2 % (c) The University of Glasgow 2006
6 {-# OPTIONS -fno-warn-incomplete-patterns #-}
7 -- The above warning supression flag is a temporary kludge.
8 -- While working on this module you are encouraged to remove it and fix
9 -- any warnings in the module. See
10 -- http://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#Warnings
13 -- | Module for type coercions, as used in System FC. See 'CoreSyn.Expr' for
14 -- more on System FC and how coercions fit into it.
16 -- Coercions are represented as types, and their kinds tell what types the
17 -- coercion works on. The coercion kind constructor is a special TyCon that must always be saturated, like so:
19 -- > typeKind (symCoercion type) :: TyConApp CoercionTyCon{...} [type, type]
24 mkCoKind, mkReflCoKind, splitCoercionKind_maybe, splitCoercionKind,
25 coercionKind, coercionKinds, coercionKindPredTy,
27 -- ** Equality predicates
28 isEqPred, mkEqPred, getEqPredTys, isEqPredTy,
30 -- ** Coercion transformations
32 mkSymCoercion, mkTransCoercion,
33 mkLeftCoercion, mkRightCoercion, mkRightCoercions,
34 mkInstCoercion, mkAppCoercion,
35 mkForAllCoercion, mkFunCoercion, mkInstsCoercion, mkUnsafeCoercion,
36 mkNewTypeCoercion, mkFamInstCoercion, mkAppsCoercion,
38 splitNewTypeRepCo_maybe, instNewTyCon_maybe, decomposeCo,
40 unsafeCoercionTyCon, symCoercionTyCon,
41 transCoercionTyCon, leftCoercionTyCon,
42 rightCoercionTyCon, instCoercionTyCon, -- needed by TysWiredIn
51 mkTyConAppCoI, mkAppTyCoI, mkFunTyCoI,
54 mkClassPPredCoI, mkIParamPredCoI, mkEqPredCoI
58 #include "HsVersions.h"
74 -- | A 'Coercion' represents a 'Type' something should be coerced to.
77 -- | A 'CoercionKind' is always of form @ty1 ~ ty2@ and indicates the
78 -- types that a 'Coercion' will work on.
79 type CoercionKind = Kind
81 ------------------------------
83 -- | This breaks a 'Coercion' with 'CoercionKind' @T A B C ~ T D E F@ into
84 -- a list of 'Coercion's of kinds @A ~ D@, @B ~ E@ and @E ~ F@. Hence:
86 -- > decomposeCo 3 c = [right (left (left c)), right (left c), right c]
87 decomposeCo :: Arity -> Coercion -> [Coercion]
92 go n co cos = go (n-1) (mkLeftCoercion co)
93 (mkRightCoercion co : cos)
95 ------------------------------
97 -------------------------------------------------------
98 -- and some coercion kind stuff
100 -- | Tests whether a type is just a type equality predicate
101 isEqPredTy :: Type -> Bool
102 isEqPredTy (PredTy pred) = isEqPred pred
105 -- | Creates a type equality predicate
106 mkEqPred :: (Type, Type) -> PredType
107 mkEqPred (ty1, ty2) = EqPred ty1 ty2
109 -- | Splits apart a type equality predicate, if the supplied 'PredType' is one.
111 getEqPredTys :: PredType -> (Type,Type)
112 getEqPredTys (EqPred ty1 ty2) = (ty1, ty2)
113 getEqPredTys other = pprPanic "getEqPredTys" (ppr other)
115 -- | Makes a 'CoercionKind' from two types: the types whose equality is proven by the relevant 'Coercion'
116 mkCoKind :: Type -> Type -> CoercionKind
117 mkCoKind ty1 ty2 = PredTy (EqPred ty1 ty2)
119 -- | Create a reflexive 'CoercionKind' that asserts that a type can be coerced to itself
120 mkReflCoKind :: Type -> CoercionKind
121 mkReflCoKind ty = mkCoKind ty ty
123 -- | Take a 'CoercionKind' apart into the two types it relates: see also 'mkCoKind'.
124 -- Panics if the argument is not a valid 'CoercionKind'
125 splitCoercionKind :: CoercionKind -> (Type, Type)
126 splitCoercionKind co | Just co' <- kindView co = splitCoercionKind co'
127 splitCoercionKind (PredTy (EqPred ty1 ty2)) = (ty1, ty2)
129 -- | Take a 'CoercionKind' apart into the two types it relates, if possible. See also 'splitCoercionKind'
130 splitCoercionKind_maybe :: Kind -> Maybe (Type, Type)
131 splitCoercionKind_maybe co | Just co' <- kindView co = splitCoercionKind_maybe co'
132 splitCoercionKind_maybe (PredTy (EqPred ty1 ty2)) = Just (ty1, ty2)
133 splitCoercionKind_maybe _ = Nothing
135 -- | If it is the case that
139 -- i.e. the kind of @c@ is a 'CoercionKind' relating @t1@ and @t2@, then @coercionKind c = (t1, t2)@.
140 -- See also 'coercionKindPredTy'
141 coercionKind :: Coercion -> (Type, Type)
142 coercionKind ty@(TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind a)
143 | otherwise = (ty, ty)
144 coercionKind (AppTy ty1 ty2)
145 = let (t1, t2) = coercionKind ty1
146 (s1, s2) = coercionKind ty2 in
147 (mkAppTy t1 s1, mkAppTy t2 s2)
148 coercionKind (TyConApp tc args)
149 | Just (ar, rule) <- isCoercionTyCon_maybe tc
150 -- CoercionTyCons carry their kinding rule, so we use it here
151 = ASSERT( length args >= ar ) -- Always saturated
152 let (ty1,ty2) = rule (take ar args) -- Apply the rule to the right number of args
153 (tys1, tys2) = coercionKinds (drop ar args)
154 in (mkAppTys ty1 tys1, mkAppTys ty2 tys2)
157 = let (lArgs, rArgs) = coercionKinds args in
158 (TyConApp tc lArgs, TyConApp tc rArgs)
159 coercionKind (FunTy ty1 ty2)
160 = let (t1, t2) = coercionKind ty1
161 (s1, s2) = coercionKind ty2 in
162 (mkFunTy t1 s1, mkFunTy t2 s2)
163 coercionKind (ForAllTy tv ty)
164 = let (ty1, ty2) = coercionKind ty in
165 (ForAllTy tv ty1, ForAllTy tv ty2)
166 coercionKind (PredTy (EqPred c1 c2))
167 = let k1 = coercionKindPredTy c1
168 k2 = coercionKindPredTy c2 in
170 coercionKind (PredTy (ClassP cl args))
171 = let (lArgs, rArgs) = coercionKinds args in
172 (PredTy (ClassP cl lArgs), PredTy (ClassP cl rArgs))
173 coercionKind (PredTy (IParam name ty))
174 = let (ty1, ty2) = coercionKind ty in
175 (PredTy (IParam name ty1), PredTy (IParam name ty2))
177 -- | Recover the 'CoercionKind' corresponding to a particular 'Coerceion'. See also 'coercionKind'
179 coercionKindPredTy :: Coercion -> CoercionKind
180 coercionKindPredTy c = let (t1, t2) = coercionKind c in mkCoKind t1 t2
182 -- | Apply 'coercionKind' to multiple 'Coercion's
183 coercionKinds :: [Coercion] -> ([Type], [Type])
184 coercionKinds tys = unzip $ map coercionKind tys
186 -------------------------------------
187 -- Coercion kind and type mk's
188 -- (make saturated TyConApp CoercionTyCon{...} args)
190 -- | Make a coercion from the specified coercion 'TyCon' and the 'Type' arguments to
191 -- that coercion. Try to use the @mk*Coercion@ family of functions instead of using this function
193 mkCoercion :: TyCon -> [Type] -> Coercion
194 mkCoercion coCon args = ASSERT( tyConArity coCon == length args )
197 -- | Apply a 'Coercion' to another 'Coercion', which is presumably a 'Coercion' constructor of some
199 mkAppCoercion :: Coercion -> Coercion -> Coercion
200 mkAppCoercion co1 co2 = mkAppTy co1 co2
202 -- | Applies multiple 'Coercion's to another 'Coercion', from left to right.
203 -- See also 'mkAppCoercion'
204 mkAppsCoercion :: Coercion -> [Coercion] -> Coercion
205 mkAppsCoercion co1 tys = foldl mkAppTy co1 tys
207 -- | Make a 'Coercion' which binds a variable within an inner 'Coercion'
208 mkForAllCoercion :: Var -> Coercion -> Coercion
209 -- note that a TyVar should be used here, not a CoVar (nor a TcTyVar)
210 mkForAllCoercion tv co = ASSERT ( isTyVar tv ) mkForAllTy tv co
212 -- | Make a function 'Coercion' between two other 'Coercion's
213 mkFunCoercion :: Coercion -> Coercion -> Coercion
214 mkFunCoercion co1 co2 = mkFunTy co1 co2
217 -------------------------------
219 mkSymCoercion :: Coercion -> Coercion
220 -- ^ Create a symmetric version of the given 'Coercion' that asserts equality between
221 -- the same types but in the other "direction", so a kind of @t1 ~ t2@ becomes the
224 -- This function attempts to simplify the generated 'Coercion' by removing redundant applications
225 -- of @sym@. This is done by pushing this new @sym@ down into the 'Coercion' and exploiting the fact that
226 -- @sym (sym co) = co@.
228 | Just co' <- coreView co = mkSymCoercion co'
230 mkSymCoercion (ForAllTy tv ty) = ForAllTy tv (mkSymCoercion ty)
231 mkSymCoercion (AppTy co1 co2) = AppTy (mkSymCoercion co1) (mkSymCoercion co2)
232 mkSymCoercion (FunTy co1 co2) = FunTy (mkSymCoercion co1) (mkSymCoercion co2)
234 mkSymCoercion (TyConApp tc cos)
235 | not (isCoercionTyCon tc) = mkTyConApp tc (map mkSymCoercion cos)
237 mkSymCoercion (TyConApp tc [co])
238 | tc `hasKey` symCoercionTyConKey = co -- sym (sym co) --> co
239 | tc `hasKey` leftCoercionTyConKey = mkLeftCoercion (mkSymCoercion co)
240 | tc `hasKey` rightCoercionTyConKey = mkRightCoercion (mkSymCoercion co)
242 mkSymCoercion (TyConApp tc [co1,co2])
243 | tc `hasKey` transCoercionTyConKey
244 -- sym (co1 `trans` co2) --> (sym co2) `trans (sym co2)
245 -- Note reversal of arguments!
246 = mkTransCoercion (mkSymCoercion co2) (mkSymCoercion co1)
248 | tc `hasKey` instCoercionTyConKey
249 -- sym (co @ ty) --> (sym co) @ ty
250 -- Note: sym is not applied to 'ty'
251 = mkInstCoercion (mkSymCoercion co1) co2
253 mkSymCoercion (TyConApp tc cos) -- Other coercion tycons, such as those
254 = mkCoercion symCoercionTyCon [TyConApp tc cos] -- arising from newtypes
256 mkSymCoercion (TyVarTy tv)
257 | isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv]
258 | otherwise = TyVarTy tv -- Reflexive
260 -------------------------------
261 -- ToDo: we should be cleverer about transitivity
263 mkTransCoercion :: Coercion -> Coercion -> Coercion
264 -- ^ Create a new 'Coercion' by exploiting transitivity on the two given 'Coercion's.
266 -- This function attempts to simplify the generated 'Coercion' by exploiting the fact that
267 -- @sym g `trans` g = id@.
268 mkTransCoercion g1 g2 -- sym g `trans` g = id
269 | (t1,_) <- coercionKind g1
270 , (_,t2) <- coercionKind g2
275 = mkCoercion transCoercionTyCon [g1, g2]
278 -------------------------------
279 -- Smart constructors for left and right
281 mkLeftCoercion :: Coercion -> Coercion
282 -- ^ From an application 'Coercion' build a 'Coercion' that asserts the equality of
283 -- the "functions" on either side of the type equality. So if @c@ has kind @f x ~ g y@ then:
285 -- > mkLeftCoercion c :: f ~ g
287 | Just (co', _) <- splitAppCoercion_maybe co = co'
288 | otherwise = mkCoercion leftCoercionTyCon [co]
290 mkRightCoercion :: Coercion -> Coercion
291 -- ^ From an application 'Coercion' build a 'Coercion' that asserts the equality of
292 -- the "arguments" on either side of the type equality. So if @c@ has kind @f x ~ g y@ then:
294 -- > mkLeftCoercion c :: x ~ y
296 | Just (_, co2) <- splitAppCoercion_maybe co = co2
297 | otherwise = mkCoercion rightCoercionTyCon [co]
299 mkRightCoercions :: Int -> Coercion -> [Coercion]
300 -- ^ As 'mkRightCoercion', but finds the 'Coercion's available on the right side of @n@
301 -- nested application 'Coercion's, manufacturing new left or right cooercions as necessary
302 -- if suffficiently many are not directly available.
303 mkRightCoercions n co
308 = case splitAppCoercion_maybe co of
309 Just (co1,co2) -> go (n-1) co1 (co2:acc)
310 Nothing -> go (n-1) (mkCoercion leftCoercionTyCon [co]) (mkCoercion rightCoercionTyCon [co]:acc)
315 mkInstCoercion :: Coercion -> Type -> Coercion
316 -- ^ Instantiates a 'Coercion' with a 'Type' argument. If possible, it immediately performs
317 -- the resulting beta-reduction, otherwise it creates a suspended instantiation.
319 | Just (tv,co') <- splitForAllTy_maybe co
320 = substTyWith [tv] [ty] co' -- (forall a.co) @ ty --> co[ty/a]
322 = mkCoercion instCoercionTyCon [co, ty]
324 mkInstsCoercion :: Coercion -> [Type] -> Coercion
325 -- ^ As 'mkInstCoercion', but instantiates the coercion with a number of type arguments, left-to-right
326 mkInstsCoercion co tys = foldl mkInstCoercion co tys
329 splitSymCoercion_maybe :: Coercion -> Maybe Coercion
330 splitSymCoercion_maybe (TyConApp tc [co]) =
331 if tc `hasKey` symCoercionTyConKey
334 splitSymCoercion_maybe co = Nothing
337 splitAppCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
338 -- ^ Splits a coercion application, being careful *not* to split @left c@ etc.
339 -- This is because those are really syntactic constructs, not applications
340 splitAppCoercion_maybe co | Just co' <- coreView co = splitAppCoercion_maybe co'
341 splitAppCoercion_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
342 splitAppCoercion_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
343 splitAppCoercion_maybe (TyConApp tc tys)
344 | not (isCoercionTyCon tc)
345 = case snocView tys of
346 Just (tys', ty') -> Just (TyConApp tc tys', ty')
348 splitAppCoercion_maybe _ = Nothing
351 splitTransCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
352 splitTransCoercion_maybe (TyConApp tc [ty1, ty2])
353 = if tc `hasKey` transCoercionTyConKey then
357 splitTransCoercion_maybe other = Nothing
359 splitInstCoercion_maybe :: Coercion -> Maybe (Coercion, Type)
360 splitInstCoercion_maybe (TyConApp tc [ty1, ty2])
361 = if tc `hasKey` instCoercionTyConKey then
365 splitInstCoercion_maybe other = Nothing
367 splitLeftCoercion_maybe :: Coercion -> Maybe Coercion
368 splitLeftCoercion_maybe (TyConApp tc [co])
369 = if tc `hasKey` leftCoercionTyConKey then
373 splitLeftCoercion_maybe other = Nothing
375 splitRightCoercion_maybe :: Coercion -> Maybe Coercion
376 splitRightCoercion_maybe (TyConApp tc [co])
377 = if tc `hasKey` rightCoercionTyConKey then
381 splitRightCoercion_maybe other = Nothing
384 -- | Manufacture a coercion from this air. Needless to say, this is not usually safe,
385 -- but it is used when we know we are dealing with bottom, which is one case in which
386 -- it is safe. This is also used implement the @unsafeCoerce#@ primitive.
387 mkUnsafeCoercion :: Type -> Type -> Coercion
388 mkUnsafeCoercion ty1 ty2
389 = mkCoercion unsafeCoercionTyCon [ty1, ty2]
392 -- See note [Newtype coercions] in TyCon
394 -- | Create a coercion suitable for the given 'TyCon'. The 'Name' should be that of a
395 -- new coercion 'TyCon', the 'TyVar's the arguments expected by the @newtype@ and the
396 -- type the appropriate right hand side of the @newtype@, with the free variables
397 -- a subset of those 'TyVar's.
398 mkNewTypeCoercion :: Name -> TyCon -> [TyVar] -> Type -> TyCon
399 mkNewTypeCoercion name tycon tvs rhs_ty
400 = mkCoercionTyCon name co_con_arity rule
402 co_con_arity = length tvs
404 rule args = ASSERT( co_con_arity == length args )
405 (TyConApp tycon args, substTyWith tvs args rhs_ty)
407 -- | Create a coercion identifying a @data@, @newtype@ or @type@ representation type
408 -- and its family instance. It has the form @Co tvs :: F ts ~ R tvs@, where @Co@ is
409 -- the coercion tycon built here, @F@ the family tycon and @R@ the (derived)
410 -- representation tycon.
411 mkFamInstCoercion :: Name -- ^ Unique name for the coercion tycon
412 -> [TyVar] -- ^ Type parameters of the coercion (@tvs@)
413 -> TyCon -- ^ Family tycon (@F@)
414 -> [Type] -- ^ Type instance (@ts@)
415 -> TyCon -- ^ Representation tycon (@R@)
416 -> TyCon -- ^ Coercion tycon (@Co@)
417 mkFamInstCoercion name tvs family instTys rep_tycon
418 = mkCoercionTyCon name coArity rule
421 rule args = (substTyWith tvs args $ -- with sigma = [tys/tvs],
422 TyConApp family instTys, -- sigma (F ts)
423 TyConApp rep_tycon args) -- ~ R tys
425 --------------------------------------
426 -- Coercion Type Constructors...
428 -- Example. The coercion ((sym c) (sym d) (sym e))
429 -- will be represented by (TyConApp sym [c, sym d, sym e])
433 -- then ((sym c) (sym d) (sym e)) :: (p1 p2 p3)=(q1 q2 q3)
435 -- | Coercion type constructors: avoid using these directly and instead use the @mk*Coercion@ and @split*Coercion@ family
436 -- of functions if possible.
437 symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, rightCoercionTyCon, instCoercionTyCon, unsafeCoercionTyCon :: TyCon
438 -- Each coercion TyCon is built with the special CoercionTyCon record and
439 -- carries its own kinding rule. Such CoercionTyCons must be fully applied
440 -- by any TyConApp in which they are applied, however they may also be over
441 -- applied (see example above) and the kinding function must deal with this.
443 mkCoercionTyCon symCoercionTyConName 1 flipCoercionKindOf
445 flipCoercionKindOf (co:rest) = ASSERT( null rest ) (ty2, ty1)
447 (ty1, ty2) = coercionKind co
450 mkCoercionTyCon transCoercionTyConName 2 composeCoercionKindsOf
452 composeCoercionKindsOf (co1:co2:rest)
453 = ASSERT( null rest )
454 WARN( not (r1 `coreEqType` a2),
455 text "Strange! Type mismatch in trans coercion, probably a bug"
457 ppr r1 <+> text "=/=" <+> ppr a2)
460 (a1, r1) = coercionKind co1
461 (a2, r2) = coercionKind co2
464 mkCoercionTyCon leftCoercionTyConName 1 leftProjectCoercionKindOf
466 leftProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2)
468 (ty1,ty2) = fst (splitCoercionKindOf co)
471 mkCoercionTyCon rightCoercionTyConName 1 rightProjectCoercionKindOf
473 rightProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2)
475 (ty1,ty2) = snd (splitCoercionKindOf co)
477 splitCoercionKindOf :: Type -> ((Type,Type), (Type,Type))
478 -- Helper for left and right. Finds coercion kind of its input and
479 -- returns the left and right projections of the coercion...
481 -- if c :: t1 s1 ~ t2 s2 then splitCoercionKindOf c = ((t1, t2), (s1, s2))
482 splitCoercionKindOf co
483 | Just (ty1, ty2) <- splitCoercionKind_maybe (coercionKindPredTy co)
484 , Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1
485 , Just (ty_fun2, ty_arg2) <- splitAppTy_maybe ty2
486 = ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2))
487 splitCoercionKindOf co
488 = pprPanic "Coercion.splitCoercionKindOf"
489 (ppr co $$ ppr (coercionKindPredTy co))
492 = mkCoercionTyCon instCoercionTyConName 2 instCoercionKind
495 let Just (tv, ty) = splitForAllTy_maybe t in
496 substTyWith [tv] [s] ty
498 instCoercionKind (co1:ty:rest) = ASSERT( null rest )
499 (instantiateCo t1 ty, instantiateCo t2 ty)
500 where (t1, t2) = coercionKind co1
503 = mkCoercionTyCon unsafeCoercionTyConName 2 unsafeCoercionKind
505 unsafeCoercionKind (ty1:ty2:rest) = ASSERT( null rest ) (ty1,ty2)
507 --------------------------------------
508 -- ...and their names
510 mkCoConName :: FastString -> Unique -> TyCon -> Name
511 mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkTcOccFS occ)
512 key (ATyCon coCon) BuiltInSyntax
514 transCoercionTyConName, symCoercionTyConName, leftCoercionTyConName, rightCoercionTyConName, instCoercionTyConName, unsafeCoercionTyConName :: Name
516 transCoercionTyConName = mkCoConName (fsLit "trans") transCoercionTyConKey transCoercionTyCon
517 symCoercionTyConName = mkCoConName (fsLit "sym") symCoercionTyConKey symCoercionTyCon
518 leftCoercionTyConName = mkCoConName (fsLit "left") leftCoercionTyConKey leftCoercionTyCon
519 rightCoercionTyConName = mkCoConName (fsLit "right") rightCoercionTyConKey rightCoercionTyCon
520 instCoercionTyConName = mkCoConName (fsLit "inst") instCoercionTyConKey instCoercionTyCon
521 unsafeCoercionTyConName = mkCoConName (fsLit "CoUnsafe") unsafeCoercionTyConKey unsafeCoercionTyCon
525 instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, CoercionI)
526 -- ^ If @co :: T ts ~ rep_ty@ then:
528 -- > instNewTyCon_maybe T ts = Just (rep_ty, co)
529 instNewTyCon_maybe tc tys
530 | Just (tvs, ty, mb_co_tc) <- unwrapNewTyCon_maybe tc
531 = ASSERT( tys `lengthIs` tyConArity tc )
532 Just (substTyWith tvs tys ty,
535 Just co_tc -> ACo (mkTyConApp co_tc tys))
539 -- this is here to avoid module loops
540 splitNewTypeRepCo_maybe :: Type -> Maybe (Type, Coercion)
541 -- ^ Sometimes we want to look through a @newtype@ and get its associated coercion.
542 -- This function only strips *one layer* of @newtype@ off, so the caller will usually call
543 -- itself recursively. Furthermore, this function should only be applied to types of kind @*@,
544 -- hence the newtype is always saturated. If @co : ty ~ ty'@ then:
546 -- > splitNewTypeRepCo_maybe ty = Just (ty', co)
548 -- The function returns @Nothing@ for non-@newtypes@ or fully-transparent @newtype@s.
549 splitNewTypeRepCo_maybe ty
550 | Just ty' <- coreView ty = splitNewTypeRepCo_maybe ty'
551 splitNewTypeRepCo_maybe (TyConApp tc tys)
552 | Just (ty', coi) <- instNewTyCon_maybe tc tys
554 ACo co -> Just (ty', co)
555 IdCo -> panic "splitNewTypeRepCo_maybe"
556 -- This case handled by coreView
557 splitNewTypeRepCo_maybe _
560 -- | Determines syntactic equality of coercions
561 coreEqCoercion :: Coercion -> Coercion -> Bool
562 coreEqCoercion = coreEqType
566 --------------------------------------
567 -- CoercionI smart constructors
568 -- lifted smart constructors of ordinary coercions
571 -- | 'CoercionI' represents a /lifted/ ordinary 'Coercion', in that it
572 -- can represent either one of:
574 -- 1. A proper 'Coercion'
576 -- 2. The identity coercion
577 data CoercionI = IdCo | ACo Coercion
579 instance Outputable CoercionI where
580 ppr IdCo = ptext (sLit "IdCo")
581 ppr (ACo co) = ppr co
583 isIdentityCoercion :: CoercionI -> Bool
584 isIdentityCoercion IdCo = True
585 isIdentityCoercion _ = False
587 -- | Tests whether all the given 'CoercionI's represent the identity coercion
588 allIdCos :: [CoercionI] -> Bool
589 allIdCos = all isIdentityCoercion
591 -- | For each 'CoercionI' in the input list, return either the 'Coercion' it
592 -- contains or the corresponding 'Type' from the other list
593 zipCoArgs :: [CoercionI] -> [Type] -> [Coercion]
594 zipCoArgs cois tys = zipWith fromCoI cois tys
596 -- | Return either the 'Coercion' contained within the 'CoercionI' or the given
597 -- 'Type' if the 'CoercionI' is the identity 'Coercion'
598 fromCoI :: CoercionI -> Type -> Type
599 fromCoI IdCo ty = ty -- Identity coercion represented
600 fromCoI (ACo co) _ = co -- by the type itself
602 -- | Smart constructor for @sym@ on 'CoercionI', see also 'mkSymCoercion'
603 mkSymCoI :: CoercionI -> CoercionI
605 mkSymCoI (ACo co) = ACo $ mkCoercion symCoercionTyCon [co]
606 -- the smart constructor
607 -- is too smart with tyvars
609 -- | Smart constructor for @trans@ on 'CoercionI', see also 'mkTransCoercion'
610 mkTransCoI :: CoercionI -> CoercionI -> CoercionI
611 mkTransCoI IdCo aco = aco
612 mkTransCoI aco IdCo = aco
613 mkTransCoI (ACo co1) (ACo co2) = ACo $ mkTransCoercion co1 co2
615 -- | Smart constructor for type constructor application on 'CoercionI', see also 'mkAppCoercion'
616 mkTyConAppCoI :: TyCon -> [Type] -> [CoercionI] -> CoercionI
617 mkTyConAppCoI tyCon tys cois
618 | allIdCos cois = IdCo
619 | otherwise = ACo (TyConApp tyCon (zipCoArgs cois tys))
621 -- | Smart constructor for honest-to-god 'Coercion' application on 'CoercionI', see also 'mkAppCoercion'
622 mkAppTyCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI
623 mkAppTyCoI _ IdCo _ IdCo = IdCo
624 mkAppTyCoI ty1 coi1 ty2 coi2 =
625 ACo $ AppTy (fromCoI coi1 ty1) (fromCoI coi2 ty2)
627 -- | Smart constructor for function-'Coercion's on 'CoercionI', see also 'mkFunCoercion'
628 mkFunTyCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI
629 mkFunTyCoI _ IdCo _ IdCo = IdCo
630 mkFunTyCoI ty1 coi1 ty2 coi2 =
631 ACo $ FunTy (fromCoI coi1 ty1) (fromCoI coi2 ty2)
633 -- | Smart constructor for quantified 'Coercion's on 'CoercionI', see also 'mkForAllCoercion'
634 mkForAllTyCoI :: TyVar -> CoercionI -> CoercionI
635 mkForAllTyCoI _ IdCo = IdCo
636 mkForAllTyCoI tv (ACo co) = ACo $ ForAllTy tv co
638 -- | Extract a 'Coercion' from a 'CoercionI' if it represents one. If it is the identity coercion,
640 fromACo :: CoercionI -> Coercion
641 fromACo (ACo co) = co
643 -- | Smart constructor for class 'Coercion's on 'CoercionI'. Satisfies:
645 -- > mkClassPPredCoI cls tys cois :: PredTy (cls tys) ~ PredTy (cls (tys `cast` cois))
646 mkClassPPredCoI :: Class -> [Type] -> [CoercionI] -> CoercionI
647 mkClassPPredCoI cls tys cois
648 | allIdCos cois = IdCo
649 | otherwise = ACo $ PredTy $ ClassP cls (zipCoArgs cois tys)
651 -- | Smart constructor for implicit parameter 'Coercion's on 'CoercionI'. Similar to 'mkClassPPredCoI'
652 mkIParamPredCoI :: (IPName Name) -> CoercionI -> CoercionI
653 mkIParamPredCoI _ IdCo = IdCo
654 mkIParamPredCoI ipn (ACo co) = ACo $ PredTy $ IParam ipn co
656 -- | Smart constructor for type equality 'Coercion's on 'CoercionI'. Similar to 'mkClassPPredCoI'
657 mkEqPredCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI
658 mkEqPredCoI _ IdCo _ IdCo = IdCo
659 mkEqPredCoI ty1 IdCo _ (ACo co2) = ACo $ PredTy $ EqPred ty1 co2
660 mkEqPredCoI _ (ACo co1) ty2 coi2 = ACo $ PredTy $ EqPred co1 (fromCoI coi2 ty2)