0764d144b7c2178626e6150ee9096e315340b928
[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, pprPrecType,
186 pprTypeApp, pprTyThingCategory, pprShortTyThing,
187 pprTvBndr, pprTvBndrs, pprForAll, pprUserForAll,
188 pprSigmaType, ppSuggestExplicitKinds,
189 pprTheta, pprThetaArrowTy, pprClassPred,
190 pprKind, pprParendKind, pprSourceTyCon,
191 TyPrec(..), maybeParen,
192 pprTyVar, pprTyVars, pprPrefixApp, pprArrowChain,
193
194 -- * Tidying type related things up for printing
195 tidyType, tidyTypes,
196 tidyOpenType, tidyOpenTypes,
197 tidyOpenKind,
198 tidyTyCoVarBndr, tidyTyCoVarBndrs, tidyFreeTyCoVars,
199 tidyOpenTyCoVar, tidyOpenTyCoVars,
200 tidyTyVarOcc,
201 tidyTopType,
202 tidyKind,
203 tidyTyVarBinder, tidyTyVarBinders
204 ) where
205
206 #include "HsVersions.h"
207
208 import BasicTypes
209
210 -- We import the representation and primitive functions from TyCoRep.
211 -- Many things are reexported, but not the representation!
212
213 import Kind
214 import TyCoRep
215
216 -- friends:
217 import Var
218 import VarEnv
219 import VarSet
220 import UniqSet
221
222 import Class
223 import TyCon
224 import TysPrim
225 import {-# SOURCE #-} TysWiredIn ( listTyCon, typeNatKind
226 , typeSymbolKind, liftedTypeKind )
227 import PrelNames
228 import CoAxiom
229 import {-# SOURCE #-} Coercion
230
231 -- others
232 import Util
233 import Outputable
234 import FastString
235 import Pair
236 import ListSetOps
237 import Digraph
238 import Unique ( nonDetCmpUnique )
239 import SrcLoc ( SrcSpan )
240 import OccName ( OccName )
241 import Name ( mkInternalName )
242
243 import Maybes ( orElse )
244 import Data.Maybe ( isJust, mapMaybe )
245 import Control.Monad ( guard )
246 import Control.Arrow ( first, second )
247
248 -- $type_classification
249 -- #type_classification#
250 --
251 -- Types are one of:
252 --
253 -- [Unboxed] Iff its representation is other than a pointer
254 -- Unboxed types are also unlifted.
255 --
256 -- [Lifted] Iff it has bottom as an element.
257 -- Closures always have lifted types: i.e. any
258 -- let-bound identifier in Core must have a lifted
259 -- type. Operationally, a lifted object is one that
260 -- can be entered.
261 -- Only lifted types may be unified with a type variable.
262 --
263 -- [Algebraic] Iff it is a type with one or more constructors, whether
264 -- declared with @data@ or @newtype@.
265 -- An algebraic type is one that can be deconstructed
266 -- with a case expression. This is /not/ the same as
267 -- lifted types, because we also include unboxed
268 -- tuples in this classification.
269 --
270 -- [Data] Iff it is a type declared with @data@, or a boxed tuple.
271 --
272 -- [Primitive] Iff it is a built-in type that can't be expressed in Haskell.
273 --
274 -- Currently, all primitive types are unlifted, but that's not necessarily
275 -- the case: for example, @Int@ could be primitive.
276 --
277 -- Some primitive types are unboxed, such as @Int#@, whereas some are boxed
278 -- but unlifted (such as @ByteArray#@). The only primitive types that we
279 -- classify as algebraic are the unboxed tuples.
280 --
281 -- Some examples of type classifications that may make this a bit clearer are:
282 --
283 -- @
284 -- Type primitive boxed lifted algebraic
285 -- -----------------------------------------------------------------------------
286 -- Int# Yes No No No
287 -- ByteArray# Yes Yes No No
288 -- (\# a, b \#) Yes No No Yes
289 -- (\# a | b \#) Yes No No Yes
290 -- ( a, b ) No Yes Yes Yes
291 -- [a] No Yes Yes Yes
292 -- @
293
294 -- $representation_types
295 -- A /source type/ is a type that is a separate type as far as the type checker is
296 -- concerned, but which has a more low-level representation as far as Core-to-Core
297 -- passes and the rest of the back end is concerned.
298 --
299 -- You don't normally have to worry about this, as the utility functions in
300 -- this module will automatically convert a source into a representation type
301 -- if they are spotted, to the best of it's abilities. If you don't want this
302 -- to happen, use the equivalent functions from the "TcType" module.
303
304 {-
305 ************************************************************************
306 * *
307 Type representation
308 * *
309 ************************************************************************
310
311 Note [coreView vs tcView]
312 ~~~~~~~~~~~~~~~~~~~~~~~~~
313 So far as the typechecker is concerned, 'Constraint' and 'TYPE LiftedRep' are distinct kinds.
314
315 But in Core these two are treated as identical.
316
317 We implement this by making 'coreView' convert 'Constraint' to 'TYPE LiftedRep' on the fly.
318 The function tcView (used in the type checker) does not do this.
319
320 See also Trac #11715, which tracks removing this inconsistency.
321
322 -}
323
324 {-# INLINE coreView #-}
325 coreView :: Type -> Maybe Type
326 -- ^ This function Strips off the /top layer only/ of a type synonym
327 -- application (if any) its underlying representation type.
328 -- Returns Nothing if there is nothing to look through.
329 -- This function considers 'Constraint' to be a synonym of @TYPE LiftedRep@.
330 --
331 -- By being non-recursive and inlined, this case analysis gets efficiently
332 -- joined onto the case analysis that the caller is already doing
333 coreView (TyConApp tc tys) | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc tys
334 = Just (mkAppTys (substTy (mkTvSubstPrs tenv) rhs) tys')
335 -- The free vars of 'rhs' should all be bound by 'tenv', so it's
336 -- ok to use 'substTy' here.
337 -- See also Note [The substitution invariant] in TyCoRep.
338 -- Its important to use mkAppTys, rather than (foldl AppTy),
339 -- because the function part might well return a
340 -- partially-applied type constructor; indeed, usually will!
341 coreView (TyConApp tc [])
342 | isStarKindSynonymTyCon tc
343 = Just liftedTypeKind
344
345 coreView _ = Nothing
346
347 -- | Gives the typechecker view of a type. This unwraps synonyms but
348 -- leaves 'Constraint' alone. c.f. coreView, which turns Constraint into
349 -- TYPE LiftedRep. Returns Nothing if no unwrapping happens.
350 -- See also Note [coreView vs tcView] in Type.
351 {-# INLINE tcView #-}
352 tcView :: Type -> Maybe Type
353 tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc tys
354 = Just (mkAppTys (substTy (mkTvSubstPrs tenv) rhs) tys')
355 -- The free vars of 'rhs' should all be bound by 'tenv', so it's
356 -- ok to use 'substTy' here.
357 -- See also Note [The substitution invariant] in TyCoRep.
358 -- Its important to use mkAppTys, rather than (foldl AppTy),
359 -- because the function part might well return a
360 -- partially-applied type constructor; indeed, usually will!
361 tcView _ = Nothing
362
363 -----------------------------------------------
364 expandTypeSynonyms :: Type -> Type
365 -- ^ Expand out all type synonyms. Actually, it'd suffice to expand out
366 -- just the ones that discard type variables (e.g. type Funny a = Int)
367 -- But we don't know which those are currently, so we just expand all.
368 --
369 -- 'expandTypeSynonyms' only expands out type synonyms mentioned in the type,
370 -- not in the kinds of any TyCon or TyVar mentioned in the type.
371 --
372 -- Keep this synchronized with 'synonymTyConsOfType'
373 expandTypeSynonyms ty
374 = go (mkEmptyTCvSubst in_scope) ty
375 where
376 in_scope = mkInScopeSet (tyCoVarsOfType ty)
377
378 go subst (TyConApp tc tys)
379 | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc expanded_tys
380 = let subst' = mkTvSubst in_scope (mkVarEnv tenv)
381 -- Make a fresh substitution; rhs has nothing to
382 -- do with anything that has happened so far
383 -- NB: if you make changes here, be sure to build an
384 -- /idempotent/ substitution, even in the nested case
385 -- type T a b = a -> b
386 -- type S x y = T y x
387 -- (Trac #11665)
388 in mkAppTys (go subst' rhs) tys'
389 | otherwise
390 = TyConApp tc expanded_tys
391 where
392 expanded_tys = (map (go subst) tys)
393
394 go _ (LitTy l) = LitTy l
395 go subst (TyVarTy tv) = substTyVar subst tv
396 go subst (AppTy t1 t2) = mkAppTy (go subst t1) (go subst t2)
397 go subst (FunTy arg res)
398 = mkFunTy (go subst arg) (go subst res)
399 go subst (ForAllTy (TvBndr tv vis) t)
400 = let (subst', tv') = substTyVarBndrCallback go subst tv in
401 ForAllTy (TvBndr tv' vis) (go subst' t)
402 go subst (CastTy ty co) = mkCastTy (go subst ty) (go_co subst co)
403 go subst (CoercionTy co) = mkCoercionTy (go_co subst co)
404
405 go_co subst (Refl r ty)
406 = mkReflCo r (go subst ty)
407 -- NB: coercions are always expanded upon creation
408 go_co subst (TyConAppCo r tc args)
409 = mkTyConAppCo r tc (map (go_co subst) args)
410 go_co subst (AppCo co arg)
411 = mkAppCo (go_co subst co) (go_co subst arg)
412 go_co subst (ForAllCo tv kind_co co)
413 = let (subst', tv', kind_co') = go_cobndr subst tv kind_co in
414 mkForAllCo tv' kind_co' (go_co subst' co)
415 go_co subst (FunCo r co1 co2)
416 = mkFunCo r (go_co subst co1) (go_co subst co2)
417 go_co subst (CoVarCo cv)
418 = substCoVar subst cv
419 go_co subst (AxiomInstCo ax ind args)
420 = mkAxiomInstCo ax ind (map (go_co subst) args)
421 go_co subst (UnivCo p r t1 t2)
422 = mkUnivCo (go_prov subst p) r (go subst t1) (go subst t2)
423 go_co subst (SymCo co)
424 = mkSymCo (go_co subst co)
425 go_co subst (TransCo co1 co2)
426 = mkTransCo (go_co subst co1) (go_co subst co2)
427 go_co subst (NthCo n co)
428 = mkNthCo n (go_co subst co)
429 go_co subst (LRCo lr co)
430 = mkLRCo lr (go_co subst co)
431 go_co subst (InstCo co arg)
432 = mkInstCo (go_co subst co) (go_co subst arg)
433 go_co subst (CoherenceCo co1 co2)
434 = mkCoherenceCo (go_co subst co1) (go_co subst co2)
435 go_co subst (KindCo co)
436 = mkKindCo (go_co subst co)
437 go_co subst (SubCo co)
438 = mkSubCo (go_co subst co)
439 go_co subst (AxiomRuleCo ax cs) = AxiomRuleCo ax (map (go_co subst) cs)
440
441 go_prov _ UnsafeCoerceProv = UnsafeCoerceProv
442 go_prov subst (PhantomProv co) = PhantomProv (go_co subst co)
443 go_prov subst (ProofIrrelProv co) = ProofIrrelProv (go_co subst co)
444 go_prov _ p@(PluginProv _) = p
445 go_prov _ (HoleProv h) = pprPanic "expandTypeSynonyms hit a hole" (ppr h)
446
447 -- the "False" and "const" are to accommodate the type of
448 -- substForAllCoBndrCallback, which is general enough to
449 -- handle coercion optimization (which sometimes swaps the
450 -- order of a coercion)
451 go_cobndr subst = substForAllCoBndrCallback False (go_co subst) subst
452
453 {-
454 ************************************************************************
455 * *
456 Analyzing types
457 * *
458 ************************************************************************
459
460 These functions do a map-like operation over types, performing some operation
461 on all variables and binding sites. Primarily used for zonking.
462
463 Note [Efficiency for mapCoercion ForAllCo case]
464 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
465 As noted in Note [Forall coercions] in TyCoRep, a ForAllCo is a bit redundant.
466 It stores a TyVar and a Coercion, where the kind of the TyVar always matches
467 the left-hand kind of the coercion. This is convenient lots of the time, but
468 not when mapping a function over a coercion.
469
470 The problem is that tcm_tybinder will affect the TyVar's kind and
471 mapCoercion will affect the Coercion, and we hope that the results will be
472 the same. Even if they are the same (which should generally happen with
473 correct algorithms), then there is an efficiency issue. In particular,
474 this problem seems to make what should be a linear algorithm into a potentially
475 exponential one. But it's only going to be bad in the case where there's
476 lots of foralls in the kinds of other foralls. Like this:
477
478 forall a : (forall b : (forall c : ...). ...). ...
479
480 This construction seems unlikely. So we'll do the inefficient, easy way
481 for now.
482
483 Note [Specialising mappers]
484 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
485 These INLINABLE pragmas are indispensable. mapType/mapCoercion are used
486 to implement zonking, and it's vital that they get specialised to the TcM
487 monad. This specialisation happens automatically (that is, without a
488 SPECIALISE pragma) as long as the definitions are INLINABLE. For example,
489 this one change made a 20% allocation difference in perf/compiler/T5030.
490
491 -}
492
493 -- | This describes how a "map" operation over a type/coercion should behave
494 data TyCoMapper env m
495 = TyCoMapper
496 { tcm_smart :: Bool -- ^ Should the new type be created with smart
497 -- constructors?
498 , tcm_tyvar :: env -> TyVar -> m Type
499 , tcm_covar :: env -> CoVar -> m Coercion
500 , tcm_hole :: env -> CoercionHole -> Role
501 -> Type -> Type -> m Coercion
502 -- ^ What to do with coercion holes. See Note [Coercion holes] in
503 -- TyCoRep.
504
505 , tcm_tybinder :: env -> TyVar -> ArgFlag -> m (env, TyVar)
506 -- ^ The returned env is used in the extended scope
507 }
508
509 {-# INLINABLE mapType #-} -- See Note [Specialising mappers]
510 mapType :: Monad m => TyCoMapper env m -> env -> Type -> m Type
511 mapType mapper@(TyCoMapper { tcm_smart = smart, tcm_tyvar = tyvar
512 , tcm_tybinder = tybinder })
513 env ty
514 = go ty
515 where
516 go (TyVarTy tv) = tyvar env tv
517 go (AppTy t1 t2) = mkappty <$> go t1 <*> go t2
518 go t@(TyConApp _ []) = return t -- avoid allocation in this exceedingly
519 -- common case (mostly, for *)
520 go (TyConApp tc tys) = mktyconapp tc <$> mapM go tys
521 go (FunTy arg res) = FunTy <$> go arg <*> go res
522 go (ForAllTy (TvBndr tv vis) inner)
523 = do { (env', tv') <- tybinder env tv vis
524 ; inner' <- mapType mapper env' inner
525 ; return $ ForAllTy (TvBndr tv' vis) inner' }
526 go ty@(LitTy {}) = return ty
527 go (CastTy ty co) = mkcastty <$> go ty <*> mapCoercion mapper env co
528 go (CoercionTy co) = CoercionTy <$> mapCoercion mapper env co
529
530 (mktyconapp, mkappty, mkcastty)
531 | smart = (mkTyConApp, mkAppTy, mkCastTy)
532 | otherwise = (TyConApp, AppTy, CastTy)
533
534 {-# INLINABLE mapCoercion #-} -- See Note [Specialising mappers]
535 mapCoercion :: Monad m
536 => TyCoMapper env m -> env -> Coercion -> m Coercion
537 mapCoercion mapper@(TyCoMapper { tcm_smart = smart, tcm_covar = covar
538 , tcm_hole = cohole, tcm_tybinder = tybinder })
539 env co
540 = go co
541 where
542 go (Refl r ty) = Refl r <$> mapType mapper env ty
543 go (TyConAppCo r tc args)
544 = mktyconappco r tc <$> mapM go args
545 go (AppCo c1 c2) = mkappco <$> go c1 <*> go c2
546 go (ForAllCo tv kind_co co)
547 = do { kind_co' <- go kind_co
548 ; (env', tv') <- tybinder env tv Inferred
549 ; co' <- mapCoercion mapper env' co
550 ; return $ mkforallco tv' kind_co' co' }
551 -- See Note [Efficiency for mapCoercion ForAllCo case]
552 go (FunCo r c1 c2) = mkFunCo r <$> go c1 <*> go c2
553 go (CoVarCo cv) = covar env cv
554 go (AxiomInstCo ax i args)
555 = mkaxiominstco ax i <$> mapM go args
556 go (UnivCo (HoleProv hole) r t1 t2)
557 = cohole env hole r t1 t2
558 go (UnivCo p r t1 t2)
559 = mkunivco <$> go_prov p <*> pure r
560 <*> mapType mapper env t1 <*> mapType mapper env t2
561 go (SymCo co) = mksymco <$> go co
562 go (TransCo c1 c2) = mktransco <$> go c1 <*> go c2
563 go (AxiomRuleCo r cos) = AxiomRuleCo r <$> mapM go cos
564 go (NthCo i co) = mknthco i <$> go co
565 go (LRCo lr co) = mklrco lr <$> go co
566 go (InstCo co arg) = mkinstco <$> go co <*> go arg
567 go (CoherenceCo c1 c2) = mkcoherenceco <$> go c1 <*> go c2
568 go (KindCo co) = mkkindco <$> go co
569 go (SubCo co) = mksubco <$> go co
570
571 go_prov UnsafeCoerceProv = return UnsafeCoerceProv
572 go_prov (PhantomProv co) = PhantomProv <$> go co
573 go_prov (ProofIrrelProv co) = ProofIrrelProv <$> go co
574 go_prov p@(PluginProv _) = return p
575 go_prov (HoleProv _) = panic "mapCoercion"
576
577 ( mktyconappco, mkappco, mkaxiominstco, mkunivco
578 , mksymco, mktransco, mknthco, mklrco, mkinstco, mkcoherenceco
579 , mkkindco, mksubco, mkforallco)
580 | smart
581 = ( mkTyConAppCo, mkAppCo, mkAxiomInstCo, mkUnivCo
582 , mkSymCo, mkTransCo, mkNthCo, mkLRCo, mkInstCo, mkCoherenceCo
583 , mkKindCo, mkSubCo, mkForAllCo )
584 | otherwise
585 = ( TyConAppCo, AppCo, AxiomInstCo, UnivCo
586 , SymCo, TransCo, NthCo, LRCo, InstCo, CoherenceCo
587 , KindCo, SubCo, ForAllCo )
588
589 {-
590 ************************************************************************
591 * *
592 \subsection{Constructor-specific functions}
593 * *
594 ************************************************************************
595
596
597 ---------------------------------------------------------------------
598 TyVarTy
599 ~~~~~~~
600 -}
601
602 -- | Attempts to obtain the type variable underlying a 'Type', and panics with the
603 -- given message if this is not a type variable type. See also 'getTyVar_maybe'
604 getTyVar :: String -> Type -> TyVar
605 getTyVar msg ty = case getTyVar_maybe ty of
606 Just tv -> tv
607 Nothing -> panic ("getTyVar: " ++ msg)
608
609 isTyVarTy :: Type -> Bool
610 isTyVarTy ty = isJust (getTyVar_maybe ty)
611
612 -- | Attempts to obtain the type variable underlying a 'Type'
613 getTyVar_maybe :: Type -> Maybe TyVar
614 getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty'
615 | otherwise = repGetTyVar_maybe ty
616
617 -- | If the type is a tyvar, possibly under a cast, returns it, along
618 -- with the coercion. Thus, the co is :: kind tv ~R kind type
619 getCastedTyVar_maybe :: Type -> Maybe (TyVar, Coercion)
620 getCastedTyVar_maybe ty | Just ty' <- coreView ty = getCastedTyVar_maybe ty'
621 getCastedTyVar_maybe (CastTy (TyVarTy tv) co) = Just (tv, co)
622 getCastedTyVar_maybe (TyVarTy tv)
623 = Just (tv, mkReflCo Nominal (tyVarKind tv))
624 getCastedTyVar_maybe _ = Nothing
625
626 -- | Attempts to obtain the type variable underlying a 'Type', without
627 -- any expansion
628 repGetTyVar_maybe :: Type -> Maybe TyVar
629 repGetTyVar_maybe (TyVarTy tv) = Just tv
630 repGetTyVar_maybe _ = Nothing
631
632 {-
633 ---------------------------------------------------------------------
634 AppTy
635 ~~~~~
636 We need to be pretty careful with AppTy to make sure we obey the
637 invariant that a TyConApp is always visibly so. mkAppTy maintains the
638 invariant: use it.
639
640 Note [Decomposing fat arrow c=>t]
641 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
642 Can we unify (a b) with (Eq a => ty)? If we do so, we end up with
643 a partial application like ((=>) Eq a) which doesn't make sense in
644 source Haskell. In contrast, we *can* unify (a b) with (t1 -> t2).
645 Here's an example (Trac #9858) of how you might do it:
646 i :: (Typeable a, Typeable b) => Proxy (a b) -> TypeRep
647 i p = typeRep p
648
649 j = i (Proxy :: Proxy (Eq Int => Int))
650 The type (Proxy (Eq Int => Int)) is only accepted with -XImpredicativeTypes,
651 but suppose we want that. But then in the call to 'i', we end
652 up decomposing (Eq Int => Int), and we definitely don't want that.
653
654 This really only applies to the type checker; in Core, '=>' and '->'
655 are the same, as are 'Constraint' and '*'. But for now I've put
656 the test in repSplitAppTy_maybe, which applies throughout, because
657 the other calls to splitAppTy are in Unify, which is also used by
658 the type checker (e.g. when matching type-function equations).
659
660 -}
661
662 -- | Applies a type to another, as in e.g. @k a@
663 mkAppTy :: Type -> Type -> Type
664 mkAppTy (TyConApp tc tys) ty2 = mkTyConApp tc (tys ++ [ty2])
665 mkAppTy ty1 ty2 = AppTy ty1 ty2
666 -- Note that the TyConApp could be an
667 -- under-saturated type synonym. GHC allows that; e.g.
668 -- type Foo k = k a -> k a
669 -- type Id x = x
670 -- foo :: Foo Id -> Foo Id
671 --
672 -- Here Id is partially applied in the type sig for Foo,
673 -- but once the type synonyms are expanded all is well
674
675 mkAppTys :: Type -> [Type] -> Type
676 mkAppTys ty1 [] = ty1
677 mkAppTys (TyConApp tc tys1) tys2 = mkTyConApp tc (tys1 ++ tys2)
678 mkAppTys ty1 tys2 = foldl AppTy ty1 tys2
679
680 -------------
681 splitAppTy_maybe :: Type -> Maybe (Type, Type)
682 -- ^ Attempt to take a type application apart, whether it is a
683 -- function, type constructor, or plain type application. Note
684 -- that type family applications are NEVER unsaturated by this!
685 splitAppTy_maybe ty | Just ty' <- coreView ty
686 = splitAppTy_maybe ty'
687 splitAppTy_maybe ty = repSplitAppTy_maybe ty
688
689 -------------
690 repSplitAppTy_maybe :: Type -> Maybe (Type,Type)
691 -- ^ Does the AppTy split as in 'splitAppTy_maybe', but assumes that
692 -- any Core view stuff is already done
693 repSplitAppTy_maybe (FunTy ty1 ty2)
694 | Just rep1 <- getRuntimeRep_maybe ty1
695 , Just rep2 <- getRuntimeRep_maybe ty2
696 = Just (TyConApp funTyCon [rep1, rep2, ty1], ty2)
697
698 | otherwise
699 = pprPanic "repSplitAppTy_maybe" (ppr ty1 $$ ppr ty2)
700 repSplitAppTy_maybe (AppTy ty1 ty2)
701 = Just (ty1, ty2)
702 repSplitAppTy_maybe (TyConApp tc tys)
703 | mightBeUnsaturatedTyCon tc || tys `lengthExceeds` tyConArity tc
704 , Just (tys', ty') <- snocView tys
705 = Just (TyConApp tc tys', ty') -- Never create unsaturated type family apps!
706 repSplitAppTy_maybe _other = Nothing
707
708 -- this one doesn't braek apart (c => t).
709 -- See Note [Decomposing fat arrow c=>t]
710 -- Defined here to avoid module loops between Unify and TcType.
711 tcRepSplitAppTy_maybe :: Type -> Maybe (Type,Type)
712 -- ^ Does the AppTy split as in 'tcSplitAppTy_maybe', but assumes that
713 -- any coreView stuff is already done. Refuses to look through (c => t)
714 tcRepSplitAppTy_maybe (FunTy ty1 ty2)
715 | isConstraintKind (typeKind ty1)
716 = Nothing -- See Note [Decomposing fat arrow c=>t]
717
718 | Just rep1 <- getRuntimeRep_maybe ty1
719 , Just rep2 <- getRuntimeRep_maybe ty2
720 = Just (TyConApp funTyCon [rep1, rep2, ty1], ty2)
721
722 | otherwise
723 = pprPanic "repSplitAppTy_maybe" (ppr ty1 $$ ppr ty2)
724 tcRepSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
725 tcRepSplitAppTy_maybe (TyConApp tc tys)
726 | mightBeUnsaturatedTyCon tc || tys `lengthExceeds` tyConArity tc
727 , Just (tys', ty') <- snocView tys
728 = Just (TyConApp tc tys', ty') -- Never create unsaturated type family apps!
729 tcRepSplitAppTy_maybe _other = Nothing
730
731 -- | Split a type constructor application into its type constructor and
732 -- applied types. Note that this may fail in the case of a 'FunTy' with an
733 -- argument of unknown kind 'FunTy' (e.g. @FunTy (a :: k) Int@. since the kind
734 -- of @a@ isn't of the form @TYPE rep@). Consequently, you may need to zonk your
735 -- type before using this function.
736 --
737 -- If you only need the 'TyCon', consider using 'tcTyConAppTyCon_maybe'.
738 tcSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type])
739 -- Defined here to avoid module loops between Unify and TcType.
740 tcSplitTyConApp_maybe ty | Just ty' <- tcView ty = tcSplitTyConApp_maybe ty'
741 tcSplitTyConApp_maybe ty = tcRepSplitTyConApp_maybe ty
742
743 -- | Like 'tcSplitTyConApp_maybe' but doesn't look through type synonyms.
744 tcRepSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type])
745 -- Defined here to avoid module loops between Unify and TcType.
746 tcRepSplitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
747 tcRepSplitTyConApp_maybe (FunTy arg res)
748 | Just arg_rep <- getRuntimeRep_maybe arg
749 , Just res_rep <- getRuntimeRep_maybe res
750 = Just (funTyCon, [arg_rep, res_rep, arg, res])
751
752 | otherwise
753 = pprPanic "tcRepSplitTyConApp_maybe" (ppr arg $$ ppr res)
754 tcRepSplitTyConApp_maybe _ = Nothing
755
756
757 -------------
758 splitAppTy :: Type -> (Type, Type)
759 -- ^ Attempts to take a type application apart, as in 'splitAppTy_maybe',
760 -- and panics if this is not possible
761 splitAppTy ty = case splitAppTy_maybe ty of
762 Just pr -> pr
763 Nothing -> panic "splitAppTy"
764
765 -------------
766 splitAppTys :: Type -> (Type, [Type])
767 -- ^ Recursively splits a type as far as is possible, leaving a residual
768 -- type being applied to and the type arguments applied to it. Never fails,
769 -- even if that means returning an empty list of type applications.
770 splitAppTys ty = split ty ty []
771 where
772 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
773 split _ (AppTy ty arg) args = split ty ty (arg:args)
774 split _ (TyConApp tc tc_args) args
775 = let -- keep type families saturated
776 n | mightBeUnsaturatedTyCon tc = 0
777 | otherwise = tyConArity tc
778 (tc_args1, tc_args2) = splitAt n tc_args
779 in
780 (TyConApp tc tc_args1, tc_args2 ++ args)
781 split _ (FunTy ty1 ty2) args
782 | Just rep1 <- getRuntimeRep_maybe ty1
783 , Just rep2 <- getRuntimeRep_maybe ty2
784 = ASSERT( null args )
785 (TyConApp funTyCon [], [rep1, rep2, ty1, ty2])
786
787 | otherwise
788 = pprPanic "splitAppTys" (ppr ty1 $$ ppr ty2 $$ ppr args)
789 split orig_ty _ args = (orig_ty, args)
790
791 -- | Like 'splitAppTys', but doesn't look through type synonyms
792 repSplitAppTys :: Type -> (Type, [Type])
793 repSplitAppTys ty = split ty []
794 where
795 split (AppTy ty arg) args = split ty (arg:args)
796 split (TyConApp tc tc_args) args
797 = let n | mightBeUnsaturatedTyCon tc = 0
798 | otherwise = tyConArity tc
799 (tc_args1, tc_args2) = splitAt n tc_args
800 in
801 (TyConApp tc tc_args1, tc_args2 ++ args)
802 split (FunTy ty1 ty2) args
803 | Just rep1 <- getRuntimeRep_maybe ty1
804 , Just rep2 <- getRuntimeRep_maybe ty2
805 = ASSERT( null args )
806 (TyConApp funTyCon [], [rep1, rep2, ty1, ty2])
807
808 | otherwise
809 = pprPanic "repSplitAppTys" (ppr ty1 $$ ppr ty2 $$ ppr args)
810 split ty args = (ty, args)
811
812 {-
813 LitTy
814 ~~~~~
815 -}
816
817 mkNumLitTy :: Integer -> Type
818 mkNumLitTy n = LitTy (NumTyLit n)
819
820 -- | Is this a numeric literal. We also look through type synonyms.
821 isNumLitTy :: Type -> Maybe Integer
822 isNumLitTy ty | Just ty1 <- coreView ty = isNumLitTy ty1
823 isNumLitTy (LitTy (NumTyLit n)) = Just n
824 isNumLitTy _ = Nothing
825
826 mkStrLitTy :: FastString -> Type
827 mkStrLitTy s = LitTy (StrTyLit s)
828
829 -- | Is this a symbol literal. We also look through type synonyms.
830 isStrLitTy :: Type -> Maybe FastString
831 isStrLitTy ty | Just ty1 <- coreView ty = isStrLitTy ty1
832 isStrLitTy (LitTy (StrTyLit s)) = Just s
833 isStrLitTy _ = Nothing
834
835
836 -- | Is this type a custom user error?
837 -- If so, give us the kind and the error message.
838 userTypeError_maybe :: Type -> Maybe Type
839 userTypeError_maybe t
840 = do { (tc, _kind : msg : _) <- splitTyConApp_maybe t
841 -- There may be more than 2 arguments, if the type error is
842 -- used as a type constructor (e.g. at kind `Type -> Type`).
843
844 ; guard (tyConName tc == errorMessageTypeErrorFamName)
845 ; return msg }
846
847 -- | Render a type corresponding to a user type error into a SDoc.
848 pprUserTypeErrorTy :: Type -> SDoc
849 pprUserTypeErrorTy ty =
850 case splitTyConApp_maybe ty of
851
852 -- Text "Something"
853 Just (tc,[txt])
854 | tyConName tc == typeErrorTextDataConName
855 , Just str <- isStrLitTy txt -> ftext str
856
857 -- ShowType t
858 Just (tc,[_k,t])
859 | tyConName tc == typeErrorShowTypeDataConName -> ppr t
860
861 -- t1 :<>: t2
862 Just (tc,[t1,t2])
863 | tyConName tc == typeErrorAppendDataConName ->
864 pprUserTypeErrorTy t1 <> pprUserTypeErrorTy t2
865
866 -- t1 :$$: t2
867 Just (tc,[t1,t2])
868 | tyConName tc == typeErrorVAppendDataConName ->
869 pprUserTypeErrorTy t1 $$ pprUserTypeErrorTy t2
870
871 -- An uneavaluated type function
872 _ -> ppr ty
873
874
875
876
877 {-
878 ---------------------------------------------------------------------
879 FunTy
880 ~~~~~
881
882 Note [Representation of function types]
883 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
884
885 Functions (e.g. Int -> Char) are can be thought of as being applications
886 of funTyCon (known in Haskell surface syntax as (->)),
887
888 (->) :: forall (r1 :: RuntimeRep) (r2 :: RuntimeRep)
889 (a :: TYPE r1) (b :: TYPE r2).
890 a -> b -> Type
891
892 However, for efficiency's sake we represent saturated applications of (->)
893 with FunTy. For instance, the type,
894
895 (->) r1 r2 a b
896
897 is equivalent to,
898
899 FunTy (Anon a) b
900
901 Note how the RuntimeReps are implied in the FunTy representation. For this
902 reason we must be careful when recontructing the TyConApp representation (see,
903 for instance, splitTyConApp_maybe).
904
905 In the compiler we maintain the invariant that all saturated applications of
906 (->) are represented with FunTy.
907
908 See #11714.
909 -}
910
911 isFunTy :: Type -> Bool
912 isFunTy ty = isJust (splitFunTy_maybe ty)
913
914 splitFunTy :: Type -> (Type, Type)
915 -- ^ Attempts to extract the argument and result types from a type, and
916 -- panics if that is not possible. See also 'splitFunTy_maybe'
917 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
918 splitFunTy (FunTy arg res) = (arg, res)
919 splitFunTy other = pprPanic "splitFunTy" (ppr other)
920
921 splitFunTy_maybe :: Type -> Maybe (Type, Type)
922 -- ^ Attempts to extract the argument and result types from a type
923 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
924 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
925 splitFunTy_maybe _ = Nothing
926
927 splitFunTys :: Type -> ([Type], Type)
928 splitFunTys ty = split [] ty ty
929 where
930 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
931 split args _ (FunTy arg res) = split (arg:args) res res
932 split args orig_ty _ = (reverse args, orig_ty)
933
934 funResultTy :: Type -> Type
935 -- ^ Extract the function result type and panic if that is not possible
936 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
937 funResultTy (FunTy _ res) = res
938 funResultTy ty = pprPanic "funResultTy" (ppr ty)
939
940 funArgTy :: Type -> Type
941 -- ^ Extract the function argument type and panic if that is not possible
942 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
943 funArgTy (FunTy arg _res) = arg
944 funArgTy ty = pprPanic "funArgTy" (ppr ty)
945
946 piResultTy :: Type -> Type -> Type
947 piResultTy ty arg = case piResultTy_maybe ty arg of
948 Just res -> res
949 Nothing -> pprPanic "piResultTy" (ppr ty $$ ppr arg)
950
951 piResultTy_maybe :: Type -> Type -> Maybe Type
952
953 -- ^ Just like 'piResultTys' but for a single argument
954 -- Try not to iterate 'piResultTy', because it's inefficient to substitute
955 -- one variable at a time; instead use 'piResultTys"
956 piResultTy_maybe ty arg
957 | Just ty' <- coreView ty = piResultTy_maybe ty' arg
958
959 | FunTy _ res <- ty
960 = Just res
961
962 | ForAllTy (TvBndr tv _) res <- ty
963 = let empty_subst = mkEmptyTCvSubst $ mkInScopeSet $
964 tyCoVarsOfTypes [arg,res]
965 in Just (substTy (extendTvSubst empty_subst tv arg) res)
966
967 | otherwise
968 = Nothing
969
970 -- | (piResultTys f_ty [ty1, .., tyn]) gives the type of (f ty1 .. tyn)
971 -- where f :: f_ty
972 -- 'piResultTys' is interesting because:
973 -- 1. 'f_ty' may have more for-alls than there are args
974 -- 2. Less obviously, it may have fewer for-alls
975 -- For case 2. think of:
976 -- piResultTys (forall a.a) [forall b.b, Int]
977 -- This really can happen, but only (I think) in situations involving
978 -- undefined. For example:
979 -- undefined :: forall a. a
980 -- Term: undefined @(forall b. b->b) @Int
981 -- This term should have type (Int -> Int), but notice that
982 -- there are more type args than foralls in 'undefined's type.
983
984 -- If you edit this function, you may need to update the GHC formalism
985 -- See Note [GHC Formalism] in coreSyn/CoreLint.hs
986
987 -- This is a heavily used function (e.g. from typeKind),
988 -- so we pay attention to efficiency, especially in the special case
989 -- where there are no for-alls so we are just dropping arrows from
990 -- a function type/kind.
991 piResultTys :: Type -> [Type] -> Type
992 piResultTys ty [] = ty
993 piResultTys ty orig_args@(arg:args)
994 | Just ty' <- coreView ty
995 = piResultTys ty' orig_args
996
997 | FunTy _ res <- ty
998 = piResultTys res args
999
1000 | ForAllTy (TvBndr tv _) res <- ty
1001 = go (extendVarEnv emptyTvSubstEnv tv arg) res args
1002
1003 | otherwise
1004 = pprPanic "piResultTys1" (ppr ty $$ ppr orig_args)
1005 where
1006 in_scope = mkInScopeSet (tyCoVarsOfTypes (ty:orig_args))
1007
1008 go :: TvSubstEnv -> Type -> [Type] -> Type
1009 go tv_env ty [] = substTy (mkTvSubst in_scope tv_env) ty
1010
1011 go tv_env ty all_args@(arg:args)
1012 | Just ty' <- coreView ty
1013 = go tv_env ty' all_args
1014
1015 | FunTy _ res <- ty
1016 = go tv_env res args
1017
1018 | ForAllTy (TvBndr tv _) res <- ty
1019 = go (extendVarEnv tv_env tv arg) res args
1020
1021 | TyVarTy tv <- ty
1022 , Just ty' <- lookupVarEnv tv_env tv
1023 -- Deals with piResultTys (forall a. a) [forall b.b, Int]
1024 = piResultTys ty' all_args
1025
1026 | otherwise
1027 = pprPanic "piResultTys2" (ppr ty $$ ppr orig_args $$ ppr all_args)
1028
1029 applyTysX :: [TyVar] -> Type -> [Type] -> Type
1030 -- applyTyxX beta-reduces (/\tvs. body_ty) arg_tys
1031 -- Assumes that (/\tvs. body_ty) is closed
1032 applyTysX tvs body_ty arg_tys
1033 = ASSERT2( arg_tys `lengthAtLeast` n_tvs, pp_stuff )
1034 ASSERT2( tyCoVarsOfType body_ty `subVarSet` mkVarSet tvs, pp_stuff )
1035 mkAppTys (substTyWith tvs (take n_tvs arg_tys) body_ty)
1036 (drop n_tvs arg_tys)
1037 where
1038 pp_stuff = vcat [ppr tvs, ppr body_ty, ppr arg_tys]
1039 n_tvs = length tvs
1040
1041 {-
1042 ---------------------------------------------------------------------
1043 TyConApp
1044 ~~~~~~~~
1045 -}
1046
1047 -- | A key function: builds a 'TyConApp' or 'FunTy' as appropriate to
1048 -- its arguments. Applies its arguments to the constructor from left to right.
1049 mkTyConApp :: TyCon -> [Type] -> Type
1050 mkTyConApp tycon tys
1051 | isFunTyCon tycon
1052 , [_rep1,_rep2,ty1,ty2] <- tys
1053 = FunTy ty1 ty2
1054
1055 | otherwise
1056 = TyConApp tycon tys
1057
1058 -- splitTyConApp "looks through" synonyms, because they don't
1059 -- mean a distinct type, but all other type-constructor applications
1060 -- including functions are returned as Just ..
1061
1062 -- | Retrieve the tycon heading this type, if there is one. Does /not/
1063 -- look through synonyms.
1064 tyConAppTyConPicky_maybe :: Type -> Maybe TyCon
1065 tyConAppTyConPicky_maybe (TyConApp tc _) = Just tc
1066 tyConAppTyConPicky_maybe (FunTy {}) = Just funTyCon
1067 tyConAppTyConPicky_maybe _ = Nothing
1068
1069
1070 -- | The same as @fst . splitTyConApp@
1071 tyConAppTyCon_maybe :: Type -> Maybe TyCon
1072 tyConAppTyCon_maybe ty | Just ty' <- coreView ty = tyConAppTyCon_maybe ty'
1073 tyConAppTyCon_maybe (TyConApp tc _) = Just tc
1074 tyConAppTyCon_maybe (FunTy {}) = Just funTyCon
1075 tyConAppTyCon_maybe _ = Nothing
1076
1077 tyConAppTyCon :: Type -> TyCon
1078 tyConAppTyCon ty = tyConAppTyCon_maybe ty `orElse` pprPanic "tyConAppTyCon" (ppr ty)
1079
1080 -- | The same as @snd . splitTyConApp@
1081 tyConAppArgs_maybe :: Type -> Maybe [Type]
1082 tyConAppArgs_maybe ty | Just ty' <- coreView ty = tyConAppArgs_maybe ty'
1083 tyConAppArgs_maybe (TyConApp _ tys) = Just tys
1084 tyConAppArgs_maybe (FunTy arg res)
1085 | Just rep1 <- getRuntimeRep_maybe arg
1086 , Just rep2 <- getRuntimeRep_maybe res
1087 = Just [rep1, rep2, arg, res]
1088 tyConAppArgs_maybe _ = Nothing
1089
1090 tyConAppArgs :: Type -> [Type]
1091 tyConAppArgs ty = tyConAppArgs_maybe ty `orElse` pprPanic "tyConAppArgs" (ppr ty)
1092
1093 tyConAppArgN :: Int -> Type -> Type
1094 -- Executing Nth
1095 tyConAppArgN n ty
1096 = case tyConAppArgs_maybe ty of
1097 Just tys -> ASSERT2( tys `lengthExceeds` n, ppr n <+> ppr tys ) tys `getNth` n
1098 Nothing -> pprPanic "tyConAppArgN" (ppr n <+> ppr ty)
1099
1100 -- | Attempts to tease a type apart into a type constructor and the application
1101 -- of a number of arguments to that constructor. Panics if that is not possible.
1102 -- See also 'splitTyConApp_maybe'
1103 splitTyConApp :: Type -> (TyCon, [Type])
1104 splitTyConApp ty = case splitTyConApp_maybe ty of
1105 Just stuff -> stuff
1106 Nothing -> pprPanic "splitTyConApp" (ppr ty)
1107
1108 -- | Attempts to tease a type apart into a type constructor and the application
1109 -- of a number of arguments to that constructor
1110 splitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
1111 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
1112 splitTyConApp_maybe ty = repSplitTyConApp_maybe ty
1113
1114 -- | Like 'splitTyConApp_maybe', but doesn't look through synonyms. This
1115 -- assumes the synonyms have already been dealt with.
1116 repSplitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
1117 repSplitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
1118 repSplitTyConApp_maybe (FunTy arg res)
1119 | Just rep1 <- getRuntimeRep_maybe arg
1120 , Just rep2 <- getRuntimeRep_maybe res
1121 = Just (funTyCon, [rep1, rep2, arg, res])
1122 | otherwise
1123 = pprPanic "repSplitTyConApp_maybe"
1124 (ppr arg $$ ppr res $$ ppr (typeKind res))
1125 repSplitTyConApp_maybe _ = Nothing
1126
1127 -- | Attempts to tease a list type apart and gives the type of the elements if
1128 -- successful (looks through type synonyms)
1129 splitListTyConApp_maybe :: Type -> Maybe Type
1130 splitListTyConApp_maybe ty = case splitTyConApp_maybe ty of
1131 Just (tc,[e]) | tc == listTyCon -> Just e
1132 _other -> Nothing
1133
1134 -- | What is the role assigned to the next parameter of this type? Usually,
1135 -- this will be 'Nominal', but if the type is a 'TyConApp', we may be able to
1136 -- do better. The type does *not* have to be well-kinded when applied for this
1137 -- to work!
1138 nextRole :: Type -> Role
1139 nextRole ty
1140 | Just (tc, tys) <- splitTyConApp_maybe ty
1141 , let num_tys = length tys
1142 , num_tys < tyConArity tc
1143 = tyConRoles tc `getNth` num_tys
1144
1145 | otherwise
1146 = Nominal
1147
1148 newTyConInstRhs :: TyCon -> [Type] -> Type
1149 -- ^ Unwrap one 'layer' of newtype on a type constructor and its
1150 -- arguments, using an eta-reduced version of the @newtype@ if possible.
1151 -- This requires tys to have at least @newTyConInstArity tycon@ elements.
1152 newTyConInstRhs tycon tys
1153 = ASSERT2( tvs `leLength` tys, ppr tycon $$ ppr tys $$ ppr tvs )
1154 applyTysX tvs rhs tys
1155 where
1156 (tvs, rhs) = newTyConEtadRhs tycon
1157
1158 {-
1159 ---------------------------------------------------------------------
1160 CastTy
1161 ~~~~~~
1162 A casted type has its *kind* casted into something new.
1163
1164 Note [No reflexive casts in types]
1165 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1166 As far as possible, we would like to maintain the following property:
1167
1168 (*) If (t1 `eqType` t2), then t1 and t2 are treated identically within GHC.
1169
1170 The (*) property is very useful, because we have a tendency to compare two
1171 types to see if they're equal, and then arbitrarily choose one. We don't
1172 want this arbitrary choice to then matter later on. Maintaining (*) means
1173 that every function that looks at a structure of a type must think about
1174 casts. In places where we directly pattern-match, this consideration is
1175 forced by consideration of the CastTy constructor.
1176
1177 But, when we call a splitXXX function, it's easy to ignore the possibility
1178 of casts. In particular, splitTyConApp is used extensively, and we don't
1179 want it to fail on (T a b c |> co). Happily, if we have
1180 (T a b c |> co) `eqType` (T d e f)
1181 then co must be reflexive. Why? eqType checks that the kinds are equal, as
1182 well as checking that (a `eqType` d), (b `eqType` e), and (c `eqType` f).
1183 By the kind check, we know that (T a b c |> co) and (T d e f) have the same
1184 kind. So the only way that co could be non-reflexive is for (T a b c) to have
1185 a different kind than (T d e f). But because T's kind is closed (all tycon kinds
1186 are closed), the only way for this to happen is that one of the arguments has
1187 to differ, leading to a contradiction. Thus, co is reflexive.
1188
1189 Accordingly, by eliminating reflexive casts, splitTyConApp need not worry
1190 about outermost casts to uphold (*).
1191
1192 Unforunately, that's not the end of the story. Consider comparing
1193 (T a b c) =? (T a b |> (co -> <Type>)) (c |> sym co)
1194 These two types have the same kind (Type), but the left type is a TyConApp
1195 while the right type is not. To handle this case, we will have to implement
1196 some variant of the dreaded KPush algorithm (c.f. CoreOpt.pushCoDataCon).
1197 This stone is left unturned for now, meaning that we don't yet uphold (*).
1198
1199 The other place where (*) will be hard to guarantee is in splitAppTy, because
1200 I (Richard E) can't think of a way to push coercions into AppTys. The good
1201 news here is that splitAppTy is not used all that much, and so all clients of
1202 that function can simply be told to use splitCastTy as well, in order to
1203 uphold (*). This, too, is left undone, for now.
1204
1205 -}
1206
1207 splitCastTy_maybe :: Type -> Maybe (Type, Coercion)
1208 splitCastTy_maybe ty | Just ty' <- coreView ty = splitCastTy_maybe ty'
1209 splitCastTy_maybe (CastTy ty co) = Just (ty, co)
1210 splitCastTy_maybe _ = Nothing
1211
1212 -- | Make a 'CastTy'. The Coercion must be nominal. Checks the
1213 -- Coercion for reflexivity, dropping it if it's reflexive.
1214 -- See Note [No reflexive casts in types]
1215 mkCastTy :: Type -> Coercion -> Type
1216 mkCastTy ty co | isReflexiveCo co = ty
1217 -- NB: Do the slow check here. This is important to keep the splitXXX
1218 -- functions working properly. Otherwise, we may end up with something
1219 -- like (((->) |> something_reflexive_but_not_obviously_so) biz baz)
1220 -- fails under splitFunTy_maybe. This happened with the cheaper check
1221 -- in test dependent/should_compile/dynamic-paper.
1222
1223 mkCastTy (CastTy ty co1) co2 = mkCastTy ty (co1 `mkTransCo` co2)
1224 mkCastTy ty co = CastTy ty co
1225
1226 tyConBindersTyBinders :: [TyConBinder] -> [TyBinder]
1227 -- Return the tyConBinders in TyBinder form
1228 tyConBindersTyBinders = map to_tyb
1229 where
1230 to_tyb (TvBndr tv (NamedTCB vis)) = Named (TvBndr tv vis)
1231 to_tyb (TvBndr tv AnonTCB) = Anon (tyVarKind tv)
1232
1233 {-
1234 --------------------------------------------------------------------
1235 CoercionTy
1236 ~~~~~~~~~~
1237 CoercionTy allows us to inject coercions into types. A CoercionTy
1238 should appear only in the right-hand side of an application.
1239 -}
1240
1241 mkCoercionTy :: Coercion -> Type
1242 mkCoercionTy = CoercionTy
1243
1244 isCoercionTy :: Type -> Bool
1245 isCoercionTy (CoercionTy _) = True
1246 isCoercionTy _ = False
1247
1248 isCoercionTy_maybe :: Type -> Maybe Coercion
1249 isCoercionTy_maybe (CoercionTy co) = Just co
1250 isCoercionTy_maybe _ = Nothing
1251
1252 stripCoercionTy :: Type -> Coercion
1253 stripCoercionTy (CoercionTy co) = co
1254 stripCoercionTy ty = pprPanic "stripCoercionTy" (ppr ty)
1255
1256 {-
1257 ---------------------------------------------------------------------
1258 SynTy
1259 ~~~~~
1260
1261 Notes on type synonyms
1262 ~~~~~~~~~~~~~~~~~~~~~~
1263 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
1264 to return type synonyms wherever possible. Thus
1265
1266 type Foo a = a -> a
1267
1268 we want
1269 splitFunTys (a -> Foo a) = ([a], Foo a)
1270 not ([a], a -> a)
1271
1272 The reason is that we then get better (shorter) type signatures in
1273 interfaces. Notably this plays a role in tcTySigs in TcBinds.hs.
1274
1275
1276 ---------------------------------------------------------------------
1277 ForAllTy
1278 ~~~~~~~~
1279 -}
1280
1281 -- | Make a dependent forall over an Inferred (as opposed to Specified)
1282 -- variable
1283 mkInvForAllTy :: TyVar -> Type -> Type
1284 mkInvForAllTy tv ty = ASSERT( isTyVar tv )
1285 ForAllTy (TvBndr tv Inferred) ty
1286
1287 -- | Like mkForAllTys, but assumes all variables are dependent and Inferred,
1288 -- a common case
1289 mkInvForAllTys :: [TyVar] -> Type -> Type
1290 mkInvForAllTys tvs ty = ASSERT( all isTyVar tvs )
1291 foldr mkInvForAllTy ty tvs
1292
1293 -- | Like mkForAllTys, but assumes all variables are dependent and specified,
1294 -- a common case
1295 mkSpecForAllTys :: [TyVar] -> Type -> Type
1296 mkSpecForAllTys tvs = ASSERT( all isTyVar tvs )
1297 mkForAllTys [ TvBndr tv Specified | tv <- tvs ]
1298
1299 -- | Like mkForAllTys, but assumes all variables are dependent and visible
1300 mkVisForAllTys :: [TyVar] -> Type -> Type
1301 mkVisForAllTys tvs = ASSERT( all isTyVar tvs )
1302 mkForAllTys [ TvBndr tv Required | tv <- tvs ]
1303
1304 mkLamType :: Var -> Type -> Type
1305 -- ^ Makes a @(->)@ type or an implicit forall type, depending
1306 -- on whether it is given a type variable or a term variable.
1307 -- This is used, for example, when producing the type of a lambda.
1308 -- Always uses Inferred binders.
1309 mkLamTypes :: [Var] -> Type -> Type
1310 -- ^ 'mkLamType' for multiple type or value arguments
1311
1312 mkLamType v ty
1313 | isTyVar v = ForAllTy (TvBndr v Inferred) ty
1314 | otherwise = FunTy (varType v) ty
1315
1316 mkLamTypes vs ty = foldr mkLamType ty vs
1317
1318 -- | Given a list of type-level vars and a result type, makes TyBinders, preferring
1319 -- anonymous binders if the variable is, in fact, not dependent.
1320 -- All binders are /visible/.
1321 mkTyConBindersPreferAnon :: [TyVar] -> Type -> [TyConBinder]
1322 mkTyConBindersPreferAnon vars inner_ty = fst (go vars)
1323 where
1324 go :: [TyVar] -> ([TyConBinder], VarSet) -- also returns the free vars
1325 go [] = ([], tyCoVarsOfType inner_ty)
1326 go (v:vs) | v `elemVarSet` fvs
1327 = ( TvBndr v (NamedTCB Required) : binders
1328 , fvs `delVarSet` v `unionVarSet` kind_vars )
1329 | otherwise
1330 = ( TvBndr v AnonTCB : binders
1331 , fvs `unionVarSet` kind_vars )
1332 where
1333 (binders, fvs) = go vs
1334 kind_vars = tyCoVarsOfType $ tyVarKind v
1335
1336 -- | Take a ForAllTy apart, returning the list of tyvars and the result type.
1337 -- This always succeeds, even if it returns only an empty list. Note that the
1338 -- result type returned may have free variables that were bound by a forall.
1339 splitForAllTys :: Type -> ([TyVar], Type)
1340 splitForAllTys ty = split ty ty []
1341 where
1342 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
1343 split _ (ForAllTy (TvBndr tv _) ty) tvs = split ty ty (tv:tvs)
1344 split orig_ty _ tvs = (reverse tvs, orig_ty)
1345
1346 -- | Like 'splitPiTys' but split off only /named/ binders.
1347 splitForAllTyVarBndrs :: Type -> ([TyVarBinder], Type)
1348 splitForAllTyVarBndrs ty = split ty ty []
1349 where
1350 split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs
1351 split _ (ForAllTy b res) bs = split res res (b:bs)
1352 split orig_ty _ bs = (reverse bs, orig_ty)
1353
1354 -- | Checks whether this is a proper forall (with a named binder)
1355 isForAllTy :: Type -> Bool
1356 isForAllTy ty | Just ty' <- coreView ty = isForAllTy ty'
1357 isForAllTy (ForAllTy {}) = True
1358 isForAllTy _ = False
1359
1360 -- | Is this a function or forall?
1361 isPiTy :: Type -> Bool
1362 isPiTy ty | Just ty' <- coreView ty = isForAllTy ty'
1363 isPiTy (ForAllTy {}) = True
1364 isPiTy (FunTy {}) = True
1365 isPiTy _ = False
1366
1367 -- | Take a forall type apart, or panics if that is not possible.
1368 splitForAllTy :: Type -> (TyVar, Type)
1369 splitForAllTy ty
1370 | Just answer <- splitForAllTy_maybe ty = answer
1371 | otherwise = pprPanic "splitForAllTy" (ppr ty)
1372
1373 -- | Drops all ForAllTys
1374 dropForAlls :: Type -> Type
1375 dropForAlls ty = go ty
1376 where
1377 go ty | Just ty' <- coreView ty = go ty'
1378 go (ForAllTy _ res) = go res
1379 go res = res
1380
1381 -- | Attempts to take a forall type apart, but only if it's a proper forall,
1382 -- with a named binder
1383 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
1384 splitForAllTy_maybe ty = go ty
1385 where
1386 go ty | Just ty' <- coreView ty = go ty'
1387 go (ForAllTy (TvBndr tv _) ty) = Just (tv, ty)
1388 go _ = Nothing
1389
1390 -- | Attempts to take a forall type apart; works with proper foralls and
1391 -- functions
1392 splitPiTy_maybe :: Type -> Maybe (TyBinder, Type)
1393 splitPiTy_maybe ty = go ty
1394 where
1395 go ty | Just ty' <- coreView ty = go ty'
1396 go (ForAllTy bndr ty) = Just (Named bndr, ty)
1397 go (FunTy arg res) = Just (Anon arg, res)
1398 go _ = Nothing
1399
1400 -- | Takes a forall type apart, or panics
1401 splitPiTy :: Type -> (TyBinder, Type)
1402 splitPiTy ty
1403 | Just answer <- splitPiTy_maybe ty = answer
1404 | otherwise = pprPanic "splitPiTy" (ppr ty)
1405
1406 -- | Split off all TyBinders to a type, splitting both proper foralls
1407 -- and functions
1408 splitPiTys :: Type -> ([TyBinder], Type)
1409 splitPiTys ty = split ty ty []
1410 where
1411 split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs
1412 split _ (ForAllTy b res) bs = split res res (Named b : bs)
1413 split _ (FunTy arg res) bs = split res res (Anon arg : bs)
1414 split orig_ty _ bs = (reverse bs, orig_ty)
1415
1416 -- Like splitPiTys, but returns only *invisible* binders, including constraints
1417 -- Stops at the first visible binder
1418 splitPiTysInvisible :: Type -> ([TyBinder], Type)
1419 splitPiTysInvisible ty = split ty ty []
1420 where
1421 split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs
1422 split _ (ForAllTy b@(TvBndr _ vis) res) bs
1423 | isInvisibleArgFlag vis = split res res (Named b : bs)
1424 split _ (FunTy arg res) bs
1425 | isPredTy arg = split res res (Anon arg : bs)
1426 split orig_ty _ bs = (reverse bs, orig_ty)
1427
1428 -- | Given a tycon and its arguments, filters out any invisible arguments
1429 filterOutInvisibleTypes :: TyCon -> [Type] -> [Type]
1430 filterOutInvisibleTypes tc tys = snd $ partitionInvisibles tc id tys
1431
1432 -- | Like 'filterOutInvisibles', but works on 'TyVar's
1433 filterOutInvisibleTyVars :: TyCon -> [TyVar] -> [TyVar]
1434 filterOutInvisibleTyVars tc tvs = snd $ partitionInvisibles tc mkTyVarTy tvs
1435
1436 -- | Given a tycon and a list of things (which correspond to arguments),
1437 -- partitions the things into
1438 -- Inferred or Specified ones and
1439 -- Required ones
1440 -- The callback function is necessary for this scenario:
1441 --
1442 -- > T :: forall k. k -> k
1443 -- > partitionInvisibles T [forall m. m -> m -> m, S, R, Q]
1444 --
1445 -- After substituting, we get
1446 --
1447 -- > T (forall m. m -> m -> m) :: (forall m. m -> m -> m) -> forall n. n -> n -> n
1448 --
1449 -- Thus, the first argument is invisible, @S@ is visible, @R@ is invisible again,
1450 -- and @Q@ is visible.
1451 --
1452 -- If you're absolutely sure that your tycon's kind doesn't end in a variable,
1453 -- it's OK if the callback function panics, as that's the only time it's
1454 -- consulted.
1455 partitionInvisibles :: TyCon -> (a -> Type) -> [a] -> ([a], [a])
1456 partitionInvisibles tc get_ty = go emptyTCvSubst (tyConKind tc)
1457 where
1458 go _ _ [] = ([], [])
1459 go subst (ForAllTy (TvBndr tv vis) res_ki) (x:xs)
1460 | isVisibleArgFlag vis = second (x :) (go subst' res_ki xs)
1461 | otherwise = first (x :) (go subst' res_ki xs)
1462 where
1463 subst' = extendTvSubst subst tv (get_ty x)
1464 go subst (TyVarTy tv) xs
1465 | Just ki <- lookupTyVar subst tv = go subst ki xs
1466 go _ _ xs = ([], xs) -- something is ill-kinded. But this can happen
1467 -- when printing errors. Assume everything is visible.
1468
1469 -- @isTauTy@ tests if a type has no foralls
1470 isTauTy :: Type -> Bool
1471 isTauTy ty | Just ty' <- coreView ty = isTauTy ty'
1472 isTauTy (TyVarTy _) = True
1473 isTauTy (LitTy {}) = True
1474 isTauTy (TyConApp tc tys) = all isTauTy tys && isTauTyCon tc
1475 isTauTy (AppTy a b) = isTauTy a && isTauTy b
1476 isTauTy (FunTy a b) = isTauTy a && isTauTy b
1477 isTauTy (ForAllTy {}) = False
1478 isTauTy (CastTy ty _) = isTauTy ty
1479 isTauTy (CoercionTy _) = False -- Not sure about this
1480
1481 {-
1482 %************************************************************************
1483 %* *
1484 TyBinders
1485 %* *
1486 %************************************************************************
1487 -}
1488
1489 -- | Make an anonymous binder
1490 mkAnonBinder :: Type -> TyBinder
1491 mkAnonBinder = Anon
1492
1493 -- | Does this binder bind a variable that is /not/ erased? Returns
1494 -- 'True' for anonymous binders.
1495 isAnonTyBinder :: TyBinder -> Bool
1496 isAnonTyBinder (Named {}) = False
1497 isAnonTyBinder (Anon {}) = True
1498
1499 isNamedTyBinder :: TyBinder -> Bool
1500 isNamedTyBinder (Named {}) = True
1501 isNamedTyBinder (Anon {}) = False
1502
1503 tyBinderType :: TyBinder -> Type
1504 -- Barely used
1505 tyBinderType (Named tvb) = binderKind tvb
1506 tyBinderType (Anon ty) = ty
1507
1508 -- | Extract a relevant type, if there is one.
1509 binderRelevantType_maybe :: TyBinder -> Maybe Type
1510 binderRelevantType_maybe (Named {}) = Nothing
1511 binderRelevantType_maybe (Anon ty) = Just ty
1512
1513 -- | Like 'maybe', but for binders.
1514 caseBinder :: TyBinder -- ^ binder to scrutinize
1515 -> (TyVarBinder -> a) -- ^ named case
1516 -> (Type -> a) -- ^ anonymous case
1517 -> a
1518 caseBinder (Named v) f _ = f v
1519 caseBinder (Anon t) _ d = d t
1520
1521 -- | Manufacture a new 'TyConBinder' from a 'TyBinder'. Anonymous
1522 -- 'TyBinder's are still assigned names as 'TyConBinder's, so we need
1523 -- the extra gunk with which to construct a 'Name'. Used when producing
1524 -- tyConTyVars from a datatype kind signature. Defined here to avoid module
1525 -- loops.
1526 mkTyBinderTyConBinder :: TyBinder -> SrcSpan -> Unique -> OccName -> TyConBinder
1527 mkTyBinderTyConBinder (Named (TvBndr tv argf)) _ _ _ = TvBndr tv (NamedTCB argf)
1528 mkTyBinderTyConBinder (Anon kind) loc uniq occ
1529 = TvBndr (mkTyVar (mkInternalName uniq occ loc) kind) AnonTCB
1530
1531 {-
1532 %************************************************************************
1533 %* *
1534 Pred
1535 * *
1536 ************************************************************************
1537
1538 Predicates on PredType
1539
1540 Note [isPredTy complications]
1541 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1542 You would think that we could define
1543 isPredTy ty = isConstraintKind (typeKind ty)
1544 But there are a number of complications:
1545
1546 * isPredTy is used when printing types, which can happen in debug
1547 printing during type checking of not-fully-zonked types. So it's
1548 not cool to say isConstraintKind (typeKind ty) because, absent
1549 zonking, the type might be ill-kinded, and typeKind crashes. Hence the
1550 rather tiresome story here
1551
1552 * isPredTy must return "True" to *unlifted* coercions, such as (t1 ~# t2)
1553 and (t1 ~R# t2), which are not of kind Constraint! Currently they are
1554 of kind #.
1555
1556 * If we do form the type '(C a => C [a]) => blah', then we'd like to
1557 print it as such. But that means that isPredTy must return True for
1558 (C a => C [a]). Admittedly that type is illegal in Haskell, but we
1559 want to print it nicely in error messages.
1560 -}
1561
1562 -- | Is the type suitable to classify a given/wanted in the typechecker?
1563 isPredTy :: Type -> Bool
1564 -- See Note [isPredTy complications]
1565 isPredTy ty = go ty []
1566 where
1567 go :: Type -> [KindOrType] -> Bool
1568 go (AppTy ty1 ty2) args = go ty1 (ty2 : args)
1569 go (TyVarTy tv) args = go_k (tyVarKind tv) args
1570 go (TyConApp tc tys) args = ASSERT( null args ) -- TyConApp invariant
1571 go_tc tc tys
1572 go (FunTy arg res) []
1573 | isPredTy arg = isPredTy res -- (Eq a => C a)
1574 | otherwise = False -- (Int -> Bool)
1575 go (ForAllTy _ ty) [] = go ty []
1576 go (CastTy _ co) args = go_k (pSnd (coercionKind co)) args
1577 go _ _ = False
1578
1579 go_tc :: TyCon -> [KindOrType] -> Bool
1580 go_tc tc args
1581 | tc `hasKey` eqPrimTyConKey || tc `hasKey` eqReprPrimTyConKey
1582 = args `lengthIs` 4 -- ~# and ~R# sadly have result kind #
1583 -- not Constraint; but we still want
1584 -- isPredTy to reply True.
1585 | otherwise = go_k (tyConKind tc) args
1586
1587 go_k :: Kind -> [KindOrType] -> Bool
1588 -- True <=> ('k' applied to 'kts') = Constraint
1589 go_k k [] = isConstraintKind k
1590 go_k k (arg:args) = case piResultTy_maybe k arg of
1591 Just k' -> go_k k' args
1592 Nothing -> WARN( True, text "isPredTy" <+> ppr ty )
1593 False
1594 -- This last case shouldn't happen under most circumstances. It can
1595 -- occur if we call isPredTy during kind checking, especially if one
1596 -- of the following happens:
1597 --
1598 -- 1. There is actually a kind error. Example in which this showed up:
1599 -- polykinds/T11399
1600 --
1601 -- 2. A type constructor application appears to be oversaturated. An
1602 -- example of this occurred in GHC Trac #13187:
1603 --
1604 -- {-# LANGUAGE PolyKinds #-}
1605 -- type Const a b = b
1606 -- f :: Const Int (,) Bool Char -> Char
1607 --
1608 -- We call isPredTy (Const k1 k2 Int (,) Bool Char
1609 -- where k1,k2 are unification variables that have been
1610 -- unified to *, and (*->*->*) resp, /but not zonked/.
1611 -- This shows that isPredTy can report a false negative
1612 -- if a constraint is similarly oversaturated, but
1613 -- it's hard to do better than isPredTy currently does without
1614 -- zonking, so we punt on such cases for now. This only happens
1615 -- during debug-printing, so it doesn't matter.
1616
1617 isClassPred, isEqPred, isNomEqPred, isIPPred :: PredType -> Bool
1618 isClassPred ty = case tyConAppTyCon_maybe ty of
1619 Just tyCon | isClassTyCon tyCon -> True
1620 _ -> False
1621 isEqPred ty = case tyConAppTyCon_maybe ty of
1622 Just tyCon -> tyCon `hasKey` eqPrimTyConKey
1623 || tyCon `hasKey` eqReprPrimTyConKey
1624 _ -> False
1625
1626 isNomEqPred ty = case tyConAppTyCon_maybe ty of
1627 Just tyCon -> tyCon `hasKey` eqPrimTyConKey
1628 _ -> False
1629
1630 isIPPred ty = case tyConAppTyCon_maybe ty of
1631 Just tc -> isIPTyCon tc
1632 _ -> False
1633
1634 isIPTyCon :: TyCon -> Bool
1635 isIPTyCon tc = tc `hasKey` ipClassKey
1636 -- Class and its corresponding TyCon have the same Unique
1637
1638 isIPClass :: Class -> Bool
1639 isIPClass cls = cls `hasKey` ipClassKey
1640
1641 isCTupleClass :: Class -> Bool
1642 isCTupleClass cls = isTupleTyCon (classTyCon cls)
1643
1644 isIPPred_maybe :: Type -> Maybe (FastString, Type)
1645 isIPPred_maybe ty =
1646 do (tc,[t1,t2]) <- splitTyConApp_maybe ty
1647 guard (isIPTyCon tc)
1648 x <- isStrLitTy t1
1649 return (x,t2)
1650
1651 {-
1652 Make PredTypes
1653
1654 --------------------- Equality types ---------------------------------
1655 -}
1656
1657 -- | Makes a lifted equality predicate at the given role
1658 mkPrimEqPredRole :: Role -> Type -> Type -> PredType
1659 mkPrimEqPredRole Nominal = mkPrimEqPred
1660 mkPrimEqPredRole Representational = mkReprPrimEqPred
1661 mkPrimEqPredRole Phantom = panic "mkPrimEqPredRole phantom"
1662
1663 -- | Creates a primitive type equality predicate.
1664 -- Invariant: the types are not Coercions
1665 mkPrimEqPred :: Type -> Type -> Type
1666 mkPrimEqPred ty1 ty2
1667 = TyConApp eqPrimTyCon [k1, k2, ty1, ty2]
1668 where
1669 k1 = typeKind ty1
1670 k2 = typeKind ty2
1671
1672 -- | Creates a primite type equality predicate with explicit kinds
1673 mkHeteroPrimEqPred :: Kind -> Kind -> Type -> Type -> Type
1674 mkHeteroPrimEqPred k1 k2 ty1 ty2 = TyConApp eqPrimTyCon [k1, k2, ty1, ty2]
1675
1676 -- | Creates a primitive representational type equality predicate
1677 -- with explicit kinds
1678 mkHeteroReprPrimEqPred :: Kind -> Kind -> Type -> Type -> Type
1679 mkHeteroReprPrimEqPred k1 k2 ty1 ty2
1680 = TyConApp eqReprPrimTyCon [k1, k2, ty1, ty2]
1681
1682 -- | Try to split up a coercion type into the types that it coerces
1683 splitCoercionType_maybe :: Type -> Maybe (Type, Type)
1684 splitCoercionType_maybe ty
1685 = do { (tc, [_, _, ty1, ty2]) <- splitTyConApp_maybe ty
1686 ; guard $ tc `hasKey` eqPrimTyConKey || tc `hasKey` eqReprPrimTyConKey
1687 ; return (ty1, ty2) }
1688
1689 mkReprPrimEqPred :: Type -> Type -> Type
1690 mkReprPrimEqPred ty1 ty2
1691 = TyConApp eqReprPrimTyCon [k1, k2, ty1, ty2]
1692 where
1693 k1 = typeKind ty1
1694 k2 = typeKind ty2
1695
1696 equalityTyCon :: Role -> TyCon
1697 equalityTyCon Nominal = eqPrimTyCon
1698 equalityTyCon Representational = eqReprPrimTyCon
1699 equalityTyCon Phantom = eqPhantPrimTyCon
1700
1701 -- --------------------- Dictionary types ---------------------------------
1702
1703 mkClassPred :: Class -> [Type] -> PredType
1704 mkClassPred clas tys = TyConApp (classTyCon clas) tys
1705
1706 isDictTy :: Type -> Bool
1707 isDictTy = isClassPred
1708
1709 isDictLikeTy :: Type -> Bool
1710 -- Note [Dictionary-like types]
1711 isDictLikeTy ty | Just ty' <- coreView ty = isDictLikeTy ty'
1712 isDictLikeTy ty = case splitTyConApp_maybe ty of
1713 Just (tc, tys) | isClassTyCon tc -> True
1714 | isTupleTyCon tc -> all isDictLikeTy tys
1715 _other -> False
1716
1717 {-
1718 Note [Dictionary-like types]
1719 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1720 Being "dictionary-like" means either a dictionary type or a tuple thereof.
1721 In GHC 6.10 we build implication constraints which construct such tuples,
1722 and if we land up with a binding
1723 t :: (C [a], Eq [a])
1724 t = blah
1725 then we want to treat t as cheap under "-fdicts-cheap" for example.
1726 (Implication constraints are normally inlined, but sadly not if the
1727 occurrence is itself inside an INLINE function! Until we revise the
1728 handling of implication constraints, that is.) This turned out to
1729 be important in getting good arities in DPH code. Example:
1730
1731 class C a
1732 class D a where { foo :: a -> a }
1733 instance C a => D (Maybe a) where { foo x = x }
1734
1735 bar :: (C a, C b) => a -> b -> (Maybe a, Maybe b)
1736 {-# INLINE bar #-}
1737 bar x y = (foo (Just x), foo (Just y))
1738
1739 Then 'bar' should jolly well have arity 4 (two dicts, two args), but
1740 we ended up with something like
1741 bar = __inline_me__ (\d1,d2. let t :: (D (Maybe a), D (Maybe b)) = ...
1742 in \x,y. <blah>)
1743
1744 This is all a bit ad-hoc; eg it relies on knowing that implication
1745 constraints build tuples.
1746
1747
1748 Decomposing PredType
1749 -}
1750
1751 -- | A choice of equality relation. This is separate from the type 'Role'
1752 -- because 'Phantom' does not define a (non-trivial) equality relation.
1753 data EqRel = NomEq | ReprEq
1754 deriving (Eq, Ord)
1755
1756 instance Outputable EqRel where
1757 ppr NomEq = text "nominal equality"
1758 ppr ReprEq = text "representational equality"
1759
1760 eqRelRole :: EqRel -> Role
1761 eqRelRole NomEq = Nominal
1762 eqRelRole ReprEq = Representational
1763
1764 data PredTree = ClassPred Class [Type]
1765 | EqPred EqRel Type Type
1766 | IrredPred PredType
1767
1768 classifyPredType :: PredType -> PredTree
1769 classifyPredType ev_ty = case splitTyConApp_maybe ev_ty of
1770 Just (tc, [_, _, ty1, ty2])
1771 | tc `hasKey` eqReprPrimTyConKey -> EqPred ReprEq ty1 ty2
1772 | tc `hasKey` eqPrimTyConKey -> EqPred NomEq ty1 ty2
1773 Just (tc, tys)
1774 | Just clas <- tyConClass_maybe tc -> ClassPred clas tys
1775 _ -> IrredPred ev_ty
1776
1777 getClassPredTys :: PredType -> (Class, [Type])
1778 getClassPredTys ty = case getClassPredTys_maybe ty of
1779 Just (clas, tys) -> (clas, tys)
1780 Nothing -> pprPanic "getClassPredTys" (ppr ty)
1781
1782 getClassPredTys_maybe :: PredType -> Maybe (Class, [Type])
1783 getClassPredTys_maybe ty = case splitTyConApp_maybe ty of
1784 Just (tc, tys) | Just clas <- tyConClass_maybe tc -> Just (clas, tys)
1785 _ -> Nothing
1786
1787 getEqPredTys :: PredType -> (Type, Type)
1788 getEqPredTys ty
1789 = case splitTyConApp_maybe ty of
1790 Just (tc, [_, _, ty1, ty2])
1791 | tc `hasKey` eqPrimTyConKey
1792 || tc `hasKey` eqReprPrimTyConKey
1793 -> (ty1, ty2)
1794 _ -> pprPanic "getEqPredTys" (ppr ty)
1795
1796 getEqPredTys_maybe :: PredType -> Maybe (Role, Type, Type)
1797 getEqPredTys_maybe ty
1798 = case splitTyConApp_maybe ty of
1799 Just (tc, [_, _, ty1, ty2])
1800 | tc `hasKey` eqPrimTyConKey -> Just (Nominal, ty1, ty2)
1801 | tc `hasKey` eqReprPrimTyConKey -> Just (Representational, ty1, ty2)
1802 _ -> Nothing
1803
1804 getEqPredRole :: PredType -> Role
1805 getEqPredRole ty = eqRelRole (predTypeEqRel ty)
1806
1807 -- | Get the equality relation relevant for a pred type.
1808 predTypeEqRel :: PredType -> EqRel
1809 predTypeEqRel ty
1810 | Just (tc, _) <- splitTyConApp_maybe ty
1811 , tc `hasKey` eqReprPrimTyConKey
1812 = ReprEq
1813 | otherwise
1814 = NomEq
1815
1816 {-
1817 %************************************************************************
1818 %* *
1819 Well-scoped tyvars
1820 * *
1821 ************************************************************************
1822 -}
1823
1824 -- | Do a topological sort on a list of tyvars,
1825 -- so that binders occur before occurrences
1826 -- E.g. given [ a::k, k::*, b::k ]
1827 -- it'll return a well-scoped list [ k::*, a::k, b::k ]
1828 --
1829 -- This is a deterministic sorting operation
1830 -- (that is, doesn't depend on Uniques).
1831 toposortTyVars :: [TyVar] -> [TyVar]
1832 toposortTyVars tvs = reverse $
1833 [ node_payload node | node <- topologicalSortG $
1834 graphFromEdgedVerticesOrd nodes ]
1835 where
1836 var_ids :: VarEnv Int
1837 var_ids = mkVarEnv (zip tvs [1..])
1838
1839 nodes :: [ Node Int TyVar ]
1840 nodes = [ DigraphNode
1841 tv
1842 (lookupVarEnv_NF var_ids tv)
1843 (mapMaybe (lookupVarEnv var_ids)
1844 (tyCoVarsOfTypeList (tyVarKind tv)))
1845 | tv <- tvs ]
1846
1847 -- | Extract a well-scoped list of variables from a deterministic set of
1848 -- variables. The result is deterministic.
1849 -- NB: There used to exist varSetElemsWellScoped :: VarSet -> [Var] which
1850 -- took a non-deterministic set and produced a non-deterministic
1851 -- well-scoped list. If you care about the list being well-scoped you also
1852 -- most likely care about it being in deterministic order.
1853 dVarSetElemsWellScoped :: DVarSet -> [Var]
1854 dVarSetElemsWellScoped = toposortTyVars . dVarSetElems
1855
1856 -- | Get the free vars of a type in scoped order
1857 tyCoVarsOfTypeWellScoped :: Type -> [TyVar]
1858 tyCoVarsOfTypeWellScoped = toposortTyVars . tyCoVarsOfTypeList
1859
1860 -- | Get the free vars of types in scoped order
1861 tyCoVarsOfTypesWellScoped :: [Type] -> [TyVar]
1862 tyCoVarsOfTypesWellScoped = toposortTyVars . tyCoVarsOfTypesList
1863
1864 {-
1865 ************************************************************************
1866 * *
1867 \subsection{Type families}
1868 * *
1869 ************************************************************************
1870 -}
1871
1872 mkFamilyTyConApp :: TyCon -> [Type] -> Type
1873 -- ^ Given a family instance TyCon and its arg types, return the
1874 -- corresponding family type. E.g:
1875 --
1876 -- > data family T a
1877 -- > data instance T (Maybe b) = MkT b
1878 --
1879 -- Where the instance tycon is :RTL, so:
1880 --
1881 -- > mkFamilyTyConApp :RTL Int = T (Maybe Int)
1882 mkFamilyTyConApp tc tys
1883 | Just (fam_tc, fam_tys) <- tyConFamInst_maybe tc
1884 , let tvs = tyConTyVars tc
1885 fam_subst = ASSERT2( tvs `equalLength` tys, ppr tc <+> ppr tys )
1886 zipTvSubst tvs tys
1887 = mkTyConApp fam_tc (substTys fam_subst fam_tys)
1888 | otherwise
1889 = mkTyConApp tc tys
1890
1891 -- | Get the type on the LHS of a coercion induced by a type/data
1892 -- family instance.
1893 coAxNthLHS :: CoAxiom br -> Int -> Type
1894 coAxNthLHS ax ind =
1895 mkTyConApp (coAxiomTyCon ax) (coAxBranchLHS (coAxiomNthBranch ax ind))
1896
1897 -- | Pretty prints a 'TyCon', using the family instance in case of a
1898 -- representation tycon. For example:
1899 --
1900 -- > data T [a] = ...
1901 --
1902 -- In that case we want to print @T [a]@, where @T@ is the family 'TyCon'
1903 pprSourceTyCon :: TyCon -> SDoc
1904 pprSourceTyCon tycon
1905 | Just (fam_tc, tys) <- tyConFamInst_maybe tycon
1906 = ppr $ fam_tc `TyConApp` tys -- can't be FunTyCon
1907 | otherwise
1908 = ppr tycon
1909
1910 -- @isTauTy@ tests if a type has no foralls
1911 isFamFreeTy :: Type -> Bool
1912 isFamFreeTy ty | Just ty' <- coreView ty = isFamFreeTy ty'
1913 isFamFreeTy (TyVarTy _) = True
1914 isFamFreeTy (LitTy {}) = True
1915 isFamFreeTy (TyConApp tc tys) = all isFamFreeTy tys && isFamFreeTyCon tc
1916 isFamFreeTy (AppTy a b) = isFamFreeTy a && isFamFreeTy b
1917 isFamFreeTy (FunTy a b) = isFamFreeTy a && isFamFreeTy b
1918 isFamFreeTy (ForAllTy _ ty) = isFamFreeTy ty
1919 isFamFreeTy (CastTy ty _) = isFamFreeTy ty
1920 isFamFreeTy (CoercionTy _) = False -- Not sure about this
1921
1922 {-
1923 ************************************************************************
1924 * *
1925 \subsection{Liftedness}
1926 * *
1927 ************************************************************************
1928 -}
1929
1930 -- | Returns Just True if this type is surely lifted, Just False
1931 -- if it is surely unlifted, Nothing if we can't be sure (i.e., it is
1932 -- levity polymorphic), and panics if the kind does not have the shape
1933 -- TYPE r.
1934 isLiftedType_maybe :: HasDebugCallStack => Type -> Maybe Bool
1935 isLiftedType_maybe ty = go (getRuntimeRep "isLiftedType_maybe" ty)
1936 where
1937 go rr | Just rr' <- coreView rr = go rr'
1938 go (TyConApp lifted_rep [])
1939 | lifted_rep `hasKey` liftedRepDataConKey = Just True
1940 go (TyConApp {}) = Just False -- everything else is unlifted
1941 go _ = Nothing -- levity polymorphic
1942
1943 -- | See "Type#type_classification" for what an unlifted type is.
1944 -- Panics on levity polymorphic types.
1945 isUnliftedType :: HasDebugCallStack => Type -> Bool
1946 -- isUnliftedType returns True for forall'd unlifted types:
1947 -- x :: forall a. Int#
1948 -- I found bindings like these were getting floated to the top level.
1949 -- They are pretty bogus types, mind you. It would be better never to
1950 -- construct them
1951 isUnliftedType ty
1952 = not (isLiftedType_maybe ty `orElse`
1953 pprPanic "isUnliftedType" (ppr ty <+> dcolon <+> ppr (typeKind ty)))
1954
1955 -- | Extract the RuntimeRep classifier of a type. For instance,
1956 -- @getRuntimeRep_maybe Int = LiftedRep@. Returns 'Nothing' if this is not
1957 -- possible.
1958 getRuntimeRep_maybe :: HasDebugCallStack
1959 => Type -> Maybe Type
1960 getRuntimeRep_maybe = getRuntimeRepFromKind_maybe . typeKind
1961
1962 -- | Extract the RuntimeRep classifier of a type. For instance,
1963 -- @getRuntimeRep_maybe Int = LiftedRep@. Panics if this is not possible.
1964 getRuntimeRep :: HasDebugCallStack
1965 => String -- ^ Printed in case of an error
1966 -> Type -> Type
1967 getRuntimeRep err ty =
1968 case getRuntimeRep_maybe ty of
1969 Just r -> r
1970 Nothing -> pprPanic "getRuntimeRep"
1971 (text err $$ ppr ty <+> dcolon <+> ppr (typeKind ty))
1972
1973 -- | Extract the RuntimeRep classifier of a type from its kind. For example,
1974 -- @getRuntimeRepFromKind * = LiftedRep@; Panics if this is not possible.
1975 getRuntimeRepFromKind :: HasDebugCallStack
1976 => String -> Type -> Type
1977 getRuntimeRepFromKind err k =
1978 case getRuntimeRepFromKind_maybe k of
1979 Just r -> r
1980 Nothing -> pprPanic "getRuntimeRepFromKind"
1981 (text err $$ ppr k <+> dcolon <+> ppr (typeKind k))
1982
1983 -- | Extract the RuntimeRep classifier of a type from its kind. For example,
1984 -- @getRuntimeRepFromKind * = LiftedRep@; Returns 'Nothing' if this is not
1985 -- possible.
1986 getRuntimeRepFromKind_maybe :: HasDebugCallStack
1987 => Type -> Maybe Type
1988 getRuntimeRepFromKind_maybe = go
1989 where
1990 go k | Just k' <- coreView k = go k'
1991 go k
1992 | Just (_tc, [arg]) <- splitTyConApp_maybe k
1993 = ASSERT2( _tc `hasKey` tYPETyConKey, ppr k )
1994 Just arg
1995 go _ = Nothing
1996
1997 isUnboxedTupleType :: Type -> Bool
1998 isUnboxedTupleType ty
1999 = tyConAppTyCon (getRuntimeRep "isUnboxedTupleType" ty) `hasKey` tupleRepDataConKey
2000 -- NB: Do not use typePrimRep, as that can't tell the difference between
2001 -- unboxed tuples and unboxed sums
2002
2003
2004 isUnboxedSumType :: Type -> Bool
2005 isUnboxedSumType ty
2006 = tyConAppTyCon (getRuntimeRep "isUnboxedSumType" ty) `hasKey` sumRepDataConKey
2007
2008 -- | See "Type#type_classification" for what an algebraic type is.
2009 -- Should only be applied to /types/, as opposed to e.g. partially
2010 -- saturated type constructors
2011 isAlgType :: Type -> Bool
2012 isAlgType ty
2013 = case splitTyConApp_maybe ty of
2014 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
2015 isAlgTyCon tc
2016 _other -> False
2017
2018 -- | See "Type#type_classification" for what an algebraic type is.
2019 -- Should only be applied to /types/, as opposed to e.g. partially
2020 -- saturated type constructors. Closed type constructors are those
2021 -- with a fixed right hand side, as opposed to e.g. associated types
2022 isClosedAlgType :: Type -> Bool
2023 isClosedAlgType ty
2024 = case splitTyConApp_maybe ty of
2025 Just (tc, ty_args) | isAlgTyCon tc && not (isFamilyTyCon tc)
2026 -> ASSERT2( ty_args `lengthIs` tyConArity tc, ppr ty ) True
2027 _other -> False
2028
2029 -- | Check whether a type is a data family type
2030 isDataFamilyAppType :: Type -> Bool
2031 isDataFamilyAppType ty = case tyConAppTyCon_maybe ty of
2032 Just tc -> isDataFamilyTyCon tc
2033 _ -> False
2034
2035 -- | Computes whether an argument (or let right hand side) should
2036 -- be computed strictly or lazily, based only on its type.
2037 -- Currently, it's just 'isUnliftedType'. Panics on levity-polymorphic types.
2038 isStrictType :: HasDebugCallStack => Type -> Bool
2039 isStrictType = isUnliftedType
2040
2041 isPrimitiveType :: Type -> Bool
2042 -- ^ Returns true of types that are opaque to Haskell.
2043 isPrimitiveType ty = case splitTyConApp_maybe ty of
2044 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
2045 isPrimTyCon tc
2046 _ -> False
2047
2048 {-
2049 ************************************************************************
2050 * *
2051 \subsection{Join points}
2052 * *
2053 ************************************************************************
2054 -}
2055
2056 -- | Determine whether a type could be the type of a join point of given total
2057 -- arity, according to the polymorphism rule. A join point cannot be polymorphic
2058 -- in its return type, since given
2059 -- join j @a @b x y z = e1 in e2,
2060 -- the types of e1 and e2 must be the same, and a and b are not in scope for e2.
2061 -- (See Note [The polymorphism rule of join points] in CoreSyn.) Returns False
2062 -- also if the type simply doesn't have enough arguments.
2063 --
2064 -- Note that we need to know how many arguments (type *and* value) the putative
2065 -- join point takes; for instance, if
2066 -- j :: forall a. a -> Int
2067 -- then j could be a binary join point returning an Int, but it could *not* be a
2068 -- unary join point returning a -> Int.
2069 --
2070 -- TODO: See Note [Excess polymorphism and join points]
2071 isValidJoinPointType :: JoinArity -> Type -> Bool
2072 isValidJoinPointType arity ty
2073 = valid_under emptyVarSet arity ty
2074 where
2075 valid_under tvs arity ty
2076 | arity == 0
2077 = isEmptyVarSet (tvs `intersectVarSet` tyCoVarsOfType ty)
2078 | Just (t, ty') <- splitForAllTy_maybe ty
2079 = valid_under (tvs `extendVarSet` t) (arity-1) ty'
2080 | Just (_, res_ty) <- splitFunTy_maybe ty
2081 = valid_under tvs (arity-1) res_ty
2082 | otherwise
2083 = False
2084
2085 {-
2086 ************************************************************************
2087 * *
2088 \subsection{Sequencing on types}
2089 * *
2090 ************************************************************************
2091 -}
2092
2093 seqType :: Type -> ()
2094 seqType (LitTy n) = n `seq` ()
2095 seqType (TyVarTy tv) = tv `seq` ()
2096 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
2097 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
2098 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
2099 seqType (ForAllTy (TvBndr tv _) ty) = seqType (tyVarKind tv) `seq` seqType ty
2100 seqType (CastTy ty co) = seqType ty `seq` seqCo co
2101 seqType (CoercionTy co) = seqCo co
2102
2103 seqTypes :: [Type] -> ()
2104 seqTypes [] = ()
2105 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
2106
2107 {-
2108 ************************************************************************
2109 * *
2110 Comparison for types
2111 (We don't use instances so that we know where it happens)
2112 * *
2113 ************************************************************************
2114
2115 Note [Equality on AppTys]
2116 ~~~~~~~~~~~~~~~~~~~~~~~~~
2117 In our cast-ignoring equality, we want to say that the following two
2118 are equal:
2119
2120 (Maybe |> co) (Int |> co') ~? Maybe Int
2121
2122 But the left is an AppTy while the right is a TyConApp. The solution is
2123 to use repSplitAppTy_maybe to break up the TyConApp into its pieces and
2124 then continue. Easy to do, but also easy to forget to do.
2125
2126 -}
2127
2128 eqType :: Type -> Type -> Bool
2129 -- ^ Type equality on source types. Does not look through @newtypes@ or
2130 -- 'PredType's, but it does look through type synonyms.
2131 -- This first checks that the kinds of the types are equal and then
2132 -- checks whether the types are equal, ignoring casts and coercions.
2133 -- (The kind check is a recursive call, but since all kinds have type
2134 -- @Type@, there is no need to check the types of kinds.)
2135 -- See also Note [Non-trivial definitional equality] in TyCoRep.
2136 eqType t1 t2 = isEqual $ nonDetCmpType t1 t2
2137 -- It's OK to use nonDetCmpType here and eqType is deterministic,
2138 -- nonDetCmpType does equality deterministically
2139
2140 -- | Compare types with respect to a (presumably) non-empty 'RnEnv2'.
2141 eqTypeX :: RnEnv2 -> Type -> Type -> Bool
2142 eqTypeX env t1 t2 = isEqual $ nonDetCmpTypeX env t1 t2
2143 -- It's OK to use nonDetCmpType here and eqTypeX is deterministic,
2144 -- nonDetCmpTypeX does equality deterministically
2145
2146 -- | Type equality on lists of types, looking through type synonyms
2147 -- but not newtypes.
2148 eqTypes :: [Type] -> [Type] -> Bool
2149 eqTypes tys1 tys2 = isEqual $ nonDetCmpTypes tys1 tys2
2150 -- It's OK to use nonDetCmpType here and eqTypes is deterministic,
2151 -- nonDetCmpTypes does equality deterministically
2152
2153 eqVarBndrs :: RnEnv2 -> [Var] -> [Var] -> Maybe RnEnv2
2154 -- Check that the var lists are the same length
2155 -- and have matching kinds; if so, extend the RnEnv2
2156 -- Returns Nothing if they don't match
2157 eqVarBndrs env [] []
2158 = Just env
2159 eqVarBndrs env (tv1:tvs1) (tv2:tvs2)
2160 | eqTypeX env (tyVarKind tv1) (tyVarKind tv2)
2161 = eqVarBndrs (rnBndr2 env tv1 tv2) tvs1 tvs2
2162 eqVarBndrs _ _ _= Nothing
2163
2164 -- Now here comes the real worker
2165
2166 {-
2167 Note [nonDetCmpType nondeterminism]
2168 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2169 nonDetCmpType is implemented in terms of nonDetCmpTypeX. nonDetCmpTypeX
2170 uses nonDetCmpTc which compares TyCons by their Unique value. Using Uniques for
2171 ordering leads to nondeterminism. We hit the same problem in the TyVarTy case,
2172 comparing type variables is nondeterministic, note the call to nonDetCmpVar in
2173 nonDetCmpTypeX.
2174 See Note [Unique Determinism] for more details.
2175 -}
2176
2177 nonDetCmpType :: Type -> Type -> Ordering
2178 nonDetCmpType t1 t2
2179 -- we know k1 and k2 have the same kind, because they both have kind *.
2180 = nonDetCmpTypeX rn_env t1 t2
2181 where
2182 rn_env = mkRnEnv2 (mkInScopeSet (tyCoVarsOfTypes [t1, t2]))
2183
2184 nonDetCmpTypes :: [Type] -> [Type] -> Ordering
2185 nonDetCmpTypes ts1 ts2 = nonDetCmpTypesX rn_env ts1 ts2
2186 where
2187 rn_env = mkRnEnv2 (mkInScopeSet (tyCoVarsOfTypes (ts1 ++ ts2)))
2188
2189 -- | An ordering relation between two 'Type's (known below as @t1 :: k1@
2190 -- and @t2 :: k2@)
2191 data TypeOrdering = TLT -- ^ @t1 < t2@
2192 | TEQ -- ^ @t1 ~ t2@ and there are no casts in either,
2193 -- therefore we can conclude @k1 ~ k2@
2194 | TEQX -- ^ @t1 ~ t2@ yet one of the types contains a cast so
2195 -- they may differ in kind.
2196 | TGT -- ^ @t1 > t2@
2197 deriving (Eq, Ord, Enum, Bounded)
2198
2199 nonDetCmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
2200 -- See Note [Non-trivial definitional equality] in TyCoRep
2201 nonDetCmpTypeX env orig_t1 orig_t2 =
2202 case go env orig_t1 orig_t2 of
2203 -- If there are casts then we also need to do a comparison of the kinds of
2204 -- the types being compared
2205 TEQX -> toOrdering $ go env k1 k2
2206 ty_ordering -> toOrdering ty_ordering
2207 where
2208 k1 = typeKind orig_t1
2209 k2 = typeKind orig_t2
2210
2211 toOrdering :: TypeOrdering -> Ordering
2212 toOrdering TLT = LT
2213 toOrdering TEQ = EQ
2214 toOrdering TEQX = EQ
2215 toOrdering TGT = GT
2216
2217 liftOrdering :: Ordering -> TypeOrdering
2218 liftOrdering LT = TLT
2219 liftOrdering EQ = TEQ
2220 liftOrdering GT = TGT
2221
2222 thenCmpTy :: TypeOrdering -> TypeOrdering -> TypeOrdering
2223 thenCmpTy TEQ rel = rel
2224 thenCmpTy TEQX rel = hasCast rel
2225 thenCmpTy rel _ = rel
2226
2227 hasCast :: TypeOrdering -> TypeOrdering
2228 hasCast TEQ = TEQX
2229 hasCast rel = rel
2230
2231 -- Returns both the resulting ordering relation between the two types
2232 -- and whether either contains a cast.
2233 go :: RnEnv2 -> Type -> Type -> TypeOrdering
2234 go env t1 t2
2235 | Just t1' <- coreView t1 = go env t1' t2
2236 | Just t2' <- coreView t2 = go env t1 t2'
2237
2238 go env (TyVarTy tv1) (TyVarTy tv2)
2239 = liftOrdering $ rnOccL env tv1 `nonDetCmpVar` rnOccR env tv2
2240 go env (ForAllTy (TvBndr tv1 _) t1) (ForAllTy (TvBndr tv2 _) t2)
2241 = go env (tyVarKind tv1) (tyVarKind tv2)
2242 `thenCmpTy` go (rnBndr2 env tv1 tv2) t1 t2
2243 -- See Note [Equality on AppTys]
2244 go env (AppTy s1 t1) ty2
2245 | Just (s2, t2) <- repSplitAppTy_maybe ty2
2246 = go env s1 s2 `thenCmpTy` go env t1 t2
2247 go env ty1 (AppTy s2 t2)
2248 | Just (s1, t1) <- repSplitAppTy_maybe ty1
2249 = go env s1 s2 `thenCmpTy` go env t1 t2
2250 go env (FunTy s1 t1) (FunTy s2 t2)
2251 = go env s1 s2 `thenCmpTy` go env t1 t2
2252 go env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
2253 = liftOrdering (tc1 `nonDetCmpTc` tc2) `thenCmpTy` gos env tys1 tys2
2254 go _ (LitTy l1) (LitTy l2) = liftOrdering (compare l1 l2)
2255 go env (CastTy t1 _) t2 = hasCast $ go env t1 t2
2256 go env t1 (CastTy t2 _) = hasCast $ go env t1 t2
2257
2258 go _ (CoercionTy {}) (CoercionTy {}) = TEQ
2259
2260 -- Deal with the rest: TyVarTy < CoercionTy < AppTy < LitTy < TyConApp < ForAllTy
2261 go _ ty1 ty2
2262 = liftOrdering $ (get_rank ty1) `compare` (get_rank ty2)
2263 where get_rank :: Type -> Int
2264 get_rank (CastTy {})
2265 = pprPanic "nonDetCmpTypeX.get_rank" (ppr [ty1,ty2])
2266 get_rank (TyVarTy {}) = 0
2267 get_rank (CoercionTy {}) = 1
2268 get_rank (AppTy {}) = 3
2269 get_rank (LitTy {}) = 4
2270 get_rank (TyConApp {}) = 5
2271 get_rank (FunTy {}) = 6
2272 get_rank (ForAllTy {}) = 7
2273
2274 gos :: RnEnv2 -> [Type] -> [Type] -> TypeOrdering
2275 gos _ [] [] = TEQ
2276 gos _ [] _ = TLT
2277 gos _ _ [] = TGT
2278 gos env (ty1:tys1) (ty2:tys2) = go env ty1 ty2 `thenCmpTy` gos env tys1 tys2
2279
2280 -------------
2281 nonDetCmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
2282 nonDetCmpTypesX _ [] [] = EQ
2283 nonDetCmpTypesX env (t1:tys1) (t2:tys2) = nonDetCmpTypeX env t1 t2
2284 `thenCmp` nonDetCmpTypesX env tys1 tys2
2285 nonDetCmpTypesX _ [] _ = LT
2286 nonDetCmpTypesX _ _ [] = GT
2287
2288 -------------
2289 -- | Compare two 'TyCon's. NB: This should /never/ see the "star synonyms",
2290 -- as recognized by Kind.isStarKindSynonymTyCon. See Note
2291 -- [Kind Constraint and kind *] in Kind.
2292 -- See Note [nonDetCmpType nondeterminism]
2293 nonDetCmpTc :: TyCon -> TyCon -> Ordering
2294 nonDetCmpTc tc1 tc2
2295 = ASSERT( not (isStarKindSynonymTyCon tc1) && not (isStarKindSynonymTyCon tc2) )
2296 u1 `nonDetCmpUnique` u2
2297 where
2298 u1 = tyConUnique tc1
2299 u2 = tyConUnique tc2
2300
2301 {-
2302 ************************************************************************
2303 * *
2304 The kind of a type
2305 * *
2306 ************************************************************************
2307 -}
2308
2309 typeKind :: Type -> Kind
2310 typeKind (TyConApp tc tys) = piResultTys (tyConKind tc) tys
2311 typeKind (AppTy fun arg) = piResultTy (typeKind fun) arg
2312 typeKind (LitTy l) = typeLiteralKind l
2313 typeKind (FunTy {}) = liftedTypeKind
2314 typeKind (ForAllTy _ ty) = typeKind ty
2315 typeKind (TyVarTy tyvar) = tyVarKind tyvar
2316 typeKind (CastTy _ty co) = pSnd $ coercionKind co
2317 typeKind (CoercionTy co) = coercionType co
2318
2319 typeLiteralKind :: TyLit -> Kind
2320 typeLiteralKind l =
2321 case l of
2322 NumTyLit _ -> typeNatKind
2323 StrTyLit _ -> typeSymbolKind
2324
2325 -- | Returns True if a type is levity polymorphic. Should be the same
2326 -- as (isKindLevPoly . typeKind) but much faster.
2327 -- Precondition: The type has kind (TYPE blah)
2328 isTypeLevPoly :: Type -> Bool
2329 isTypeLevPoly = go
2330 where
2331 go ty@(TyVarTy {}) = check_kind ty
2332 go ty@(AppTy {}) = check_kind ty
2333 go ty@(TyConApp tc _) | not (isTcLevPoly tc) = False
2334 | otherwise = check_kind ty
2335 go (ForAllTy _ ty) = go ty
2336 go (FunTy {}) = False
2337 go (LitTy {}) = False
2338 go ty@(CastTy {}) = check_kind ty
2339 go ty@(CoercionTy {}) = pprPanic "isTypeLevPoly co" (ppr ty)
2340
2341 check_kind = isKindLevPoly . typeKind
2342
2343 -- | Looking past all pi-types, is the end result potentially levity polymorphic?
2344 -- Example: True for (forall r (a :: TYPE r). String -> a)
2345 -- Example: False for (forall r1 r2 (a :: TYPE r1) (b :: TYPE r2). a -> b -> Type)
2346 resultIsLevPoly :: Type -> Bool
2347 resultIsLevPoly = isTypeLevPoly . snd . splitPiTys
2348
2349 {-
2350 %************************************************************************
2351 %* *
2352 Miscellaneous functions
2353 %* *
2354 %************************************************************************
2355
2356 -}
2357 -- | All type constructors occurring in the type; looking through type
2358 -- synonyms, but not newtypes.
2359 -- When it finds a Class, it returns the class TyCon.
2360 tyConsOfType :: Type -> UniqSet TyCon
2361 tyConsOfType ty
2362 = go ty
2363 where
2364 go :: Type -> UniqSet TyCon -- The UniqSet does duplicate elim
2365 go ty | Just ty' <- coreView ty = go ty'
2366 go (TyVarTy {}) = emptyUniqSet
2367 go (LitTy {}) = emptyUniqSet
2368 go (TyConApp tc tys) = go_tc tc `unionUniqSets` go_s tys
2369 go (AppTy a b) = go a `unionUniqSets` go b
2370 go (FunTy a b) = go a `unionUniqSets` go b `unionUniqSets` go_tc funTyCon
2371 go (ForAllTy (TvBndr tv _) ty) = go ty `unionUniqSets` go (tyVarKind tv)
2372 go (CastTy ty co) = go ty `unionUniqSets` go_co co
2373 go (CoercionTy co) = go_co co
2374
2375 go_co (Refl _ ty) = go ty
2376 go_co (TyConAppCo _ tc args) = go_tc tc `unionUniqSets` go_cos args
2377 go_co (AppCo co arg) = go_co co `unionUniqSets` go_co arg
2378 go_co (ForAllCo _ kind_co co) = go_co kind_co `unionUniqSets` go_co co
2379 go_co (FunCo _ co1 co2) = go_co co1 `unionUniqSets` go_co co2
2380 go_co (AxiomInstCo ax _ args) = go_ax ax `unionUniqSets` go_cos args
2381 go_co (UnivCo p _ t1 t2) = go_prov p `unionUniqSets` go t1 `unionUniqSets` go t2
2382 go_co (CoVarCo {}) = emptyUniqSet
2383 go_co (SymCo co) = go_co co
2384 go_co (TransCo co1 co2) = go_co co1 `unionUniqSets` go_co co2
2385 go_co (NthCo _ co) = go_co co
2386 go_co (LRCo _ co) = go_co co
2387 go_co (InstCo co arg) = go_co co `unionUniqSets` go_co arg
2388 go_co (CoherenceCo co1 co2) = go_co co1 `unionUniqSets` go_co co2
2389 go_co (KindCo co) = go_co co
2390 go_co (SubCo co) = go_co co
2391 go_co (AxiomRuleCo _ cs) = go_cos cs
2392
2393 go_prov UnsafeCoerceProv = emptyUniqSet
2394 go_prov (PhantomProv co) = go_co co
2395 go_prov (ProofIrrelProv co) = go_co co
2396 go_prov (PluginProv _) = emptyUniqSet
2397 go_prov (HoleProv _) = emptyUniqSet
2398 -- this last case can happen from the tyConsOfType used from
2399 -- checkTauTvUpdate
2400
2401 go_s tys = foldr (unionUniqSets . go) emptyUniqSet tys
2402 go_cos cos = foldr (unionUniqSets . go_co) emptyUniqSet cos
2403
2404 go_tc tc = unitUniqSet tc
2405 go_ax ax = go_tc $ coAxiomTyCon ax
2406
2407 -- | Find the result 'Kind' of a type synonym,
2408 -- after applying it to its 'arity' number of type variables
2409 -- Actually this function works fine on data types too,
2410 -- but they'd always return '*', so we never need to ask
2411 synTyConResKind :: TyCon -> Kind
2412 synTyConResKind tycon = piResultTys (tyConKind tycon) (mkTyVarTys (tyConTyVars tycon))
2413
2414 -- | Retrieve the free variables in this type, splitting them based
2415 -- on whether they are used visibly or invisibly. Invisible ones come
2416 -- first.
2417 splitVisVarsOfType :: Type -> Pair TyCoVarSet
2418 splitVisVarsOfType orig_ty = Pair invis_vars vis_vars
2419 where
2420 Pair invis_vars1 vis_vars = go orig_ty
2421 invis_vars = invis_vars1 `minusVarSet` vis_vars
2422
2423 go (TyVarTy tv) = Pair (tyCoVarsOfType $ tyVarKind tv) (unitVarSet tv)
2424 go (AppTy t1 t2) = go t1 `mappend` go t2
2425 go (TyConApp tc tys) = go_tc tc tys
2426 go (FunTy t1 t2) = go t1 `mappend` go t2
2427 go (ForAllTy (TvBndr tv _) ty)
2428 = ((`delVarSet` tv) <$> go ty) `mappend`
2429 (invisible (tyCoVarsOfType $ tyVarKind tv))
2430 go (LitTy {}) = mempty
2431 go (CastTy ty co) = go ty `mappend` invisible (tyCoVarsOfCo co)
2432 go (CoercionTy co) = invisible $ tyCoVarsOfCo co
2433
2434 invisible vs = Pair vs emptyVarSet
2435
2436 go_tc tc tys = let (invis, vis) = partitionInvisibles tc id tys in
2437 invisible (tyCoVarsOfTypes invis) `mappend` foldMap go vis
2438
2439 splitVisVarsOfTypes :: [Type] -> Pair TyCoVarSet
2440 splitVisVarsOfTypes = foldMap splitVisVarsOfType
2441
2442 modifyJoinResTy :: Int -- Number of binders to skip
2443 -> (Type -> Type) -- Function to apply to result type
2444 -> Type -- Type of join point
2445 -> Type -- New type
2446 -- INVARIANT: If any of the first n binders are foralls, those tyvars cannot
2447 -- appear in the original result type. See isValidJoinPointType.
2448 modifyJoinResTy orig_ar f orig_ty
2449 = go orig_ar orig_ty
2450 where
2451 go 0 ty = f ty
2452 go n ty | Just (arg_bndr, res_ty) <- splitPiTy_maybe ty
2453 = mkPiTy arg_bndr (go (n-1) res_ty)
2454 | otherwise
2455 = pprPanic "modifyJoinResTy" (ppr orig_ar <+> ppr orig_ty)
2456
2457 setJoinResTy :: Int -- Number of binders to skip
2458 -> Type -- New result type
2459 -> Type -- Type of join point
2460 -> Type -- New type
2461 -- INVARIANT: Same as for modifyJoinResTy
2462 setJoinResTy ar new_res_ty ty
2463 = modifyJoinResTy ar (const new_res_ty) ty