <$> go co
573 go_prov p@(PluginProv _) = return p
574 go_prov (HoleProv _) = panic "mapCoercion"
575
576 ( mktyconappco, mkappco, mkaxiominstco, mkunivco
577 , mksymco, mktransco, mknthco, mklrco, mkinstco, mkcoherenceco
578 , mkkindco, mksubco, mkforallco)
579 | smart
580 = ( mkTyConAppCo, mkAppCo, mkAxiomInstCo, mkUnivCo
581 , mkSymCo, mkTransCo, mkNthCo, mkLRCo, mkInstCo, mkCoherenceCo
582 , mkKindCo, mkSubCo, mkForAllCo )
583 | otherwise
584 = ( TyConAppCo, AppCo, AxiomInstCo, UnivCo
585 , SymCo, TransCo, NthCo, LRCo, InstCo, CoherenceCo
586 , KindCo, SubCo, ForAllCo )
587
588 {-
589 ************************************************************************
590 * *
591 \subsection{Constructor-specific functions}
592 * *
593 ************************************************************************
594
595
596 ---------------------------------------------------------------------
597 TyVarTy
598 ~~~~~~~
599 -}
600
601 -- | Attempts to obtain the type variable underlying a 'Type', and panics with the
602 -- given message if this is not a type variable type. See also 'getTyVar_maybe'
603 getTyVar :: String -> Type -> TyVar
604 getTyVar msg ty = case getTyVar_maybe ty of
605 Just tv -> tv
606 Nothing -> panic ("getTyVar: " ++ msg)
607
608 isTyVarTy :: Type -> Bool
609 isTyVarTy ty = isJust (getTyVar_maybe ty)
610
611 -- | Attempts to obtain the type variable underlying a 'Type'
612 getTyVar_maybe :: Type -> Maybe TyVar
613 getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty'
614 | otherwise = repGetTyVar_maybe ty
615
616 -- | If the type is a tyvar, possibly under a cast, returns it, along
617 -- with the coercion. Thus, the co is :: kind tv ~R kind type
618 getCastedTyVar_maybe :: Type -> Maybe (TyVar, Coercion)
619 getCastedTyVar_maybe ty | Just ty' <- coreView ty = getCastedTyVar_maybe ty'
620 getCastedTyVar_maybe (CastTy (TyVarTy tv) co) = Just (tv, co)
621 getCastedTyVar_maybe (TyVarTy tv)
622 = Just (tv, mkReflCo Nominal (tyVarKind tv))
623 getCastedTyVar_maybe _ = Nothing
624
625 -- | Attempts to obtain the type variable underlying a 'Type', without
626 -- any expansion
627 repGetTyVar_maybe :: Type -> Maybe TyVar
628 repGetTyVar_maybe (TyVarTy tv) = Just tv
629 repGetTyVar_maybe _ = Nothing
630
631 {-
632 ---------------------------------------------------------------------
633 AppTy
634 ~~~~~
635 We need to be pretty careful with AppTy to make sure we obey the
636 invariant that a TyConApp is always visibly so. mkAppTy maintains the
637 invariant: use it.
638
639 Note [Decomposing fat arrow c=>t]
640 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
641 Can we unify (a b) with (Eq a => ty)? If we do so, we end up with
642 a partial application like ((=>) Eq a) which doesn't make sense in
643 source Haskell. In contrast, we *can* unify (a b) with (t1 -> t2).
644 Here's an example (Trac #9858) of how you might do it:
645 i :: (Typeable a, Typeable b) => Proxy (a b) -> TypeRep
646 i p = typeRep p
647
648 j = i (Proxy :: Proxy (Eq Int => Int))
649 The type (Proxy (Eq Int => Int)) is only accepted with -XImpredicativeTypes,
650 but suppose we want that. But then in the call to 'i', we end
651 up decomposing (Eq Int => Int), and we definitely don't want that.
652
653 This really only applies to the type checker; in Core, '=>' and '->'
654 are the same, as are 'Constraint' and '*'. But for now I've put
655 the test in repSplitAppTy_maybe, which applies throughout, because
656 the other calls to splitAppTy are in Unify, which is also used by
657 the type checker (e.g. when matching type-function equations).
658
659 -}
660
661 -- | Applies a type to another, as in e.g. @k a@
662 mkAppTy :: Type -> Type -> Type
663 mkAppTy (TyConApp tc tys) ty2 = mkTyConApp tc (tys ++ [ty2])
664 mkAppTy ty1 ty2 = AppTy ty1 ty2
665 -- Note that the TyConApp could be an
666 -- under-saturated type synonym. GHC allows that; e.g.
667 -- type Foo k = k a -> k a
668 -- type Id x = x
669 -- foo :: Foo Id -> Foo Id
670 --
671 -- Here Id is partially applied in the type sig for Foo,
672 -- but once the type synonyms are expanded all is well
673
674 mkAppTys :: Type -> [Type] -> Type
675 mkAppTys ty1 [] = ty1
676 mkAppTys (TyConApp tc tys1) tys2 = mkTyConApp tc (tys1 ++ tys2)
677 mkAppTys ty1 tys2 = foldl AppTy ty1 tys2
678
679 -------------
680 splitAppTy_maybe :: Type -> Maybe (Type, Type)
681 -- ^ Attempt to take a type application apart, whether it is a
682 -- function, type constructor, or plain type application. Note
683 -- that type family applications are NEVER unsaturated by this!
684 splitAppTy_maybe ty | Just ty' <- coreView ty
685 = splitAppTy_maybe ty'
686 splitAppTy_maybe ty = repSplitAppTy_maybe ty
687
688 -------------
689 repSplitAppTy_maybe :: Type -> Maybe (Type,Type)
690 -- ^ Does the AppTy split as in 'splitAppTy_maybe', but assumes that
691 -- any Core view stuff is already done
692 repSplitAppTy_maybe (FunTy ty1 ty2)
693 | Just rep1 <- getRuntimeRep_maybe ty1
694 , Just rep2 <- getRuntimeRep_maybe ty2
695 = Just (TyConApp funTyCon [rep1, rep2, ty1], ty2)
696
697 | otherwise
698 = pprPanic "repSplitAppTy_maybe" (ppr ty1 $$ ppr ty2)
699 repSplitAppTy_maybe (AppTy ty1 ty2)
700 = Just (ty1, ty2)
701 repSplitAppTy_maybe (TyConApp tc tys)
702 | mightBeUnsaturatedTyCon tc || tys `lengthExceeds` tyConArity tc
703 , Just (tys', ty') <- snocView tys
704 = Just (TyConApp tc tys', ty') -- Never create unsaturated type family apps!
705 repSplitAppTy_maybe _other = Nothing
706
707 -- this one doesn't braek apart (c => t).
708 -- See Note [Decomposing fat arrow c=>t]
709 -- Defined here to avoid module loops between Unify and TcType.
710 tcRepSplitAppTy_maybe :: Type -> Maybe (Type,Type)
711 -- ^ Does the AppTy split as in 'tcSplitAppTy_maybe', but assumes that
712 -- any coreView stuff is already done. Refuses to look through (c => t)
713 tcRepSplitAppTy_maybe (FunTy ty1 ty2)
714 | isConstraintKind (typeKind ty1)
715 = Nothing -- See Note [Decomposing fat arrow c=>t]
716
717 | Just rep1 <- getRuntimeRep_maybe ty1
718 , Just rep2 <- getRuntimeRep_maybe ty2
719 = Just (TyConApp funTyCon [rep1, rep2, ty1], ty2)
720
721 | otherwise
722 = pprPanic "repSplitAppTy_maybe" (ppr ty1 $$ ppr ty2)
723 tcRepSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
724 tcRepSplitAppTy_maybe (TyConApp tc tys)
725 | mightBeUnsaturatedTyCon tc || tys `lengthExceeds` tyConArity tc
726 , Just (tys', ty') <- snocView tys
727 = Just (TyConApp tc tys', ty') -- Never create unsaturated type family apps!
728 tcRepSplitAppTy_maybe _other = Nothing
729
730 -- | Split a type constructor application into its type constructor and
731 -- applied types. Note that this may fail in the case of a 'FunTy' with an
732 -- argument of unknown kind 'FunTy' (e.g. @FunTy (a :: k) Int@. since the kind
733 -- of @a@ isn't of the form @TYPE rep@). Consequently, you may need to zonk your
734 -- type before using this function.
735 --
736 -- If you only need the 'TyCon', consider using 'tcTyConAppTyCon_maybe'.
737 tcSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type])
738 -- Defined here to avoid module loops between Unify and TcType.
739 tcSplitTyConApp_maybe ty | Just ty' <- tcView ty = tcSplitTyConApp_maybe ty'
740 tcSplitTyConApp_maybe ty = tcRepSplitTyConApp_maybe ty
741
742 -- | Like 'tcSplitTyConApp_maybe' but doesn't look through type synonyms.
743 tcRepSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type])
744 -- Defined here to avoid module loops between Unify and TcType.
745 tcRepSplitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
746 tcRepSplitTyConApp_maybe (FunTy arg res)
747 | Just arg_rep <- getRuntimeRep_maybe arg
748 , Just res_rep <- getRuntimeRep_maybe res
749 = Just (funTyCon, [arg_rep, res_rep, arg, res])
750
751 | otherwise
752 = pprPanic "tcRepSplitTyConApp_maybe" (ppr arg $$ ppr res)
753 tcRepSplitTyConApp_maybe _ = Nothing
754
755
756 -------------
757 splitAppTy :: Type -> (Type, Type)
758 -- ^ Attempts to take a type application apart, as in 'splitAppTy_maybe',
759 -- and panics if this is not possible
760 splitAppTy ty = case splitAppTy_maybe ty of
761 Just pr -> pr
762 Nothing -> panic "splitAppTy"
763
764 -------------
765 splitAppTys :: Type -> (Type, [Type])
766 -- ^ Recursively splits a type as far as is possible, leaving a residual
767 -- type being applied to and the type arguments applied to it. Never fails,
768 -- even if that means returning an empty list of type applications.
769 splitAppTys ty = split ty ty []
770 where
771 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
772 split _ (AppTy ty arg) args = split ty ty (arg:args)
773 split _ (TyConApp tc tc_args) args
774 = let -- keep type families saturated
775 n | mightBeUnsaturatedTyCon tc = 0
776 | otherwise = tyConArity tc
777 (tc_args1, tc_args2) = splitAt n tc_args
778 in
779 (TyConApp tc tc_args1, tc_args2 ++ args)
780 split _ (FunTy ty1 ty2) args
781 | Just rep1 <- getRuntimeRep_maybe ty1
782 , Just rep2 <- getRuntimeRep_maybe ty2
783 = ASSERT( null args )
784 (TyConApp funTyCon [], [rep1, rep2, ty1, ty2])
785
786 | otherwise
787 = pprPanic "splitAppTys" (ppr ty1 $$ ppr ty2 $$ ppr args)
788 split orig_ty _ args = (orig_ty, args)
789
790 -- | Like 'splitAppTys', but doesn't look through type synonyms
791 repSplitAppTys :: Type -> (Type, [Type])
792 repSplitAppTys ty = split ty []
793 where
794 split (AppTy ty arg) args = split ty (arg:args)
795 split (TyConApp tc tc_args) args
796 = let n | mightBeUnsaturatedTyCon tc = 0
797 | otherwise = tyConArity tc
798 (tc_args1, tc_args2) = splitAt n tc_args
799 in
800 (TyConApp tc tc_args1, tc_args2 ++ args)
801 split (FunTy ty1 ty2) args
802 | Just rep1 <- getRuntimeRep_maybe ty1
803 , Just rep2 <- getRuntimeRep_maybe ty2
804 = ASSERT( null args )
805 (TyConApp funTyCon [], [rep1, rep2, ty1, ty2])
806
807 | otherwise
808 = pprPanic "repSplitAppTys" (ppr ty1 $$ ppr ty2 $$ ppr args)
809 split ty args = (ty, args)
810
811 {-
812 LitTy
813 ~~~~~
814 -}
815
816 mkNumLitTy :: Integer -> Type
817 mkNumLitTy n = LitTy (NumTyLit n)
818
819 -- | Is this a numeric literal. We also look through type synonyms.
820 isNumLitTy :: Type -> Maybe Integer
821 isNumLitTy ty | Just ty1 <- coreView ty = isNumLitTy ty1
822 isNumLitTy (LitTy (NumTyLit n)) = Just n
823 isNumLitTy _ = Nothing
824
825 mkStrLitTy :: FastString -> Type
826 mkStrLitTy s = LitTy (StrTyLit s)
827
828 -- | Is this a symbol literal. We also look through type synonyms.
829 isStrLitTy :: Type -> Maybe FastString
830 isStrLitTy ty | Just ty1 <- coreView ty = isStrLitTy ty1
831 isStrLitTy (LitTy (StrTyLit s)) = Just s
832 isStrLitTy _ = Nothing
833
834
835 -- | Is this type a custom user error?
836 -- If so, give us the kind and the error message.
837 userTypeError_maybe :: Type -> Maybe Type
838 userTypeError_maybe t
839 = do { (tc, _kind : msg : _) <- splitTyConApp_maybe t
840 -- There may be more than 2 arguments, if the type error is
841 -- used as a type constructor (e.g. at kind `Type -> Type`).
842
843 ; guard (tyConName tc == errorMessageTypeErrorFamName)
844 ; return msg }
845
846 -- | Render a type corresponding to a user type error into a SDoc.
847 pprUserTypeErrorTy :: Type -> SDoc
848 pprUserTypeErrorTy ty =
849 case splitTyConApp_maybe ty of
850
851 -- Text "Something"
852 Just (tc,[txt])
853 | tyConName tc == typeErrorTextDataConName
854 , Just str <- isStrLitTy txt -> ftext str
855
856 -- ShowType t
857 Just (tc,[_k,t])
858 | tyConName tc == typeErrorShowTypeDataConName -> ppr t
859
860 -- t1 :<>: t2
861 Just (tc,[t1,t2])
862 | tyConName tc == typeErrorAppendDataConName ->
863 pprUserTypeErrorTy t1 <> pprUserTypeErrorTy t2
864
865 -- t1 :$$: t2
866 Just (tc,[t1,t2])
867 | tyConName tc == typeErrorVAppendDataConName ->
868 pprUserTypeErrorTy t1 $$ pprUserTypeErrorTy t2
869
870 -- An uneavaluated type function
871 _ -> ppr ty
872
873
874
875
876 {-
877 ---------------------------------------------------------------------
878 FunTy
879 ~~~~~
880
881 Note [Representation of function types]
882 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
883
884 Functions (e.g. Int -> Char) are can be thought of as being applications
885 of funTyCon (known in Haskell surface syntax as (->)),
886
887 (->) :: forall (r1 :: RuntimeRep) (r2 :: RuntimeRep)
888 (a :: TYPE r1) (b :: TYPE r2).
889 a -> b -> Type
890
891 However, for efficiency's sake we represent saturated applications of (->)
892 with FunTy. For instance, the type,
893
894 (->) r1 r2 a b
895
896 is equivalent to,
897
898 FunTy (Anon a) b
899
900 Note how the RuntimeReps are implied in the FunTy representation. For this
901 reason we must be careful when recontructing the TyConApp representation (see,
902 for instance, splitTyConApp_maybe).
903
904 In the compiler we maintain the invariant that all saturated applications of
905 (->) are represented with FunTy.
906
907 See #11714.
908 -}
909
910 isFunTy :: Type -> Bool
911 isFunTy ty = isJust (splitFunTy_maybe ty)
912
913 splitFunTy :: Type -> (Type, Type)
914 -- ^ Attempts to extract the argument and result types from a type, and
915 -- panics if that is not possible. See also 'splitFunTy_maybe'
916 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
917 splitFunTy (FunTy arg res) = (arg, res)
918 splitFunTy other = pprPanic "splitFunTy" (ppr other)
919
920 splitFunTy_maybe :: Type -> Maybe (Type, Type)
921 -- ^ Attempts to extract the argument and result types from a type
922 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
923 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
924 splitFunTy_maybe _ = Nothing
925
926 splitFunTys :: Type -> ([Type], Type)
927 splitFunTys ty = split [] ty ty
928 where
929 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
930 split args _ (FunTy arg res) = split (arg:args) res res
931 split args orig_ty _ = (reverse args, orig_ty)
932
933 funResultTy :: Type -> Type
934 -- ^ Extract the function result type and panic if that is not possible
935 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
936 funResultTy (FunTy _ res) = res
937 funResultTy ty = pprPanic "funResultTy" (ppr ty)
938
939 funArgTy :: Type -> Type
940 -- ^ Extract the function argument type and panic if that is not possible
941 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
942 funArgTy (FunTy arg _res) = arg
943 funArgTy ty = pprPanic "funArgTy" (ppr ty)
944
945 piResultTy :: Type -> Type -> Type
946 piResultTy ty arg = case piResultTy_maybe ty arg of
947 Just res -> res
948 Nothing -> pprPanic "piResultTy" (ppr ty $$ ppr arg)
949
950 piResultTy_maybe :: Type -> Type -> Maybe Type
951
952 -- ^ Just like 'piResultTys' but for a single argument
953 -- Try not to iterate 'piResultTy', because it's inefficient to substitute
954 -- one variable at a time; instead use 'piResultTys"
955 piResultTy_maybe ty arg
956 | Just ty' <- coreView ty = piResultTy_maybe ty' arg
957
958 | FunTy _ res <- ty
959 = Just res
960
961 | ForAllTy (TvBndr tv _) res <- ty
962 = let empty_subst = mkEmptyTCvSubst $ mkInScopeSet $
963 tyCoVarsOfTypes [arg,res]
964 in Just (substTy (extendTvSubst empty_subst tv arg) res)
965
966 | otherwise
967 = Nothing
968
969 -- | (piResultTys f_ty [ty1, .., tyn]) gives the type of (f ty1 .. tyn)
970 -- where f :: f_ty
971 -- 'piResultTys' is interesting because:
972 -- 1. 'f_ty' may have more for-alls than there are args
973 -- 2. Less obviously, it may have fewer for-alls
974 -- For case 2. think of:
975 -- piResultTys (forall a.a) [forall b.b, Int]
976 -- This really can happen, but only (I think) in situations involving
977 -- undefined. For example:
978 -- undefined :: forall a. a
979 -- Term: undefined @(forall b. b->b) @Int
980 -- This term should have type (Int -> Int), but notice that
981 -- there are more type args than foralls in 'undefined's type.
982
983 -- If you edit this function, you may need to update the GHC formalism
984 -- See Note [GHC Formalism] in coreSyn/CoreLint.hs
985
986 -- This is a heavily used function (e.g. from typeKind),
987 -- so we pay attention to efficiency, especially in the special case
988 -- where there are no for-alls so we are just dropping arrows from
989 -- a function type/kind.
990 piResultTys :: Type -> [Type] -> Type
991 piResultTys ty [] = ty
992 piResultTys ty orig_args@(arg:args)
993 | Just ty' <- coreView ty
994 = piResultTys ty' orig_args
995
996 | FunTy _ res <- ty
997 = piResultTys res args
998
999 | ForAllTy (TvBndr tv _) res <- ty
1000 = go (extendVarEnv emptyTvSubstEnv tv arg) res args
1001
1002 | otherwise
1003 = pprPanic "piResultTys1" (ppr ty $$ ppr orig_args)
1004 where
1005 in_scope = mkInScopeSet (tyCoVarsOfTypes (ty:orig_args))
1006
1007 go :: TvSubstEnv -> Type -> [Type] -> Type
1008 go tv_env ty [] = substTy (mkTvSubst in_scope tv_env) ty
1009
1010 go tv_env ty all_args@(arg:args)
1011 | Just ty' <- coreView ty
1012 = go tv_env ty' all_args
1013
1014 | FunTy _ res <- ty
1015 = go tv_env res args
1016
1017 | ForAllTy (TvBndr tv _) res <- ty
1018 = go (extendVarEnv tv_env tv arg) res args
1019
1020 | TyVarTy tv <- ty
1021 , Just ty' <- lookupVarEnv tv_env tv
1022 -- Deals with piResultTys (forall a. a) [forall b.b, Int]
1023 = piResultTys ty' all_args
1024
1025 | otherwise
1026 = pprPanic "piResultTys2" (ppr ty $$ ppr orig_args $$ ppr all_args)
1027
1028 applyTysX :: [TyVar] -> Type -> [Type] -> Type
1029 -- applyTyxX beta-reduces (/\tvs. body_ty) arg_tys
1030 -- Assumes that (/\tvs. body_ty) is closed
1031 applyTysX tvs body_ty arg_tys
1032 = ASSERT2( length arg_tys >= n_tvs, pp_stuff )
1033 ASSERT2( tyCoVarsOfType body_ty `subVarSet` mkVarSet tvs, pp_stuff )
1034 mkAppTys (substTyWith tvs (take n_tvs arg_tys) body_ty)
1035 (drop n_tvs arg_tys)
1036 where
1037 pp_stuff = vcat [ppr tvs, ppr body_ty, ppr arg_tys]
1038 n_tvs = length tvs
1039
1040 {-
1041 ---------------------------------------------------------------------
1042 TyConApp
1043 ~~~~~~~~
1044 -}
1045
1046 -- | A key function: builds a 'TyConApp' or 'FunTy' as appropriate to
1047 -- its arguments. Applies its arguments to the constructor from left to right.
1048 mkTyConApp :: TyCon -> [Type] -> Type
1049 mkTyConApp tycon tys
1050 | isFunTyCon tycon
1051 , [_rep1,_rep2,ty1,ty2] <- tys
1052 = FunTy ty1 ty2
1053
1054 | otherwise
1055 = TyConApp tycon tys
1056
1057 -- splitTyConApp "looks through" synonyms, because they don't
1058 -- mean a distinct type, but all other type-constructor applications
1059 -- including functions are returned as Just ..
1060
1061 -- | Retrieve the tycon heading this type, if there is one. Does /not/
1062 -- look through synonyms.
1063 tyConAppTyConPicky_maybe :: Type -> Maybe TyCon
1064 tyConAppTyConPicky_maybe (TyConApp tc _) = Just tc
1065 tyConAppTyConPicky_maybe (FunTy {}) = Just funTyCon
1066 tyConAppTyConPicky_maybe _ = Nothing
1067
1068
1069 -- | The same as @fst . splitTyConApp@
1070 tyConAppTyCon_maybe :: Type -> Maybe TyCon
1071 tyConAppTyCon_maybe ty | Just ty' <- coreView ty = tyConAppTyCon_maybe ty'
1072 tyConAppTyCon_maybe (TyConApp tc _) = Just tc
1073 tyConAppTyCon_maybe (FunTy {}) = Just funTyCon
1074 tyConAppTyCon_maybe _ = Nothing
1075
1076 tyConAppTyCon :: Type -> TyCon
1077 tyConAppTyCon ty = tyConAppTyCon_maybe ty `orElse` pprPanic "tyConAppTyCon" (ppr ty)
1078
1079 -- | The same as @snd . splitTyConApp@
1080 tyConAppArgs_maybe :: Type -> Maybe [Type]
1081 tyConAppArgs_maybe ty | Just ty' <- coreView ty = tyConAppArgs_maybe ty'
1082 tyConAppArgs_maybe (TyConApp _ tys) = Just tys
1083 tyConAppArgs_maybe (FunTy arg res)
1084 | Just rep1 <- getRuntimeRep_maybe arg
1085 , Just rep2 <- getRuntimeRep_maybe res
1086 = Just [rep1, rep2, arg, res]
1087 tyConAppArgs_maybe _ = Nothing
1088
1089 tyConAppArgs :: Type -> [Type]
1090 tyConAppArgs ty = tyConAppArgs_maybe ty `orElse` pprPanic "tyConAppArgs" (ppr ty)
1091
1092 tyConAppArgN :: Int -> Type -> Type
1093 -- Executing Nth
1094 tyConAppArgN n ty
1095 = case tyConAppArgs_maybe ty of
1096 Just tys -> ASSERT2( n < length tys, ppr n <+> ppr tys ) tys `getNth` n
1097 Nothing -> pprPanic "tyConAppArgN" (ppr n <+> ppr ty)
1098
1099 -- | Attempts to tease a type apart into a type constructor and the application
1100 -- of a number of arguments to that constructor. Panics if that is not possible.
1101 -- See also 'splitTyConApp_maybe'
1102 splitTyConApp :: Type -> (TyCon, [Type])
1103 splitTyConApp ty = case splitTyConApp_maybe ty of
1104 Just stuff -> stuff
1105 Nothing -> pprPanic "splitTyConApp" (ppr ty)
1106
1107 -- | Attempts to tease a type apart into a type constructor and the application
1108 -- of a number of arguments to that constructor
1109 splitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
1110 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
1111 splitTyConApp_maybe ty = repSplitTyConApp_maybe ty
1112
1113 -- | Like 'splitTyConApp_maybe', but doesn't look through synonyms. This
1114 -- assumes the synonyms have already been dealt with.
1115 repSplitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
1116 repSplitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
1117 repSplitTyConApp_maybe (FunTy arg res)
1118 | Just rep1 <- getRuntimeRep_maybe arg
1119 , Just rep2 <- getRuntimeRep_maybe res
1120 = Just (funTyCon, [rep1, rep2, arg, res])
1121 | otherwise
1122 = pprPanic "repSplitTyConApp_maybe"
1123 (ppr arg $$ ppr res $$ ppr (typeKind res))
1124 repSplitTyConApp_maybe _ = Nothing
1125
1126 -- | Attempts to tease a list type apart and gives the type of the elements if
1127 -- successful (looks through type synonyms)
1128 splitListTyConApp_maybe :: Type -> Maybe Type
1129 splitListTyConApp_maybe ty = case splitTyConApp_maybe ty of
1130 Just (tc,[e]) | tc == listTyCon -> Just e
1131 _other -> Nothing
1132
1133 -- | What is the role assigned to the next parameter of this type? Usually,
1134 -- this will be 'Nominal', but if the type is a 'TyConApp', we may be able to
1135 -- do better. The type does *not* have to be well-kinded when applied for this
1136 -- to work!
1137 nextRole :: Type -> Role
1138 nextRole ty
1139 | Just (tc, tys) <- splitTyConApp_maybe ty
1140 , let num_tys = length tys
1141 , num_tys < tyConArity tc
1142 = tyConRoles tc `getNth` num_tys
1143
1144 | otherwise
1145 = Nominal
1146
1147 newTyConInstRhs :: TyCon -> [Type] -> Type
1148 -- ^ Unwrap one 'layer' of newtype on a type constructor and its
1149 -- arguments, using an eta-reduced version of the @newtype@ if possible.
1150 -- This requires tys to have at least @newTyConInstArity tycon@ elements.
1151 newTyConInstRhs tycon tys
1152 = ASSERT2( tvs `leLength` tys, ppr tycon $$ ppr tys $$ ppr tvs )
1153 applyTysX tvs rhs tys
1154 where
1155 (tvs, rhs) = newTyConEtadRhs tycon
1156
1157 {-
1158 ---------------------------------------------------------------------
1159 CastTy
1160 ~~~~~~
1161 A casted type has its *kind* casted into something new.
1162
1163 Note [No reflexive casts in types]
1164 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1165 As far as possible, we would like to maintain the following property:
1166
1167 (*) If (t1 `eqType` t2), then t1 and t2 are treated identically within GHC.
1168
1169 The (*) property is very useful, because we have a tendency to compare two
1170 types to see if they're equal, and then arbitrarily choose one. We don't
1171 want this arbitrary choice to then matter later on. Maintaining (*) means
1172 that every function that looks at a structure of a type must think about
1173 casts. In places where we directly pattern-match, this consideration is
1174 forced by consideration of the CastTy constructor.
1175
1176 But, when we call a splitXXX function, it's easy to ignore the possibility
1177 of casts. In particular, splitTyConApp is used extensively, and we don't
1178 want it to fail on (T a b c |> co). Happily, if we have
1179 (T a b c |> co) `eqType` (T d e f)
1180 then co must be reflexive. Why? eqType checks that the kinds are equal, as
1181 well as checking that (a `eqType` d), (b `eqType` e), and (c `eqType` f).
1182 By the kind check, we know that (T a b c |> co) and (T d e f) have the same
1183 kind. So the only way that co could be non-reflexive is for (T a b c) to have
1184 a different kind than (T d e f). But because T's kind is closed (all tycon kinds
1185 are closed), the only way for this to happen is that one of the arguments has
1186 to differ, leading to a contradiction. Thus, co is reflexive.
1187
1188 Accordingly, by eliminating reflexive casts, splitTyConApp need not worry
1189 about outermost casts to uphold (*).
1190
1191 Unforunately, that's not the end of the story. Consider comparing
1192 (T a b c) =? (T a b |> (co -> <Type>)) (c |> sym co)
1193 These two types have the same kind (Type), but the left type is a TyConApp
1194 while the right type is not. To handle this case, we will have to implement
1195 some variant of the dreaded KPush algorithm (c.f. CoreOpt.pushCoDataCon).
1196 This stone is left unturned for now, meaning that we don't yet uphold (*).
1197
1198 The other place where (*) will be hard to guarantee is in splitAppTy, because
1199 I (Richard E) can't think of a way to push coercions into AppTys. The good
1200 news here is that splitAppTy is not used all that much, and so all clients of
1201 that function can simply be told to use splitCastTy as well, in order to
1202 uphold (*). This, too, is left undone, for now.
1203
1204 -}
1205
1206 splitCastTy_maybe :: Type -> Maybe (Type, Coercion)
1207 splitCastTy_maybe ty | Just ty' <- coreView ty = splitCastTy_maybe ty'
1208 splitCastTy_maybe (CastTy ty co) = Just (ty, co)
1209 splitCastTy_maybe _ = Nothing
1210
1211 -- | Make a 'CastTy'. The Coercion must be nominal. Checks the
1212 -- Coercion for reflexivity, dropping it if it's reflexive.
1213 -- See Note [No reflexive casts in types]
1214 mkCastTy :: Type -> Coercion -> Type
1215 mkCastTy ty co | isReflexiveCo co = ty
1216 -- NB: Do the slow check here. This is important to keep the splitXXX
1217 -- functions working properly. Otherwise, we may end up with something
1218 -- like (((->) |> something_reflexive_but_not_obviously_so) biz baz)
1219 -- fails under splitFunTy_maybe. This happened with the cheaper check
1220 -- in test dependent/should_compile/dynamic-paper.
1221
1222 mkCastTy (CastTy ty co1) co2 = mkCastTy ty (co1 `mkTransCo` co2)
1223 mkCastTy ty co = CastTy ty co
1224
1225 tyConBindersTyBinders :: [TyConBinder] -> [TyBinder]
1226 -- Return the tyConBinders in TyBinder form
1227 tyConBindersTyBinders = map to_tyb
1228 where
1229 to_tyb (TvBndr tv (NamedTCB vis)) = Named (TvBndr tv vis)
1230 to_tyb (TvBndr tv AnonTCB) = Anon (tyVarKind tv)
1231
1232 {-
1233 --------------------------------------------------------------------
1234 CoercionTy
1235 ~~~~~~~~~~
1236 CoercionTy allows us to inject coercions into types. A CoercionTy
1237 should appear only in the right-hand side of an application.
1238 -}
1239
1240 mkCoercionTy :: Coercion -> Type
1241 mkCoercionTy = CoercionTy
1242
1243 isCoercionTy :: Type -> Bool
1244 isCoercionTy (CoercionTy _) = True
1245 isCoercionTy _ = False
1246
1247 isCoercionTy_maybe :: Type -> Maybe Coercion
1248 isCoercionTy_maybe (CoercionTy co) = Just co
1249 isCoercionTy_maybe _ = Nothing
1250
1251 stripCoercionTy :: Type -> Coercion
1252 stripCoercionTy (CoercionTy co) = co
1253 stripCoercionTy ty = pprPanic "stripCoercionTy" (ppr ty)
1254
1255 {-
1256 ---------------------------------------------------------------------
1257 SynTy
1258 ~~~~~
1259
1260 Notes on type synonyms
1261 ~~~~~~~~~~~~~~~~~~~~~~
1262 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
1263 to return type synonyms wherever possible. Thus
1264
1265 type Foo a = a -> a
1266
1267 we want
1268 splitFunTys (a -> Foo a) = ([a], Foo a)
1269 not ([a], a -> a)
1270
1271 The reason is that we then get better (shorter) type signatures in
1272 interfaces. Notably this plays a role in tcTySigs in TcBinds.hs.
1273
1274
1275 ---------------------------------------------------------------------
1276 ForAllTy
1277 ~~~~~~~~
1278 -}
1279
1280 -- | Make a dependent forall over an Inferred (as opposed to Specified)
1281 -- variable
1282 mkInvForAllTy :: TyVar -> Type -> Type
1283 mkInvForAllTy tv ty = ASSERT( isTyVar tv )
1284 ForAllTy (TvBndr tv Inferred) ty
1285
1286 -- | Like mkForAllTys, but assumes all variables are dependent and Inferred,
1287 -- a common case
1288 mkInvForAllTys :: [TyVar] -> Type -> Type
1289 mkInvForAllTys tvs ty = ASSERT( all isTyVar tvs )
1290 foldr mkInvForAllTy ty tvs
1291
1292 -- | Like mkForAllTys, but assumes all variables are dependent and specified,
1293 -- a common case
1294 mkSpecForAllTys :: [TyVar] -> Type -> Type
1295 mkSpecForAllTys tvs = ASSERT( all isTyVar tvs )
1296 mkForAllTys [ TvBndr tv Specified | tv <- tvs ]
1297
1298 -- | Like mkForAllTys, but assumes all variables are dependent and visible
1299 mkVisForAllTys :: [TyVar] -> Type -> Type
1300 mkVisForAllTys tvs = ASSERT( all isTyVar tvs )
1301 mkForAllTys [ TvBndr tv Required | tv <- tvs ]
1302
1303 mkLamType :: Var -> Type -> Type
1304 -- ^ Makes a @(->)@ type or an implicit forall type, depending
1305 -- on whether it is given a type variable or a term variable.
1306 -- This is used, for example, when producing the type of a lambda.
1307 -- Always uses Inferred binders.
1308 mkLamTypes :: [Var] -> Type -> Type
1309 -- ^ 'mkLamType' for multiple type or value arguments
1310
1311 mkLamType v ty
1312 | isTyVar v = ForAllTy (TvBndr v Inferred) ty
1313 | otherwise = FunTy (varType v) ty
1314
1315 mkLamTypes vs ty = foldr mkLamType ty vs
1316
1317 -- | Given a list of type-level vars and a result type, makes TyBinders, preferring
1318 -- anonymous binders if the variable is, in fact, not dependent.
1319 -- All binders are /visible/.
1320 mkTyConBindersPreferAnon :: [TyVar] -> Type -> [TyConBinder]
1321 mkTyConBindersPreferAnon vars inner_ty = fst (go vars)
1322 where
1323 go :: [TyVar] -> ([TyConBinder], VarSet) -- also returns the free vars
1324 go [] = ([], tyCoVarsOfType inner_ty)
1325 go (v:vs) | v `elemVarSet` fvs
1326 = ( TvBndr v (NamedTCB Required) : binders
1327 , fvs `delVarSet` v `unionVarSet` kind_vars )
1328 | otherwise
1329 = ( TvBndr v AnonTCB : binders
1330 , fvs `unionVarSet` kind_vars )
1331 where
1332 (binders, fvs) = go vs
1333 kind_vars = tyCoVarsOfType $ tyVarKind v
1334
1335 -- | Take a ForAllTy apart, returning the list of tyvars and the result type.
1336 -- This always succeeds, even if it returns only an empty list. Note that the
1337 -- result type returned may have free variables that were bound by a forall.
1338 splitForAllTys :: Type -> ([TyVar], Type)
1339 splitForAllTys ty = split ty ty []
1340 where
1341 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
1342 split _ (ForAllTy (TvBndr tv _) ty) tvs = split ty ty (tv:tvs)
1343 split orig_ty _ tvs = (reverse tvs, orig_ty)
1344
1345 -- | Like 'splitPiTys' but split off only /named/ binders.
1346 splitForAllTyVarBndrs :: Type -> ([TyVarBinder], Type)
1347 splitForAllTyVarBndrs ty = split ty ty []
1348 where
1349 split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs
1350 split _ (ForAllTy b res) bs = split res res (b:bs)
1351 split orig_ty _ bs = (reverse bs, orig_ty)
1352
1353 -- | Checks whether this is a proper forall (with a named binder)
1354 isForAllTy :: Type -> Bool
1355 isForAllTy ty | Just ty' <- coreView ty = isForAllTy ty'
1356 isForAllTy (ForAllTy {}) = True
1357 isForAllTy _ = False
1358
1359 -- | Is this a function or forall?
1360 isPiTy :: Type -> Bool
1361 isPiTy ty | Just ty' <- coreView ty = isForAllTy ty'
1362 isPiTy (ForAllTy {}) = True
1363 isPiTy (FunTy {}) = True
1364 isPiTy _ = False
1365
1366 -- | Take a forall type apart, or panics if that is not possible.
1367 splitForAllTy :: Type -> (TyVar, Type)
1368 splitForAllTy ty
1369 | Just answer <- splitForAllTy_maybe ty = answer
1370 | otherwise = pprPanic "splitForAllTy" (ppr ty)
1371
1372 -- | Drops all ForAllTys
1373 dropForAlls :: Type -> Type
1374 dropForAlls ty = go ty
1375 where
1376 go ty | Just ty' <- coreView ty = go ty'
1377 go (ForAllTy _ res) = go res
1378 go res = res
1379
1380 -- | Attempts to take a forall type apart, but only if it's a proper forall,
1381 -- with a named binder
1382 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
1383 splitForAllTy_maybe ty = go ty
1384 where
1385 go ty | Just ty' <- coreView ty = go ty'
1386 go (ForAllTy (TvBndr tv _) ty) = Just (tv, ty)
1387 go _ = Nothing
1388
1389 -- | Attempts to take a forall type apart; works with proper foralls and
1390 -- functions
1391 splitPiTy_maybe :: Type -> Maybe (TyBinder, Type)
1392 splitPiTy_maybe ty = go ty
1393 where
1394 go ty | Just ty' <- coreView ty = go ty'
1395 go (ForAllTy bndr ty) = Just (Named bndr, ty)
1396 go (FunTy arg res) = Just (Anon arg, res)
1397 go _ = Nothing
1398
1399 -- | Takes a forall type apart, or panics
1400 splitPiTy :: Type -> (TyBinder, Type)
1401 splitPiTy ty
1402 | Just answer <- splitPiTy_maybe ty = answer
1403 | otherwise = pprPanic "splitPiTy" (ppr ty)
1404
1405 -- | Split off all TyBinders to a type, splitting both proper foralls
1406 -- and functions
1407 splitPiTys :: Type -> ([TyBinder], Type)
1408 splitPiTys ty = split ty ty []
1409 where
1410 split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs
1411 split _ (ForAllTy b res) bs = split res res (Named b : bs)
1412 split _ (FunTy arg res) bs = split res res (Anon arg : bs)
1413 split orig_ty _ bs = (reverse bs, orig_ty)
1414
1415 -- Like splitPiTys, but returns only *invisible* binders, including constraints
1416 -- Stops at the first visible binder
1417 splitPiTysInvisible :: Type -> ([TyBinder], Type)
1418 splitPiTysInvisible ty = split ty ty []
1419 where
1420 split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs
1421 split _ (ForAllTy b@(TvBndr _ vis) res) bs
1422 | isInvisibleArgFlag vis = split res res (Named b : bs)
1423 split _ (FunTy arg res) bs
1424 | isPredTy arg = split res res (Anon arg : bs)
1425 split orig_ty _ bs = (reverse bs, orig_ty)
1426
1427 -- | Given a tycon and its arguments, filters out any invisible arguments
1428 filterOutInvisibleTypes :: TyCon -> [Type] -> [Type]
1429 filterOutInvisibleTypes tc tys = snd $ partitionInvisibles tc id tys
1430
1431 -- | Like 'filterOutInvisibles', but works on 'TyVar's
1432 filterOutInvisibleTyVars :: TyCon -> [TyVar] -> [TyVar]
1433 filterOutInvisibleTyVars tc tvs = snd $ partitionInvisibles tc mkTyVarTy tvs
1434
1435 -- | Given a tycon and a list of things (which correspond to arguments),
1436 -- partitions the things into
1437 -- Inferred or Specified ones and
1438 -- Required ones
1439 -- The callback function is necessary for this scenario:
1440 --
1441 -- > T :: forall k. k -> k
1442 -- > partitionInvisibles T [forall m. m -> m -> m, S, R, Q]
1443 --
1444 -- After substituting, we get
1445 --
1446 -- > T (forall m. m -> m -> m) :: (forall m. m -> m -> m) -> forall n. n -> n -> n
1447 --
1448 -- Thus, the first argument is invisible, @S@ is visible, @R@ is invisible again,
1449 -- and @Q@ is visible.
1450 --
1451 -- If you're absolutely sure that your tycon's kind doesn't end in a variable,
1452 -- it's OK if the callback function panics, as that's the only time it's
1453 -- consulted.
1454 partitionInvisibles :: TyCon -> (a -> Type) -> [a] -> ([a], [a])
1455 partitionInvisibles tc get_ty = go emptyTCvSubst (tyConKind tc)
1456 where
1457 go _ _ [] = ([], [])
1458 go subst (ForAllTy (TvBndr tv vis) res_ki) (x:xs)
1459 | isVisibleArgFlag vis = second (x :) (go subst' res_ki xs)
1460 | otherwise = first (x :) (go subst' res_ki xs)
1461 where
1462 subst' = extendTvSubst subst tv (get_ty x)
1463 go subst (TyVarTy tv) xs
1464 | Just ki <- lookupTyVar subst tv = go subst ki xs
1465 go _ _ xs = ([], xs) -- something is ill-kinded. But this can happen
1466 -- when printing errors. Assume everything is visible.
1467
1468 -- @isTauTy@ tests if a type has no foralls
1469 isTauTy :: Type -> Bool
1470 isTauTy ty | Just ty' <- coreView ty = isTauTy ty'
1471 isTauTy (TyVarTy _) = True
1472 isTauTy (LitTy {}) = True
1473 isTauTy (TyConApp tc tys) = all isTauTy tys && isTauTyCon tc
1474 isTauTy (AppTy a b) = isTauTy a && isTauTy b
1475 isTauTy (FunTy a b) = isTauTy a && isTauTy b
1476 isTauTy (ForAllTy {}) = False
1477 isTauTy (CastTy ty _) = isTauTy ty
1478 isTauTy (CoercionTy _) = False -- Not sure about this
1479
1480 {-
1481 %************************************************************************
1482 %* *
1483 TyBinders
1484 %* *
1485 %************************************************************************
1486 -}
1487
1488 -- | Make a named binder
1489 mkTyVarBinder :: ArgFlag -> Var -> TyVarBinder
1490 mkTyVarBinder vis var = TvBndr var vis
1491
1492 -- | Make many named binders
1493 mkTyVarBinders :: ArgFlag -> [TyVar] -> [TyVarBinder]
1494 mkTyVarBinders vis = map (mkTyVarBinder vis)
1495
1496 -- | Make an anonymous binder
1497 mkAnonBinder :: Type -> TyBinder
1498 mkAnonBinder = Anon
1499
1500 -- | Does this binder bind a variable that is /not/ erased? Returns
1501 -- 'True' for anonymous binders.
1502 isAnonTyBinder :: TyBinder -> Bool
1503 isAnonTyBinder (Named {}) = False
1504 isAnonTyBinder (Anon {}) = True
1505
1506 isNamedTyBinder :: TyBinder -> Bool
1507 isNamedTyBinder (Named {}) = True
1508 isNamedTyBinder (Anon {}) = False
1509
1510 tyBinderType :: TyBinder -> Type
1511 -- Barely used
1512 tyBinderType (Named tvb) = binderKind tvb
1513 tyBinderType (Anon ty) = ty
1514
1515 -- | Extract a relevant type, if there is one.
1516 binderRelevantType_maybe :: TyBinder -> Maybe Type
1517 binderRelevantType_maybe (Named {}) = Nothing
1518 binderRelevantType_maybe (Anon ty) = Just ty
1519
1520 -- | Like 'maybe', but for binders.
1521 caseBinder :: TyBinder -- ^ binder to scrutinize
1522 -> (TyVarBinder -> a) -- ^ named case
1523 -> (Type -> a) -- ^ anonymous case
1524 -> a
1525 caseBinder (Named v) f _ = f v
1526 caseBinder (Anon t) _ d = d t
1527
1528 -- | Manufacture a new 'TyConBinder' from a 'TyBinder'. Anonymous
1529 -- 'TyBinder's are still assigned names as 'TyConBinder's, so we need
1530 -- the extra gunk with which to construct a 'Name'. Used when producing
1531 -- tyConTyVars from a datatype kind signature. Defined here to avoid module
1532 -- loops.
1533 mkTyBinderTyConBinder :: TyBinder -> SrcSpan -> Unique -> OccName -> TyConBinder
1534 mkTyBinderTyConBinder (Named (TvBndr tv argf)) _ _ _ = TvBndr tv (NamedTCB argf)
1535 mkTyBinderTyConBinder (Anon kind) loc uniq occ
1536 = TvBndr (mkTyVar (mkInternalName uniq occ loc) kind) AnonTCB
1537
1538 {-
1539 %************************************************************************
1540 %* *
1541 Pred
1542 * *
1543 ************************************************************************
1544
1545 Predicates on PredType
1546
1547 Note [isPredTy complications]
1548 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1549 You would think that we could define
1550 isPredTy ty = isConstraintKind (typeKind ty)
1551 But there are a number of complications:
1552
1553 * isPredTy is used when printing types, which can happen in debug
1554 printing during type checking of not-fully-zonked types. So it's
1555 not cool to say isConstraintKind (typeKind ty) because, absent
1556 zonking, the type might be ill-kinded, and typeKind crashes. Hence the
1557 rather tiresome story here
1558
1559 * isPredTy must return "True" to *unlifted* coercions, such as (t1 ~# t2)
1560 and (t1 ~R# t2), which are not of kind Constraint! Currently they are
1561 of kind #.
1562
1563 * If we do form the type '(C a => C [a]) => blah', then we'd like to
1564 print it as such. But that means that isPredTy must return True for
1565 (C a => C [a]). Admittedly that type is illegal in Haskell, but we
1566 want to print it nicely in error messages.
1567 -}
1568
1569 -- | Is the type suitable to classify a given/wanted in the typechecker?
1570 isPredTy :: Type -> Bool
1571 -- See Note [isPredTy complications]
1572 isPredTy ty = go ty []
1573 where
1574 go :: Type -> [KindOrType] -> Bool
1575 go (AppTy ty1 ty2) args = go ty1 (ty2 : args)
1576 go (TyVarTy tv) args = go_k (tyVarKind tv) args
1577 go (TyConApp tc tys) args = ASSERT( null args ) -- TyConApp invariant
1578 go_tc tc tys
1579 go (FunTy arg res) []
1580 | isPredTy arg = isPredTy res -- (Eq a => C a)
1581 | otherwise = False -- (Int -> Bool)
1582 go (ForAllTy _ ty) [] = go ty []
1583 go (CastTy _ co) args = go_k (pSnd (coercionKind co)) args
1584 go _ _ = False
1585
1586 go_tc :: TyCon -> [KindOrType] -> Bool
1587 go_tc tc args
1588 | tc `hasKey` eqPrimTyConKey || tc `hasKey` eqReprPrimTyConKey
1589 = length args == 4 -- ~# and ~R# sadly have result kind #
1590 -- not Constraint; but we still want
1591 -- isPredTy to reply True.
1592 | otherwise = go_k (tyConKind tc) args
1593
1594 go_k :: Kind -> [KindOrType] -> Bool
1595 -- True <=> ('k' applied to 'kts') = Constraint
1596 go_k k [] = isConstraintKind k
1597 go_k k (arg:args) = case piResultTy_maybe k arg of
1598 Just k' -> go_k k' args
1599 Nothing -> WARN( True, text "isPredTy" <+> ppr ty )
1600 False
1601 -- This last case shouldn't happen under most circumstances. It can
1602 -- occur if we call isPredTy during kind checking, especially if one
1603 -- of the following happens:
1604 --
1605 -- 1. There is actually a kind error. Example in which this showed up:
1606 -- polykinds/T11399
1607 --
1608 -- 2. A type constructor application appears to be oversaturated. An
1609 -- example of this occurred in GHC Trac #13187:
1610 --
1611 -- {-# LANGUAGE PolyKinds #-}
1612 -- type Const a b = b
1613 -- f :: Const Int (,) Bool Char -> Char
1614 --
1615 -- We call isPredTy (Const k1 k2 Int (,) Bool Char
1616 -- where k1,k2 are unification variables that have been
1617 -- unified to *, and (*->*->*) resp, /but not zonked/.
1618 -- This shows that isPredTy can report a false negative
1619 -- if a constraint is similarly oversaturated, but
1620 -- it's hard to do better than isPredTy currently does without
1621 -- zonking, so we punt on such cases for now. This only happens
1622 -- during debug-printing, so it doesn't matter.
1623
1624 isClassPred, isEqPred, isNomEqPred, isIPPred :: PredType -> Bool
1625 isClassPred ty = case tyConAppTyCon_maybe ty of
1626 Just tyCon | isClassTyCon tyCon -> True
1627 _ -> False
1628 isEqPred ty = case tyConAppTyCon_maybe ty of
1629 Just tyCon -> tyCon `hasKey` eqPrimTyConKey
1630 || tyCon `hasKey` eqReprPrimTyConKey
1631 _ -> False
1632
1633 isNomEqPred ty = case tyConAppTyCon_maybe ty of
1634 Just tyCon -> tyCon `hasKey` eqPrimTyConKey
1635 _ -> False
1636
1637 isIPPred ty = case tyConAppTyCon_maybe ty of
1638 Just tc -> isIPTyCon tc
1639 _ -> False
1640
1641 isIPTyCon :: TyCon -> Bool
1642 isIPTyCon tc = tc `hasKey` ipClassKey
1643 -- Class and its corresponding TyCon have the same Unique
1644
1645 isIPClass :: Class -> Bool
1646 isIPClass cls = cls `hasKey` ipClassKey
1647
1648 isCTupleClass :: Class -> Bool
1649 isCTupleClass cls = isTupleTyCon (classTyCon cls)
1650
1651 isIPPred_maybe :: Type -> Maybe (FastString, Type)
1652 isIPPred_maybe ty =
1653 do (tc,[t1,t2]) <- splitTyConApp_maybe ty
1654 guard (isIPTyCon tc)
1655 x <- isStrLitTy t1
1656 return (x,t2)
1657
1658 {-
1659 Make PredTypes
1660
1661 --------------------- Equality types ---------------------------------
1662 -}
1663
1664 -- | Makes a lifted equality predicate at the given role
1665 mkPrimEqPredRole :: Role -> Type -> Type -> PredType
1666 mkPrimEqPredRole Nominal = mkPrimEqPred
1667 mkPrimEqPredRole Representational = mkReprPrimEqPred
1668 mkPrimEqPredRole Phantom = panic "mkPrimEqPredRole phantom"
1669
1670 -- | Creates a primitive type equality predicate.
1671 -- Invariant: the types are not Coercions
1672 mkPrimEqPred :: Type -> Type -> Type
1673 mkPrimEqPred ty1 ty2
1674 = TyConApp eqPrimTyCon [k1, k2, ty1, ty2]
1675 where
1676 k1 = typeKind ty1
1677 k2 = typeKind ty2
1678
1679 -- | Creates a primite type equality predicate with explicit kinds
1680 mkHeteroPrimEqPred :: Kind -> Kind -> Type -> Type -> Type
1681 mkHeteroPrimEqPred k1 k2 ty1 ty2 = TyConApp eqPrimTyCon [k1, k2, ty1, ty2]
1682
1683 -- | Creates a primitive representational type equality predicate
1684 -- with explicit kinds
1685 mkHeteroReprPrimEqPred :: Kind -> Kind -> Type -> Type -> Type
1686 mkHeteroReprPrimEqPred k1 k2 ty1 ty2
1687 = TyConApp eqReprPrimTyCon [k1, k2, ty1, ty2]
1688
1689 -- | Try to split up a coercion type into the types that it coerces
1690 splitCoercionType_maybe :: Type -> Maybe (Type, Type)
1691 splitCoercionType_maybe ty
1692 = do { (tc, [_, _, ty1, ty2]) <- splitTyConApp_maybe ty
1693 ; guard $ tc `hasKey` eqPrimTyConKey || tc `hasKey` eqReprPrimTyConKey
1694 ; return (ty1, ty2) }
1695
1696 mkReprPrimEqPred :: Type -> Type -> Type
1697 mkReprPrimEqPred ty1 ty2
1698 = TyConApp eqReprPrimTyCon [k1, k2, ty1, ty2]
1699 where
1700 k1 = typeKind ty1
1701 k2 = typeKind ty2
1702
1703 equalityTyCon :: Role -> TyCon
1704 equalityTyCon Nominal = eqPrimTyCon
1705 equalityTyCon Representational = eqReprPrimTyCon
1706 equalityTyCon Phantom = eqPhantPrimTyCon
1707
1708 -- --------------------- Dictionary types ---------------------------------
1709
1710 mkClassPred :: Class -> [Type] -> PredType
1711 mkClassPred clas tys = TyConApp (classTyCon clas) tys
1712
1713 isDictTy :: Type -> Bool
1714 isDictTy = isClassPred
1715
1716 isDictLikeTy :: Type -> Bool
1717 -- Note [Dictionary-like types]
1718 isDictLikeTy ty | Just ty' <- coreView ty = isDictLikeTy ty'
1719 isDictLikeTy ty = case splitTyConApp_maybe ty of
1720 Just (tc, tys) | isClassTyCon tc -> True
1721 | isTupleTyCon tc -> all isDictLikeTy tys
1722 _other -> False
1723
1724 {-
1725 Note [Dictionary-like types]
1726 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1727 Being "dictionary-like" means either a dictionary type or a tuple thereof.
1728 In GHC 6.10 we build implication constraints which construct such tuples,
1729 and if we land up with a binding
1730 t :: (C [a], Eq [a])
1731 t = blah
1732 then we want to treat t as cheap under "-fdicts-cheap" for example.
1733 (Implication constraints are normally inlined, but sadly not if the
1734 occurrence is itself inside an INLINE function! Until we revise the
1735 handling of implication constraints, that is.) This turned out to
1736 be important in getting good arities in DPH code. Example:
1737
1738 class C a
1739 class D a where { foo :: a -> a }
1740 instance C a => D (Maybe a) where { foo x = x }
1741
1742 bar :: (C a, C b) => a -> b -> (Maybe a, Maybe b)
1743 {-# INLINE bar #-}
1744 bar x y = (foo (Just x), foo (Just y))
1745
1746 Then 'bar' should jolly well have arity 4 (two dicts, two args), but
1747 we ended up with something like
1748 bar = __inline_me__ (\d1,d2. let t :: (D (Maybe a), D (Maybe b)) = ...
1749 in \x,y. <blah>)
1750
1751 This is all a bit ad-hoc; eg it relies on knowing that implication
1752 constraints build tuples.
1753
1754
1755 Decomposing PredType
1756 -}
1757
1758 -- | A choice of equality relation. This is separate from the type 'Role'
1759 -- because 'Phantom' does not define a (non-trivial) equality relation.
1760 data EqRel = NomEq | ReprEq
1761 deriving (Eq, Ord)
1762
1763 instance Outputable EqRel where
1764 ppr NomEq = text "nominal equality"
1765 ppr ReprEq = text "representational equality"
1766
1767 eqRelRole :: EqRel -> Role
1768 eqRelRole NomEq = Nominal
1769 eqRelRole ReprEq = Representational
1770
1771 data PredTree = ClassPred Class [Type]
1772 | EqPred EqRel Type Type
1773 | IrredPred PredType
1774
1775 classifyPredType :: PredType -> PredTree
1776 classifyPredType ev_ty = case splitTyConApp_maybe ev_ty of
1777 Just (tc, [_, _, ty1, ty2])
1778 | tc `hasKey` eqReprPrimTyConKey -> EqPred ReprEq ty1 ty2
1779 | tc `hasKey` eqPrimTyConKey -> EqPred NomEq ty1 ty2
1780 Just (tc, tys)
1781 | Just clas <- tyConClass_maybe tc -> ClassPred clas tys
1782 _ -> IrredPred ev_ty
1783
1784 getClassPredTys :: PredType -> (Class, [Type])
1785 getClassPredTys ty = case getClassPredTys_maybe ty of
1786 Just (clas, tys) -> (clas, tys)
1787 Nothing -> pprPanic "getClassPredTys" (ppr ty)
1788
1789 getClassPredTys_maybe :: PredType -> Maybe (Class, [Type])
1790 getClassPredTys_maybe ty = case splitTyConApp_maybe ty of
1791 Just (tc, tys) | Just clas <- tyConClass_maybe tc -> Just (clas, tys)
1792 _ -> Nothing
1793
1794 getEqPredTys :: PredType -> (Type, Type)
1795 getEqPredTys ty
1796 = case splitTyConApp_maybe ty of
1797 Just (tc, [_, _, ty1, ty2])
1798 | tc `hasKey` eqPrimTyConKey
1799 || tc `hasKey` eqReprPrimTyConKey
1800 -> (ty1, ty2)
1801 _ -> pprPanic "getEqPredTys" (ppr ty)
1802
1803 getEqPredTys_maybe :: PredType -> Maybe (Role, Type, Type)
1804 getEqPredTys_maybe ty
1805 = case splitTyConApp_maybe ty of
1806 Just (tc, [_, _, ty1, ty2])
1807 | tc `hasKey` eqPrimTyConKey -> Just (Nominal, ty1, ty2)
1808 | tc `hasKey` eqReprPrimTyConKey -> Just (Representational, ty1, ty2)
1809 _ -> Nothing
1810
1811 getEqPredRole :: PredType -> Role
1812 getEqPredRole ty = eqRelRole (predTypeEqRel ty)
1813
1814 -- | Get the equality relation relevant for a pred type.
1815 predTypeEqRel :: PredType -> EqRel
1816 predTypeEqRel ty
1817 | Just (tc, _) <- splitTyConApp_maybe ty
1818 , tc `hasKey` eqReprPrimTyConKey
1819 = ReprEq
1820 | otherwise
1821 = NomEq
1822
1823 {-
1824 %************************************************************************
1825 %* *
1826 Well-scoped tyvars
1827 * *
1828 ************************************************************************
1829 -}
1830
1831 -- | Do a topological sort on a list of tyvars,
1832 -- so that binders occur before occurrences
1833 -- E.g. given [ a::k, k::*, b::k ]
1834 -- it'll return a well-scoped list [ k::*, a::k, b::k ]
1835 --
1836 -- This is a deterministic sorting operation
1837 -- (that is, doesn't depend on Uniques).
1838 toposortTyVars :: [TyVar] -> [TyVar]
1839 toposortTyVars tvs = reverse $
1840 [ node_payload node | node <- topologicalSortG $
1841 graphFromEdgedVerticesOrd nodes ]
1842 where
1843 var_ids :: VarEnv Int
1844 var_ids = mkVarEnv (zip tvs [1..])
1845
1846 nodes :: [ Node Int TyVar ]
1847 nodes = [ DigraphNode
1848 tv
1849 (lookupVarEnv_NF var_ids tv)
1850 (mapMaybe (lookupVarEnv var_ids)
1851 (tyCoVarsOfTypeList (tyVarKind tv)))
1852 | tv <- tvs ]
1853
1854 -- | Extract a well-scoped list of variables from a deterministic set of
1855 -- variables. The result is deterministic.
1856 -- NB: There used to exist varSetElemsWellScoped :: VarSet -> [Var] which
1857 -- took a non-deterministic set and produced a non-deterministic
1858 -- well-scoped list. If you care about the list being well-scoped you also
1859 -- most likely care about it being in deterministic order.
1860 dVarSetElemsWellScoped :: DVarSet -> [Var]
1861 dVarSetElemsWellScoped = toposortTyVars . dVarSetElems
1862
1863 -- | Get the free vars of a type in scoped order
1864 tyCoVarsOfTypeWellScoped :: Type -> [TyVar]
1865 tyCoVarsOfTypeWellScoped = toposortTyVars . tyCoVarsOfTypeList
1866
1867 -- | Get the free vars of types in scoped order
1868 tyCoVarsOfTypesWellScoped :: [Type] -> [TyVar]
1869 tyCoVarsOfTypesWellScoped = toposortTyVars . tyCoVarsOfTypesList
1870
1871 {-
1872 ************************************************************************
1873 * *
1874 \subsection{Type families}
1875 * *
1876 ************************************************************************
1877 -}
1878
1879 mkFamilyTyConApp :: TyCon -> [Type] -> Type
1880 -- ^ Given a family instance TyCon and its arg types, return the
1881 -- corresponding family type. E.g:
1882 --
1883 -- > data family T a
1884 -- > data instance T (Maybe b) = MkT b
1885 --
1886 -- Where the instance tycon is :RTL, so:
1887 --
1888 -- > mkFamilyTyConApp :RTL Int = T (Maybe Int)
1889 mkFamilyTyConApp tc tys
1890 | Just (fam_tc, fam_tys) <- tyConFamInst_maybe tc
1891 , let tvs = tyConTyVars tc
1892 fam_subst = ASSERT2( length tvs == length tys, ppr tc <+> ppr tys )
1893 zipTvSubst tvs tys
1894 = mkTyConApp fam_tc (substTys fam_subst fam_tys)
1895 | otherwise
1896 = mkTyConApp tc tys
1897
1898 -- | Get the type on the LHS of a coercion induced by a type/data
1899 -- family instance.
1900 coAxNthLHS :: CoAxiom br -> Int -> Type
1901 coAxNthLHS ax ind =
1902 mkTyConApp (coAxiomTyCon ax) (coAxBranchLHS (coAxiomNthBranch ax ind))
1903
1904 -- | Pretty prints a 'TyCon', using the family instance in case of a
1905 -- representation tycon. For example:
1906 --
1907 -- > data T [a] = ...
1908 --
1909 -- In that case we want to print @T [a]@, where @T@ is the family 'TyCon'
1910 pprSourceTyCon :: TyCon -> SDoc
1911 pprSourceTyCon tycon
1912 | Just (fam_tc, tys) <- tyConFamInst_maybe tycon
1913 = ppr $ fam_tc `TyConApp` tys -- can't be FunTyCon
1914 | otherwise
1915 = ppr tycon
1916
1917 -- @isTauTy@ tests if a type has no foralls
1918 isFamFreeTy :: Type -> Bool
1919 isFamFreeTy ty | Just ty' <- coreView ty = isFamFreeTy ty'
1920 isFamFreeTy (TyVarTy _) = True
1921 isFamFreeTy (LitTy {}) = True
1922 isFamFreeTy (TyConApp tc tys) = all isFamFreeTy tys && isFamFreeTyCon tc
1923 isFamFreeTy (AppTy a b) = isFamFreeTy a && isFamFreeTy b
1924 isFamFreeTy (FunTy a b) = isFamFreeTy a && isFamFreeTy b
1925 isFamFreeTy (ForAllTy _ ty) = isFamFreeTy ty
1926 isFamFreeTy (CastTy ty _) = isFamFreeTy ty
1927 isFamFreeTy (CoercionTy _) = False -- Not sure about this
1928
1929 {-
1930 ************************************************************************
1931 * *
1932 \subsection{Liftedness}
1933 * *
1934 ************************************************************************
1935 -}
1936
1937 -- | Returns Just True if this type is surely lifted, Just False
1938 -- if it is surely unlifted, Nothing if we can't be sure (i.e., it is
1939 -- levity polymorphic), and panics if the kind does not have the shape
1940 -- TYPE r.
1941 isLiftedType_maybe :: HasDebugCallStack => Type -> Maybe Bool
1942 isLiftedType_maybe ty = go (getRuntimeRep "isLiftedType_maybe" ty)
1943 where
1944 go rr | Just rr' <- coreView rr = go rr'
1945 go (TyConApp lifted_rep [])
1946 | lifted_rep `hasKey` liftedRepDataConKey = Just True
1947 go (TyConApp {}) = Just False -- everything else is unlifted
1948 go _ = Nothing -- levity polymorphic
1949
1950 -- | See "Type#type_classification" for what an unlifted type is.
1951 -- Panics on levity polymorphic types.
1952 isUnliftedType :: HasDebugCallStack => Type -> Bool
1953 -- isUnliftedType returns True for forall'd unlifted types:
1954 -- x :: forall a. Int#
1955 -- I found bindings like these were getting floated to the top level.
1956 -- They are pretty bogus types, mind you. It would be better never to
1957 -- construct them
1958 isUnliftedType ty
1959 = not (isLiftedType_maybe ty `orElse`
1960 pprPanic "isUnliftedType" (ppr ty <+> dcolon <+> ppr (typeKind ty)))
1961
1962 -- | Extract the RuntimeRep classifier of a type. For instance,
1963 -- @getRuntimeRep_maybe Int = LiftedRep@. Returns 'Nothing' if this is not
1964 -- possible.
1965 getRuntimeRep_maybe :: HasDebugCallStack
1966 => Type -> Maybe Type
1967 getRuntimeRep_maybe = getRuntimeRepFromKind_maybe . typeKind
1968
1969 -- | Extract the RuntimeRep classifier of a type. For instance,
1970 -- @getRuntimeRep_maybe Int = LiftedRep@. Panics if this is not possible.
1971 getRuntimeRep :: HasDebugCallStack
1972 => String -- ^ Printed in case of an error
1973 -> Type -> Type
1974 getRuntimeRep err ty =
1975 case getRuntimeRep_maybe ty of
1976 Just r -> r
1977 Nothing -> pprPanic "getRuntimeRep"
1978 (text err $$ ppr ty <+> dcolon <+> ppr (typeKind ty))
1979
1980 -- | Extract the RuntimeRep classifier of a type from its kind. For example,
1981 -- @getRuntimeRepFromKind * = LiftedRep@; Panics if this is not possible.
1982 getRuntimeRepFromKind :: HasDebugCallStack
1983 => String -> Type -> Type
1984 getRuntimeRepFromKind err k =
1985 case getRuntimeRepFromKind_maybe k of
1986 Just r -> r
1987 Nothing -> pprPanic "getRuntimeRepFromKind"
1988 (text err $$ ppr k <+> dcolon <+> ppr (typeKind k))
1989
1990 -- | Extract the RuntimeRep classifier of a type from its kind. For example,
1991 -- @getRuntimeRepFromKind * = LiftedRep@; Returns 'Nothing' if this is not
1992 -- possible.
1993 getRuntimeRepFromKind_maybe :: HasDebugCallStack
1994 => Type -> Maybe Type
1995 getRuntimeRepFromKind_maybe = go
1996 where
1997 go k | Just k' <- coreView k = go k'
1998 go k
1999 | Just (_tc, [arg]) <- splitTyConApp_maybe k
2000 = ASSERT2( _tc `hasKey` tYPETyConKey, ppr k )
2001 Just arg
2002 go _ = Nothing
2003
2004 isUnboxedTupleType :: Type -> Bool
2005 isUnboxedTupleType ty
2006 = tyConAppTyCon (getRuntimeRep "isUnboxedTupleType" ty) `hasKey` tupleRepDataConKey
2007 -- NB: Do not use typePrimRep, as that can't tell the difference between
2008 -- unboxed tuples and unboxed sums
2009
2010
2011 isUnboxedSumType :: Type -> Bool
2012 isUnboxedSumType ty
2013 = tyConAppTyCon (getRuntimeRep "isUnboxedSumType" ty) `hasKey` sumRepDataConKey
2014
2015 -- | See "Type#type_classification" for what an algebraic type is.
2016 -- Should only be applied to /types/, as opposed to e.g. partially
2017 -- saturated type constructors
2018 isAlgType :: Type -> Bool
2019 isAlgType ty
2020 = case splitTyConApp_maybe ty of
2021 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
2022 isAlgTyCon tc
2023 _other -> False
2024
2025 -- | See "Type#type_classification" for what an algebraic type is.
2026 -- Should only be applied to /types/, as opposed to e.g. partially
2027 -- saturated type constructors. Closed type constructors are those
2028 -- with a fixed right hand side, as opposed to e.g. associated types
2029 isClosedAlgType :: Type -> Bool
2030 isClosedAlgType ty
2031 = case splitTyConApp_maybe ty of
2032 Just (tc, ty_args) | isAlgTyCon tc && not (isFamilyTyCon tc)
2033 -> ASSERT2( ty_args `lengthIs` tyConArity tc, ppr ty ) True
2034 _other -> False
2035
2036 -- | Check whether a type is a data family type
2037 isDataFamilyAppType :: Type -> Bool
2038 isDataFamilyAppType ty = case tyConAppTyCon_maybe ty of
2039 Just tc -> isDataFamilyTyCon tc
2040 _ -> False
2041
2042 -- | Computes whether an argument (or let right hand side) should
2043 -- be computed strictly or lazily, based only on its type.
2044 -- Currently, it's just 'isUnliftedType'. Panics on levity-polymorphic types.
2045 isStrictType :: HasDebugCallStack => Type -> Bool
2046 isStrictType = isUnliftedType
2047
2048 isPrimitiveType :: Type -> Bool
2049 -- ^ Returns true of types that are opaque to Haskell.
2050 isPrimitiveType ty = case splitTyConApp_maybe ty of
2051 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
2052 isPrimTyCon tc
2053 _ -> False
2054
2055 {-
2056 ************************************************************************
2057 * *
2058 \subsection{Join points}
2059 * *
2060 ************************************************************************
2061 -}
2062
2063 -- | Determine whether a type could be the type of a join point of given total
2064 -- arity, according to the polymorphism rule. A join point cannot be polymorphic
2065 -- in its return type, since given
2066 -- join j @a @b x y z = e1 in e2,
2067 -- the types of e1 and e2 must be the same, and a and b are not in scope for e2.
2068 -- (See Note [The polymorphism rule of join points] in CoreSyn.) Returns False
2069 -- also if the type simply doesn't have enough arguments.
2070 --
2071 -- Note that we need to know how many arguments (type *and* value) the putative
2072 -- join point takes; for instance, if
2073 -- j :: forall a. a -> Int
2074 -- then j could be a binary join point returning an Int, but it could *not* be a
2075 -- unary join point returning a -> Int.
2076 --
2077 -- TODO: See Note [Excess polymorphism and join points]
2078 isValidJoinPointType :: JoinArity -> Type -> Bool
2079 isValidJoinPointType arity ty
2080 = valid_under emptyVarSet arity ty
2081 where
2082 valid_under tvs arity ty
2083 | arity == 0
2084 = isEmptyVarSet (tvs `intersectVarSet` tyCoVarsOfType ty)
2085 | Just (t, ty') <- splitForAllTy_maybe ty
2086 = valid_under (tvs `extendVarSet` t) (arity-1) ty'
2087 | Just (_, res_ty) <- splitFunTy_maybe ty
2088 = valid_under tvs (arity-1) res_ty
2089 | otherwise
2090 = False
2091
2092 {-
2093 ************************************************************************
2094 * *
2095 \subsection{Sequencing on types}
2096 * *
2097 ************************************************************************
2098 -}
2099
2100 seqType :: Type -> ()
2101 seqType (LitTy n) = n `seq` ()
2102 seqType (TyVarTy tv) = tv `seq` ()
2103 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
2104 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
2105 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
2106 seqType (ForAllTy (TvBndr tv _) ty) = seqType (tyVarKind tv) `seq` seqType ty
2107 seqType (CastTy ty co) = seqType ty `seq` seqCo co
2108 seqType (CoercionTy co) = seqCo co
2109
2110 seqTypes :: [Type] -> ()
2111 seqTypes [] = ()
2112 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
2113
2114 {-
2115 ************************************************************************
2116 * *
2117 Comparison for types
2118 (We don't use instances so that we know where it happens)
2119 * *
2120 ************************************************************************
2121
2122 Note [Equality on AppTys]
2123 ~~~~~~~~~~~~~~~~~~~~~~~~~
2124 In our cast-ignoring equality, we want to say that the following two
2125 are equal:
2126
2127 (Maybe |> co) (Int |> co') ~? Maybe Int
2128
2129 But the left is an AppTy while the right is a TyConApp. The solution is
2130 to use repSplitAppTy_maybe to break up the TyConApp into its pieces and
2131 then continue. Easy to do, but also easy to forget to do.
2132
2133 -}
2134
2135 eqType :: Type -> Type -> Bool
2136 -- ^ Type equality on source types. Does not look through @newtypes@ or
2137 -- 'PredType's, but it does look through type synonyms.
2138 -- This first checks that the kinds of the types are equal and then
2139 -- checks whether the types are equal, ignoring casts and coercions.
2140 -- (The kind check is a recursive call, but since all kinds have type
2141 -- @Type@, there is no need to check the types of kinds.)
2142 -- See also Note [Non-trivial definitional equality] in TyCoRep.
2143 eqType t1 t2 = isEqual $ nonDetCmpType t1 t2
2144 -- It's OK to use nonDetCmpType here and eqType is deterministic,
2145 -- nonDetCmpType does equality deterministically
2146
2147 -- | Compare types with respect to a (presumably) non-empty 'RnEnv2'.
2148 eqTypeX :: RnEnv2 -> Type -> Type -> Bool
2149 eqTypeX env t1 t2 = isEqual $ nonDetCmpTypeX env t1 t2
2150 -- It's OK to use nonDetCmpType here and eqTypeX is deterministic,
2151 -- nonDetCmpTypeX does equality deterministically
2152
2153 -- | Type equality on lists of types, looking through type synonyms
2154 -- but not newtypes.
2155 eqTypes :: [Type] -> [Type] -> Bool
2156 eqTypes tys1 tys2 = isEqual $ nonDetCmpTypes tys1 tys2
2157 -- It's OK to use nonDetCmpType here and eqTypes is deterministic,
2158 -- nonDetCmpTypes does equality deterministically
2159
2160 eqVarBndrs :: RnEnv2 -> [Var] -> [Var] -> Maybe RnEnv2
2161 -- Check that the var lists are the same length
2162 -- and have matching kinds; if so, extend the RnEnv2
2163 -- Returns Nothing if they don't match
2164 eqVarBndrs env [] []
2165 = Just env
2166 eqVarBndrs env (tv1:tvs1) (tv2:tvs2)
2167 | eqTypeX env (tyVarKind tv1) (tyVarKind tv2)
2168 = eqVarBndrs (rnBndr2 env tv1 tv2) tvs1 tvs2
2169 eqVarBndrs _ _ _= Nothing
2170
2171 -- Now here comes the real worker
2172
2173 {-
2174 Note [nonDetCmpType nondeterminism]
2175 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2176 nonDetCmpType is implemented in terms of nonDetCmpTypeX. nonDetCmpTypeX
2177 uses nonDetCmpTc which compares TyCons by their Unique value. Using Uniques for
2178 ordering leads to nondeterminism. We hit the same problem in the TyVarTy case,
2179 comparing type variables is nondeterministic, note the call to nonDetCmpVar in
2180 nonDetCmpTypeX.
2181 See Note [Unique Determinism] for more details.
2182 -}
2183
2184 nonDetCmpType :: Type -> Type -> Ordering
2185 nonDetCmpType t1 t2
2186 -- we know k1 and k2 have the same kind, because they both have kind *.
2187 = nonDetCmpTypeX rn_env t1 t2
2188 where
2189 rn_env = mkRnEnv2 (mkInScopeSet (tyCoVarsOfTypes [t1, t2]))
2190
2191 nonDetCmpTypes :: [Type] -> [Type] -> Ordering
2192 nonDetCmpTypes ts1 ts2 = nonDetCmpTypesX rn_env ts1 ts2
2193 where
2194 rn_env = mkRnEnv2 (mkInScopeSet (tyCoVarsOfTypes (ts1 ++ ts2)))
2195
2196 -- | An ordering relation between two 'Type's (known below as @t1 :: k1@
2197 -- and @t2 :: k2@)
2198 data TypeOrdering = TLT -- ^ @t1 < t2@
2199 | TEQ -- ^ @t1 ~ t2@ and there are no casts in either,
2200 -- therefore we can conclude @k1 ~ k2@
2201 | TEQX -- ^ @t1 ~ t2@ yet one of the types contains a cast so
2202 -- they may differ in kind.
2203 | TGT -- ^ @t1 > t2@
2204 deriving (Eq, Ord, Enum, Bounded)
2205
2206 nonDetCmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
2207 -- See Note [Non-trivial definitional equality] in TyCoRep
2208 nonDetCmpTypeX env orig_t1 orig_t2 =
2209 case go env orig_t1 orig_t2 of
2210 -- If there are casts then we also need to do a comparison of the kinds of
2211 -- the types being compared
2212 TEQX -> toOrdering $ go env k1 k2
2213 ty_ordering -> toOrdering ty_ordering
2214 where
2215 k1 = typeKind orig_t1
2216 k2 = typeKind orig_t2
2217
2218 toOrdering :: TypeOrdering -> Ordering
2219 toOrdering TLT = LT
2220 toOrdering TEQ = EQ
2221 toOrdering TEQX = EQ
2222 toOrdering TGT = GT
2223
2224 liftOrdering :: Ordering -> TypeOrdering
2225 liftOrdering LT = TLT
2226 liftOrdering EQ = TEQ
2227 liftOrdering GT = TGT
2228
2229 thenCmpTy :: TypeOrdering -> TypeOrdering -> TypeOrdering
2230 thenCmpTy TEQ rel = rel
2231 thenCmpTy TEQX rel = hasCast rel
2232 thenCmpTy rel _ = rel
2233
2234 hasCast :: TypeOrdering -> TypeOrdering
2235 hasCast TEQ = TEQX
2236 hasCast rel = rel
2237
2238 -- Returns both the resulting ordering relation between the two types
2239 -- and whether either contains a cast.
2240 go :: RnEnv2 -> Type -> Type -> TypeOrdering
2241 go env t1 t2
2242 | Just t1' <- coreView t1 = go env t1' t2
2243 | Just t2' <- coreView t2 = go env t1 t2'
2244
2245 go env (TyVarTy tv1) (TyVarTy tv2)
2246 = liftOrdering $ rnOccL env tv1 `nonDetCmpVar` rnOccR env tv2
2247 go env (ForAllTy (TvBndr tv1 _) t1) (ForAllTy (TvBndr tv2 _) t2)
2248 = go env (tyVarKind tv1) (tyVarKind tv2)
2249 `thenCmpTy` go (rnBndr2 env tv1 tv2) t1 t2
2250 -- See Note [Equality on AppTys]
2251 go env (AppTy s1 t1) ty2
2252 | Just (s2, t2) <- repSplitAppTy_maybe ty2
2253 = go env s1 s2 `thenCmpTy` go env t1 t2
2254 go env ty1 (AppTy s2 t2)
2255 | Just (s1, t1) <- repSplitAppTy_maybe ty1
2256 = go env s1 s2 `thenCmpTy` go env t1 t2
2257 go env (FunTy s1 t1) (FunTy s2 t2)
2258 = go env s1 s2 `thenCmpTy` go env t1 t2
2259 go env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
2260 = liftOrdering (tc1 `nonDetCmpTc` tc2) `thenCmpTy` gos env tys1 tys2
2261 go _ (LitTy l1) (LitTy l2) = liftOrdering (compare l1 l2)
2262 go env (CastTy t1 _) t2 = hasCast $ go env t1 t2
2263 go env t1 (CastTy t2 _) = hasCast $ go env t1 t2
2264
2265 go _ (CoercionTy {}) (CoercionTy {}) = TEQ
2266
2267 -- Deal with the rest: TyVarTy < CoercionTy < AppTy < LitTy < TyConApp < ForAllTy
2268 go _ ty1 ty2
2269 = liftOrdering $ (get_rank ty1) `compare` (get_rank ty2)
2270 where get_rank :: Type -> Int
2271 get_rank (CastTy {})
2272 = pprPanic "nonDetCmpTypeX.get_rank" (ppr [ty1,ty2])
2273 get_rank (TyVarTy {}) = 0
2274 get_rank (CoercionTy {}) = 1
2275 get_rank (AppTy {}) = 3
2276 get_rank (LitTy {}) = 4
2277 get_rank (TyConApp {}) = 5
2278 get_rank (FunTy {}) = 6
2279 get_rank (ForAllTy {}) = 7
2280
2281 gos :: RnEnv2 -> [Type] -> [Type] -> TypeOrdering
2282 gos _ [] [] = TEQ
2283 gos _ [] _ = TLT
2284 gos _ _ [] = TGT
2285 gos env (ty1:tys1) (ty2:tys2) = go env ty1 ty2 `thenCmpTy` gos env tys1 tys2
2286
2287 -------------
2288 nonDetCmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
2289 nonDetCmpTypesX _ [] [] = EQ
2290 nonDetCmpTypesX env (t1:tys1) (t2:tys2) = nonDetCmpTypeX env t1 t2
2291 `thenCmp` nonDetCmpTypesX env tys1 tys2
2292 nonDetCmpTypesX _ [] _ = LT
2293 nonDetCmpTypesX _ _ [] = GT
2294
2295 -------------
2296 -- | Compare two 'TyCon's. NB: This should /never/ see the "star synonyms",
2297 -- as recognized by Kind.isStarKindSynonymTyCon. See Note
2298 -- [Kind Constraint and kind *] in Kind.
2299 -- See Note [nonDetCmpType nondeterminism]
2300 nonDetCmpTc :: TyCon -> TyCon -> Ordering
2301 nonDetCmpTc tc1 tc2
2302 = ASSERT( not (isStarKindSynonymTyCon tc1) && not (isStarKindSynonymTyCon tc2) )
2303 u1 `nonDetCmpUnique` u2
2304 where
2305 u1 = tyConUnique tc1
2306 u2 = tyConUnique tc2
2307
2308 {-
2309 ************************************************************************
2310 * *
2311 The kind of a type
2312 * *
2313 ************************************************************************
2314 -}
2315
2316 typeKind :: Type -> Kind
2317 typeKind (TyConApp tc tys) = piResultTys (tyConKind tc) tys
2318 typeKind (AppTy fun arg) = piResultTy (typeKind fun) arg
2319 typeKind (LitTy l) = typeLiteralKind l
2320 typeKind (FunTy {}) = liftedTypeKind
2321 typeKind (ForAllTy _ ty) = typeKind ty
2322 typeKind (TyVarTy tyvar) = tyVarKind tyvar
2323 typeKind (CastTy _ty co) = pSnd $ coercionKind co
2324 typeKind (CoercionTy co) = coercionType co
2325
2326 typeLiteralKind :: TyLit -> Kind
2327 typeLiteralKind l =
2328 case l of
2329 NumTyLit _ -> typeNatKind
2330 StrTyLit _ -> typeSymbolKind
2331
2332 -- | Returns True if a type is levity polymorphic. Should be the same
2333 -- as (isKindLevPoly . typeKind) but much faster.
2334 -- Precondition: The type has kind (TYPE blah)
2335 isTypeLevPoly :: Type -> Bool
2336 isTypeLevPoly = go
2337 where
2338 go ty@(TyVarTy {}) = check_kind ty
2339 go ty@(AppTy {}) = check_kind ty
2340 go ty@(TyConApp tc _) | not (isTcLevPoly tc) = False
2341 | otherwise = check_kind ty
2342 go (ForAllTy _ ty) = go ty
2343 go (FunTy {}) = False
2344 go (LitTy {}) = False
2345 go ty@(CastTy {}) = check_kind ty
2346 go ty@(CoercionTy {}) = pprPanic "isTypeLevPoly co" (ppr ty)
2347
2348 check_kind = isKindLevPoly . typeKind
2349
2350 -- | Looking past all pi-types, is the end result potentially levity polymorphic?
2351 -- Example: True for (forall r (a :: TYPE r). String -> a)
2352 -- Example: False for (forall r1 r2 (a :: TYPE r1) (b :: TYPE r2). a -> b -> Type)
2353 resultIsLevPoly :: Type -> Bool
2354 resultIsLevPoly = isTypeLevPoly . snd . splitPiTys
2355
2356 {-
2357 %************************************************************************
2358 %* *
2359 Miscellaneous functions
2360 %* *
2361 %************************************************************************
2362
2363 -}
2364 -- | All type constructors occurring in the type; looking through type
2365 -- synonyms, but not newtypes.
2366 -- When it finds a Class, it returns the class TyCon.
2367 tyConsOfType :: Type -> UniqSet TyCon
2368 tyConsOfType ty
2369 = go ty
2370 where
2371 go :: Type -> UniqSet TyCon -- The UniqSet does duplicate elim
2372 go ty | Just ty' <- coreView ty = go ty'
2373 go (TyVarTy {}) = emptyUniqSet
2374 go (LitTy {}) = emptyUniqSet
2375 go (TyConApp tc tys) = go_tc tc `unionUniqSets` go_s tys
2376 go (AppTy a b) = go a `unionUniqSets` go b
2377 go (FunTy a b) = go a `unionUniqSets` go b `unionUniqSets` go_tc funTyCon
2378 go (ForAllTy (TvBndr tv _) ty) = go ty `unionUniqSets` go (tyVarKind tv)
2379 go (CastTy ty co) = go ty `unionUniqSets` go_co co
2380 go (CoercionTy co) = go_co co
2381
2382 go_co (Refl _ ty) = go ty
2383 go_co (TyConAppCo _ tc args) = go_tc tc `unionUniqSets` go_cos args
2384 go_co (AppCo co arg) = go_co co `unionUniqSets` go_co arg
2385 go_co (ForAllCo _ kind_co co) = go_co kind_co `unionUniqSets` go_co co
2386 go_co (FunCo _ co1 co2) = go_co co1 `unionUniqSets` go_co co2
2387 go_co (AxiomInstCo ax _ args) = go_ax ax `unionUniqSets` go_cos args
2388 go_co (UnivCo p _ t1 t2) = go_prov p `unionUniqSets` go t1 `unionUniqSets` go t2
2389 go_co (CoVarCo {}) = emptyUniqSet
2390 go_co (SymCo co) = go_co co
2391 go_co (TransCo co1 co2) = go_co co1 `unionUniqSets` go_co co2
2392 go_co (NthCo _ co) = go_co co
2393 go_co (LRCo _ co) = go_co co
2394 go_co (InstCo co arg) = go_co co `unionUniqSets` go_co arg
2395 go_co (CoherenceCo co1 co2) = go_co co1 `unionUniqSets` go_co co2
2396 go_co (KindCo co) = go_co co
2397 go_co (SubCo co) = go_co co
2398 go_co (AxiomRuleCo _ cs) = go_cos cs
2399
2400 go_prov UnsafeCoerceProv = emptyUniqSet
2401 go_prov (PhantomProv co) = go_co co
2402 go_prov (ProofIrrelProv co) = go_co co
2403 go_prov (PluginProv _) = emptyUniqSet
2404 go_prov (HoleProv _) = emptyUniqSet
2405 -- this last case can happen from the tyConsOfType used from
2406 -- checkTauTvUpdate
2407
2408 go_s tys = foldr (unionUniqSets . go) emptyUniqSet tys
2409 go_cos cos = foldr (unionUniqSets . go_co) emptyUniqSet cos
2410
2411 go_tc tc = unitUniqSet tc
2412 go_ax ax = go_tc $ coAxiomTyCon ax
2413
2414 -- | Find the result 'Kind' of a type synonym,
2415 -- after applying it to its 'arity' number of type variables
2416 -- Actually this function works fine on data types too,
2417 -- but they'd always return '*', so we never need to ask
2418 synTyConResKind :: TyCon -> Kind
2419 synTyConResKind tycon = piResultTys (tyConKind tycon) (mkTyVarTys (tyConTyVars tycon))
2420
2421 -- | Retrieve the free variables in this type, splitting them based
2422 -- on whether they are used visibly or invisibly. Invisible ones come
2423 -- first.
2424 splitVisVarsOfType :: Type -> Pair TyCoVarSet
2425 splitVisVarsOfType orig_ty = Pair invis_vars vis_vars
2426 where
2427 Pair invis_vars1 vis_vars = go orig_ty
2428 invis_vars = invis_vars1 `minusVarSet` vis_vars
2429
2430 go (TyVarTy tv) = Pair (tyCoVarsOfType $ tyVarKind tv) (unitVarSet tv)
2431 go (AppTy t1 t2) = go t1 `mappend` go t2
2432 go (TyConApp tc tys) = go_tc tc tys
2433 go (FunTy t1 t2) = go t1 `mappend` go t2
2434 go (ForAllTy (TvBndr tv _) ty)
2435 = ((`delVarSet` tv) <$> go ty) `mappend`
2436 (invisible (tyCoVarsOfType $ tyVarKind tv))
2437 go (LitTy {}) = mempty
2438 go (CastTy ty co) = go ty `mappend` invisible (tyCoVarsOfCo co)
2439 go (CoercionTy co) = invisible $ tyCoVarsOfCo co
2440
2441 invisible vs = Pair vs emptyVarSet
2442
2443 go_tc tc tys = let (invis, vis) = partitionInvisibles tc id tys in
2444 invisible (tyCoVarsOfTypes invis) `mappend` foldMap go vis
2445
2446 splitVisVarsOfTypes :: [Type] -> Pair TyCoVarSet
2447 splitVisVarsOfTypes = foldMap splitVisVarsOfType
2448
2449 modifyJoinResTy :: Int -- Number of binders to skip
2450 -> (Type -> Type) -- Function to apply to result type
2451 -> Type -- Type of join point
2452 -> Type -- New type
2453 -- INVARIANT: If any of the first n binders are foralls, those tyvars cannot
2454 -- appear in the original result type. See isValidJoinPointType.
2455 modifyJoinResTy orig_ar f orig_ty
2456 = go orig_ar orig_ty
2457 where
2458 go 0 ty = f ty
2459 go n ty | Just (arg_bndr, res_ty) <- splitPiTy_maybe ty
2460 = mkPiTy arg_bndr (go (n-1) res_ty)
2461 | otherwise
2462 = pprPanic "modifyJoinResTy" (ppr orig_ar <+> ppr orig_ty)
2463
2464 setJoinResTy :: Int -- Number of binders to skip
2465 -> Type -- New result type
2466 -> Type -- Type of join point
2467 -> Type -- New type
2468 -- INVARIANT: Same as for modifyJoinResTy
2469 setJoinResTy ar new_res_ty ty
2470 = modifyJoinResTy ar (const new_res_ty) ty