2 Module for type coercions, as in System FC.
4 Coercions are represented as types, and their kinds tell what types the
7 The coercion kind constructor is a special TyCon that must always be saturated
9 typeKind (symCoercion type) :: TyConApp CoercionTyCon{...} [type, type]
15 mkCoKind, mkReflCoKind, splitCoercionKind_maybe, splitCoercionKind,
16 coercionKind, coercionKinds, coercionKindPredTy,
18 -- Equality predicates
19 isEqPred, mkEqPred, getEqPredTys, isEqPredTy,
21 -- Coercion transformations
22 mkSymCoercion, mkTransCoercion,
23 mkLeftCoercion, mkRightCoercion, mkInstCoercion, mkAppCoercion,
24 mkForAllCoercion, mkFunCoercion, mkInstsCoercion, mkUnsafeCoercion,
25 mkNewTypeCoercion, mkDataInstCoercion, mkAppsCoercion,
27 splitNewTypeRepCo_maybe, decomposeCo,
29 unsafeCoercionTyCon, symCoercionTyCon,
30 transCoercionTyCon, leftCoercionTyCon,
31 rightCoercionTyCon, instCoercionTyCon -- needed by TysWiredIn
34 #include "HsVersions.h"
37 import Type ( Type, Kind, PredType, substTyWith, mkAppTy, mkForAllTy,
38 mkFunTy, splitAppTy_maybe, splitForAllTy_maybe, coreView,
39 kindView, mkTyConApp, isCoercionKind, isEqPred, mkAppTys,
40 coreEqType, splitAppTys, isTyVarTy, splitTyConApp_maybe,
41 tyVarsOfType, mkTyVarTys
43 import TyCon ( TyCon, tyConArity, mkCoercionTyCon, isClosedNewTyCon,
44 newTyConRhs, newTyConCo_maybe,
45 isCoercionTyCon, isCoercionTyCon_maybe )
46 import Var ( Var, TyVar, isTyVar, tyVarKind )
47 import VarSet ( elemVarSet )
48 import Name ( BuiltInSyntax(..), Name, mkWiredInName, tcName )
49 import OccName ( mkOccNameFS )
50 import PrelNames ( symCoercionTyConKey,
51 transCoercionTyConKey, leftCoercionTyConKey,
52 rightCoercionTyConKey, instCoercionTyConKey,
53 unsafeCoercionTyConKey, gHC_PRIM
55 import Util ( lengthIs, snocView )
56 import Unique ( hasKey )
57 import BasicTypes ( Arity )
62 ------------------------------
63 decomposeCo :: Arity -> Coercion -> [Coercion]
64 -- (decomposeCo 3 c) = [right (left (left c)), right (left c), right c]
65 -- So this breaks a coercion with kind T A B C :=: T D E F into
66 -- a list of coercions of kinds A :=: D, B :=: E and E :=: F
71 go n co cos = go (n-1) (mkLeftCoercion co)
72 (mkRightCoercion co : cos)
74 ------------------------------
76 -------------------------------------------------------
77 -- and some coercion kind stuff
79 isEqPredTy (PredTy pred) = isEqPred pred
80 isEqPredTy other = False
82 mkEqPred :: (Type, Type) -> PredType
83 mkEqPred (ty1, ty2) = EqPred ty1 ty2
85 getEqPredTys :: PredType -> (Type,Type)
86 getEqPredTys (EqPred ty1 ty2) = (ty1, ty2)
87 getEqPredTys other = pprPanic "getEqPredTys" (ppr other)
89 mkCoKind :: Type -> Type -> CoercionKind
90 mkCoKind ty1 ty2 = PredTy (EqPred ty1 ty2)
92 mkReflCoKind :: Type -> CoercionKind
93 mkReflCoKind ty = mkCoKind ty ty
95 splitCoercionKind :: CoercionKind -> (Type, Type)
96 splitCoercionKind co | Just co' <- kindView co = splitCoercionKind co'
97 splitCoercionKind (PredTy (EqPred ty1 ty2)) = (ty1, ty2)
99 splitCoercionKind_maybe :: Kind -> Maybe (Type, Type)
100 splitCoercionKind_maybe co | Just co' <- kindView co = splitCoercionKind_maybe co'
101 splitCoercionKind_maybe (PredTy (EqPred ty1 ty2)) = Just (ty1, ty2)
102 splitCoercionKind_maybe other = Nothing
104 isCoVar :: Var -> Bool
105 isCoVar tv = isTyVar tv && isCoercionKind (tyVarKind tv)
108 type CoercionKind = Kind -- A CoercionKind is always of form (ty1 :=: ty2)
110 coercionKind :: Coercion -> (Type, Type)
112 -- Then (coercionKind c) = (t1,t2)
113 coercionKind (TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind a)
114 | otherwise = let t = (TyVarTy a) in (t, t)
115 coercionKind (AppTy ty1 ty2)
116 = let (t1, t2) = coercionKind ty1
117 (s1, s2) = coercionKind ty2 in
118 (mkAppTy t1 s1, mkAppTy t2 s2)
119 coercionKind (TyConApp tc args)
120 | Just (ar, rule) <- isCoercionTyCon_maybe tc
121 -- CoercionTyCons carry their kinding rule, so we use it here
122 = if length args >= ar
123 then splitCoercionKind (rule args)
124 else pprPanic ("arity/arguments mismatch in coercionKind:")
125 (ppr ar $$ ppr tc <+> ppr args)
127 = let (lArgs, rArgs) = coercionKinds args in
128 (TyConApp tc lArgs, TyConApp tc rArgs)
129 coercionKind (FunTy ty1 ty2)
130 = let (t1, t2) = coercionKind ty1
131 (s1, s2) = coercionKind ty2 in
132 (mkFunTy t1 s1, mkFunTy t2 s2)
133 coercionKind (ForAllTy tv ty)
134 = let (ty1, ty2) = coercionKind ty in
135 (ForAllTy tv ty1, ForAllTy tv ty2)
136 coercionKind (NoteTy _ ty) = coercionKind ty
137 coercionKind (PredTy (EqPred c1 c2))
138 = let k1 = coercionKindPredTy c1
139 k2 = coercionKindPredTy c2 in
141 coercionKind (PredTy (ClassP cl args))
142 = let (lArgs, rArgs) = coercionKinds args in
143 (PredTy (ClassP cl lArgs), PredTy (ClassP cl rArgs))
144 coercionKind (PredTy (IParam name ty))
145 = let (ty1, ty2) = coercionKind ty in
146 (PredTy (IParam name ty1), PredTy (IParam name ty2))
148 coercionKindPredTy :: Coercion -> CoercionKind
149 coercionKindPredTy c = let (t1, t2) = coercionKind c in mkCoKind t1 t2
151 coercionKinds :: [Coercion] -> ([Type], [Type])
152 coercionKinds tys = unzip $ map coercionKind tys
154 -------------------------------------
155 -- Coercion kind and type mk's
156 -- (make saturated TyConApp CoercionTyCon{...} args)
158 mkCoercion coCon args = ASSERT( tyConArity coCon == length args )
161 mkAppCoercion, mkFunCoercion, mkTransCoercion, mkInstCoercion :: Coercion -> Coercion -> Coercion
162 mkSymCoercion, mkLeftCoercion, mkRightCoercion :: Coercion -> Coercion
164 mkAppCoercion co1 co2 = mkAppTy co1 co2
165 mkAppsCoercion co1 tys = foldl mkAppTy co1 tys
166 -- note that a TyVar should be used here, not a CoVar (nor a TcTyVar)
167 mkForAllCoercion tv co = ASSERT ( isTyVar tv ) mkForAllTy tv co
168 mkFunCoercion co1 co2 = mkFunTy co1 co2
171 -- This smart constructor creates a sym'ed version its argument,
172 -- but tries to push the sym's down to the leaves. If we come to
173 -- sym tv or sym tycon then we can drop the sym because tv and tycon
174 -- are reflexive coercions
176 | Just co2 <- splitSymCoercion_maybe co = co2
177 -- sym (sym co) --> co
178 | Just (co1, arg_tys) <- splitTyConApp_maybe co
179 , not (isCoercionTyCon co1) = mkTyConApp co1 (map mkSymCoercion arg_tys)
180 -- we can drop the sym for a TyCon
181 -- sym (ty [t1, ..., tn]) --> ty [sym t1, ..., sym tn]
182 | (co1, arg_tys) <- splitAppTys co
183 , isTyVarTy co1 = mkAppTys (maybe_drop co1) (map mkSymCoercion arg_tys)
184 -- sym (tv [t1, ..., tn]) --> tv [sym t1, ..., sym tn]
185 -- if tv type variable
186 -- sym (cv [t1, ..., tn]) --> (sym cv) [sym t1, ..., sym tn]
187 -- if cv is a coercion variable
188 -- fall through if head is a CoercionTyCon
189 | Just (co1, co2) <- splitTransCoercion_maybe co
190 -- sym (co1 `trans` co2) --> (sym co2) `trans (sym co2)
191 = mkTransCoercion (mkSymCoercion co2) (mkSymCoercion co1)
192 | Just (co, ty) <- splitInstCoercion_maybe co
193 -- sym (co @ ty) --> (sym co) @ ty
194 = mkInstCoercion (mkSymCoercion co) ty
195 | Just co <- splitLeftCoercion_maybe co
196 -- sym (left co) --> left (sym co)
197 = mkLeftCoercion (mkSymCoercion co)
198 | Just co <- splitRightCoercion_maybe co
199 -- sym (right co) --> right (sym co)
200 = mkRightCoercion (mkSymCoercion co)
202 maybe_drop (TyVarTy tv)
203 | isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv]
204 | otherwise = TyVarTy tv
205 maybe_drop other = other
206 mkSymCoercion (ForAllTy tv ty) = ForAllTy tv (mkSymCoercion ty)
207 -- for atomic types and constructors, we can just ignore sym since these
208 -- are reflexive coercions
209 mkSymCoercion (TyVarTy tv)
210 | isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv]
211 | otherwise = TyVarTy tv
212 mkSymCoercion co = mkCoercion symCoercionTyCon [co]
214 -- Smart constructors for left and right
216 | Just (co', _) <- splitAppCoercion_maybe co = co'
217 | otherwise = mkCoercion leftCoercionTyCon [co]
220 | Just (co1, co2) <- splitAppCoercion_maybe co = co2
221 | otherwise = mkCoercion rightCoercionTyCon [co]
223 mkTransCoercion co1 co2 = mkCoercion transCoercionTyCon [co1, co2]
225 mkInstCoercion co ty = mkCoercion instCoercionTyCon [co, ty]
227 mkInstsCoercion co tys = foldl mkInstCoercion co tys
229 splitSymCoercion_maybe :: Coercion -> Maybe Coercion
230 splitSymCoercion_maybe (TyConApp tc [co]) =
231 if tc `hasKey` symCoercionTyConKey
234 splitSymCoercion_maybe co = Nothing
236 splitAppCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
237 -- Splits a coercion application, being careful *not* to split (left c), etc
238 -- which are really sytactic constructs, not applications
239 splitAppCoercion_maybe co | Just co' <- coreView co = splitAppCoercion_maybe co'
240 splitAppCoercion_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
241 splitAppCoercion_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
242 splitAppCoercion_maybe (TyConApp tc tys)
243 | not (isCoercionTyCon tc)
244 = case snocView tys of
245 Just (tys', ty') -> Just (TyConApp tc tys', ty')
247 splitAppCoercion_maybe co = Nothing
249 splitTransCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
250 splitTransCoercion_maybe (TyConApp tc [ty1, ty2])
251 = if tc `hasKey` transCoercionTyConKey then
255 splitTransCoercion_maybe other = Nothing
257 splitInstCoercion_maybe :: Coercion -> Maybe (Coercion, Type)
258 splitInstCoercion_maybe (TyConApp tc [ty1, ty2])
259 = if tc `hasKey` instCoercionTyConKey then
263 splitInstCoercion_maybe other = Nothing
265 splitLeftCoercion_maybe :: Coercion -> Maybe Coercion
266 splitLeftCoercion_maybe (TyConApp tc [co])
267 = if tc `hasKey` leftCoercionTyConKey then
271 splitLeftCoercion_maybe other = Nothing
273 splitRightCoercion_maybe :: Coercion -> Maybe Coercion
274 splitRightCoercion_maybe (TyConApp tc [co])
275 = if tc `hasKey` rightCoercionTyConKey then
279 splitRightCoercion_maybe other = Nothing
281 -- Unsafe coercion is not safe, it is used when we know we are dealing with
282 -- bottom, which is one case in which it is safe. It is also used to
283 -- implement the unsafeCoerce# primitive.
284 mkUnsafeCoercion :: Type -> Type -> Coercion
285 mkUnsafeCoercion ty1 ty2
286 = mkCoercion unsafeCoercionTyCon [ty1, ty2]
289 -- See note [Newtype coercions] in TyCon
290 mkNewTypeCoercion :: Name -> TyCon -> [TyVar] -> Type -> TyCon
291 mkNewTypeCoercion name tycon tvs rhs_ty
292 = ASSERT (length tvs == tyConArity tycon)
293 mkCoercionTyCon name co_con_arity (mkKindingFun rule)
295 rule args = (TyConApp tycon tys, substTyWith tvs_eta tys rhs_eta, rest)
297 tys = take co_con_arity args
298 rest = drop co_con_arity args
300 -- if the rhs_ty is a type application and it has a tail equal to a tail
301 -- of the tvs, then we eta-contract the type of the coercion
302 rhs_args = let (ty, ty_args) = splitAppTys rhs_ty in ty_args
304 n_eta_tys = count_eta (reverse rhs_args) (reverse tvs)
306 count_eta ((TyVarTy tv):rest_ty) (tv':rest_tv)
307 | tv == tv' && (not $ any (elemVarSet tv . tyVarsOfType) rest_ty)
308 -- if the last types are the same, and not free anywhere else
310 = 1 + (count_eta rest_ty rest_tv)
316 eqVar (TyVarTy tv) tv' = tv == tv'
319 co_con_arity = (tyConArity tycon) - n_eta_tys
321 tvs_eta = (reverse (drop n_eta_tys (reverse tvs)))
324 | (ty, ty_args) <- splitAppTys rhs_ty
325 = mkAppTys ty (reverse (drop n_eta_tys (reverse ty_args)))
327 -- Coercion identifying a data/newtype representation type and its family
328 -- instance. It has the form `Co tvs :: F ts :=: R tvs', where `Co' is the
329 -- coercion tycon built here, `F' the family tycon and `R' the (derived)
330 -- representation tycon.
332 mkDataInstCoercion :: Name -- unique name for the coercion tycon
333 -> [TyVar] -- type parameters of the coercion (`tvs')
334 -> TyCon -- family tycon (`F')
335 -> [Type] -- type instance (`ts')
336 -> TyCon -- representation tycon (`R')
337 -> TyCon -- => coercion tycon (`Co')
338 mkDataInstCoercion name tvs family instTys rep_tycon
339 = mkCoercionTyCon name coArity (mkKindingFun rule)
343 rule args = (substTyWith tvs tys $ -- with sigma = [tys/tvs],
344 TyConApp family instTys, -- sigma (F ts)
345 TyConApp rep_tycon tys, -- :=: R tys
346 rest) -- surplus arguments
348 tys = take coArity args
349 rest = drop coArity args
351 --------------------------------------
352 -- Coercion Type Constructors...
354 -- Example. The coercion ((sym c) (sym d) (sym e))
355 -- will be represented by (TyConApp sym [c, sym d, sym e])
359 -- then ((sym c) (sym d) (sym e)) :: (p1 p2 p3)=(q1 q2 q3)
361 -- (mkKindingFun f) is given the args [c, sym d, sym e]
362 mkKindingFun :: ([Type] -> (Type, Type, [Type])) -> [Type] -> Kind
363 mkKindingFun f args =
364 let (ty1, ty2, rest) = f args in
365 let (argtys1, argtys2) = unzip (map coercionKind rest) in
366 mkCoKind (mkAppTys ty1 argtys1) (mkAppTys ty2 argtys2)
369 symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, rightCoercionTyCon, instCoercionTyCon :: TyCon
370 -- Each coercion TyCon is built with the special CoercionTyCon record and
371 -- carries its own kinding rule. Such CoercionTyCons must be fully applied
372 -- by any TyConApp in which they are applied, however they may also be over
373 -- applied (see example above) and the kinding function must deal with this.
375 mkCoercionTyCon symCoercionTyConName 1 (mkKindingFun flipCoercionKindOf)
377 flipCoercionKindOf (co:rest) = (ty2, ty1, rest)
379 (ty1, ty2) = coercionKind co
382 mkCoercionTyCon transCoercionTyConName 2 (mkKindingFun composeCoercionKindsOf)
384 composeCoercionKindsOf (co1:co2:rest) =
385 WARN( not (r1 `coreEqType` a2), text "Strange! Type mismatch in trans coercion, probably a bug")
388 (a1, r1) = coercionKind co1
389 (a2, r2) = coercionKind co2
392 mkCoercionTyCon leftCoercionTyConName 1 (mkKindingFun leftProjectCoercionKindOf)
394 leftProjectCoercionKindOf (co:rest) = (ty1, ty2, rest)
396 (ty1,ty2) = fst (splitCoercionKindOf co)
399 mkCoercionTyCon rightCoercionTyConName 1 (mkKindingFun rightProjectCoercionKindOf)
401 rightProjectCoercionKindOf (co:rest) = (ty1, ty2, rest)
403 (ty1,ty2) = snd (splitCoercionKindOf co)
405 splitCoercionKindOf :: Type -> ((Type,Type), (Type,Type))
406 -- Helper for left and right. Finds coercion kind of its input and
407 -- returns the left and right projections of the coercion...
409 -- if c :: t1 s1 :=: t2 s2 then splitCoercionKindOf c = ((t1, t2), (s1, s2))
410 splitCoercionKindOf co
411 | Just (ty1, ty2) <- splitCoercionKind_maybe (coercionKindPredTy co)
412 , Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1
413 , Just (ty_fun2, ty_arg2) <- splitAppTy_maybe ty2
414 = ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2))
417 = mkCoercionTyCon instCoercionTyConName 2 (mkKindingFun instCoercionKind)
420 let Just (tv, ty) = splitForAllTy_maybe t in
421 substTyWith [tv] [s] ty
423 instCoercionKind (co1:ty:rest) = (instantiateCo t1 ty, instantiateCo t2 ty, rest)
424 where (t1, t2) = coercionKind co1
427 = mkCoercionTyCon unsafeCoercionTyConName 2 (mkKindingFun unsafeCoercionKind)
429 unsafeCoercionKind (ty1:ty2:rest) = (ty1,ty2,rest)
431 --------------------------------------
432 -- ...and their names
434 mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkOccNameFS tcName occ)
435 key Nothing (ATyCon coCon) BuiltInSyntax
437 transCoercionTyConName = mkCoConName FSLIT("trans") transCoercionTyConKey transCoercionTyCon
438 symCoercionTyConName = mkCoConName FSLIT("sym") symCoercionTyConKey symCoercionTyCon
439 leftCoercionTyConName = mkCoConName FSLIT("left") leftCoercionTyConKey leftCoercionTyCon
440 rightCoercionTyConName = mkCoConName FSLIT("right") rightCoercionTyConKey rightCoercionTyCon
441 instCoercionTyConName = mkCoConName FSLIT("inst") instCoercionTyConKey instCoercionTyCon
442 unsafeCoercionTyConName = mkCoConName FSLIT("CoUnsafe") unsafeCoercionTyConKey unsafeCoercionTyCon
446 -- this is here to avoid module loops
447 splitNewTypeRepCo_maybe :: Type -> Maybe (Type, Coercion)
448 -- Sometimes we want to look through a newtype and get its associated coercion
449 -- It only strips *one layer* off, so the caller will usually call itself recursively
450 -- Only applied to types of kind *, hence the newtype is always saturated
451 splitNewTypeRepCo_maybe ty
452 | Just ty' <- coreView ty = splitNewTypeRepCo_maybe ty'
453 splitNewTypeRepCo_maybe (TyConApp tc tys)
454 | isClosedNewTyCon tc
455 = ASSERT( tys `lengthIs` tyConArity tc ) -- splitNewTypeRepCo_maybe only be applied
456 -- to *types* (of kind *)
457 case newTyConRhs tc of
459 ASSERT( length tvs == length tys )
460 Just (substTyWith tvs tys rep_ty, mkTyConApp co_con tys)
462 co_con = maybe (pprPanic "splitNewTypeRepCo_maybe" (ppr tc)) id (newTyConCo_maybe tc)
463 splitNewTypeRepCo_maybe other = Nothing