95c2e0a26b01fdcdbde1a8a383ef7b236367bf6d
[ghc.git] / compiler / types / TyCoRep.hs
1 {-
2 (c) The University of Glasgow 2006
3 (c) The GRASP/AQUA Project, Glasgow University, 1998
4 \section[TyCoRep]{Type and Coercion - friends' interface}
5
6 Note [The Type-related module hierarchy]
7 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
8 Class
9 CoAxiom
10 TyCon imports Class, CoAxiom
11 TyCoRep imports Class, CoAxiom, TyCon
12 TysPrim imports TyCoRep ( including mkTyConTy )
13 Kind imports TysPrim ( mainly for primitive kinds )
14 Type imports Kind
15 Coercion imports Type
16 -}
17
18 -- We expose the relevant stuff from this module via the Type module
19 {-# OPTIONS_HADDOCK hide #-}
20 {-# LANGUAGE CPP, DeriveDataTypeable, MultiWayIf #-}
21
22 module TyCoRep (
23 TyThing(..), tyThingCategory, pprTyThingCategory, pprShortTyThing,
24
25 -- * Types
26 Type(..),
27 TyLit(..),
28 KindOrType, Kind,
29 PredType, ThetaType, -- Synonyms
30 ArgFlag(..),
31
32 -- * Coercions
33 Coercion(..),
34 UnivCoProvenance(..),
35 CoercionHole(..), coHoleCoVar,
36 CoercionN, CoercionR, CoercionP, KindCoercion,
37
38 -- * Functions over types
39 mkTyConTy, mkTyVarTy, mkTyVarTys,
40 mkFunTy, mkFunTys, mkForAllTy, mkForAllTys,
41 mkPiTy, mkPiTys,
42 isTYPE, tcIsTYPE,
43 isLiftedTypeKind, isUnliftedTypeKind,
44 isCoercionType, isRuntimeRepTy, isRuntimeRepVar,
45 sameVis,
46
47 -- * Functions over binders
48 TyBinder(..), TyVarBinder,
49 binderVar, binderVars, binderKind, binderArgFlag,
50 delBinderVar,
51 isInvisibleArgFlag, isVisibleArgFlag,
52 isInvisibleBinder, isVisibleBinder,
53
54 -- * Functions over coercions
55 pickLR,
56
57 -- * Pretty-printing
58 pprType, pprParendType, pprPrecType,
59 pprTypeApp, pprTvBndr, pprTvBndrs,
60 pprSigmaType,
61 pprTheta, pprParendTheta, pprForAll, pprUserForAll,
62 pprTyVar, pprTyVars,
63 pprThetaArrowTy, pprClassPred,
64 pprKind, pprParendKind, pprTyLit,
65 TyPrec(..), maybeParen,
66 pprDataCons, ppSuggestExplicitKinds,
67
68 pprCo, pprParendCo,
69
70 debugPprType,
71
72 -- * Free variables
73 tyCoVarsOfType, tyCoVarsOfTypeDSet, tyCoVarsOfTypes, tyCoVarsOfTypesDSet,
74 tyCoFVsBndr, tyCoFVsOfType, tyCoVarsOfTypeList,
75 tyCoFVsOfTypes, tyCoVarsOfTypesList,
76 closeOverKindsDSet, closeOverKindsFV, closeOverKindsList,
77 coVarsOfType, coVarsOfTypes,
78 coVarsOfCo, coVarsOfCos,
79 tyCoVarsOfCo, tyCoVarsOfCos,
80 tyCoVarsOfCoDSet,
81 tyCoFVsOfCo, tyCoFVsOfCos,
82 tyCoVarsOfCoList, tyCoVarsOfProv,
83 closeOverKinds,
84 injectiveVarsOfBinder, injectiveVarsOfType,
85
86 noFreeVarsOfType, noFreeVarsOfCo,
87
88 -- * Substitutions
89 TCvSubst(..), TvSubstEnv, CvSubstEnv,
90 emptyTvSubstEnv, emptyCvSubstEnv, composeTCvSubstEnv, composeTCvSubst,
91 emptyTCvSubst, mkEmptyTCvSubst, isEmptyTCvSubst,
92 mkTCvSubst, mkTvSubst,
93 getTvSubstEnv,
94 getCvSubstEnv, getTCvInScope, getTCvSubstRangeFVs,
95 isInScope, notElemTCvSubst,
96 setTvSubstEnv, setCvSubstEnv, zapTCvSubst,
97 extendTCvInScope, extendTCvInScopeList, extendTCvInScopeSet,
98 extendTCvSubst,
99 extendCvSubst, extendCvSubstWithClone,
100 extendTvSubst, extendTvSubstBinderAndInScope, extendTvSubstWithClone,
101 extendTvSubstList, extendTvSubstAndInScope,
102 unionTCvSubst, zipTyEnv, zipCoEnv, mkTyCoInScopeSet,
103 zipTvSubst, zipCvSubst,
104 mkTvSubstPrs,
105
106 substTyWith, substTyWithCoVars, substTysWith, substTysWithCoVars,
107 substCoWith,
108 substTy, substTyAddInScope,
109 substTyUnchecked, substTysUnchecked, substThetaUnchecked,
110 substTyWithUnchecked,
111 substCoUnchecked, substCoWithUnchecked,
112 substTyWithInScope,
113 substTys, substTheta,
114 lookupTyVar, substTyVarBndr,
115 substCo, substCos, substCoVar, substCoVars, lookupCoVar,
116 substCoVarBndr, cloneTyVarBndr, cloneTyVarBndrs,
117 substTyVar, substTyVars,
118 substForAllCoBndr,
119 substTyVarBndrCallback, substForAllCoBndrCallback,
120 checkValidSubst, isValidTCvSubst,
121
122 -- * Tidying type related things up for printing
123 tidyType, tidyTypes,
124 tidyOpenType, tidyOpenTypes,
125 tidyOpenKind,
126 tidyTyCoVarBndr, tidyTyCoVarBndrs, tidyFreeTyCoVars,
127 tidyOpenTyCoVar, tidyOpenTyCoVars,
128 tidyTyVarOcc,
129 tidyTopType,
130 tidyKind,
131 tidyCo, tidyCos,
132 tidyTyVarBinder, tidyTyVarBinders,
133
134 -- * Sizes
135 typeSize, coercionSize, provSize
136 ) where
137
138 #include "HsVersions.h"
139
140 import GhcPrelude
141
142 import {-# SOURCE #-} DataCon( dataConFullSig
143 , dataConUserTyVarBinders
144 , DataCon )
145 import {-# SOURCE #-} Type( isPredTy, isCoercionTy, mkAppTy, mkCastTy
146 , tyCoVarsOfTypeWellScoped
147 , tyCoVarsOfTypesWellScoped
148 , toposortTyVars
149 , coreView, tcView )
150 -- Transitively pulls in a LOT of stuff, better to break the loop
151
152 import {-# SOURCE #-} Coercion
153 import {-# SOURCE #-} ConLike ( ConLike(..), conLikeName )
154 import {-# SOURCE #-} ToIface( toIfaceTypeX, toIfaceTyLit, toIfaceForAllBndr
155 , toIfaceTyCon, toIfaceTcArgs, toIfaceCoercionX )
156
157 -- friends:
158 import IfaceType
159 import Var
160 import VarEnv
161 import VarSet
162 import Name hiding ( varName )
163 import TyCon
164 import Class
165 import CoAxiom
166 import FV
167
168 -- others
169 import BasicTypes ( LeftOrRight(..), TyPrec(..), maybeParen, pickLR )
170 import PrelNames
171 import Outputable
172 import DynFlags
173 import FastString
174 import Pair
175 import UniqSupply
176 import Util
177 import UniqFM
178 import UniqSet
179
180 -- libraries
181 import qualified Data.Data as Data hiding ( TyCon )
182 import Data.List
183 import Data.IORef ( IORef ) -- for CoercionHole
184
185 {-
186 %************************************************************************
187 %* *
188 TyThing
189 %* *
190 %************************************************************************
191
192 Despite the fact that DataCon has to be imported via a hi-boot route,
193 this module seems the right place for TyThing, because it's needed for
194 funTyCon and all the types in TysPrim.
195
196 It is also SOURCE-imported into Name.hs
197
198
199 Note [ATyCon for classes]
200 ~~~~~~~~~~~~~~~~~~~~~~~~~
201 Both classes and type constructors are represented in the type environment
202 as ATyCon. You can tell the difference, and get to the class, with
203 isClassTyCon :: TyCon -> Bool
204 tyConClass_maybe :: TyCon -> Maybe Class
205 The Class and its associated TyCon have the same Name.
206 -}
207
208 -- | A global typecheckable-thing, essentially anything that has a name.
209 -- Not to be confused with a 'TcTyThing', which is also a typecheckable
210 -- thing but in the *local* context. See 'TcEnv' for how to retrieve
211 -- a 'TyThing' given a 'Name'.
212 data TyThing
213 = AnId Id
214 | AConLike ConLike
215 | ATyCon TyCon -- TyCons and classes; see Note [ATyCon for classes]
216 | ACoAxiom (CoAxiom Branched)
217
218 instance Outputable TyThing where
219 ppr = pprShortTyThing
220
221 instance NamedThing TyThing where -- Can't put this with the type
222 getName (AnId id) = getName id -- decl, because the DataCon instance
223 getName (ATyCon tc) = getName tc -- isn't visible there
224 getName (ACoAxiom cc) = getName cc
225 getName (AConLike cl) = conLikeName cl
226
227 pprShortTyThing :: TyThing -> SDoc
228 -- c.f. PprTyThing.pprTyThing, which prints all the details
229 pprShortTyThing thing
230 = pprTyThingCategory thing <+> quotes (ppr (getName thing))
231
232 pprTyThingCategory :: TyThing -> SDoc
233 pprTyThingCategory = text . capitalise . tyThingCategory
234
235 tyThingCategory :: TyThing -> String
236 tyThingCategory (ATyCon tc)
237 | isClassTyCon tc = "class"
238 | otherwise = "type constructor"
239 tyThingCategory (ACoAxiom _) = "coercion axiom"
240 tyThingCategory (AnId _) = "identifier"
241 tyThingCategory (AConLike (RealDataCon _)) = "data constructor"
242 tyThingCategory (AConLike (PatSynCon _)) = "pattern synonym"
243
244
245 {- **********************************************************************
246 * *
247 Type
248 * *
249 ********************************************************************** -}
250
251 -- | The key representation of types within the compiler
252
253 type KindOrType = Type -- See Note [Arguments to type constructors]
254
255 -- | The key type representing kinds in the compiler.
256 type Kind = Type
257
258 -- If you edit this type, you may need to update the GHC formalism
259 -- See Note [GHC Formalism] in coreSyn/CoreLint.hs
260 data Type
261 -- See Note [Non-trivial definitional equality]
262 = TyVarTy Var -- ^ Vanilla type or kind variable (*never* a coercion variable)
263
264 | AppTy
265 Type
266 Type -- ^ Type application to something other than a 'TyCon'. Parameters:
267 --
268 -- 1) Function: must /not/ be a 'TyConApp' or 'CastTy',
269 -- must be another 'AppTy', or 'TyVarTy'
270 -- See Note [Respecting definitional equality] (EQ1) about the
271 -- no 'CastTy' requirement
272 --
273 -- 2) Argument type
274
275 | TyConApp
276 TyCon
277 [KindOrType] -- ^ Application of a 'TyCon', including newtypes /and/ synonyms.
278 -- Invariant: saturated applications of 'FunTyCon' must
279 -- use 'FunTy' and saturated synonyms must use their own
280 -- constructors. However, /unsaturated/ 'FunTyCon's
281 -- do appear as 'TyConApp's.
282 -- Parameters:
283 --
284 -- 1) Type constructor being applied to.
285 --
286 -- 2) Type arguments. Might not have enough type arguments
287 -- here to saturate the constructor.
288 -- Even type synonyms are not necessarily saturated;
289 -- for example unsaturated type synonyms
290 -- can appear as the right hand side of a type synonym.
291
292 | ForAllTy
293 {-# UNPACK #-} !TyVarBinder
294 Type -- ^ A Π type.
295
296 | FunTy Type Type -- ^ t1 -> t2 Very common, so an important special case
297
298 | LitTy TyLit -- ^ Type literals are similar to type constructors.
299
300 | CastTy
301 Type
302 KindCoercion -- ^ A kind cast. The coercion is always nominal.
303 -- INVARIANT: The cast is never refl.
304 -- INVARIANT: The Type is not a CastTy (use TransCo instead)
305 -- See Note [Respecting definitional equality] (EQ2) and (EQ3)
306
307 | CoercionTy
308 Coercion -- ^ Injection of a Coercion into a type
309 -- This should only ever be used in the RHS of an AppTy,
310 -- in the list of a TyConApp, when applying a promoted
311 -- GADT data constructor
312
313 deriving Data.Data
314
315
316 -- NOTE: Other parts of the code assume that type literals do not contain
317 -- types or type variables.
318 data TyLit
319 = NumTyLit Integer
320 | StrTyLit FastString
321 deriving (Eq, Ord, Data.Data)
322
323 {- Note [Arguments to type constructors]
324 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
325 Because of kind polymorphism, in addition to type application we now
326 have kind instantiation. We reuse the same notations to do so.
327
328 For example:
329
330 Just (* -> *) Maybe
331 Right * Nat Zero
332
333 are represented by:
334
335 TyConApp (PromotedDataCon Just) [* -> *, Maybe]
336 TyConApp (PromotedDataCon Right) [*, Nat, (PromotedDataCon Zero)]
337
338 Important note: Nat is used as a *kind* and not as a type. This can be
339 confusing, since type-level Nat and kind-level Nat are identical. We
340 use the kind of (PromotedDataCon Right) to know if its arguments are
341 kinds or types.
342
343 This kind instantiation only happens in TyConApp currently.
344
345 Note [Non-trivial definitional equality]
346 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
347 Is Int |> <*> the same as Int? YES! In order to reduce headaches,
348 we decide that any reflexive casts in types are just ignored.
349 (Indeed they must be. See Note [Respecting definitional equality].)
350 More generally, the `eqType` function, which defines Core's type equality
351 relation, ignores casts and coercion arguments, as long as the
352 two types have the same kind. This allows us to be a little sloppier
353 in keeping track of coercions, which is a good thing. It also means
354 that eqType does not depend on eqCoercion, which is also a good thing.
355
356 Why is this sensible? That is, why is something different than α-equivalence
357 appropriate for the implementation of eqType?
358
359 Anything smaller than ~ and homogeneous is an appropriate definition for
360 equality. The type safety of FC depends only on ~. Let's say η : τ ~ σ. Any
361 expression of type τ can be transmuted to one of type σ at any point by
362 casting. The same is true of types of type τ. So in some sense, τ and σ are
363 interchangeable.
364
365 But let's be more precise. If we examine the typing rules of FC (say, those in
366 http://www.cis.upenn.edu/~eir/papers/2015/equalities/equalities-extended.pdf)
367 there are several places where the same metavariable is used in two different
368 premises to a rule. (For example, see Ty_App.) There is an implicit equality
369 check here. What definition of equality should we use? By convention, we use
370 α-equivalence. Take any rule with one (or more) of these implicit equality
371 checks. Then there is an admissible rule that uses ~ instead of the implicit
372 check, adding in casts as appropriate.
373
374 The only problem here is that ~ is heterogeneous. To make the kinds work out
375 in the admissible rule that uses ~, it is necessary to homogenize the
376 coercions. That is, if we have η : (τ : κ1) ~ (σ : κ2), then we don't use η;
377 we use η |> kind η, which is homogeneous.
378
379 The effect of this all is that eqType, the implementation of the implicit
380 equality check, can use any homogeneous relation that is smaller than ~, as
381 those rules must also be admissible.
382
383 A more drawn out argument around all of this is presented in Section 7.2 of
384 Richard E's thesis (http://cs.brynmawr.edu/~rae/papers/2016/thesis/eisenberg-thesis.pdf).
385
386 What would go wrong if we insisted on the casts matching? See the beginning of
387 Section 8 in the unpublished paper above. Theoretically, nothing at all goes
388 wrong. But in practical terms, getting the coercions right proved to be
389 nightmarish. And types would explode: during kind-checking, we often produce
390 reflexive kind coercions. When we try to cast by these, mkCastTy just discards
391 them. But if we used an eqType that distinguished between Int and Int |> <*>,
392 then we couldn't discard -- the output of kind-checking would be enormous,
393 and we would need enormous casts with lots of CoherenceCo's to straighten
394 them out.
395
396 Would anything go wrong if eqType respected type families? No, not at all. But
397 that makes eqType rather hard to implement.
398
399 Thus, the guideline for eqType is that it should be the largest
400 easy-to-implement relation that is still smaller than ~ and homogeneous. The
401 precise choice of relation is somewhat incidental, as long as the smart
402 constructors and destructors in Type respect whatever relation is chosen.
403
404 Another helpful principle with eqType is this:
405
406 (EQ) If (t1 `eqType` t2) then I can replace t1 by t2 anywhere.
407
408 This principle also tells us that eqType must relate only types with the
409 same kinds.
410
411 Note [Respecting definitional equality]
412 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
413 Note [Non-trivial definitional equality] introduces the property (EQ).
414 How is this upheld?
415
416 Any function that pattern matches on all the constructors will have to
417 consider the possibility of CastTy. Presumably, those functions will handle
418 CastTy appropriately and we'll be OK.
419
420 More dangerous are the splitXXX functions. Let's focus on splitTyConApp.
421 We don't want it to fail on (T a b c |> co). Happily, if we have
422 (T a b c |> co) `eqType` (T d e f)
423 then co must be reflexive. Why? eqType checks that the kinds are equal, as
424 well as checking that (a `eqType` d), (b `eqType` e), and (c `eqType` f).
425 By the kind check, we know that (T a b c |> co) and (T d e f) have the same
426 kind. So the only way that co could be non-reflexive is for (T a b c) to have
427 a different kind than (T d e f). But because T's kind is closed (all tycon kinds
428 are closed), the only way for this to happen is that one of the arguments has
429 to differ, leading to a contradiction. Thus, co is reflexive.
430
431 Accordingly, by eliminating reflexive casts, splitTyConApp need not worry
432 about outermost casts to uphold (EQ). Eliminating reflexive casts is done
433 in mkCastTy.
434
435 Unforunately, that's not the end of the story. Consider comparing
436 (T a b c) =? (T a b |> (co -> <Type>)) (c |> co)
437 These two types have the same kind (Type), but the left type is a TyConApp
438 while the right type is not. To handle this case, we say that the right-hand
439 type is ill-formed, requiring an AppTy never to have a casted TyConApp
440 on its left. It is easy enough to pull around the coercions to maintain
441 this invariant, as done in Type.mkAppTy. In the example above, trying to
442 form the right-hand type will instead yield (T a b (c |> co |> sym co) |> <Type>).
443 Both the casts there are reflexive and will be dropped. Huzzah.
444
445 This idea of pulling coercions to the right works for splitAppTy as well.
446
447 However, there is one hiccup: it's possible that a coercion doesn't relate two
448 Pi-types. For example, if we have @type family Fun a b where Fun a b = a -> b@,
449 then we might have (T :: Fun Type Type) and (T |> axFun) Int. That axFun can't
450 be pulled to the right. But we don't need to pull it: (T |> axFun) Int is not
451 `eqType` to any proper TyConApp -- thus, leaving it where it is doesn't violate
452 our (EQ) property.
453
454 Lastly, in order to detect reflexive casts reliably, we must make sure not
455 to have nested casts: we update (t |> co1 |> co2) to (t |> (co1 `TransCo` co2)).
456
457 In sum, in order to uphold (EQ), we need the following three invariants:
458
459 (EQ1) No decomposable CastTy to the left of an AppTy, where a decomposable
460 cast is one that relates either a FunTy to a FunTy or a
461 ForAllTy to a ForAllTy.
462 (EQ2) No reflexive casts in CastTy.
463 (EQ3) No nested CastTys.
464
465 These invariants are all documented above, in the declaration for Type.
466
467 -}
468
469 {- **********************************************************************
470 * *
471 TyBinder and ArgFlag
472 * *
473 ********************************************************************** -}
474
475 -- | A 'TyBinder' represents an argument to a function. TyBinders can be dependent
476 -- ('Named') or nondependent ('Anon'). They may also be visible or not.
477 -- See Note [TyBinders]
478 data TyBinder
479 = Named TyVarBinder -- A type-lambda binder
480 | Anon Type -- A term-lambda binder
481 -- Visibility is determined by the type (Constraint vs. *)
482 deriving Data.Data
483
484 -- | Remove the binder's variable from the set, if the binder has
485 -- a variable.
486 delBinderVar :: VarSet -> TyVarBinder -> VarSet
487 delBinderVar vars (TvBndr tv _) = vars `delVarSet` tv
488
489 -- | Does this binder bind an invisible argument?
490 isInvisibleBinder :: TyBinder -> Bool
491 isInvisibleBinder (Named (TvBndr _ vis)) = isInvisibleArgFlag vis
492 isInvisibleBinder (Anon ty) = isPredTy ty
493
494 -- | Does this binder bind a visible argument?
495 isVisibleBinder :: TyBinder -> Bool
496 isVisibleBinder = not . isInvisibleBinder
497
498
499 {- Note [TyBinders]
500 ~~~~~~~~~~~~~~~~~~~
501 A ForAllTy contains a TyVarBinder. But a type can be decomposed
502 to a telescope consisting of a [TyBinder]
503
504 A TyBinder represents the type of binders -- that is, the type of an
505 argument to a Pi-type. GHC Core currently supports two different
506 Pi-types:
507
508 * A non-dependent function type,
509 written with ->, e.g. ty1 -> ty2
510 represented as FunTy ty1 ty2. These are
511 lifted to Coercions with the corresponding FunCo.
512
513 * A dependent compile-time-only polytype,
514 written with forall, e.g. forall (a:*). ty
515 represented as ForAllTy (TvBndr a v) ty
516
517 Both Pi-types classify terms/types that take an argument. In other
518 words, if `x` is either a function or a polytype, `x arg` makes sense
519 (for an appropriate `arg`).
520
521
522 Note [TyVarBndrs, TyVarBinders, TyConBinders, and visibility]
523 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
524 * A ForAllTy (used for both types and kinds) contains a TyVarBinder.
525 Each TyVarBinder
526 TvBndr a tvis
527 is equipped with tvis::ArgFlag, which says whether or not arguments
528 for this binder should be visible (explicit) in source Haskell.
529
530 * A TyCon contains a list of TyConBinders. Each TyConBinder
531 TvBndr a cvis
532 is equipped with cvis::TyConBndrVis, which says whether or not type
533 and kind arguments for this TyCon should be visible (explicit) in
534 source Haskell.
535
536 This table summarises the visibility rules:
537 ---------------------------------------------------------------------------------------
538 | Occurrences look like this
539 | GHC displays type as in Haskell source code
540 |-----------------------------------------------------------------------
541 | TvBndr a tvis :: TyVarBinder, in the binder of ForAllTy for a term
542 | tvis :: ArgFlag
543 | tvis = Inferred: f :: forall {a}. type Arg not allowed: f
544 | tvis = Specified: f :: forall a. type Arg optional: f or f @Int
545 | tvis = Required: T :: forall k -> type Arg required: T *
546 | This last form is illegal in terms: See Note [No Required TyBinder in terms]
547 |
548 | TvBndr k cvis :: TyConBinder, in the TyConBinders of a TyCon
549 | cvis :: TyConBndrVis
550 | cvis = AnonTCB: T :: kind -> kind Required: T *
551 | cvis = NamedTCB Inferred: T :: forall {k}. kind Arg not allowed: T
552 | cvis = NamedTCB Specified: T :: forall k. kind Arg not allowed[1]: T
553 | cvis = NamedTCB Required: T :: forall k -> kind Required: T *
554 ---------------------------------------------------------------------------------------
555
556 [1] In types, in the Specified case, it would make sense to allow
557 optional kind applications, thus (T @*), but we have not
558 yet implemented that
559
560 ---- Examples of where the different visibilities come from -----
561
562 In term declarations:
563
564 * Inferred. Function defn, with no signature: f1 x = x
565 We infer f1 :: forall {a}. a -> a, with 'a' Inferred
566 It's Inferred because it doesn't appear in any
567 user-written signature for f1
568
569 * Specified. Function defn, with signature (implicit forall):
570 f2 :: a -> a; f2 x = x
571 So f2 gets the type f2 :: forall a. a->a, with 'a' Specified
572 even though 'a' is not bound in the source code by an explicit forall
573
574 * Specified. Function defn, with signature (explicit forall):
575 f3 :: forall a. a -> a; f3 x = x
576 So f3 gets the type f3 :: forall a. a->a, with 'a' Specified
577
578 * Inferred/Specified. Function signature with inferred kind polymorphism.
579 f4 :: a b -> Int
580 So 'f4' gets the type f4 :: forall {k} (a:k->*) (b:k). a b -> Int
581 Here 'k' is Inferred (it's not mentioned in the type),
582 but 'a' and 'b' are Specified.
583
584 * Specified. Function signature with explicit kind polymorphism
585 f5 :: a (b :: k) -> Int
586 This time 'k' is Specified, because it is mentioned explicitly,
587 so we get f5 :: forall (k:*) (a:k->*) (b:k). a b -> Int
588
589 * Similarly pattern synonyms:
590 Inferred - from inferred types (e.g. no pattern type signature)
591 - or from inferred kind polymorphism
592
593 In type declarations:
594
595 * Inferred (k)
596 data T1 a b = MkT1 (a b)
597 Here T1's kind is T1 :: forall {k:*}. (k->*) -> k -> *
598 The kind variable 'k' is Inferred, since it is not mentioned
599
600 Note that 'a' and 'b' correspond to /Anon/ TyBinders in T1's kind,
601 and Anon binders don't have a visibility flag. (Or you could think
602 of Anon having an implicit Required flag.)
603
604 * Specified (k)
605 data T2 (a::k->*) b = MkT (a b)
606 Here T's kind is T :: forall (k:*). (k->*) -> k -> *
607 The kind variable 'k' is Specified, since it is mentioned in
608 the signature.
609
610 * Required (k)
611 data T k (a::k->*) b = MkT (a b)
612 Here T's kind is T :: forall k:* -> (k->*) -> k -> *
613 The kind is Required, since it bound in a positional way in T's declaration
614 Every use of T must be explicitly applied to a kind
615
616 * Inferred (k1), Specified (k)
617 data T a b (c :: k) = MkT (a b) (Proxy c)
618 Here T's kind is T :: forall {k1:*} (k:*). (k1->*) -> k1 -> k -> *
619 So 'k' is Specified, because it appears explicitly,
620 but 'k1' is Inferred, because it does not
621
622 ---- Printing -----
623
624 We print forall types with enough syntax to tell you their visibility
625 flag. But this is not source Haskell, and these types may not all
626 be parsable.
627
628 Specified: a list of Specified binders is written between `forall` and `.`:
629 const :: forall a b. a -> b -> a
630
631 Inferred: with -fprint-explicit-foralls, Inferred binders are written
632 in braces:
633 f :: forall {k} (a:k). S k a -> Int
634 Otherwise, they are printed like Specified binders.
635
636 Required: binders are put between `forall` and `->`:
637 T :: forall k -> *
638
639 ---- Other points -----
640
641 * In classic Haskell, all named binders (that is, the type variables in
642 a polymorphic function type f :: forall a. a -> a) have been Inferred.
643
644 * Inferred variables correspond to "generalized" variables from the
645 Visible Type Applications paper (ESOP'16).
646
647 Note [No Required TyBinder in terms]
648 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
649 We don't allow Required foralls for term variables, including pattern
650 synonyms and data constructors. Why? Because then an application
651 would need a /compulsory/ type argument (possibly without an "@"?),
652 thus (f Int); and we don't have concrete syntax for that.
653
654 We could change this decision, but Required, Named TyBinders are rare
655 anyway. (Most are Anons.)
656 -}
657
658
659 {- **********************************************************************
660 * *
661 PredType
662 * *
663 ********************************************************************** -}
664
665
666 -- | A type of the form @p@ of kind @Constraint@ represents a value whose type is
667 -- the Haskell predicate @p@, where a predicate is what occurs before
668 -- the @=>@ in a Haskell type.
669 --
670 -- We use 'PredType' as documentation to mark those types that we guarantee to have
671 -- this kind.
672 --
673 -- It can be expanded into its representation, but:
674 --
675 -- * The type checker must treat it as opaque
676 --
677 -- * The rest of the compiler treats it as transparent
678 --
679 -- Consider these examples:
680 --
681 -- > f :: (Eq a) => a -> Int
682 -- > g :: (?x :: Int -> Int) => a -> Int
683 -- > h :: (r\l) => {r} => {l::Int | r}
684 --
685 -- Here the @Eq a@ and @?x :: Int -> Int@ and @r\l@ are all called \"predicates\"
686 type PredType = Type
687
688 -- | A collection of 'PredType's
689 type ThetaType = [PredType]
690
691 {-
692 (We don't support TREX records yet, but the setup is designed
693 to expand to allow them.)
694
695 A Haskell qualified type, such as that for f,g,h above, is
696 represented using
697 * a FunTy for the double arrow
698 * with a type of kind Constraint as the function argument
699
700 The predicate really does turn into a real extra argument to the
701 function. If the argument has type (p :: Constraint) then the predicate p is
702 represented by evidence of type p.
703
704
705 %************************************************************************
706 %* *
707 Simple constructors
708 %* *
709 %************************************************************************
710
711 These functions are here so that they can be used by TysPrim,
712 which in turn is imported by Type
713 -}
714
715 -- named with "Only" to prevent naive use of mkTyVarTy
716 mkTyVarTy :: TyVar -> Type
717 mkTyVarTy v = ASSERT2( isTyVar v, ppr v <+> dcolon <+> ppr (tyVarKind v) )
718 TyVarTy v
719
720 mkTyVarTys :: [TyVar] -> [Type]
721 mkTyVarTys = map mkTyVarTy -- a common use of mkTyVarTy
722
723 infixr 3 `mkFunTy` -- Associates to the right
724 -- | Make an arrow type
725 mkFunTy :: Type -> Type -> Type
726 mkFunTy arg res = FunTy arg res
727
728 -- | Make nested arrow types
729 mkFunTys :: [Type] -> Type -> Type
730 mkFunTys tys ty = foldr mkFunTy ty tys
731
732 mkForAllTy :: TyVar -> ArgFlag -> Type -> Type
733 mkForAllTy tv vis ty = ForAllTy (TvBndr tv vis) ty
734
735 -- | Wraps foralls over the type using the provided 'TyVar's from left to right
736 mkForAllTys :: [TyVarBinder] -> Type -> Type
737 mkForAllTys tyvars ty = foldr ForAllTy ty tyvars
738
739 mkPiTy :: TyBinder -> Type -> Type
740 mkPiTy (Anon ty1) ty2 = FunTy ty1 ty2
741 mkPiTy (Named tvb) ty = ForAllTy tvb ty
742
743 mkPiTys :: [TyBinder] -> Type -> Type
744 mkPiTys tbs ty = foldr mkPiTy ty tbs
745
746 -- | Does this type classify a core (unlifted) Coercion?
747 -- At either role nominal or representational
748 -- (t1 ~# t2) or (t1 ~R# t2)
749 isCoercionType :: Type -> Bool
750 isCoercionType (TyConApp tc tys)
751 | (tc `hasKey` eqPrimTyConKey) || (tc `hasKey` eqReprPrimTyConKey)
752 , tys `lengthIs` 4
753 = True
754 isCoercionType _ = False
755
756
757 -- | Create the plain type constructor type which has been applied to no type arguments at all.
758 mkTyConTy :: TyCon -> Type
759 mkTyConTy tycon = TyConApp tycon []
760
761 {-
762 Some basic functions, put here to break loops eg with the pretty printer
763 -}
764
765 -- | If a type is @'TYPE' r@ for some @r@, run the predicate argument on @r@.
766 -- Otherwise, return 'False'.
767 --
768 -- This function does not distinguish between 'Constraint' and 'Type'. For a
769 -- version which does distinguish between the two, see 'tcIsTYPE'.
770 isTYPE :: ( Type -- the single argument to TYPE; not a synonym
771 -> Bool ) -- what to return
772 -> Kind -> Bool
773 isTYPE f ki | Just ki' <- coreView ki = isTYPE f ki'
774 isTYPE f (TyConApp tc [arg])
775 | tc `hasKey` tYPETyConKey
776 = go arg
777 where
778 go ty | Just ty' <- coreView ty = go ty'
779 go ty = f ty
780 isTYPE _ _ = False
781
782 -- | If a type is @'TYPE' r@ for some @r@, run the predicate argument on @r@.
783 -- Otherwise, return 'False'.
784 --
785 -- This function distinguishes between 'Constraint' and 'Type' (and will return
786 -- 'False' for 'Constraint'). For a version which does not distinguish between
787 -- the two, see 'isTYPE'.
788 tcIsTYPE :: ( Type -- the single argument to TYPE; not a synonym
789 -> Bool ) -- what to return
790 -> Kind -> Bool
791 tcIsTYPE f ki | Just ki' <- tcView ki = tcIsTYPE f ki'
792 tcIsTYPE f (TyConApp tc [arg])
793 | tc `hasKey` tYPETyConKey
794 = go arg
795 where
796 go ty | Just ty' <- tcView ty = go ty'
797 go ty = f ty
798 tcIsTYPE _ _ = False
799
800 -- | This version considers Constraint to be the same as *. Returns True
801 -- if the argument is equivalent to Type/Constraint and False otherwise.
802 isLiftedTypeKind :: Kind -> Bool
803 isLiftedTypeKind = isTYPE is_lifted
804 where
805 is_lifted (TyConApp lifted_rep []) = lifted_rep `hasKey` liftedRepDataConKey
806 is_lifted _ = False
807
808 -- | Returns True if the kind classifies unlifted types and False otherwise.
809 -- Note that this returns False for levity-polymorphic kinds, which may
810 -- be specialized to a kind that classifies unlifted types.
811 isUnliftedTypeKind :: Kind -> Bool
812 isUnliftedTypeKind = isTYPE is_unlifted
813 where
814 is_unlifted (TyConApp rr _args) = not (rr `hasKey` liftedRepDataConKey)
815 is_unlifted _ = False
816
817 -- | Is this the type 'RuntimeRep'?
818 isRuntimeRepTy :: Type -> Bool
819 isRuntimeRepTy ty | Just ty' <- coreView ty = isRuntimeRepTy ty'
820 isRuntimeRepTy (TyConApp tc []) = tc `hasKey` runtimeRepTyConKey
821 isRuntimeRepTy _ = False
822
823 -- | Is a tyvar of type 'RuntimeRep'?
824 isRuntimeRepVar :: TyVar -> Bool
825 isRuntimeRepVar = isRuntimeRepTy . tyVarKind
826
827 {-
828 %************************************************************************
829 %* *
830 Coercions
831 %* *
832 %************************************************************************
833 -}
834
835 -- | A 'Coercion' is concrete evidence of the equality/convertibility
836 -- of two types.
837
838 -- If you edit this type, you may need to update the GHC formalism
839 -- See Note [GHC Formalism] in coreSyn/CoreLint.hs
840 data Coercion
841 -- Each constructor has a "role signature", indicating the way roles are
842 -- propagated through coercions.
843 -- - P, N, and R stand for coercions of the given role
844 -- - e stands for a coercion of a specific unknown role
845 -- (think "role polymorphism")
846 -- - "e" stands for an explicit role parameter indicating role e.
847 -- - _ stands for a parameter that is not a Role or Coercion.
848
849 -- These ones mirror the shape of types
850 = -- Refl :: "e" -> _ -> e
851 Refl Role Type -- See Note [Refl invariant]
852 -- Invariant: applications of (Refl T) to a bunch of identity coercions
853 -- always show up as Refl.
854 -- For example (Refl T) (Refl a) (Refl b) shows up as (Refl (T a b)).
855
856 -- Applications of (Refl T) to some coercions, at least one of
857 -- which is NOT the identity, show up as TyConAppCo.
858 -- (They may not be fully saturated however.)
859 -- ConAppCo coercions (like all coercions other than Refl)
860 -- are NEVER the identity.
861
862 -- Use (Refl Representational _), not (SubCo (Refl Nominal _))
863
864 -- These ones simply lift the correspondingly-named
865 -- Type constructors into Coercions
866
867 -- TyConAppCo :: "e" -> _ -> ?? -> e
868 -- See Note [TyConAppCo roles]
869 | TyConAppCo Role TyCon [Coercion] -- lift TyConApp
870 -- The TyCon is never a synonym;
871 -- we expand synonyms eagerly
872 -- But it can be a type function
873
874 | AppCo Coercion CoercionN -- lift AppTy
875 -- AppCo :: e -> N -> e
876
877 -- See Note [Forall coercions]
878 | ForAllCo TyVar KindCoercion Coercion
879 -- ForAllCo :: _ -> N -> e -> e
880
881 | FunCo Role Coercion Coercion -- lift FunTy
882 -- FunCo :: "e" -> e -> e -> e
883
884 -- These are special
885 | CoVarCo CoVar -- :: _ -> (N or R)
886 -- result role depends on the tycon of the variable's type
887
888 -- AxiomInstCo :: e -> _ -> [N] -> e
889 | AxiomInstCo (CoAxiom Branched) BranchIndex [Coercion]
890 -- See also [CoAxiom index]
891 -- The coercion arguments always *precisely* saturate
892 -- arity of (that branch of) the CoAxiom. If there are
893 -- any left over, we use AppCo.
894 -- See [Coercion axioms applied to coercions]
895
896 | AxiomRuleCo CoAxiomRule [Coercion]
897 -- AxiomRuleCo is very like AxiomInstCo, but for a CoAxiomRule
898 -- The number coercions should match exactly the expectations
899 -- of the CoAxiomRule (i.e., the rule is fully saturated).
900
901 | UnivCo UnivCoProvenance Role Type Type
902 -- :: _ -> "e" -> _ -> _ -> e
903
904 | SymCo Coercion -- :: e -> e
905 | TransCo Coercion Coercion -- :: e -> e -> e
906
907 | NthCo Int Coercion -- Zero-indexed; decomposes (T t0 ... tn)
908 -- :: _ -> e -> ?? (inverse of TyConAppCo, see Note [TyConAppCo roles])
909 -- Using NthCo on a ForAllCo gives an N coercion always
910 -- See Note [NthCo and newtypes]
911
912 | LRCo LeftOrRight CoercionN -- Decomposes (t_left t_right)
913 -- :: _ -> N -> N
914 | InstCo Coercion CoercionN
915 -- :: e -> N -> e
916 -- See Note [InstCo roles]
917
918 -- Coherence applies a coercion to the left-hand type of another coercion
919 -- See Note [Coherence]
920 | CoherenceCo Coercion KindCoercion
921 -- :: e -> N -> e
922
923 -- Extract a kind coercion from a (heterogeneous) type coercion
924 -- NB: all kind coercions are Nominal
925 | KindCo Coercion
926 -- :: e -> N
927
928 | SubCo CoercionN -- Turns a ~N into a ~R
929 -- :: N -> R
930
931 | HoleCo CoercionHole -- ^ See Note [Coercion holes]
932 -- Only present during typechecking
933 deriving Data.Data
934
935 type CoercionN = Coercion -- always nominal
936 type CoercionR = Coercion -- always representational
937 type CoercionP = Coercion -- always phantom
938 type KindCoercion = CoercionN -- always nominal
939
940 {-
941 Note [Refl invariant]
942 ~~~~~~~~~~~~~~~~~~~~~
943 Invariant 1:
944
945 Coercions have the following invariant
946 Refl is always lifted as far as possible.
947
948 You might think that a consequencs is:
949 Every identity coercions has Refl at the root
950
951 But that's not quite true because of coercion variables. Consider
952 g where g :: Int~Int
953 Left h where h :: Maybe Int ~ Maybe Int
954 etc. So the consequence is only true of coercions that
955 have no coercion variables.
956
957 Note [Coercion axioms applied to coercions]
958 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
959 The reason coercion axioms can be applied to coercions and not just
960 types is to allow for better optimization. There are some cases where
961 we need to be able to "push transitivity inside" an axiom in order to
962 expose further opportunities for optimization.
963
964 For example, suppose we have
965
966 C a : t[a] ~ F a
967 g : b ~ c
968
969 and we want to optimize
970
971 sym (C b) ; t[g] ; C c
972
973 which has the kind
974
975 F b ~ F c
976
977 (stopping through t[b] and t[c] along the way).
978
979 We'd like to optimize this to just F g -- but how? The key is
980 that we need to allow axioms to be instantiated by *coercions*,
981 not just by types. Then we can (in certain cases) push
982 transitivity inside the axiom instantiations, and then react
983 opposite-polarity instantiations of the same axiom. In this
984 case, e.g., we match t[g] against the LHS of (C c)'s kind, to
985 obtain the substitution a |-> g (note this operation is sort
986 of the dual of lifting!) and hence end up with
987
988 C g : t[b] ~ F c
989
990 which indeed has the same kind as t[g] ; C c.
991
992 Now we have
993
994 sym (C b) ; C g
995
996 which can be optimized to F g.
997
998 Note [CoAxiom index]
999 ~~~~~~~~~~~~~~~~~~~~
1000 A CoAxiom has 1 or more branches. Each branch has contains a list
1001 of the free type variables in that branch, the LHS type patterns,
1002 and the RHS type for that branch. When we apply an axiom to a list
1003 of coercions, we must choose which branch of the axiom we wish to
1004 use, as the different branches may have different numbers of free
1005 type variables. (The number of type patterns is always the same
1006 among branches, but that doesn't quite concern us here.)
1007
1008 The Int in the AxiomInstCo constructor is the 0-indexed number
1009 of the chosen branch.
1010
1011 Note [Forall coercions]
1012 ~~~~~~~~~~~~~~~~~~~~~~~
1013 Constructing coercions between forall-types can be a bit tricky,
1014 because the kinds of the bound tyvars can be different.
1015
1016 The typing rule is:
1017
1018
1019 kind_co : k1 ~ k2
1020 tv1:k1 |- co : t1 ~ t2
1021 -------------------------------------------------------------------
1022 ForAllCo tv1 kind_co co : all tv1:k1. t1 ~
1023 all tv1:k2. (t2[tv1 |-> tv1 |> sym kind_co])
1024
1025 First, the TyVar stored in a ForAllCo is really an optimisation: this field
1026 should be a Name, as its kind is redundant. Thinking of the field as a Name
1027 is helpful in understanding what a ForAllCo means.
1028
1029 The idea is that kind_co gives the two kinds of the tyvar. See how, in the
1030 conclusion, tv1 is assigned kind k1 on the left but kind k2 on the right.
1031
1032 Of course, a type variable can't have different kinds at the same time. So,
1033 we arbitrarily prefer the first kind when using tv1 in the inner coercion
1034 co, which shows that t1 equals t2.
1035
1036 The last wrinkle is that we need to fix the kinds in the conclusion. In
1037 t2, tv1 is assumed to have kind k1, but it has kind k2 in the conclusion of
1038 the rule. So we do a kind-fixing substitution, replacing (tv1:k1) with
1039 (tv1:k2) |> sym kind_co. This substitution is slightly bizarre, because it
1040 mentions the same name with different kinds, but it *is* well-kinded, noting
1041 that `(tv1:k2) |> sym kind_co` has kind k1.
1042
1043 This all really would work storing just a Name in the ForAllCo. But we can't
1044 add Names to, e.g., VarSets, and there generally is just an impedance mismatch
1045 in a bunch of places. So we use tv1. When we need tv2, we can use
1046 setTyVarKind.
1047
1048 Note [Coherence]
1049 ~~~~~~~~~~~~~~~~
1050 The Coherence typing rule is thus:
1051
1052 g1 : s ~ t s : k1 g2 : k1 ~ k2
1053 ------------------------------------
1054 CoherenceCo g1 g2 : (s |> g2) ~ t
1055
1056 While this looks (and is) unsymmetric, a combination of other coercion
1057 combinators can make the symmetric version.
1058
1059 For role information, see Note [Roles and kind coercions].
1060
1061 Note [Predicate coercions]
1062 ~~~~~~~~~~~~~~~~~~~~~~~~~~
1063 Suppose we have
1064 g :: a~b
1065 How can we coerce between types
1066 ([c]~a) => [a] -> c
1067 and
1068 ([c]~b) => [b] -> c
1069 where the equality predicate *itself* differs?
1070
1071 Answer: we simply treat (~) as an ordinary type constructor, so these
1072 types really look like
1073
1074 ((~) [c] a) -> [a] -> c
1075 ((~) [c] b) -> [b] -> c
1076
1077 So the coercion between the two is obviously
1078
1079 ((~) [c] g) -> [g] -> c
1080
1081 Another way to see this to say that we simply collapse predicates to
1082 their representation type (see Type.coreView and Type.predTypeRep).
1083
1084 This collapse is done by mkPredCo; there is no PredCo constructor
1085 in Coercion. This is important because we need Nth to work on
1086 predicates too:
1087 Nth 1 ((~) [c] g) = g
1088 See Simplify.simplCoercionF, which generates such selections.
1089
1090 Note [Roles]
1091 ~~~~~~~~~~~~
1092 Roles are a solution to the GeneralizedNewtypeDeriving problem, articulated
1093 in Trac #1496. The full story is in docs/core-spec/core-spec.pdf. Also, see
1094 http://ghc.haskell.org/trac/ghc/wiki/RolesImplementation
1095
1096 Here is one way to phrase the problem:
1097
1098 Given:
1099 newtype Age = MkAge Int
1100 type family F x
1101 type instance F Age = Bool
1102 type instance F Int = Char
1103
1104 This compiles down to:
1105 axAge :: Age ~ Int
1106 axF1 :: F Age ~ Bool
1107 axF2 :: F Int ~ Char
1108
1109 Then, we can make:
1110 (sym (axF1) ; F axAge ; axF2) :: Bool ~ Char
1111
1112 Yikes!
1113
1114 The solution is _roles_, as articulated in "Generative Type Abstraction and
1115 Type-level Computation" (POPL 2010), available at
1116 http://www.seas.upenn.edu/~sweirich/papers/popl163af-weirich.pdf
1117
1118 The specification for roles has evolved somewhat since that paper. For the
1119 current full details, see the documentation in docs/core-spec. Here are some
1120 highlights.
1121
1122 We label every equality with a notion of type equivalence, of which there are
1123 three options: Nominal, Representational, and Phantom. A ground type is
1124 nominally equivalent only with itself. A newtype (which is considered a ground
1125 type in Haskell) is representationally equivalent to its representation.
1126 Anything is "phantomly" equivalent to anything else. We use "N", "R", and "P"
1127 to denote the equivalences.
1128
1129 The axioms above would be:
1130 axAge :: Age ~R Int
1131 axF1 :: F Age ~N Bool
1132 axF2 :: F Age ~N Char
1133
1134 Then, because transitivity applies only to coercions proving the same notion
1135 of equivalence, the above construction is impossible.
1136
1137 However, there is still an escape hatch: we know that any two types that are
1138 nominally equivalent are representationally equivalent as well. This is what
1139 the form SubCo proves -- it "demotes" a nominal equivalence into a
1140 representational equivalence. So, it would seem the following is possible:
1141
1142 sub (sym axF1) ; F axAge ; sub axF2 :: Bool ~R Char -- WRONG
1143
1144 What saves us here is that the arguments to a type function F, lifted into a
1145 coercion, *must* prove nominal equivalence. So, (F axAge) is ill-formed, and
1146 we are safe.
1147
1148 Roles are attached to parameters to TyCons. When lifting a TyCon into a
1149 coercion (through TyConAppCo), we need to ensure that the arguments to the
1150 TyCon respect their roles. For example:
1151
1152 data T a b = MkT a (F b)
1153
1154 If we know that a1 ~R a2, then we know (T a1 b) ~R (T a2 b). But, if we know
1155 that b1 ~R b2, we know nothing about (T a b1) and (T a b2)! This is because
1156 the type function F branches on b's *name*, not representation. So, we say
1157 that 'a' has role Representational and 'b' has role Nominal. The third role,
1158 Phantom, is for parameters not used in the type's definition. Given the
1159 following definition
1160
1161 data Q a = MkQ Int
1162
1163 the Phantom role allows us to say that (Q Bool) ~R (Q Char), because we
1164 can construct the coercion Bool ~P Char (using UnivCo).
1165
1166 See the paper cited above for more examples and information.
1167
1168 Note [TyConAppCo roles]
1169 ~~~~~~~~~~~~~~~~~~~~~~~
1170 The TyConAppCo constructor has a role parameter, indicating the role at
1171 which the coercion proves equality. The choice of this parameter affects
1172 the required roles of the arguments of the TyConAppCo. To help explain
1173 it, assume the following definition:
1174
1175 type instance F Int = Bool -- Axiom axF : F Int ~N Bool
1176 newtype Age = MkAge Int -- Axiom axAge : Age ~R Int
1177 data Foo a = MkFoo a -- Role on Foo's parameter is Representational
1178
1179 TyConAppCo Nominal Foo axF : Foo (F Int) ~N Foo Bool
1180 For (TyConAppCo Nominal) all arguments must have role Nominal. Why?
1181 So that Foo Age ~N Foo Int does *not* hold.
1182
1183 TyConAppCo Representational Foo (SubCo axF) : Foo (F Int) ~R Foo Bool
1184 TyConAppCo Representational Foo axAge : Foo Age ~R Foo Int
1185 For (TyConAppCo Representational), all arguments must have the roles
1186 corresponding to the result of tyConRoles on the TyCon. This is the
1187 whole point of having roles on the TyCon to begin with. So, we can
1188 have Foo Age ~R Foo Int, if Foo's parameter has role R.
1189
1190 If a Representational TyConAppCo is over-saturated (which is otherwise fine),
1191 the spill-over arguments must all be at Nominal. This corresponds to the
1192 behavior for AppCo.
1193
1194 TyConAppCo Phantom Foo (UnivCo Phantom Int Bool) : Foo Int ~P Foo Bool
1195 All arguments must have role Phantom. This one isn't strictly
1196 necessary for soundness, but this choice removes ambiguity.
1197
1198 The rules here dictate the roles of the parameters to mkTyConAppCo
1199 (should be checked by Lint).
1200
1201 Note [NthCo and newtypes]
1202 ~~~~~~~~~~~~~~~~~~~~~~~~~
1203 Suppose we have
1204
1205 newtype N a = MkN Int
1206 type role N representational
1207
1208 This yields axiom
1209
1210 NTCo:N :: forall a. N a ~R Int
1211
1212 We can then build
1213
1214 co :: forall a b. N a ~R N b
1215 co = NTCo:N a ; sym (NTCo:N b)
1216
1217 for any `a` and `b`. Because of the role annotation on N, if we use
1218 NthCo, we'll get out a representational coercion. That is:
1219
1220 NthCo 0 co :: forall a b. a ~R b
1221
1222 Yikes! Clearly, this is terrible. The solution is simple: forbid
1223 NthCo to be used on newtypes if the internal coercion is representational.
1224
1225 This is not just some corner case discovered by a segfault somewhere;
1226 it was discovered in the proof of soundness of roles and described
1227 in the "Safe Coercions" paper (ICFP '14).
1228
1229 Note [InstCo roles]
1230 ~~~~~~~~~~~~~~~~~~~
1231 Here is (essentially) the typing rule for InstCo:
1232
1233 g :: (forall a. t1) ~r (forall a. t2)
1234 w :: s1 ~N s2
1235 ------------------------------- InstCo
1236 InstCo g w :: (t1 [a |-> s1]) ~r (t2 [a |-> s2])
1237
1238 Note that the Coercion w *must* be nominal. This is necessary
1239 because the variable a might be used in a "nominal position"
1240 (that is, a place where role inference would require a nominal
1241 role) in t1 or t2. If we allowed w to be representational, we
1242 could get bogus equalities.
1243
1244 A more nuanced treatment might be able to relax this condition
1245 somewhat, by checking if t1 and/or t2 use their bound variables
1246 in nominal ways. If not, having w be representational is OK.
1247
1248
1249 %************************************************************************
1250 %* *
1251 UnivCoProvenance
1252 %* *
1253 %************************************************************************
1254
1255 A UnivCo is a coercion whose proof does not directly express its role
1256 and kind (indeed for some UnivCos, like UnsafeCoerceProv, there /is/
1257 no proof).
1258
1259 The different kinds of UnivCo are described by UnivCoProvenance. Really
1260 each is entirely separate, but they all share the need to represent their
1261 role and kind, which is done in the UnivCo constructor.
1262
1263 -}
1264
1265 -- | For simplicity, we have just one UnivCo that represents a coercion from
1266 -- some type to some other type, with (in general) no restrictions on the
1267 -- type. The UnivCoProvenance specifies more exactly what the coercion really
1268 -- is and why a program should (or shouldn't!) trust the coercion.
1269 -- It is reasonable to consider each constructor of 'UnivCoProvenance'
1270 -- as a totally independent coercion form; their only commonality is
1271 -- that they don't tell you what types they coercion between. (That info
1272 -- is in the 'UnivCo' constructor of 'Coercion'.
1273 data UnivCoProvenance
1274 = UnsafeCoerceProv -- ^ From @unsafeCoerce#@. These are unsound.
1275
1276 | PhantomProv KindCoercion -- ^ See Note [Phantom coercions]. Only in Phantom
1277 -- roled coercions
1278
1279 | ProofIrrelProv KindCoercion -- ^ From the fact that any two coercions are
1280 -- considered equivalent. See Note [ProofIrrelProv].
1281 -- Can be used in Nominal or Representational coercions
1282
1283 | PluginProv String -- ^ From a plugin, which asserts that this coercion
1284 -- is sound. The string is for the use of the plugin.
1285
1286 deriving Data.Data
1287
1288 instance Outputable UnivCoProvenance where
1289 ppr UnsafeCoerceProv = text "(unsafeCoerce#)"
1290 ppr (PhantomProv _) = text "(phantom)"
1291 ppr (ProofIrrelProv _) = text "(proof irrel.)"
1292 ppr (PluginProv str) = parens (text "plugin" <+> brackets (text str))
1293
1294 -- | A coercion to be filled in by the type-checker. See Note [Coercion holes]
1295 data CoercionHole
1296 = CoercionHole { ch_co_var :: CoVar
1297 -- See Note [CoercionHoles and coercion free variables]
1298
1299 , ch_ref :: IORef (Maybe Coercion)
1300 }
1301
1302 coHoleCoVar :: CoercionHole -> CoVar
1303 coHoleCoVar = ch_co_var
1304
1305 instance Data.Data CoercionHole where
1306 -- don't traverse?
1307 toConstr _ = abstractConstr "CoercionHole"
1308 gunfold _ _ = error "gunfold"
1309 dataTypeOf _ = mkNoRepType "CoercionHole"
1310
1311 instance Outputable CoercionHole where
1312 ppr (CoercionHole { ch_co_var = cv }) = braces (ppr cv)
1313
1314
1315 {- Note [Phantom coercions]
1316 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
1317 Consider
1318 data T a = T1 | T2
1319 Then we have
1320 T s ~R T t
1321 for any old s,t. The witness for this is (TyConAppCo T Rep co),
1322 where (co :: s ~P t) is a phantom coercion built with PhantomProv.
1323 The role of the UnivCo is always Phantom. The Coercion stored is the
1324 (nominal) kind coercion between the types
1325 kind(s) ~N kind (t)
1326
1327 Note [Coercion holes]
1328 ~~~~~~~~~~~~~~~~~~~~~~~~
1329 During typechecking, constraint solving for type classes works by
1330 - Generate an evidence Id, d7 :: Num a
1331 - Wrap it in a Wanted constraint, [W] d7 :: Num a
1332 - Use the evidence Id where the evidence is needed
1333 - Solve the constraint later
1334 - When solved, add an enclosing let-binding let d7 = .... in ....
1335 which actually binds d7 to the (Num a) evidence
1336
1337 For equality constraints we use a different strategy. See Note [The
1338 equality types story] in TysPrim for background on equality constraints.
1339 - For /boxed/ equality constraints, (t1 ~N t2) and (t1 ~R t2), it's just
1340 like type classes above. (Indeed, boxed equality constraints *are* classes.)
1341 - But for /unboxed/ equality constraints (t1 ~R# t2) and (t1 ~N# t2)
1342 we use a different plan
1343
1344 For unboxed equalities:
1345 - Generate a CoercionHole, a mutable variable just like a unification
1346 variable
1347 - Wrap the CoercionHole in a Wanted constraint; see TcRnTypes.TcEvDest
1348 - Use the CoercionHole in a Coercion, via HoleCo
1349 - Solve the constraint later
1350 - When solved, fill in the CoercionHole by side effect, instead of
1351 doing the let-binding thing
1352
1353 The main reason for all this is that there may be no good place to let-bind
1354 the evidence for unboxed equalities:
1355
1356 - We emit constraints for kind coercions, to be used to cast a
1357 type's kind. These coercions then must be used in types. Because
1358 they might appear in a top-level type, there is no place to bind
1359 these (unlifted) coercions in the usual way.
1360
1361 - A coercion for (forall a. t1) ~ (forall a. t2) will look like
1362 forall a. (coercion for t1~t2)
1363 But the coercion for (t1~t2) may mention 'a', and we don't have
1364 let-bindings within coercions. We could add them, but coercion
1365 holes are easier.
1366
1367 - Moreover, nothing is lost from the lack of let-bindings. For
1368 dicionaries want to achieve sharing to avoid recomoputing the
1369 dictionary. But coercions are entirely erased, so there's little
1370 benefit to sharing. Indeed, even if we had a let-binding, we
1371 always inline types and coercions at every use site and drop the
1372 binding.
1373
1374 Other notes about HoleCo:
1375
1376 * INVARIANT: CoercionHole and HoleCo are used only during type checking,
1377 and should never appear in Core. Just like unification variables; a Type
1378 can contain a TcTyVar, but only during type checking. If, one day, we
1379 use type-level information to separate out forms that can appear during
1380 type-checking vs forms that can appear in core proper, holes in Core will
1381 be ruled out.
1382
1383 * See Note [CoercionHoles and coercion free variables]
1384
1385 * Coercion holes can be compared for equality like other coercions:
1386 by looking at the types coerced.
1387
1388
1389 Note [CoercionHoles and coercion free variables]
1390 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1391 Why does a CoercionHole contain a CoVar, as well as reference to
1392 fill in? Because we want to treat that CoVar as a free variable of
1393 the coercion. See Trac #14584, and Note [What prevents a
1394 constraint from floating] in TcSimplify, item (4):
1395
1396 forall k. [W] co1 :: t1 ~# t2 |> co2
1397 [W] co2 :: k ~# *
1398
1399 Here co2 is a CoercionHole. But we /must/ know that it is free in
1400 co1, because that's all that stops it floating outside the
1401 implication.
1402
1403
1404 Note [ProofIrrelProv]
1405 ~~~~~~~~~~~~~~~~~~~~~
1406 A ProofIrrelProv is a coercion between coercions. For example:
1407
1408 data G a where
1409 MkG :: G Bool
1410
1411 In core, we get
1412
1413 G :: * -> *
1414 MkG :: forall (a :: *). (a ~ Bool) -> G a
1415
1416 Now, consider 'MkG -- that is, MkG used in a type -- and suppose we want
1417 a proof that ('MkG co1 a1) ~ ('MkG co2 a2). This will have to be
1418
1419 TyConAppCo Nominal MkG [co3, co4]
1420 where
1421 co3 :: co1 ~ co2
1422 co4 :: a1 ~ a2
1423
1424 Note that
1425 co1 :: a1 ~ Bool
1426 co2 :: a2 ~ Bool
1427
1428 Here,
1429 co3 = UnivCo (ProofIrrelProv co5) Nominal (CoercionTy co1) (CoercionTy co2)
1430 where
1431 co5 :: (a1 ~ Bool) ~ (a2 ~ Bool)
1432 co5 = TyConAppCo Nominal (~) [<*>, <*>, co4, <Bool>]
1433
1434
1435 %************************************************************************
1436 %* *
1437 Free variables of types and coercions
1438 %* *
1439 %************************************************************************
1440 -}
1441
1442 {- Note [Free variables of types]
1443 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1444 The family of functions tyCoVarsOfType, tyCoVarsOfTypes etc, returns
1445 a VarSet that is closed over the types of its variables. More precisely,
1446 if S = tyCoVarsOfType( t )
1447 and (a:k) is in S
1448 then tyCoVarsOftype( k ) is a subset of S
1449
1450 Example: The tyCoVars of this ((a:* -> k) Int) is {a, k}.
1451
1452 We could /not/ close over the kinds of the variable occurrences, and
1453 instead do so at call sites, but it seems that we always want to do
1454 so, so it's easiest to do it here.
1455 -}
1456
1457
1458 -- | Returns free variables of a type, including kind variables as
1459 -- a non-deterministic set. For type synonyms it does /not/ expand the
1460 -- synonym.
1461 tyCoVarsOfType :: Type -> TyCoVarSet
1462 -- See Note [Free variables of types]
1463 tyCoVarsOfType ty = fvVarSet $ tyCoFVsOfType ty
1464
1465 -- | `tyCoFVsOfType` that returns free variables of a type in a deterministic
1466 -- set. For explanation of why using `VarSet` is not deterministic see
1467 -- Note [Deterministic FV] in FV.
1468 tyCoVarsOfTypeDSet :: Type -> DTyCoVarSet
1469 -- See Note [Free variables of types]
1470 tyCoVarsOfTypeDSet ty = fvDVarSet $ tyCoFVsOfType ty
1471
1472 -- | `tyCoFVsOfType` that returns free variables of a type in deterministic
1473 -- order. For explanation of why using `VarSet` is not deterministic see
1474 -- Note [Deterministic FV] in FV.
1475 tyCoVarsOfTypeList :: Type -> [TyCoVar]
1476 -- See Note [Free variables of types]
1477 tyCoVarsOfTypeList ty = fvVarList $ tyCoFVsOfType ty
1478
1479 -- | The worker for `tyCoFVsOfType` and `tyCoFVsOfTypeList`.
1480 -- The previous implementation used `unionVarSet` which is O(n+m) and can
1481 -- make the function quadratic.
1482 -- It's exported, so that it can be composed with
1483 -- other functions that compute free variables.
1484 -- See Note [FV naming conventions] in FV.
1485 --
1486 -- Eta-expanded because that makes it run faster (apparently)
1487 -- See Note [FV eta expansion] in FV for explanation.
1488 tyCoFVsOfType :: Type -> FV
1489 -- See Note [Free variables of types]
1490 tyCoFVsOfType (TyVarTy v) a b c = (unitFV v `unionFV` tyCoFVsOfType (tyVarKind v)) a b c
1491 tyCoFVsOfType (TyConApp _ tys) a b c = tyCoFVsOfTypes tys a b c
1492 tyCoFVsOfType (LitTy {}) a b c = emptyFV a b c
1493 tyCoFVsOfType (AppTy fun arg) a b c = (tyCoFVsOfType fun `unionFV` tyCoFVsOfType arg) a b c
1494 tyCoFVsOfType (FunTy arg res) a b c = (tyCoFVsOfType arg `unionFV` tyCoFVsOfType res) a b c
1495 tyCoFVsOfType (ForAllTy bndr ty) a b c = tyCoFVsBndr bndr (tyCoFVsOfType ty) a b c
1496 tyCoFVsOfType (CastTy ty co) a b c = (tyCoFVsOfType ty `unionFV` tyCoFVsOfCo co) a b c
1497 tyCoFVsOfType (CoercionTy co) a b c = tyCoFVsOfCo co a b c
1498
1499 tyCoFVsBndr :: TyVarBinder -> FV -> FV
1500 -- Free vars of (forall b. <thing with fvs>)
1501 tyCoFVsBndr (TvBndr tv _) fvs = (delFV tv fvs)
1502 `unionFV` tyCoFVsOfType (tyVarKind tv)
1503
1504 -- | Returns free variables of types, including kind variables as
1505 -- a non-deterministic set. For type synonyms it does /not/ expand the
1506 -- synonym.
1507 tyCoVarsOfTypes :: [Type] -> TyCoVarSet
1508 -- See Note [Free variables of types]
1509 tyCoVarsOfTypes tys = fvVarSet $ tyCoFVsOfTypes tys
1510
1511 -- | Returns free variables of types, including kind variables as
1512 -- a non-deterministic set. For type synonyms it does /not/ expand the
1513 -- synonym.
1514 tyCoVarsOfTypesSet :: TyVarEnv Type -> TyCoVarSet
1515 -- See Note [Free variables of types]
1516 tyCoVarsOfTypesSet tys = fvVarSet $ tyCoFVsOfTypes $ nonDetEltsUFM tys
1517 -- It's OK to use nonDetEltsUFM here because we immediately forget the
1518 -- ordering by returning a set
1519
1520 -- | Returns free variables of types, including kind variables as
1521 -- a deterministic set. For type synonyms it does /not/ expand the
1522 -- synonym.
1523 tyCoVarsOfTypesDSet :: [Type] -> DTyCoVarSet
1524 -- See Note [Free variables of types]
1525 tyCoVarsOfTypesDSet tys = fvDVarSet $ tyCoFVsOfTypes tys
1526
1527 -- | Returns free variables of types, including kind variables as
1528 -- a deterministically ordered list. For type synonyms it does /not/ expand the
1529 -- synonym.
1530 tyCoVarsOfTypesList :: [Type] -> [TyCoVar]
1531 -- See Note [Free variables of types]
1532 tyCoVarsOfTypesList tys = fvVarList $ tyCoFVsOfTypes tys
1533
1534 tyCoFVsOfTypes :: [Type] -> FV
1535 -- See Note [Free variables of types]
1536 tyCoFVsOfTypes (ty:tys) fv_cand in_scope acc = (tyCoFVsOfType ty `unionFV` tyCoFVsOfTypes tys) fv_cand in_scope acc
1537 tyCoFVsOfTypes [] fv_cand in_scope acc = emptyFV fv_cand in_scope acc
1538
1539 tyCoVarsOfCo :: Coercion -> TyCoVarSet
1540 -- See Note [Free variables of types]
1541 tyCoVarsOfCo co = fvVarSet $ tyCoFVsOfCo co
1542
1543 -- | Get a deterministic set of the vars free in a coercion
1544 tyCoVarsOfCoDSet :: Coercion -> DTyCoVarSet
1545 -- See Note [Free variables of types]
1546 tyCoVarsOfCoDSet co = fvDVarSet $ tyCoFVsOfCo co
1547
1548 tyCoVarsOfCoList :: Coercion -> [TyCoVar]
1549 -- See Note [Free variables of types]
1550 tyCoVarsOfCoList co = fvVarList $ tyCoFVsOfCo co
1551
1552 tyCoFVsOfCo :: Coercion -> FV
1553 -- Extracts type and coercion variables from a coercion
1554 -- See Note [Free variables of types]
1555 tyCoFVsOfCo (Refl _ ty) fv_cand in_scope acc = tyCoFVsOfType ty fv_cand in_scope acc
1556 tyCoFVsOfCo (TyConAppCo _ _ cos) fv_cand in_scope acc = tyCoFVsOfCos cos fv_cand in_scope acc
1557 tyCoFVsOfCo (AppCo co arg) fv_cand in_scope acc
1558 = (tyCoFVsOfCo co `unionFV` tyCoFVsOfCo arg) fv_cand in_scope acc
1559 tyCoFVsOfCo (ForAllCo tv kind_co co) fv_cand in_scope acc
1560 = (delFV tv (tyCoFVsOfCo co) `unionFV` tyCoFVsOfCo kind_co) fv_cand in_scope acc
1561 tyCoFVsOfCo (FunCo _ co1 co2) fv_cand in_scope acc
1562 = (tyCoFVsOfCo co1 `unionFV` tyCoFVsOfCo co2) fv_cand in_scope acc
1563 tyCoFVsOfCo (CoVarCo v) fv_cand in_scope acc
1564 = tyCoFVsOfCoVar v fv_cand in_scope acc
1565 tyCoFVsOfCo (HoleCo h) fv_cand in_scope acc
1566 = tyCoFVsOfCoVar (coHoleCoVar h) fv_cand in_scope acc
1567 -- See Note [CoercionHoles and coercion free variables]
1568 tyCoFVsOfCo (AxiomInstCo _ _ cos) fv_cand in_scope acc = tyCoFVsOfCos cos fv_cand in_scope acc
1569 tyCoFVsOfCo (UnivCo p _ t1 t2) fv_cand in_scope acc
1570 = (tyCoFVsOfProv p `unionFV` tyCoFVsOfType t1
1571 `unionFV` tyCoFVsOfType t2) fv_cand in_scope acc
1572 tyCoFVsOfCo (SymCo co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1573 tyCoFVsOfCo (TransCo co1 co2) fv_cand in_scope acc = (tyCoFVsOfCo co1 `unionFV` tyCoFVsOfCo co2) fv_cand in_scope acc
1574 tyCoFVsOfCo (NthCo _ co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1575 tyCoFVsOfCo (LRCo _ co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1576 tyCoFVsOfCo (InstCo co arg) fv_cand in_scope acc = (tyCoFVsOfCo co `unionFV` tyCoFVsOfCo arg) fv_cand in_scope acc
1577 tyCoFVsOfCo (CoherenceCo c1 c2) fv_cand in_scope acc = (tyCoFVsOfCo c1 `unionFV` tyCoFVsOfCo c2) fv_cand in_scope acc
1578 tyCoFVsOfCo (KindCo co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1579 tyCoFVsOfCo (SubCo co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1580 tyCoFVsOfCo (AxiomRuleCo _ cs) fv_cand in_scope acc = tyCoFVsOfCos cs fv_cand in_scope acc
1581
1582 tyCoFVsOfCoVar :: CoVar -> FV
1583 tyCoFVsOfCoVar v fv_cand in_scope acc
1584 = (unitFV v `unionFV` tyCoFVsOfType (varType v)) fv_cand in_scope acc
1585
1586 tyCoVarsOfProv :: UnivCoProvenance -> TyCoVarSet
1587 tyCoVarsOfProv prov = fvVarSet $ tyCoFVsOfProv prov
1588
1589 tyCoFVsOfProv :: UnivCoProvenance -> FV
1590 tyCoFVsOfProv UnsafeCoerceProv fv_cand in_scope acc = emptyFV fv_cand in_scope acc
1591 tyCoFVsOfProv (PhantomProv co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1592 tyCoFVsOfProv (ProofIrrelProv co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1593 tyCoFVsOfProv (PluginProv _) fv_cand in_scope acc = emptyFV fv_cand in_scope acc
1594
1595 tyCoVarsOfCos :: [Coercion] -> TyCoVarSet
1596 tyCoVarsOfCos cos = fvVarSet $ tyCoFVsOfCos cos
1597
1598 tyCoVarsOfCosSet :: CoVarEnv Coercion -> TyCoVarSet
1599 tyCoVarsOfCosSet cos = fvVarSet $ tyCoFVsOfCos $ nonDetEltsUFM cos
1600 -- It's OK to use nonDetEltsUFM here because we immediately forget the
1601 -- ordering by returning a set
1602
1603 tyCoFVsOfCos :: [Coercion] -> FV
1604 tyCoFVsOfCos [] fv_cand in_scope acc = emptyFV fv_cand in_scope acc
1605 tyCoFVsOfCos (co:cos) fv_cand in_scope acc = (tyCoFVsOfCo co `unionFV` tyCoFVsOfCos cos) fv_cand in_scope acc
1606
1607 coVarsOfType :: Type -> CoVarSet
1608 coVarsOfType (TyVarTy v) = coVarsOfType (tyVarKind v)
1609 coVarsOfType (TyConApp _ tys) = coVarsOfTypes tys
1610 coVarsOfType (LitTy {}) = emptyVarSet
1611 coVarsOfType (AppTy fun arg) = coVarsOfType fun `unionVarSet` coVarsOfType arg
1612 coVarsOfType (FunTy arg res) = coVarsOfType arg `unionVarSet` coVarsOfType res
1613 coVarsOfType (ForAllTy (TvBndr tv _) ty)
1614 = (coVarsOfType ty `delVarSet` tv)
1615 `unionVarSet` coVarsOfType (tyVarKind tv)
1616 coVarsOfType (CastTy ty co) = coVarsOfType ty `unionVarSet` coVarsOfCo co
1617 coVarsOfType (CoercionTy co) = coVarsOfCo co
1618
1619 coVarsOfTypes :: [Type] -> TyCoVarSet
1620 coVarsOfTypes tys = mapUnionVarSet coVarsOfType tys
1621
1622 coVarsOfCo :: Coercion -> CoVarSet
1623 -- Extract *coercion* variables only. Tiresome to repeat the code, but easy.
1624 coVarsOfCo (Refl _ ty) = coVarsOfType ty
1625 coVarsOfCo (TyConAppCo _ _ args) = coVarsOfCos args
1626 coVarsOfCo (AppCo co arg) = coVarsOfCo co `unionVarSet` coVarsOfCo arg
1627 coVarsOfCo (ForAllCo tv kind_co co)
1628 = coVarsOfCo co `delVarSet` tv `unionVarSet` coVarsOfCo kind_co
1629 coVarsOfCo (FunCo _ co1 co2) = coVarsOfCo co1 `unionVarSet` coVarsOfCo co2
1630 coVarsOfCo (CoVarCo v) = coVarsOfCoVar v
1631 coVarsOfCo (HoleCo h) = coVarsOfCoVar (coHoleCoVar h)
1632 -- See Note [CoercionHoles and coercion free variables]
1633 coVarsOfCo (AxiomInstCo _ _ as) = coVarsOfCos as
1634 coVarsOfCo (UnivCo p _ t1 t2) = coVarsOfProv p `unionVarSet` coVarsOfTypes [t1, t2]
1635 coVarsOfCo (SymCo co) = coVarsOfCo co
1636 coVarsOfCo (TransCo co1 co2) = coVarsOfCo co1 `unionVarSet` coVarsOfCo co2
1637 coVarsOfCo (NthCo _ co) = coVarsOfCo co
1638 coVarsOfCo (LRCo _ co) = coVarsOfCo co
1639 coVarsOfCo (InstCo co arg) = coVarsOfCo co `unionVarSet` coVarsOfCo arg
1640 coVarsOfCo (CoherenceCo c1 c2) = coVarsOfCos [c1, c2]
1641 coVarsOfCo (KindCo co) = coVarsOfCo co
1642 coVarsOfCo (SubCo co) = coVarsOfCo co
1643 coVarsOfCo (AxiomRuleCo _ cs) = coVarsOfCos cs
1644
1645 coVarsOfCoVar :: CoVar -> CoVarSet
1646 coVarsOfCoVar v = unitVarSet v `unionVarSet` coVarsOfType (varType v)
1647
1648 coVarsOfProv :: UnivCoProvenance -> CoVarSet
1649 coVarsOfProv UnsafeCoerceProv = emptyVarSet
1650 coVarsOfProv (PhantomProv co) = coVarsOfCo co
1651 coVarsOfProv (ProofIrrelProv co) = coVarsOfCo co
1652 coVarsOfProv (PluginProv _) = emptyVarSet
1653
1654 coVarsOfCos :: [Coercion] -> CoVarSet
1655 coVarsOfCos cos = mapUnionVarSet coVarsOfCo cos
1656
1657 -- | Add the kind variables free in the kinds of the tyvars in the given set.
1658 -- Returns a non-deterministic set.
1659 closeOverKinds :: TyVarSet -> TyVarSet
1660 closeOverKinds = fvVarSet . closeOverKindsFV . nonDetEltsUniqSet
1661 -- It's OK to use nonDetEltsUniqSet here because we immediately forget
1662 -- about the ordering by returning a set.
1663
1664 -- | Given a list of tyvars returns a deterministic FV computation that
1665 -- returns the given tyvars with the kind variables free in the kinds of the
1666 -- given tyvars.
1667 closeOverKindsFV :: [TyVar] -> FV
1668 closeOverKindsFV tvs =
1669 mapUnionFV (tyCoFVsOfType . tyVarKind) tvs `unionFV` mkFVs tvs
1670
1671 -- | Add the kind variables free in the kinds of the tyvars in the given set.
1672 -- Returns a deterministically ordered list.
1673 closeOverKindsList :: [TyVar] -> [TyVar]
1674 closeOverKindsList tvs = fvVarList $ closeOverKindsFV tvs
1675
1676 -- | Add the kind variables free in the kinds of the tyvars in the given set.
1677 -- Returns a deterministic set.
1678 closeOverKindsDSet :: DTyVarSet -> DTyVarSet
1679 closeOverKindsDSet = fvDVarSet . closeOverKindsFV . dVarSetElems
1680
1681 -- | Returns the free variables of a 'TyConBinder' that are in injective
1682 -- positions. (See @Note [Kind annotations on TyConApps]@ in "TcSplice" for an
1683 -- explanation of what an injective position is.)
1684 injectiveVarsOfBinder :: TyConBinder -> FV
1685 injectiveVarsOfBinder (TvBndr tv vis) =
1686 case vis of
1687 AnonTCB -> injectiveVarsOfType (tyVarKind tv)
1688 NamedTCB Required -> unitFV tv `unionFV`
1689 injectiveVarsOfType (tyVarKind tv)
1690 NamedTCB _ -> emptyFV
1691
1692 -- | Returns the free variables of a 'Type' that are in injective positions.
1693 -- (See @Note [Kind annotations on TyConApps]@ in "TcSplice" for an explanation
1694 -- of what an injective position is.)
1695 injectiveVarsOfType :: Type -> FV
1696 injectiveVarsOfType = go
1697 where
1698 go ty | Just ty' <- coreView ty
1699 = go ty'
1700 go (TyVarTy v) = unitFV v `unionFV` go (tyVarKind v)
1701 go (AppTy f a) = go f `unionFV` go a
1702 go (FunTy ty1 ty2) = go ty1 `unionFV` go ty2
1703 go (TyConApp tc tys) =
1704 case tyConInjectivityInfo tc of
1705 NotInjective -> emptyFV
1706 Injective inj -> mapUnionFV go $
1707 filterByList (inj ++ repeat True) tys
1708 -- Oversaturated arguments to a tycon are
1709 -- always injective, hence the repeat True
1710 go (ForAllTy tvb ty) = tyCoFVsBndr tvb $ go (tyVarKind (binderVar tvb))
1711 `unionFV` go ty
1712 go LitTy{} = emptyFV
1713 go (CastTy ty _) = go ty
1714 go CoercionTy{} = emptyFV
1715
1716 -- | Returns True if this type has no free variables. Should be the same as
1717 -- isEmptyVarSet . tyCoVarsOfType, but faster in the non-forall case.
1718 noFreeVarsOfType :: Type -> Bool
1719 noFreeVarsOfType (TyVarTy _) = False
1720 noFreeVarsOfType (AppTy t1 t2) = noFreeVarsOfType t1 && noFreeVarsOfType t2
1721 noFreeVarsOfType (TyConApp _ tys) = all noFreeVarsOfType tys
1722 noFreeVarsOfType ty@(ForAllTy {}) = isEmptyVarSet (tyCoVarsOfType ty)
1723 noFreeVarsOfType (FunTy t1 t2) = noFreeVarsOfType t1 && noFreeVarsOfType t2
1724 noFreeVarsOfType (LitTy _) = True
1725 noFreeVarsOfType (CastTy ty co) = noFreeVarsOfType ty && noFreeVarsOfCo co
1726 noFreeVarsOfType (CoercionTy co) = noFreeVarsOfCo co
1727
1728 -- | Returns True if this coercion has no free variables. Should be the same as
1729 -- isEmptyVarSet . tyCoVarsOfCo, but faster in the non-forall case.
1730 noFreeVarsOfCo :: Coercion -> Bool
1731 noFreeVarsOfCo (Refl _ ty) = noFreeVarsOfType ty
1732 noFreeVarsOfCo (TyConAppCo _ _ args) = all noFreeVarsOfCo args
1733 noFreeVarsOfCo (AppCo c1 c2) = noFreeVarsOfCo c1 && noFreeVarsOfCo c2
1734 noFreeVarsOfCo co@(ForAllCo {}) = isEmptyVarSet (tyCoVarsOfCo co)
1735 noFreeVarsOfCo (FunCo _ c1 c2) = noFreeVarsOfCo c1 && noFreeVarsOfCo c2
1736 noFreeVarsOfCo (CoVarCo _) = False
1737 noFreeVarsOfCo (HoleCo {}) = True -- I'm unsure; probably never happens
1738 noFreeVarsOfCo (AxiomInstCo _ _ args) = all noFreeVarsOfCo args
1739 noFreeVarsOfCo (UnivCo p _ t1 t2) = noFreeVarsOfProv p &&
1740 noFreeVarsOfType t1 &&
1741 noFreeVarsOfType t2
1742 noFreeVarsOfCo (SymCo co) = noFreeVarsOfCo co
1743 noFreeVarsOfCo (TransCo co1 co2) = noFreeVarsOfCo co1 && noFreeVarsOfCo co2
1744 noFreeVarsOfCo (NthCo _ co) = noFreeVarsOfCo co
1745 noFreeVarsOfCo (LRCo _ co) = noFreeVarsOfCo co
1746 noFreeVarsOfCo (InstCo co1 co2) = noFreeVarsOfCo co1 && noFreeVarsOfCo co2
1747 noFreeVarsOfCo (CoherenceCo co1 co2) = noFreeVarsOfCo co1 && noFreeVarsOfCo co2
1748 noFreeVarsOfCo (KindCo co) = noFreeVarsOfCo co
1749 noFreeVarsOfCo (SubCo co) = noFreeVarsOfCo co
1750 noFreeVarsOfCo (AxiomRuleCo _ cs) = all noFreeVarsOfCo cs
1751
1752 -- | Returns True if this UnivCoProv has no free variables. Should be the same as
1753 -- isEmptyVarSet . tyCoVarsOfProv, but faster in the non-forall case.
1754 noFreeVarsOfProv :: UnivCoProvenance -> Bool
1755 noFreeVarsOfProv UnsafeCoerceProv = True
1756 noFreeVarsOfProv (PhantomProv co) = noFreeVarsOfCo co
1757 noFreeVarsOfProv (ProofIrrelProv co) = noFreeVarsOfCo co
1758 noFreeVarsOfProv (PluginProv {}) = True
1759
1760 {-
1761 %************************************************************************
1762 %* *
1763 Substitutions
1764 Data type defined here to avoid unnecessary mutual recursion
1765 %* *
1766 %************************************************************************
1767 -}
1768
1769 -- | Type & coercion substitution
1770 --
1771 -- #tcvsubst_invariant#
1772 -- The following invariants must hold of a 'TCvSubst':
1773 --
1774 -- 1. The in-scope set is needed /only/ to
1775 -- guide the generation of fresh uniques
1776 --
1777 -- 2. In particular, the /kind/ of the type variables in
1778 -- the in-scope set is not relevant
1779 --
1780 -- 3. The substitution is only applied ONCE! This is because
1781 -- in general such application will not reach a fixed point.
1782 data TCvSubst
1783 = TCvSubst InScopeSet -- The in-scope type and kind variables
1784 TvSubstEnv -- Substitutes both type and kind variables
1785 CvSubstEnv -- Substitutes coercion variables
1786 -- See Note [Apply Once]
1787 -- and Note [Extending the TvSubstEnv]
1788 -- and Note [Substituting types and coercions]
1789 -- and Note [The substitution invariant]
1790
1791 -- | A substitution of 'Type's for 'TyVar's
1792 -- and 'Kind's for 'KindVar's
1793 type TvSubstEnv = TyVarEnv Type
1794 -- A TvSubstEnv is used both inside a TCvSubst (with the apply-once
1795 -- invariant discussed in Note [Apply Once]), and also independently
1796 -- in the middle of matching, and unification (see Types.Unify)
1797 -- So you have to look at the context to know if it's idempotent or
1798 -- apply-once or whatever
1799
1800 -- | A substitution of 'Coercion's for 'CoVar's
1801 type CvSubstEnv = CoVarEnv Coercion
1802
1803 {-
1804 Note [Apply Once]
1805 ~~~~~~~~~~~~~~~~~
1806 We use TCvSubsts to instantiate things, and we might instantiate
1807 forall a b. ty
1808 \with the types
1809 [a, b], or [b, a].
1810 So the substitution might go [a->b, b->a]. A similar situation arises in Core
1811 when we find a beta redex like
1812 (/\ a /\ b -> e) b a
1813 Then we also end up with a substitution that permutes type variables. Other
1814 variations happen to; for example [a -> (a, b)].
1815
1816 ****************************************************
1817 *** So a TCvSubst must be applied precisely once ***
1818 ****************************************************
1819
1820 A TCvSubst is not idempotent, but, unlike the non-idempotent substitution
1821 we use during unifications, it must not be repeatedly applied.
1822
1823 Note [Extending the TvSubstEnv]
1824 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1825 See #tcvsubst_invariant# for the invariants that must hold.
1826
1827 This invariant allows a short-cut when the subst envs are empty:
1828 if the TvSubstEnv and CvSubstEnv are empty --- i.e. (isEmptyTCvSubst subst)
1829 holds --- then (substTy subst ty) does nothing.
1830
1831 For example, consider:
1832 (/\a. /\b:(a~Int). ...b..) Int
1833 We substitute Int for 'a'. The Unique of 'b' does not change, but
1834 nevertheless we add 'b' to the TvSubstEnv, because b's kind does change
1835
1836 This invariant has several crucial consequences:
1837
1838 * In substTyVarBndr, we need extend the TvSubstEnv
1839 - if the unique has changed
1840 - or if the kind has changed
1841
1842 * In substTyVar, we do not need to consult the in-scope set;
1843 the TvSubstEnv is enough
1844
1845 * In substTy, substTheta, we can short-circuit when the TvSubstEnv is empty
1846
1847 Note [Substituting types and coercions]
1848 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1849 Types and coercions are mutually recursive, and either may have variables
1850 "belonging" to the other. Thus, every time we wish to substitute in a
1851 type, we may also need to substitute in a coercion, and vice versa.
1852 However, the constructor used to create type variables is distinct from
1853 that of coercion variables, so we carry two VarEnvs in a TCvSubst. Note
1854 that it would be possible to use the CoercionTy constructor to combine
1855 these environments, but that seems like a false economy.
1856
1857 Note that the TvSubstEnv should *never* map a CoVar (built with the Id
1858 constructor) and the CvSubstEnv should *never* map a TyVar. Furthermore,
1859 the range of the TvSubstEnv should *never* include a type headed with
1860 CoercionTy.
1861
1862 Note [The substitution invariant]
1863 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1864 When calling (substTy subst ty) it should be the case that
1865 the in-scope set in the substitution is a superset of both:
1866
1867 * The free vars of the range of the substitution
1868 * The free vars of ty minus the domain of the substitution
1869
1870 If we want to substitute [a -> ty1, b -> ty2] I used to
1871 think it was enough to generate an in-scope set that includes
1872 fv(ty1,ty2). But that's not enough; we really should also take the
1873 free vars of the type we are substituting into! Example:
1874 (forall b. (a,b,x)) [a -> List b]
1875 Then if we use the in-scope set {b}, there is a danger we will rename
1876 the forall'd variable to 'x' by mistake, getting this:
1877 (forall x. (List b, x, x))
1878
1879 Breaking this invariant caused the bug from #11371.
1880 -}
1881
1882 emptyTvSubstEnv :: TvSubstEnv
1883 emptyTvSubstEnv = emptyVarEnv
1884
1885 emptyCvSubstEnv :: CvSubstEnv
1886 emptyCvSubstEnv = emptyVarEnv
1887
1888 composeTCvSubstEnv :: InScopeSet
1889 -> (TvSubstEnv, CvSubstEnv)
1890 -> (TvSubstEnv, CvSubstEnv)
1891 -> (TvSubstEnv, CvSubstEnv)
1892 -- ^ @(compose env1 env2)(x)@ is @env1(env2(x))@; i.e. apply @env2@ then @env1@.
1893 -- It assumes that both are idempotent.
1894 -- Typically, @env1@ is the refinement to a base substitution @env2@
1895 composeTCvSubstEnv in_scope (tenv1, cenv1) (tenv2, cenv2)
1896 = ( tenv1 `plusVarEnv` mapVarEnv (substTy subst1) tenv2
1897 , cenv1 `plusVarEnv` mapVarEnv (substCo subst1) cenv2 )
1898 -- First apply env1 to the range of env2
1899 -- Then combine the two, making sure that env1 loses if
1900 -- both bind the same variable; that's why env1 is the
1901 -- *left* argument to plusVarEnv, because the right arg wins
1902 where
1903 subst1 = TCvSubst in_scope tenv1 cenv1
1904
1905 -- | Composes two substitutions, applying the second one provided first,
1906 -- like in function composition.
1907 composeTCvSubst :: TCvSubst -> TCvSubst -> TCvSubst
1908 composeTCvSubst (TCvSubst is1 tenv1 cenv1) (TCvSubst is2 tenv2 cenv2)
1909 = TCvSubst is3 tenv3 cenv3
1910 where
1911 is3 = is1 `unionInScope` is2
1912 (tenv3, cenv3) = composeTCvSubstEnv is3 (tenv1, cenv1) (tenv2, cenv2)
1913
1914 emptyTCvSubst :: TCvSubst
1915 emptyTCvSubst = TCvSubst emptyInScopeSet emptyTvSubstEnv emptyCvSubstEnv
1916
1917 mkEmptyTCvSubst :: InScopeSet -> TCvSubst
1918 mkEmptyTCvSubst is = TCvSubst is emptyTvSubstEnv emptyCvSubstEnv
1919
1920 isEmptyTCvSubst :: TCvSubst -> Bool
1921 -- See Note [Extending the TvSubstEnv]
1922 isEmptyTCvSubst (TCvSubst _ tenv cenv) = isEmptyVarEnv tenv && isEmptyVarEnv cenv
1923
1924 mkTCvSubst :: InScopeSet -> (TvSubstEnv, CvSubstEnv) -> TCvSubst
1925 mkTCvSubst in_scope (tenv, cenv) = TCvSubst in_scope tenv cenv
1926
1927 mkTvSubst :: InScopeSet -> TvSubstEnv -> TCvSubst
1928 -- ^ Make a TCvSubst with specified tyvar subst and empty covar subst
1929 mkTvSubst in_scope tenv = TCvSubst in_scope tenv emptyCvSubstEnv
1930
1931 getTvSubstEnv :: TCvSubst -> TvSubstEnv
1932 getTvSubstEnv (TCvSubst _ env _) = env
1933
1934 getCvSubstEnv :: TCvSubst -> CvSubstEnv
1935 getCvSubstEnv (TCvSubst _ _ env) = env
1936
1937 getTCvInScope :: TCvSubst -> InScopeSet
1938 getTCvInScope (TCvSubst in_scope _ _) = in_scope
1939
1940 -- | Returns the free variables of the types in the range of a substitution as
1941 -- a non-deterministic set.
1942 getTCvSubstRangeFVs :: TCvSubst -> VarSet
1943 getTCvSubstRangeFVs (TCvSubst _ tenv cenv)
1944 = unionVarSet tenvFVs cenvFVs
1945 where
1946 tenvFVs = tyCoVarsOfTypesSet tenv
1947 cenvFVs = tyCoVarsOfCosSet cenv
1948
1949 isInScope :: Var -> TCvSubst -> Bool
1950 isInScope v (TCvSubst in_scope _ _) = v `elemInScopeSet` in_scope
1951
1952 notElemTCvSubst :: Var -> TCvSubst -> Bool
1953 notElemTCvSubst v (TCvSubst _ tenv cenv)
1954 | isTyVar v
1955 = not (v `elemVarEnv` tenv)
1956 | otherwise
1957 = not (v `elemVarEnv` cenv)
1958
1959 setTvSubstEnv :: TCvSubst -> TvSubstEnv -> TCvSubst
1960 setTvSubstEnv (TCvSubst in_scope _ cenv) tenv = TCvSubst in_scope tenv cenv
1961
1962 setCvSubstEnv :: TCvSubst -> CvSubstEnv -> TCvSubst
1963 setCvSubstEnv (TCvSubst in_scope tenv _) cenv = TCvSubst in_scope tenv cenv
1964
1965 zapTCvSubst :: TCvSubst -> TCvSubst
1966 zapTCvSubst (TCvSubst in_scope _ _) = TCvSubst in_scope emptyVarEnv emptyVarEnv
1967
1968 extendTCvInScope :: TCvSubst -> Var -> TCvSubst
1969 extendTCvInScope (TCvSubst in_scope tenv cenv) var
1970 = TCvSubst (extendInScopeSet in_scope var) tenv cenv
1971
1972 extendTCvInScopeList :: TCvSubst -> [Var] -> TCvSubst
1973 extendTCvInScopeList (TCvSubst in_scope tenv cenv) vars
1974 = TCvSubst (extendInScopeSetList in_scope vars) tenv cenv
1975
1976 extendTCvInScopeSet :: TCvSubst -> VarSet -> TCvSubst
1977 extendTCvInScopeSet (TCvSubst in_scope tenv cenv) vars
1978 = TCvSubst (extendInScopeSetSet in_scope vars) tenv cenv
1979
1980 extendTCvSubst :: TCvSubst -> TyCoVar -> Type -> TCvSubst
1981 extendTCvSubst subst v ty
1982 | isTyVar v
1983 = extendTvSubst subst v ty
1984 | CoercionTy co <- ty
1985 = extendCvSubst subst v co
1986 | otherwise
1987 = pprPanic "extendTCvSubst" (ppr v <+> text "|->" <+> ppr ty)
1988
1989 extendTvSubst :: TCvSubst -> TyVar -> Type -> TCvSubst
1990 extendTvSubst (TCvSubst in_scope tenv cenv) tv ty
1991 = TCvSubst in_scope (extendVarEnv tenv tv ty) cenv
1992
1993 extendTvSubstBinderAndInScope :: TCvSubst -> TyBinder -> Type -> TCvSubst
1994 extendTvSubstBinderAndInScope subst (Named bndr) ty
1995 = extendTvSubstAndInScope subst (binderVar bndr) ty
1996 extendTvSubstBinderAndInScope subst (Anon _) _
1997 = subst
1998
1999 extendTvSubstWithClone :: TCvSubst -> TyVar -> TyVar -> TCvSubst
2000 -- Adds a new tv -> tv mapping, /and/ extends the in-scope set
2001 extendTvSubstWithClone (TCvSubst in_scope tenv cenv) tv tv'
2002 = TCvSubst (extendInScopeSetSet in_scope new_in_scope)
2003 (extendVarEnv tenv tv (mkTyVarTy tv'))
2004 cenv
2005 where
2006 new_in_scope = tyCoVarsOfType (tyVarKind tv') `extendVarSet` tv'
2007
2008 extendCvSubst :: TCvSubst -> CoVar -> Coercion -> TCvSubst
2009 extendCvSubst (TCvSubst in_scope tenv cenv) v co
2010 = TCvSubst in_scope tenv (extendVarEnv cenv v co)
2011
2012 extendCvSubstWithClone :: TCvSubst -> CoVar -> CoVar -> TCvSubst
2013 extendCvSubstWithClone (TCvSubst in_scope tenv cenv) cv cv'
2014 = TCvSubst (extendInScopeSetSet in_scope new_in_scope)
2015 tenv
2016 (extendVarEnv cenv cv (mkCoVarCo cv'))
2017 where
2018 new_in_scope = tyCoVarsOfType (varType cv') `extendVarSet` cv'
2019
2020 extendTvSubstAndInScope :: TCvSubst -> TyVar -> Type -> TCvSubst
2021 -- Also extends the in-scope set
2022 extendTvSubstAndInScope (TCvSubst in_scope tenv cenv) tv ty
2023 = TCvSubst (in_scope `extendInScopeSetSet` tyCoVarsOfType ty)
2024 (extendVarEnv tenv tv ty)
2025 cenv
2026
2027 extendTvSubstList :: TCvSubst -> [Var] -> [Type] -> TCvSubst
2028 extendTvSubstList subst tvs tys
2029 = foldl2 extendTvSubst subst tvs tys
2030
2031 unionTCvSubst :: TCvSubst -> TCvSubst -> TCvSubst
2032 -- Works when the ranges are disjoint
2033 unionTCvSubst (TCvSubst in_scope1 tenv1 cenv1) (TCvSubst in_scope2 tenv2 cenv2)
2034 = ASSERT( not (tenv1 `intersectsVarEnv` tenv2)
2035 && not (cenv1 `intersectsVarEnv` cenv2) )
2036 TCvSubst (in_scope1 `unionInScope` in_scope2)
2037 (tenv1 `plusVarEnv` tenv2)
2038 (cenv1 `plusVarEnv` cenv2)
2039
2040 -- mkTvSubstPrs and zipTvSubst generate the in-scope set from
2041 -- the types given; but it's just a thunk so with a bit of luck
2042 -- it'll never be evaluated
2043
2044 -- | Generates an in-scope set from the free variables in a list of types
2045 -- and a list of coercions
2046 mkTyCoInScopeSet :: [Type] -> [Coercion] -> InScopeSet
2047 mkTyCoInScopeSet tys cos
2048 = mkInScopeSet (tyCoVarsOfTypes tys `unionVarSet` tyCoVarsOfCos cos)
2049
2050 -- | Generates the in-scope set for the 'TCvSubst' from the types in the incoming
2051 -- environment. No CoVars, please!
2052 zipTvSubst :: [TyVar] -> [Type] -> TCvSubst
2053 zipTvSubst tvs tys
2054 | debugIsOn
2055 , not (all isTyVar tvs) || neLength tvs tys
2056 = pprTrace "zipTvSubst" (ppr tvs $$ ppr tys) emptyTCvSubst
2057 | otherwise
2058 = mkTvSubst (mkInScopeSet (tyCoVarsOfTypes tys)) tenv
2059 where
2060 tenv = zipTyEnv tvs tys
2061
2062 -- | Generates the in-scope set for the 'TCvSubst' from the types in the incoming
2063 -- environment. No TyVars, please!
2064 zipCvSubst :: [CoVar] -> [Coercion] -> TCvSubst
2065 zipCvSubst cvs cos
2066 | debugIsOn
2067 , not (all isCoVar cvs) || neLength cvs cos
2068 = pprTrace "zipCvSubst" (ppr cvs $$ ppr cos) emptyTCvSubst
2069 | otherwise
2070 = TCvSubst (mkInScopeSet (tyCoVarsOfCos cos)) emptyTvSubstEnv cenv
2071 where
2072 cenv = zipCoEnv cvs cos
2073
2074 -- | Generates the in-scope set for the 'TCvSubst' from the types in the
2075 -- incoming environment. No CoVars, please!
2076 mkTvSubstPrs :: [(TyVar, Type)] -> TCvSubst
2077 mkTvSubstPrs prs =
2078 ASSERT2( onlyTyVarsAndNoCoercionTy, text "prs" <+> ppr prs )
2079 mkTvSubst in_scope tenv
2080 where tenv = mkVarEnv prs
2081 in_scope = mkInScopeSet $ tyCoVarsOfTypes $ map snd prs
2082 onlyTyVarsAndNoCoercionTy =
2083 and [ isTyVar tv && not (isCoercionTy ty)
2084 | (tv, ty) <- prs ]
2085
2086 zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
2087 zipTyEnv tyvars tys
2088 = ASSERT( all (not . isCoercionTy) tys )
2089 mkVarEnv (zipEqual "zipTyEnv" tyvars tys)
2090 -- There used to be a special case for when
2091 -- ty == TyVarTy tv
2092 -- (a not-uncommon case) in which case the substitution was dropped.
2093 -- But the type-tidier changes the print-name of a type variable without
2094 -- changing the unique, and that led to a bug. Why? Pre-tidying, we had
2095 -- a type {Foo t}, where Foo is a one-method class. So Foo is really a newtype.
2096 -- And it happened that t was the type variable of the class. Post-tiding,
2097 -- it got turned into {Foo t2}. The ext-core printer expanded this using
2098 -- sourceTypeRep, but that said "Oh, t == t2" because they have the same unique,
2099 -- and so generated a rep type mentioning t not t2.
2100 --
2101 -- Simplest fix is to nuke the "optimisation"
2102
2103 zipCoEnv :: [CoVar] -> [Coercion] -> CvSubstEnv
2104 zipCoEnv cvs cos = mkVarEnv (zipEqual "zipCoEnv" cvs cos)
2105
2106 instance Outputable TCvSubst where
2107 ppr (TCvSubst ins tenv cenv)
2108 = brackets $ sep[ text "TCvSubst",
2109 nest 2 (text "In scope:" <+> ppr ins),
2110 nest 2 (text "Type env:" <+> ppr tenv),
2111 nest 2 (text "Co env:" <+> ppr cenv) ]
2112
2113 {-
2114 %************************************************************************
2115 %* *
2116 Performing type or kind substitutions
2117 %* *
2118 %************************************************************************
2119
2120 Note [Sym and ForAllCo]
2121 ~~~~~~~~~~~~~~~~~~~~~~~
2122 In OptCoercion, we try to push "sym" out to the leaves of a coercion. But,
2123 how do we push sym into a ForAllCo? It's a little ugly.
2124
2125 Here is the typing rule:
2126
2127 h : k1 ~# k2
2128 (tv : k1) |- g : ty1 ~# ty2
2129 ----------------------------
2130 ForAllCo tv h g : (ForAllTy (tv : k1) ty1) ~#
2131 (ForAllTy (tv : k2) (ty2[tv |-> tv |> sym h]))
2132
2133 Here is what we want:
2134
2135 ForAllCo tv h' g' : (ForAllTy (tv : k2) (ty2[tv |-> tv |> sym h])) ~#
2136 (ForAllTy (tv : k1) ty1)
2137
2138
2139 Because the kinds of the type variables to the right of the colon are the kinds
2140 coerced by h', we know (h' : k2 ~# k1). Thus, (h' = sym h).
2141
2142 Now, we can rewrite ty1 to be (ty1[tv |-> tv |> sym h' |> h']). We thus want
2143
2144 ForAllCo tv h' g' :
2145 (ForAllTy (tv : k2) (ty2[tv |-> tv |> h'])) ~#
2146 (ForAllTy (tv : k1) (ty1[tv |-> tv |> h'][tv |-> tv |> sym h']))
2147
2148 We thus see that we want
2149
2150 g' : ty2[tv |-> tv |> h'] ~# ty1[tv |-> tv |> h']
2151
2152 and thus g' = sym (g[tv |-> tv |> h']).
2153
2154 Putting it all together, we get this:
2155
2156 sym (ForAllCo tv h g)
2157 ==>
2158 ForAllCo tv (sym h) (sym g[tv |-> tv |> sym h])
2159
2160 -}
2161
2162 -- | Type substitution, see 'zipTvSubst'
2163 substTyWith :: HasCallStack => [TyVar] -> [Type] -> Type -> Type
2164 -- Works only if the domain of the substitution is a
2165 -- superset of the type being substituted into
2166 substTyWith tvs tys = {-#SCC "substTyWith" #-}
2167 ASSERT( tvs `equalLength` tys )
2168 substTy (zipTvSubst tvs tys)
2169
2170 -- | Type substitution, see 'zipTvSubst'. Disables sanity checks.
2171 -- The problems that the sanity checks in substTy catch are described in
2172 -- Note [The substitution invariant].
2173 -- The goal of #11371 is to migrate all the calls of substTyUnchecked to
2174 -- substTy and remove this function. Please don't use in new code.
2175 substTyWithUnchecked :: [TyVar] -> [Type] -> Type -> Type
2176 substTyWithUnchecked tvs tys
2177 = ASSERT( tvs `equalLength` tys )
2178 substTyUnchecked (zipTvSubst tvs tys)
2179
2180 -- | Substitute tyvars within a type using a known 'InScopeSet'.
2181 -- Pre-condition: the 'in_scope' set should satisfy Note [The substitution
2182 -- invariant]; specifically it should include the free vars of 'tys',
2183 -- and of 'ty' minus the domain of the subst.
2184 substTyWithInScope :: InScopeSet -> [TyVar] -> [Type] -> Type -> Type
2185 substTyWithInScope in_scope tvs tys ty =
2186 ASSERT( tvs `equalLength` tys )
2187 substTy (mkTvSubst in_scope tenv) ty
2188 where tenv = zipTyEnv tvs tys
2189
2190 -- | Coercion substitution, see 'zipTvSubst'
2191 substCoWith :: HasCallStack => [TyVar] -> [Type] -> Coercion -> Coercion
2192 substCoWith tvs tys = ASSERT( tvs `equalLength` tys )
2193 substCo (zipTvSubst tvs tys)
2194
2195 -- | Coercion substitution, see 'zipTvSubst'. Disables sanity checks.
2196 -- The problems that the sanity checks in substCo catch are described in
2197 -- Note [The substitution invariant].
2198 -- The goal of #11371 is to migrate all the calls of substCoUnchecked to
2199 -- substCo and remove this function. Please don't use in new code.
2200 substCoWithUnchecked :: [TyVar] -> [Type] -> Coercion -> Coercion
2201 substCoWithUnchecked tvs tys
2202 = ASSERT( tvs `equalLength` tys )
2203 substCoUnchecked (zipTvSubst tvs tys)
2204
2205
2206
2207 -- | Substitute covars within a type
2208 substTyWithCoVars :: [CoVar] -> [Coercion] -> Type -> Type
2209 substTyWithCoVars cvs cos = substTy (zipCvSubst cvs cos)
2210
2211 -- | Type substitution, see 'zipTvSubst'
2212 substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type]
2213 substTysWith tvs tys = ASSERT( tvs `equalLength` tys )
2214 substTys (zipTvSubst tvs tys)
2215
2216 -- | Type substitution, see 'zipTvSubst'
2217 substTysWithCoVars :: [CoVar] -> [Coercion] -> [Type] -> [Type]
2218 substTysWithCoVars cvs cos = ASSERT( cvs `equalLength` cos )
2219 substTys (zipCvSubst cvs cos)
2220
2221 -- | Substitute within a 'Type' after adding the free variables of the type
2222 -- to the in-scope set. This is useful for the case when the free variables
2223 -- aren't already in the in-scope set or easily available.
2224 -- See also Note [The substitution invariant].
2225 substTyAddInScope :: TCvSubst -> Type -> Type
2226 substTyAddInScope subst ty =
2227 substTy (extendTCvInScopeSet subst $ tyCoVarsOfType ty) ty
2228
2229 -- | When calling `substTy` it should be the case that the in-scope set in
2230 -- the substitution is a superset of the free vars of the range of the
2231 -- substitution.
2232 -- See also Note [The substitution invariant].
2233 isValidTCvSubst :: TCvSubst -> Bool
2234 isValidTCvSubst (TCvSubst in_scope tenv cenv) =
2235 (tenvFVs `varSetInScope` in_scope) &&
2236 (cenvFVs `varSetInScope` in_scope)
2237 where
2238 tenvFVs = tyCoVarsOfTypesSet tenv
2239 cenvFVs = tyCoVarsOfCosSet cenv
2240
2241 -- | This checks if the substitution satisfies the invariant from
2242 -- Note [The substitution invariant].
2243 checkValidSubst :: HasCallStack => TCvSubst -> [Type] -> [Coercion] -> a -> a
2244 checkValidSubst subst@(TCvSubst in_scope tenv cenv) tys cos a
2245 = WARN( not ({-#SCC "isValidTCvSubst" #-} isValidTCvSubst subst),
2246 text "in_scope" <+> ppr in_scope $$
2247 text "tenv" <+> ppr tenv $$
2248 text "tenvFVs"
2249 <+> ppr (tyCoVarsOfTypesSet tenv) $$
2250 text "cenv" <+> ppr cenv $$
2251 text "cenvFVs"
2252 <+> ppr (tyCoVarsOfCosSet cenv) $$
2253 text "tys" <+> ppr tys $$
2254 text "cos" <+> ppr cos )
2255 WARN( not ({-#SCC "tysCosFVsInScope" #-} tysCosFVsInScope),
2256 text "in_scope" <+> ppr in_scope $$
2257 text "tenv" <+> ppr tenv $$
2258 text "cenv" <+> ppr cenv $$
2259 text "tys" <+> ppr tys $$
2260 text "cos" <+> ppr cos $$
2261 text "needInScope" <+> ppr needInScope )
2262 a
2263 where
2264 substDomain = nonDetKeysUFM tenv ++ nonDetKeysUFM cenv
2265 -- It's OK to use nonDetKeysUFM here, because we only use this list to
2266 -- remove some elements from a set
2267 needInScope = (tyCoVarsOfTypes tys `unionVarSet` tyCoVarsOfCos cos)
2268 `delListFromUniqSet_Directly` substDomain
2269 tysCosFVsInScope = needInScope `varSetInScope` in_scope
2270
2271
2272 -- | Substitute within a 'Type'
2273 -- The substitution has to satisfy the invariants described in
2274 -- Note [The substitution invariant].
2275 substTy :: HasCallStack => TCvSubst -> Type -> Type
2276 substTy subst ty
2277 | isEmptyTCvSubst subst = ty
2278 | otherwise = checkValidSubst subst [ty] [] $
2279 subst_ty subst ty
2280
2281 -- | Substitute within a 'Type' disabling the sanity checks.
2282 -- The problems that the sanity checks in substTy catch are described in
2283 -- Note [The substitution invariant].
2284 -- The goal of #11371 is to migrate all the calls of substTyUnchecked to
2285 -- substTy and remove this function. Please don't use in new code.
2286 substTyUnchecked :: TCvSubst -> Type -> Type
2287 substTyUnchecked subst ty
2288 | isEmptyTCvSubst subst = ty
2289 | otherwise = subst_ty subst ty
2290
2291 -- | Substitute within several 'Type's
2292 -- The substitution has to satisfy the invariants described in
2293 -- Note [The substitution invariant].
2294 substTys :: HasCallStack => TCvSubst -> [Type] -> [Type]
2295 substTys subst tys
2296 | isEmptyTCvSubst subst = tys
2297 | otherwise = checkValidSubst subst tys [] $ map (subst_ty subst) tys
2298
2299 -- | Substitute within several 'Type's disabling the sanity checks.
2300 -- The problems that the sanity checks in substTys catch are described in
2301 -- Note [The substitution invariant].
2302 -- The goal of #11371 is to migrate all the calls of substTysUnchecked to
2303 -- substTys and remove this function. Please don't use in new code.
2304 substTysUnchecked :: TCvSubst -> [Type] -> [Type]
2305 substTysUnchecked subst tys
2306 | isEmptyTCvSubst subst = tys
2307 | otherwise = map (subst_ty subst) tys
2308
2309 -- | Substitute within a 'ThetaType'
2310 -- The substitution has to satisfy the invariants described in
2311 -- Note [The substitution invariant].
2312 substTheta :: HasCallStack => TCvSubst -> ThetaType -> ThetaType
2313 substTheta = substTys
2314
2315 -- | Substitute within a 'ThetaType' disabling the sanity checks.
2316 -- The problems that the sanity checks in substTys catch are described in
2317 -- Note [The substitution invariant].
2318 -- The goal of #11371 is to migrate all the calls of substThetaUnchecked to
2319 -- substTheta and remove this function. Please don't use in new code.
2320 substThetaUnchecked :: TCvSubst -> ThetaType -> ThetaType
2321 substThetaUnchecked = substTysUnchecked
2322
2323
2324 subst_ty :: TCvSubst -> Type -> Type
2325 -- subst_ty is the main workhorse for type substitution
2326 --
2327 -- Note that the in_scope set is poked only if we hit a forall
2328 -- so it may often never be fully computed
2329 subst_ty subst ty
2330 = {-#SCC "subst_ty" #-} go ty
2331 where
2332 go (TyVarTy tv) = substTyVar subst tv
2333 go (AppTy fun arg) = mkAppTy (go fun) $! (go arg)
2334 -- The mkAppTy smart constructor is important
2335 -- we might be replacing (a Int), represented with App
2336 -- by [Int], represented with TyConApp
2337 go (TyConApp tc tys) = let args = map go tys
2338 in args `seqList` TyConApp tc args
2339 go (FunTy arg res) = (FunTy $! go arg) $! go res
2340 go (ForAllTy (TvBndr tv vis) ty)
2341 = case substTyVarBndrUnchecked subst tv of
2342 (subst', tv') ->
2343 (ForAllTy $! ((TvBndr $! tv') vis)) $!
2344 (subst_ty subst' ty)
2345 go (LitTy n) = LitTy $! n
2346 go (CastTy ty co) = (mkCastTy $! (go ty)) $! (subst_co subst co)
2347 go (CoercionTy co) = CoercionTy $! (subst_co subst co)
2348
2349 substTyVar :: TCvSubst -> TyVar -> Type
2350 substTyVar (TCvSubst _ tenv _) tv
2351 = ASSERT( isTyVar tv )
2352 case lookupVarEnv tenv tv of
2353 Just ty -> ty
2354 Nothing -> TyVarTy tv
2355
2356 substTyVars :: TCvSubst -> [TyVar] -> [Type]
2357 substTyVars subst = map $ substTyVar subst
2358
2359 lookupTyVar :: TCvSubst -> TyVar -> Maybe Type
2360 -- See Note [Extending the TCvSubst]
2361 lookupTyVar (TCvSubst _ tenv _) tv
2362 = ASSERT( isTyVar tv )
2363 lookupVarEnv tenv tv
2364
2365 -- | Substitute within a 'Coercion'
2366 -- The substitution has to satisfy the invariants described in
2367 -- Note [The substitution invariant].
2368 substCo :: HasCallStack => TCvSubst -> Coercion -> Coercion
2369 substCo subst co
2370 | isEmptyTCvSubst subst = co
2371 | otherwise = checkValidSubst subst [] [co] $ subst_co subst co
2372
2373 -- | Substitute within a 'Coercion' disabling sanity checks.
2374 -- The problems that the sanity checks in substCo catch are described in
2375 -- Note [The substitution invariant].
2376 -- The goal of #11371 is to migrate all the calls of substCoUnchecked to
2377 -- substCo and remove this function. Please don't use in new code.
2378 substCoUnchecked :: TCvSubst -> Coercion -> Coercion
2379 substCoUnchecked subst co
2380 | isEmptyTCvSubst subst = co
2381 | otherwise = subst_co subst co
2382
2383 -- | Substitute within several 'Coercion's
2384 -- The substitution has to satisfy the invariants described in
2385 -- Note [The substitution invariant].
2386 substCos :: HasCallStack => TCvSubst -> [Coercion] -> [Coercion]
2387 substCos subst cos
2388 | isEmptyTCvSubst subst = cos
2389 | otherwise = checkValidSubst subst [] cos $ map (subst_co subst) cos
2390
2391 subst_co :: TCvSubst -> Coercion -> Coercion
2392 subst_co subst co
2393 = go co
2394 where
2395 go_ty :: Type -> Type
2396 go_ty = subst_ty subst
2397
2398 go :: Coercion -> Coercion
2399 go (Refl r ty) = mkReflCo r $! go_ty ty
2400 go (TyConAppCo r tc args)= let args' = map go args
2401 in args' `seqList` mkTyConAppCo r tc args'
2402 go (AppCo co arg) = (mkAppCo $! go co) $! go arg
2403 go (ForAllCo tv kind_co co)
2404 = case substForAllCoBndrUnchecked subst tv kind_co of { (subst', tv', kind_co') ->
2405 ((mkForAllCo $! tv') $! kind_co') $! subst_co subst' co }
2406 go (FunCo r co1 co2) = (mkFunCo r $! go co1) $! go co2
2407 go (CoVarCo cv) = substCoVar subst cv
2408 go (AxiomInstCo con ind cos) = mkAxiomInstCo con ind $! map go cos
2409 go (UnivCo p r t1 t2) = (((mkUnivCo $! go_prov p) $! r) $!
2410 (go_ty t1)) $! (go_ty t2)
2411 go (SymCo co) = mkSymCo $! (go co)
2412 go (TransCo co1 co2) = (mkTransCo $! (go co1)) $! (go co2)
2413 go (NthCo d co) = mkNthCo d $! (go co)
2414 go (LRCo lr co) = mkLRCo lr $! (go co)
2415 go (InstCo co arg) = (mkInstCo $! (go co)) $! go arg
2416 go (CoherenceCo co1 co2) = (mkCoherenceCo $! (go co1)) $! (go co2)
2417 go (KindCo co) = mkKindCo $! (go co)
2418 go (SubCo co) = mkSubCo $! (go co)
2419 go (AxiomRuleCo c cs) = let cs1 = map go cs
2420 in cs1 `seqList` AxiomRuleCo c cs1
2421 go (HoleCo h) = HoleCo h
2422 -- NB: this last case is a little suspicious, but we need it. Originally,
2423 -- there was a panic here, but it triggered from deeplySkolemise. Because
2424 -- we only skolemise tyvars that are manually bound, this operation makes
2425 -- sense, even over a coercion with holes. We don't need to substitute
2426 -- in the type of the coHoleCoVar because it wouldn't makes sense to have
2427 -- forall a. ....(ty |> {hole_cv::a})....
2428
2429 go_prov UnsafeCoerceProv = UnsafeCoerceProv
2430 go_prov (PhantomProv kco) = PhantomProv (go kco)
2431 go_prov (ProofIrrelProv kco) = ProofIrrelProv (go kco)
2432 go_prov p@(PluginProv _) = p
2433
2434 substForAllCoBndr :: TCvSubst -> TyVar -> Coercion -> (TCvSubst, TyVar, Coercion)
2435 substForAllCoBndr subst
2436 = substForAllCoBndrCallback False (substCo subst) subst
2437
2438 -- | Like 'substForAllCoBndr', but disables sanity checks.
2439 -- The problems that the sanity checks in substCo catch are described in
2440 -- Note [The substitution invariant].
2441 -- The goal of #11371 is to migrate all the calls of substCoUnchecked to
2442 -- substCo and remove this function. Please don't use in new code.
2443 substForAllCoBndrUnchecked :: TCvSubst -> TyVar -> Coercion -> (TCvSubst, TyVar, Coercion)
2444 substForAllCoBndrUnchecked subst
2445 = substForAllCoBndrCallback False (substCoUnchecked subst) subst
2446
2447 -- See Note [Sym and ForAllCo]
2448 substForAllCoBndrCallback :: Bool -- apply sym to binder?
2449 -> (Coercion -> Coercion) -- transformation to kind co
2450 -> TCvSubst -> TyVar -> Coercion
2451 -> (TCvSubst, TyVar, Coercion)
2452 substForAllCoBndrCallback sym sco (TCvSubst in_scope tenv cenv)
2453 old_var old_kind_co
2454 = ( TCvSubst (in_scope `extendInScopeSet` new_var) new_env cenv
2455 , new_var, new_kind_co )
2456 where
2457 new_env | no_change && not sym = delVarEnv tenv old_var
2458 | sym = extendVarEnv tenv old_var $
2459 TyVarTy new_var `CastTy` new_kind_co
2460 | otherwise = extendVarEnv tenv old_var (TyVarTy new_var)
2461
2462 no_kind_change = noFreeVarsOfCo old_kind_co
2463 no_change = no_kind_change && (new_var == old_var)
2464
2465 new_kind_co | no_kind_change = old_kind_co
2466 | otherwise = sco old_kind_co
2467
2468 Pair new_ki1 _ = coercionKind new_kind_co
2469
2470 new_var = uniqAway in_scope (setTyVarKind old_var new_ki1)
2471
2472 substCoVar :: TCvSubst -> CoVar -> Coercion
2473 substCoVar (TCvSubst _ _ cenv) cv
2474 = case lookupVarEnv cenv cv of
2475 Just co -> co
2476 Nothing -> CoVarCo cv
2477
2478 substCoVars :: TCvSubst -> [CoVar] -> [Coercion]
2479 substCoVars subst cvs = map (substCoVar subst) cvs
2480
2481 lookupCoVar :: TCvSubst -> Var -> Maybe Coercion
2482 lookupCoVar (TCvSubst _ _ cenv) v = lookupVarEnv cenv v
2483
2484 substTyVarBndr :: HasCallStack => TCvSubst -> TyVar -> (TCvSubst, TyVar)
2485 substTyVarBndr = substTyVarBndrCallback substTy
2486
2487 -- | Like 'substTyVarBndr' but disables sanity checks.
2488 -- The problems that the sanity checks in substTy catch are described in
2489 -- Note [The substitution invariant].
2490 -- The goal of #11371 is to migrate all the calls of substTyUnchecked to
2491 -- substTy and remove this function. Please don't use in new code.
2492 substTyVarBndrUnchecked :: TCvSubst -> TyVar -> (TCvSubst, TyVar)
2493 substTyVarBndrUnchecked = substTyVarBndrCallback substTyUnchecked
2494
2495 -- | Substitute a tyvar in a binding position, returning an
2496 -- extended subst and a new tyvar.
2497 substTyVarBndrCallback :: (TCvSubst -> Type -> Type) -- ^ the subst function
2498 -> TCvSubst -> TyVar -> (TCvSubst, TyVar)
2499 substTyVarBndrCallback subst_fn subst@(TCvSubst in_scope tenv cenv) old_var
2500 = ASSERT2( _no_capture, pprTyVar old_var $$ pprTyVar new_var $$ ppr subst )
2501 ASSERT( isTyVar old_var )
2502 (TCvSubst (in_scope `extendInScopeSet` new_var) new_env cenv, new_var)
2503 where
2504 new_env | no_change = delVarEnv tenv old_var
2505 | otherwise = extendVarEnv tenv old_var (TyVarTy new_var)
2506
2507 _no_capture = not (new_var `elemVarSet` tyCoVarsOfTypesSet tenv)
2508 -- Assertion check that we are not capturing something in the substitution
2509
2510 old_ki = tyVarKind old_var
2511 no_kind_change = noFreeVarsOfType old_ki -- verify that kind is closed
2512 no_change = no_kind_change && (new_var == old_var)
2513 -- no_change means that the new_var is identical in
2514 -- all respects to the old_var (same unique, same kind)
2515 -- See Note [Extending the TCvSubst]
2516 --
2517 -- In that case we don't need to extend the substitution
2518 -- to map old to new. But instead we must zap any
2519 -- current substitution for the variable. For example:
2520 -- (\x.e) with id_subst = [x |-> e']
2521 -- Here we must simply zap the substitution for x
2522
2523 new_var | no_kind_change = uniqAway in_scope old_var
2524 | otherwise = uniqAway in_scope $
2525 setTyVarKind old_var (subst_fn subst old_ki)
2526 -- The uniqAway part makes sure the new variable is not already in scope
2527
2528 substCoVarBndr :: TCvSubst -> CoVar -> (TCvSubst, CoVar)
2529 substCoVarBndr subst@(TCvSubst in_scope tenv cenv) old_var
2530 = ASSERT( isCoVar old_var )
2531 (TCvSubst (in_scope `extendInScopeSet` new_var) tenv new_cenv, new_var)
2532 where
2533 new_co = mkCoVarCo new_var
2534 no_kind_change = all noFreeVarsOfType [t1, t2]
2535 no_change = new_var == old_var && no_kind_change
2536
2537 new_cenv | no_change = delVarEnv cenv old_var
2538 | otherwise = extendVarEnv cenv old_var new_co
2539
2540 new_var = uniqAway in_scope subst_old_var
2541 subst_old_var = mkCoVar (varName old_var) new_var_type
2542
2543 (_, _, t1, t2, role) = coVarKindsTypesRole old_var
2544 t1' = substTy subst t1
2545 t2' = substTy subst t2
2546 new_var_type = mkCoercionType role t1' t2'
2547 -- It's important to do the substitution for coercions,
2548 -- because they can have free type variables
2549
2550 cloneTyVarBndr :: TCvSubst -> TyVar -> Unique -> (TCvSubst, TyVar)
2551 cloneTyVarBndr subst@(TCvSubst in_scope tv_env cv_env) tv uniq
2552 = ASSERT2( isTyVar tv, ppr tv ) -- I think it's only called on TyVars
2553 (TCvSubst (extendInScopeSet in_scope tv')
2554 (extendVarEnv tv_env tv (mkTyVarTy tv')) cv_env, tv')
2555 where
2556 old_ki = tyVarKind tv
2557 no_kind_change = noFreeVarsOfType old_ki -- verify that kind is closed
2558
2559 tv1 | no_kind_change = tv
2560 | otherwise = setTyVarKind tv (substTy subst old_ki)
2561
2562 tv' = setVarUnique tv1 uniq
2563
2564 cloneTyVarBndrs :: TCvSubst -> [TyVar] -> UniqSupply -> (TCvSubst, [TyVar])
2565 cloneTyVarBndrs subst [] _usupply = (subst, [])
2566 cloneTyVarBndrs subst (t:ts) usupply = (subst'', tv:tvs)
2567 where
2568 (uniq, usupply') = takeUniqFromSupply usupply
2569 (subst' , tv ) = cloneTyVarBndr subst t uniq
2570 (subst'', tvs) = cloneTyVarBndrs subst' ts usupply'
2571
2572 {-
2573 %************************************************************************
2574 %* *
2575 Pretty-printing types
2576
2577 Defined very early because of debug printing in assertions
2578 %* *
2579 %************************************************************************
2580
2581 @pprType@ is the standard @Type@ printer; the overloaded @ppr@ function is
2582 defined to use this. @pprParendType@ is the same, except it puts
2583 parens around the type, except for the atomic cases. @pprParendType@
2584 works just by setting the initial context precedence very high.
2585
2586 See Note [Precedence in types] in BasicTypes.
2587 -}
2588
2589 ------------------
2590
2591 pprType, pprParendType :: Type -> SDoc
2592 pprType = pprPrecType TopPrec
2593 pprParendType = pprPrecType TyConPrec
2594
2595 pprPrecType :: TyPrec -> Type -> SDoc
2596 pprPrecType prec ty
2597 = getPprStyle $ \sty ->
2598 if debugStyle sty -- Use pprDebugType when in
2599 then debug_ppr_ty prec ty -- when in debug-style
2600 else pprPrecIfaceType prec (tidyToIfaceTypeSty ty sty)
2601
2602 pprTyLit :: TyLit -> SDoc
2603 pprTyLit = pprIfaceTyLit . toIfaceTyLit
2604
2605 pprKind, pprParendKind :: Kind -> SDoc
2606 pprKind = pprType
2607 pprParendKind = pprParendType
2608
2609 tidyToIfaceTypeSty :: Type -> PprStyle -> IfaceType
2610 tidyToIfaceTypeSty ty sty
2611 | userStyle sty = tidyToIfaceType ty
2612 | otherwise = toIfaceTypeX (tyCoVarsOfType ty) ty
2613 -- in latter case, don't tidy, as we'll be printing uniques.
2614
2615 tidyToIfaceType :: Type -> IfaceType
2616 -- It's vital to tidy before converting to an IfaceType
2617 -- or nested binders will become indistinguishable!
2618 --
2619 -- Also for the free type variables, tell toIfaceTypeX to
2620 -- leave them as IfaceFreeTyVar. This is super-important
2621 -- for debug printing.
2622 tidyToIfaceType ty = toIfaceTypeX (mkVarSet free_tcvs) (tidyType env ty)
2623 where
2624 env = tidyFreeTyCoVars emptyTidyEnv free_tcvs
2625 free_tcvs = tyCoVarsOfTypeWellScoped ty
2626
2627 ------------
2628 pprCo, pprParendCo :: Coercion -> SDoc
2629 pprCo co = getPprStyle $ \ sty -> pprIfaceCoercion (tidyToIfaceCoSty co sty)
2630 pprParendCo co = getPprStyle $ \ sty -> pprParendIfaceCoercion (tidyToIfaceCoSty co sty)
2631
2632 tidyToIfaceCoSty :: Coercion -> PprStyle -> IfaceCoercion
2633 tidyToIfaceCoSty co sty
2634 | userStyle sty = tidyToIfaceCo co
2635 | otherwise = toIfaceCoercionX (tyCoVarsOfCo co) co
2636 -- in latter case, don't tidy, as we'll be printing uniques.
2637
2638 tidyToIfaceCo :: Coercion -> IfaceCoercion
2639 -- It's vital to tidy before converting to an IfaceType
2640 -- or nested binders will become indistinguishable!
2641 --
2642 -- Also for the free type variables, tell toIfaceCoercionX to
2643 -- leave them as IfaceFreeCoVar. This is super-important
2644 -- for debug printing.
2645 tidyToIfaceCo co = toIfaceCoercionX (mkVarSet free_tcvs) (tidyCo env co)
2646 where
2647 env = tidyFreeTyCoVars emptyTidyEnv free_tcvs
2648 free_tcvs = toposortTyVars $ tyCoVarsOfCoList co
2649
2650 ------------
2651 pprClassPred :: Class -> [Type] -> SDoc
2652 pprClassPred clas tys = pprTypeApp (classTyCon clas) tys
2653
2654 ------------
2655 pprTheta :: ThetaType -> SDoc
2656 pprTheta = pprIfaceContext TopPrec . map tidyToIfaceType
2657
2658 pprParendTheta :: ThetaType -> SDoc
2659 pprParendTheta = pprIfaceContext TyConPrec . map tidyToIfaceType
2660
2661 pprThetaArrowTy :: ThetaType -> SDoc
2662 pprThetaArrowTy = pprIfaceContextArr . map tidyToIfaceType
2663
2664 ------------------
2665 instance Outputable Type where
2666 ppr ty = pprType ty
2667
2668 instance Outputable TyLit where
2669 ppr = pprTyLit
2670
2671 ------------------
2672 pprSigmaType :: Type -> SDoc
2673 pprSigmaType = pprIfaceSigmaType ShowForAllWhen . tidyToIfaceType
2674
2675 pprForAll :: [TyVarBinder] -> SDoc
2676 pprForAll tvs = pprIfaceForAll (map toIfaceForAllBndr tvs)
2677
2678 -- | Print a user-level forall; see Note [When to print foralls]
2679 pprUserForAll :: [TyVarBinder] -> SDoc
2680 pprUserForAll = pprUserIfaceForAll . map toIfaceForAllBndr
2681
2682 pprTvBndrs :: [TyVarBinder] -> SDoc
2683 pprTvBndrs tvs = sep (map pprTvBndr tvs)
2684
2685 pprTvBndr :: TyVarBinder -> SDoc
2686 pprTvBndr = pprTyVar . binderVar
2687
2688 pprTyVars :: [TyVar] -> SDoc
2689 pprTyVars tvs = sep (map pprTyVar tvs)
2690
2691 pprTyVar :: TyVar -> SDoc
2692 -- Print a type variable binder with its kind (but not if *)
2693 -- Here we do not go via IfaceType, because the duplication with
2694 -- pprIfaceTvBndr is minimal, and the loss of uniques etc in
2695 -- debug printing is disastrous
2696 pprTyVar tv
2697 | isLiftedTypeKind kind = ppr tv
2698 | otherwise = parens (ppr tv <+> dcolon <+> ppr kind)
2699 where
2700 kind = tyVarKind tv
2701
2702 instance Outputable TyBinder where
2703 ppr (Anon ty) = text "[anon]" <+> ppr ty
2704 ppr (Named (TvBndr v Required)) = ppr v
2705 ppr (Named (TvBndr v Specified)) = char '@' <> ppr v
2706 ppr (Named (TvBndr v Inferred)) = braces (ppr v)
2707
2708 -----------------
2709 instance Outputable Coercion where -- defined here to avoid orphans
2710 ppr = pprCo
2711
2712 debugPprType :: Type -> SDoc
2713 -- ^ debugPprType is a simple pretty printer that prints a type
2714 -- without going through IfaceType. It does not format as prettily
2715 -- as the normal route, but it's much more direct, and that can
2716 -- be useful for debugging. E.g. with -dppr-debug it prints the
2717 -- kind on type-variable /occurrences/ which the normal route
2718 -- fundamentally cannot do.
2719 debugPprType ty = debug_ppr_ty TopPrec ty
2720
2721 debug_ppr_ty :: TyPrec -> Type -> SDoc
2722 debug_ppr_ty _ (LitTy l)
2723 = ppr l
2724
2725 debug_ppr_ty _ (TyVarTy tv)
2726 = ppr tv -- With -dppr-debug we get (tv :: kind)
2727
2728 debug_ppr_ty prec (FunTy arg res)
2729 = maybeParen prec FunPrec $
2730 sep [debug_ppr_ty FunPrec arg, arrow <+> debug_ppr_ty prec res]
2731
2732 debug_ppr_ty prec (TyConApp tc tys)
2733 | null tys = ppr tc
2734 | otherwise = maybeParen prec TyConPrec $
2735 hang (ppr tc) 2 (sep (map (debug_ppr_ty TyConPrec) tys))
2736
2737 debug_ppr_ty prec (AppTy t1 t2)
2738 = hang (debug_ppr_ty prec t1)
2739 2 (debug_ppr_ty TyConPrec t2)
2740
2741 debug_ppr_ty prec (CastTy ty co)
2742 = maybeParen prec TopPrec $
2743 hang (debug_ppr_ty TopPrec ty)
2744 2 (text "|>" <+> ppr co)
2745
2746 debug_ppr_ty _ (CoercionTy co)
2747 = parens (text "CO" <+> ppr co)
2748
2749 debug_ppr_ty prec ty@(ForAllTy {})
2750 | (tvs, body) <- split ty
2751 = maybeParen prec FunPrec $
2752 hang (text "forall" <+> fsep (map ppr tvs) <> dot)
2753 -- The (map ppr tvs) will print kind-annotated
2754 -- tvs, because we are (usually) in debug-style
2755 2 (ppr body)
2756 where
2757 split ty | ForAllTy tv ty' <- ty
2758 , (tvs, body) <- split ty'
2759 = (tv:tvs, body)
2760 | otherwise
2761 = ([], ty)
2762
2763 {-
2764 Note [When to print foralls]
2765 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2766 Mostly we want to print top-level foralls when (and only when) the user specifies
2767 -fprint-explicit-foralls. But when kind polymorphism is at work, that suppresses
2768 too much information; see Trac #9018.
2769
2770 So I'm trying out this rule: print explicit foralls if
2771 a) User specifies -fprint-explicit-foralls, or
2772 b) Any of the quantified type variables has a kind
2773 that mentions a kind variable
2774
2775 This catches common situations, such as a type siguature
2776 f :: m a
2777 which means
2778 f :: forall k. forall (m :: k->*) (a :: k). m a
2779 We really want to see both the "forall k" and the kind signatures
2780 on m and a. The latter comes from pprTvBndr.
2781
2782 Note [Infix type variables]
2783 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
2784 With TypeOperators you can say
2785
2786 f :: (a ~> b) -> b
2787
2788 and the (~>) is considered a type variable. However, the type
2789 pretty-printer in this module will just see (a ~> b) as
2790
2791 App (App (TyVarTy "~>") (TyVarTy "a")) (TyVarTy "b")
2792
2793 So it'll print the type in prefix form. To avoid confusion we must
2794 remember to parenthesise the operator, thus
2795
2796 (~>) a b -> b
2797
2798 See Trac #2766.
2799 -}
2800
2801 pprDataCons :: TyCon -> SDoc
2802 pprDataCons = sepWithVBars . fmap pprDataConWithArgs . tyConDataCons
2803 where
2804 sepWithVBars [] = empty
2805 sepWithVBars docs = sep (punctuate (space <> vbar) docs)
2806
2807 pprDataConWithArgs :: DataCon -> SDoc
2808 pprDataConWithArgs dc = sep [forAllDoc, thetaDoc, ppr dc <+> argsDoc]
2809 where
2810 (_univ_tvs, _ex_tvs, _eq_spec, theta, arg_tys, _res_ty) = dataConFullSig dc
2811 user_bndrs = dataConUserTyVarBinders dc
2812 forAllDoc = pprUserForAll user_bndrs
2813 thetaDoc = pprThetaArrowTy theta
2814 argsDoc = hsep (fmap pprParendType arg_tys)
2815
2816
2817 pprTypeApp :: TyCon -> [Type] -> SDoc
2818 pprTypeApp tc tys
2819 = pprIfaceTypeApp TopPrec (toIfaceTyCon tc)
2820 (toIfaceTcArgs tc tys)
2821 -- TODO: toIfaceTcArgs seems rather wasteful here
2822
2823 ------------------
2824 ppSuggestExplicitKinds :: SDoc
2825 -- Print a helpful suggstion about -fprint-explicit-kinds,
2826 -- if it is not already on
2827 ppSuggestExplicitKinds
2828 = sdocWithDynFlags $ \ dflags ->
2829 ppUnless (gopt Opt_PrintExplicitKinds dflags) $
2830 text "Use -fprint-explicit-kinds to see the kind arguments"
2831
2832 {-
2833 %************************************************************************
2834 %* *
2835 \subsection{TidyType}
2836 %* *
2837 %************************************************************************
2838 -}
2839
2840 -- | This tidies up a type for printing in an error message, or in
2841 -- an interface file.
2842 --
2843 -- It doesn't change the uniques at all, just the print names.
2844 tidyTyCoVarBndrs :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar])
2845 tidyTyCoVarBndrs (occ_env, subst) tvs
2846 = mapAccumL tidyTyCoVarBndr tidy_env' tvs
2847 where
2848 -- Seed the occ_env with clashes among the names, see
2849 -- Node [Tidying multiple names at once] in OccName
2850 -- Se still go through tidyTyCoVarBndr so that each kind variable is tidied
2851 -- with the correct tidy_env
2852 occs = map getHelpfulOccName tvs
2853 tidy_env' = (avoidClashesOccEnv occ_env occs, subst)
2854
2855 tidyTyCoVarBndr :: TidyEnv -> TyCoVar -> (TidyEnv, TyCoVar)
2856 tidyTyCoVarBndr tidy_env@(occ_env, subst) tyvar
2857 = case tidyOccName occ_env (getHelpfulOccName tyvar) of
2858 (occ_env', occ') -> ((occ_env', subst'), tyvar')
2859 where
2860 subst' = extendVarEnv subst tyvar tyvar'
2861 tyvar' = setTyVarKind (setTyVarName tyvar name') kind'
2862 kind' = tidyKind tidy_env (tyVarKind tyvar)
2863 name' = tidyNameOcc name occ'
2864 name = tyVarName tyvar
2865
2866 getHelpfulOccName :: TyCoVar -> OccName
2867 getHelpfulOccName tyvar = occ1
2868 where
2869 name = tyVarName tyvar
2870 occ = getOccName name
2871 -- A TcTyVar with a System Name is probably a unification variable;
2872 -- when we tidy them we give them a trailing "0" (or 1 etc)
2873 -- so that they don't take precedence for the un-modified name
2874 -- Plus, indicating a unification variable in this way is a
2875 -- helpful clue for users
2876 occ1 | isSystemName name
2877 , isTcTyVar tyvar
2878 = mkTyVarOcc (occNameString occ ++ "0")
2879 | otherwise
2880 = occ
2881
2882 tidyTyVarBinder :: TidyEnv -> TyVarBndr TyVar vis
2883 -> (TidyEnv, TyVarBndr TyVar vis)
2884 tidyTyVarBinder tidy_env (TvBndr tv vis)
2885 = (tidy_env', TvBndr tv' vis)
2886 where
2887 (tidy_env', tv') = tidyTyCoVarBndr tidy_env tv
2888
2889 tidyTyVarBinders :: TidyEnv -> [TyVarBndr TyVar vis]
2890 -> (TidyEnv, [TyVarBndr TyVar vis])
2891 tidyTyVarBinders = mapAccumL tidyTyVarBinder
2892
2893 ---------------
2894 tidyFreeTyCoVars :: TidyEnv -> [TyCoVar] -> TidyEnv
2895 -- ^ Add the free 'TyVar's to the env in tidy form,
2896 -- so that we can tidy the type they are free in
2897 tidyFreeTyCoVars (full_occ_env, var_env) tyvars
2898 = fst (tidyOpenTyCoVars (full_occ_env, var_env) tyvars)
2899
2900 ---------------
2901 tidyOpenTyCoVars :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar])
2902 tidyOpenTyCoVars env tyvars = mapAccumL tidyOpenTyCoVar env tyvars
2903
2904 ---------------
2905 tidyOpenTyCoVar :: TidyEnv -> TyCoVar -> (TidyEnv, TyCoVar)
2906 -- ^ Treat a new 'TyCoVar' as a binder, and give it a fresh tidy name
2907 -- using the environment if one has not already been allocated. See
2908 -- also 'tidyTyCoVarBndr'
2909 tidyOpenTyCoVar env@(_, subst) tyvar
2910 = case lookupVarEnv subst tyvar of
2911 Just tyvar' -> (env, tyvar') -- Already substituted
2912 Nothing ->
2913 let env' = tidyFreeTyCoVars env (tyCoVarsOfTypeList (tyVarKind tyvar))
2914 in tidyTyCoVarBndr env' tyvar -- Treat it as a binder
2915
2916 ---------------
2917 tidyTyVarOcc :: TidyEnv -> TyVar -> TyVar
2918 tidyTyVarOcc env@(_, subst) tv
2919 = case lookupVarEnv subst tv of
2920 Nothing -> updateTyVarKind (tidyType env) tv
2921 Just tv' -> tv'
2922
2923 ---------------
2924 tidyTypes :: TidyEnv -> [Type] -> [Type]
2925 tidyTypes env tys = map (tidyType env) tys
2926
2927 ---------------
2928 tidyType :: TidyEnv -> Type -> Type
2929 tidyType _ (LitTy n) = LitTy n
2930 tidyType env (TyVarTy tv) = TyVarTy (tidyTyVarOcc env tv)
2931 tidyType env (TyConApp tycon tys) = let args = tidyTypes env tys
2932 in args `seqList` TyConApp tycon args
2933 tidyType env (AppTy fun arg) = (AppTy $! (tidyType env fun)) $! (tidyType env arg)
2934 tidyType env (FunTy fun arg) = (FunTy $! (tidyType env fun)) $! (tidyType env arg)
2935 tidyType env (ty@(ForAllTy{})) = mkForAllTys' (zip tvs' vis) $! tidyType env' body_ty
2936 where
2937 (tvs, vis, body_ty) = splitForAllTys' ty
2938 (env', tvs') = tidyTyCoVarBndrs env tvs
2939 tidyType env (CastTy ty co) = (CastTy $! tidyType env ty) $! (tidyCo env co)
2940 tidyType env (CoercionTy co) = CoercionTy $! (tidyCo env co)
2941
2942
2943 -- The following two functions differ from mkForAllTys and splitForAllTys in that
2944 -- they expect/preserve the ArgFlag argument. Thes belong to types/Type.hs, but
2945 -- how should they be named?
2946 mkForAllTys' :: [(TyVar, ArgFlag)] -> Type -> Type
2947 mkForAllTys' tvvs ty = foldr strictMkForAllTy ty tvvs
2948 where
2949 strictMkForAllTy (tv,vis) ty = (ForAllTy $! ((TvBndr $! tv) $! vis)) $! ty
2950
2951 splitForAllTys' :: Type -> ([TyVar], [ArgFlag], Type)
2952 splitForAllTys' ty = go ty [] []
2953 where
2954 go (ForAllTy (TvBndr tv vis) ty) tvs viss = go ty (tv:tvs) (vis:viss)
2955 go ty tvs viss = (reverse tvs, reverse viss, ty)
2956
2957
2958 ---------------
2959 -- | Grabs the free type variables, tidies them
2960 -- and then uses 'tidyType' to work over the type itself
2961 tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
2962 tidyOpenTypes env tys
2963 = (env', tidyTypes (trimmed_occ_env, var_env) tys)
2964 where
2965 (env'@(_, var_env), tvs') = tidyOpenTyCoVars env $
2966 tyCoVarsOfTypesWellScoped tys
2967 trimmed_occ_env = initTidyOccEnv (map getOccName tvs')
2968 -- The idea here was that we restrict the new TidyEnv to the
2969 -- _free_ vars of the types, so that we don't gratuitously rename
2970 -- the _bound_ variables of the types.
2971
2972 ---------------
2973 tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
2974 tidyOpenType env ty = let (env', [ty']) = tidyOpenTypes env [ty] in
2975 (env', ty')
2976
2977 ---------------
2978 -- | Calls 'tidyType' on a top-level type (i.e. with an empty tidying environment)
2979 tidyTopType :: Type -> Type
2980 tidyTopType ty = tidyType emptyTidyEnv ty
2981
2982 ---------------
2983 tidyOpenKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
2984 tidyOpenKind = tidyOpenType
2985
2986 tidyKind :: TidyEnv -> Kind -> Kind
2987 tidyKind = tidyType
2988
2989 ----------------
2990 tidyCo :: TidyEnv -> Coercion -> Coercion
2991 tidyCo env@(_, subst) co
2992 = go co
2993 where
2994 go (Refl r ty) = Refl r (tidyType env ty)
2995 go (TyConAppCo r tc cos) = let args = map go cos
2996 in args `seqList` TyConAppCo r tc args
2997 go (AppCo co1 co2) = (AppCo $! go co1) $! go co2
2998 go (ForAllCo tv h co) = ((ForAllCo $! tvp) $! (go h)) $! (tidyCo envp co)
2999 where (envp, tvp) = tidyTyCoVarBndr env tv
3000 -- the case above duplicates a bit of work in tidying h and the kind
3001 -- of tv. But the alternative is to use coercionKind, which seems worse.
3002 go (FunCo r co1 co2) = (FunCo r $! go co1) $! go co2
3003 go (CoVarCo cv) = case lookupVarEnv subst cv of
3004 Nothing -> CoVarCo cv
3005 Just cv' -> CoVarCo cv'
3006 go (HoleCo h) = HoleCo h
3007 go (AxiomInstCo con ind cos) = let args = map go cos
3008 in args `seqList` AxiomInstCo con ind args
3009 go (UnivCo p r t1 t2) = (((UnivCo $! (go_prov p)) $! r) $!
3010 tidyType env t1) $! tidyType env t2
3011 go (SymCo co) = SymCo $! go co
3012 go (TransCo co1 co2) = (TransCo $! go co1) $! go co2
3013 go (NthCo d co) = NthCo d $! go co
3014 go (LRCo lr co) = LRCo lr $! go co
3015 go (InstCo co ty) = (InstCo $! go co) $! go ty
3016 go (CoherenceCo co1 co2) = (CoherenceCo $! go co1) $! go co2
3017 go (KindCo co) = KindCo $! go co
3018 go (SubCo co) = SubCo $! go co
3019 go (AxiomRuleCo ax cos) = let cos1 = tidyCos env cos
3020 in cos1 `seqList` AxiomRuleCo ax cos1
3021
3022 go_prov UnsafeCoerceProv = UnsafeCoerceProv
3023 go_prov (PhantomProv co) = PhantomProv (go co)
3024 go_prov (ProofIrrelProv co) = ProofIrrelProv (go co)
3025 go_prov p@(PluginProv _) = p
3026
3027 tidyCos :: TidyEnv -> [Coercion] -> [Coercion]
3028 tidyCos env = map (tidyCo env)
3029
3030
3031 {- *********************************************************************
3032 * *
3033 typeSize, coercionSize
3034 * *
3035 ********************************************************************* -}
3036
3037 -- NB: We put typeSize/coercionSize here because they are mutually
3038 -- recursive, and have the CPR property. If we have mutual
3039 -- recursion across a hi-boot file, we don't get the CPR property
3040 -- and these functions allocate a tremendous amount of rubbish.
3041 -- It's not critical (because typeSize is really only used in
3042 -- debug mode, but I tripped over an example (T5642) in which
3043 -- typeSize was one of the biggest single allocators in all of GHC.
3044 -- And it's easy to fix, so I did.
3045
3046 -- NB: typeSize does not respect `eqType`, in that two types that
3047 -- are `eqType` may return different sizes. This is OK, because this
3048 -- function is used only in reporting, not decision-making.
3049
3050 typeSize :: Type -> Int
3051 typeSize (LitTy {}) = 1
3052 typeSize (TyVarTy {}) = 1
3053 typeSize (AppTy t1 t2) = typeSize t1 + typeSize t2
3054 typeSize (FunTy t1 t2) = typeSize t1 + typeSize t2
3055 typeSize (ForAllTy (TvBndr tv _) t) = typeSize (tyVarKind tv) + typeSize t
3056 typeSize (TyConApp _ ts) = 1 + sum (map typeSize ts)
3057 typeSize (CastTy ty co) = typeSize ty + coercionSize co
3058 typeSize (CoercionTy co) = coercionSize co
3059
3060 coercionSize :: Coercion -> Int
3061 coercionSize (Refl _ ty) = typeSize ty
3062 coercionSize (TyConAppCo _ _ args) = 1 + sum (map coercionSize args)
3063 coercionSize (AppCo co arg) = coercionSize co + coercionSize arg
3064 coercionSize (ForAllCo _ h co) = 1 + coercionSize co + coercionSize h
3065 coercionSize (FunCo _ co1 co2) = 1 + coercionSize co1 + coercionSize co2
3066 coercionSize (CoVarCo _) = 1
3067 coercionSize (HoleCo _) = 1
3068 coercionSize (AxiomInstCo _ _ args) = 1 + sum (map coercionSize args)
3069 coercionSize (UnivCo p _ t1 t2) = 1 + provSize p + typeSize t1 + typeSize t2
3070 coercionSize (SymCo co) = 1 + coercionSize co
3071 coercionSize (TransCo co1 co2) = 1 + coercionSize co1 + coercionSize co2
3072 coercionSize (NthCo _ co) = 1 + coercionSize co
3073 coercionSize (LRCo _ co) = 1 + coercionSize co
3074 coercionSize (InstCo co arg) = 1 + coercionSize co + coercionSize arg
3075 coercionSize (CoherenceCo c1 c2) = 1 + coercionSize c1 + coercionSize c2
3076 coercionSize (KindCo co) = 1 + coercionSize co
3077 coercionSize (SubCo co) = 1 + coercionSize co
3078 coercionSize (AxiomRuleCo _ cs) = 1 + sum (map coercionSize cs)
3079
3080 provSize :: UnivCoProvenance -> Int
3081 provSize UnsafeCoerceProv = 1
3082 provSize (PhantomProv co) = 1 + coercionSize co
3083 provSize (ProofIrrelProv co) = 1 + coercionSize co
3084 provSize (PluginProv _) = 1