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, 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
41 import TyCon ( TyCon, tyConArity, mkCoercionTyCon, isNewTyCon,
42 newTyConRhs, newTyConCo,
43 isCoercionTyCon, isCoercionTyCon_maybe )
44 import Var ( Var, TyVar, isTyVar, tyVarKind )
45 import Name ( BuiltInSyntax(..), Name, mkWiredInName, tcName )
46 import OccName ( mkOccNameFS )
47 import PrelNames ( symCoercionTyConKey,
48 transCoercionTyConKey, leftCoercionTyConKey,
49 rightCoercionTyConKey, instCoercionTyConKey,
50 unsafeCoercionTyConKey, gHC_PRIM
52 import Util ( lengthIs, snocView )
53 import Unique ( hasKey )
54 import BasicTypes ( Arity )
59 ------------------------------
60 decomposeCo :: Arity -> Coercion -> [Coercion]
61 -- (decomposeCo 3 c) = [right (left (left c)), right (left c), right c]
66 go n co cos = go (n-1) (mkLeftCoercion co)
67 (mkRightCoercion co : cos)
69 ------------------------------
71 -------------------------------------------------------
72 -- and some coercion kind stuff
74 isEqPredTy (PredTy pred) = isEqPred pred
75 isEqPredTy other = False
77 mkEqPred :: (Type, Type) -> PredType
78 mkEqPred (ty1, ty2) = EqPred ty1 ty2
80 getEqPredTys :: PredType -> (Type,Type)
81 getEqPredTys (EqPred ty1 ty2) = (ty1, ty2)
82 getEqPredTys other = pprPanic "getEqPredTys" (ppr other)
84 mkCoKind :: Type -> Type -> CoercionKind
85 mkCoKind ty1 ty2 = PredTy (EqPred ty1 ty2)
87 mkReflCoKind :: Type -> CoercionKind
88 mkReflCoKind ty = mkCoKind ty ty
90 splitCoercionKind :: CoercionKind -> (Type, Type)
91 splitCoercionKind co | Just co' <- kindView co = splitCoercionKind co'
92 splitCoercionKind (PredTy (EqPred ty1 ty2)) = (ty1, ty2)
94 splitCoercionKind_maybe :: Kind -> Maybe (Type, Type)
95 splitCoercionKind_maybe co | Just co' <- kindView co = splitCoercionKind_maybe co'
96 splitCoercionKind_maybe (PredTy (EqPred ty1 ty2)) = Just (ty1, ty2)
97 splitCoercionKind_maybe other = Nothing
99 isCoVar :: Var -> Bool
100 isCoVar tv = isTyVar tv && isCoercionKind (tyVarKind tv)
103 type CoercionKind = Kind -- A CoercionKind is always of form (ty1 :=: ty2)
105 coercionKind :: Coercion -> (Type, Type)
107 -- Then (coercionKind c) = (t1,t2)
109 coercionKind (TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind a)
110 | otherwise = let t = (TyVarTy a) in (t, t)
111 coercionKind (AppTy ty1 ty2)
112 = let (t1, t2) = coercionKind ty1
113 (s1, s2) = coercionKind ty2 in
114 (mkAppTy t1 s1, mkAppTy t2 s2)
115 coercionKind (TyConApp tc args)
116 | Just (ar, rule) <- isCoercionTyCon_maybe tc
117 = if length args >= ar
118 then splitCoercionKind (rule args)
119 else pprPanic ("arity/arguments mismatch in coercionKind:")
120 (ppr ar $$ ppr tc <+> ppr args)
122 = let (lArgs, rArgs) = coercionKinds args in
123 (TyConApp tc lArgs, TyConApp tc rArgs)
124 coercionKind (FunTy ty1 ty2)
125 = let (t1, t2) = coercionKind ty1
126 (s1, s2) = coercionKind ty2 in
127 (mkFunTy t1 s1, mkFunTy t2 s2)
128 coercionKind (ForAllTy tv ty)
129 = let (ty1, ty2) = coercionKind ty in
130 (ForAllTy tv ty1, ForAllTy tv ty2)
131 coercionKind (NoteTy _ ty) = coercionKind ty
132 coercionKind (PredTy (EqPred c1 c2))
133 = let k1 = coercionKindPredTy c1
134 k2 = coercionKindPredTy c2 in
136 coercionKind (PredTy (ClassP cl args))
137 = let (lArgs, rArgs) = coercionKinds args in
138 (PredTy (ClassP cl lArgs), PredTy (ClassP cl rArgs))
139 coercionKind (PredTy (IParam name ty))
140 = let (ty1, ty2) = coercionKind ty in
141 (PredTy (IParam name ty1), PredTy (IParam name ty2))
143 coercionKindPredTy :: Coercion -> CoercionKind
144 coercionKindPredTy c = let (t1, t2) = coercionKind c in mkCoKind t1 t2
146 coercionKinds :: [Coercion] -> ([Type], [Type])
147 coercionKinds tys = unzip $ map coercionKind tys
149 -------------------------------------
150 -- Coercion kind and type mk's
151 -- (make saturated TyConApp CoercionTyCon{...} args)
153 mkCoercion coCon args = ASSERT( tyConArity coCon == length args )
156 mkAppCoercion, mkFunCoercion, mkTransCoercion, mkInstCoercion :: Coercion -> Coercion -> Coercion
157 mkSymCoercion, mkLeftCoercion, mkRightCoercion :: Coercion -> Coercion
159 mkAppCoercion co1 co2 = mkAppTy co1 co2
160 mkAppsCoercion co1 tys = foldl mkAppTy co1 tys
161 -- note that a TyVar should be used here, not a CoVar (nor a TcTyVar)
162 mkForAllCoercion tv co = ASSERT ( isTyVar tv ) mkForAllTy tv co
163 mkFunCoercion co1 co2 = mkFunTy co1 co2
166 | Just co2 <- splitSymCoercion_maybe co = co2
167 | Just (co1, co2) <- splitAppCoercion_maybe co
168 -- should make this case better
169 = mkAppCoercion (mkSymCoercion co1) (mkSymCoercion co2)
170 | Just (co1, co2) <- splitTransCoercion_maybe co
171 = mkTransCoercion (mkSymCoercion co2) (mkSymCoercion co1)
172 | Just (co, ty) <- splitInstCoercion_maybe co
173 = mkInstCoercion (mkSymCoercion co) ty
174 | Just co <- splitLeftCoercion_maybe co
175 = mkLeftCoercion (mkSymCoercion co)
176 | Just co <- splitRightCoercion_maybe co
177 = mkRightCoercion (mkSymCoercion co)
178 mkSymCoercion (ForAllTy tv ty) = ForAllTy tv (mkSymCoercion ty)
179 -- for atomic types and constructors, we can just ignore sym since these
180 -- are reflexive coercions
181 mkSymCoercion (TyVarTy tv)
182 | isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv]
183 | otherwise = TyVarTy tv
184 mkSymCoercion co = mkCoercion symCoercionTyCon [co]
185 -- this should not happen but does
187 -- Smart constructors for left and right
189 | Just (co', _) <- splitAppCoercion_maybe co = co'
190 | otherwise = mkCoercion leftCoercionTyCon [co]
193 | Just (co1, co2) <- splitAppCoercion_maybe co = co2
194 | otherwise = mkCoercion rightCoercionTyCon [co]
196 mkTransCoercion co1 co2 = mkCoercion transCoercionTyCon [co1, co2]
198 mkInstCoercion co ty = mkCoercion instCoercionTyCon [co, ty]
200 mkInstsCoercion co tys = foldl mkInstCoercion co tys
202 splitSymCoercion_maybe :: Coercion -> Maybe Coercion
203 splitSymCoercion_maybe (TyConApp tc [co]) =
204 if tc `hasKey` symCoercionTyConKey
207 splitSymCoercion_maybe co = Nothing
209 splitAppCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
210 -- Splits a coercion application, being careful *not* to split (left c), etc
211 -- which are really sytactic constructs, not applications
212 splitAppCoercion_maybe co | Just co' <- coreView co = splitAppCoercion_maybe co'
213 splitAppCoercion_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
214 splitAppCoercion_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
215 splitAppCoercion_maybe (TyConApp tc tys)
216 | not (isCoercionTyCon tc)
217 = case snocView tys of
218 Just (tys', ty') -> Just (TyConApp tc tys', ty')
220 splitAppCoercion_maybe co = Nothing
222 splitTransCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
223 splitTransCoercion_maybe (TyConApp tc [ty1, ty2])
224 = if tc `hasKey` transCoercionTyConKey then
228 splitTransCoercion_maybe other = Nothing
230 splitInstCoercion_maybe :: Coercion -> Maybe (Coercion, Type)
231 splitInstCoercion_maybe (TyConApp tc [ty1, ty2])
232 = if tc `hasKey` instCoercionTyConKey then
236 splitInstCoercion_maybe other = Nothing
238 splitLeftCoercion_maybe :: Coercion -> Maybe Coercion
239 splitLeftCoercion_maybe (TyConApp tc [co])
240 = if tc `hasKey` leftCoercionTyConKey then
244 splitLeftCoercion_maybe other = Nothing
246 splitRightCoercion_maybe :: Coercion -> Maybe Coercion
247 splitRightCoercion_maybe (TyConApp tc [co])
248 = if tc `hasKey` rightCoercionTyConKey then
252 splitRightCoercion_maybe other = Nothing
254 -- Unsafe coercion is not safe, it is used when we know we are dealing with
255 -- bottom, which is the one case in which it is safe
256 mkUnsafeCoercion :: Type -> Type -> Coercion
257 mkUnsafeCoercion ty1 ty2
258 = mkCoercion unsafeCoercionTyCon [ty1, ty2]
261 -- make the coercion associated with a newtype
262 mkNewTypeCoercion :: Name -> TyCon -> [TyVar] -> Type -> TyCon
263 mkNewTypeCoercion name tycon tvs rhs_ty
264 = ASSERT (length tvs == tyConArity tycon)
265 mkCoercionTyCon name (tyConArity tycon) rule
267 rule args = mkCoKind (substTyWith tvs args rhs_ty) (TyConApp tycon args)
269 --------------------------------------
270 -- Coercion Type Constructors...
272 -- Example. The coercion ((sym c) (sym d) (sym e))
273 -- will be represented by (TyConApp sym [c, sym d, sym e])
277 -- then ((sym c) (sym d) (sym e)) :: (p1 p2 p3)=(q1 q2 q3)
279 -- (mkKindingFun f) is given the args [c, sym d, sym e]
280 mkKindingFun :: ([Type] -> (Type, Type, [Type])) -> [Type] -> Kind
281 mkKindingFun f args =
282 let (ty1, ty2, rest) = f args in
283 let (argtys1, argtys2) = unzip (map coercionKind rest) in
284 mkCoKind (mkAppTys ty1 argtys1) (mkAppTys ty2 argtys2)
287 symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, rightCoercionTyCon, instCoercionTyCon :: TyCon
288 -- Each coercion TyCon is built with the special CoercionTyCon record and
289 -- carries its won kinding rule. Such CoercionTyCons must be fully applied
290 -- by any TyConApp in which they are applied, however they may also be over
291 -- applied (see example above) and the kinding function must deal with this.
293 mkCoercionTyCon symCoercionTyConName 1 (mkKindingFun flipCoercionKindOf)
295 flipCoercionKindOf (co:rest) = (ty2, ty1, rest)
297 (ty1, ty2) = coercionKind co
300 mkCoercionTyCon transCoercionTyConName 2 (mkKindingFun composeCoercionKindsOf)
302 composeCoercionKindsOf (co1:co2:rest) = (a1, r2, rest)
304 (a1, r1) = coercionKind co1
305 (a2, r2) = coercionKind co2
308 mkCoercionTyCon leftCoercionTyConName 1 (mkKindingFun leftProjectCoercionKindOf)
310 leftProjectCoercionKindOf (co:rest) = (ty1, ty2, rest)
312 (ty1,ty2) = fst (splitCoercionKindOf co)
315 mkCoercionTyCon rightCoercionTyConName 1 (mkKindingFun rightProjectCoercionKindOf)
317 rightProjectCoercionKindOf (co:rest) = (ty1, ty2, rest)
319 (ty1,ty2) = snd (splitCoercionKindOf co)
321 splitCoercionKindOf :: Type -> ((Type,Type), (Type,Type))
322 -- Helper for left and right. Finds coercion kind of its input and
323 -- returns the left and right projections of the coercion...
325 -- if c :: t1 s1 :=: t2 s2 then splitCoercionKindOf c = ((t1, t2), (s1, s2))
326 splitCoercionKindOf co
327 | Just (ty1, ty2) <- splitCoercionKind_maybe (coercionKindPredTy co)
328 , Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1
329 , Just (ty_fun2, ty_arg2) <- splitAppTy_maybe ty2
330 = ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2))
333 = mkCoercionTyCon instCoercionTyConName 2 (mkKindingFun instCoercionKind)
336 let Just (tv, ty) = splitForAllTy_maybe t in
337 substTyWith [tv] [s] ty
339 instCoercionKind (co1:ty:rest) = (instantiateCo t1 ty, instantiateCo t2 ty, rest)
340 where (t1, t2) = coercionKind co1
343 = mkCoercionTyCon unsafeCoercionTyConName 2 (mkKindingFun unsafeCoercionKind)
345 unsafeCoercionKind (ty1:ty2:rest) = (ty1,ty2,rest)
347 --------------------------------------
348 -- ...and their names
350 mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkOccNameFS tcName occ)
351 key Nothing (ATyCon coCon) BuiltInSyntax
353 transCoercionTyConName = mkCoConName FSLIT("trans") transCoercionTyConKey transCoercionTyCon
354 symCoercionTyConName = mkCoConName FSLIT("sym") symCoercionTyConKey symCoercionTyCon
355 leftCoercionTyConName = mkCoConName FSLIT("left") leftCoercionTyConKey leftCoercionTyCon
356 rightCoercionTyConName = mkCoConName FSLIT("right") rightCoercionTyConKey rightCoercionTyCon
357 instCoercionTyConName = mkCoConName FSLIT("inst") instCoercionTyConKey instCoercionTyCon
358 unsafeCoercionTyConName = mkCoConName FSLIT("CoUnsafe") unsafeCoercionTyConKey unsafeCoercionTyCon
362 -- this is here to avoid module loops
363 splitNewTypeRepCo_maybe :: Type -> Maybe (Type, Coercion)
364 -- Sometimes we want to look through a recursive newtype, and that's what happens here
365 -- It only strips *one layer* off, so the caller will usually call itself recursively
366 -- Only applied to types of kind *, hence the newtype is always saturated
367 splitNewTypeRepCo_maybe ty
368 | Just ty' <- coreView ty = splitNewTypeRepCo_maybe ty'
369 splitNewTypeRepCo_maybe (TyConApp tc tys)
371 = ASSERT( tys `lengthIs` tyConArity tc ) -- splitNewTypeRepCo_maybe only be applied
372 -- to *types* (of kind *)
373 case newTyConRhs tc of
375 ASSERT( length tvs == length tys )
376 Just (substTyWith tvs tys rep_ty, mkTyConApp co_con tys)
378 co_con = maybe (pprPanic "splitNewTypeRepCo_maybe" (ppr tc)) id (newTyConCo tc)
380 splitNewTypeRepCo_maybe other = Nothing