2 % (c) The University of Glasgow 2006
5 Module for type coercions, as in System FC.
7 Coercions are represented as types, and their kinds tell what types the
10 The coercion kind constructor is a special TyCon that must always be saturated
12 typeKind (symCoercion type) :: TyConApp CoercionTyCon{...} [type, type]
18 mkCoKind, mkReflCoKind, splitCoercionKind_maybe, splitCoercionKind,
19 coercionKind, coercionKinds, coercionKindPredTy,
21 -- Equality predicates
22 isEqPred, mkEqPred, getEqPredTys, isEqPredTy,
24 -- Coercion transformations
25 mkSymCoercion, mkTransCoercion,
26 mkLeftCoercion, mkRightCoercion, mkInstCoercion, mkAppCoercion,
27 mkForAllCoercion, mkFunCoercion, mkInstsCoercion, mkUnsafeCoercion,
28 mkNewTypeCoercion, mkDataInstCoercion, mkAppsCoercion,
30 splitNewTypeRepCo_maybe, decomposeCo,
32 unsafeCoercionTyCon, symCoercionTyCon,
33 transCoercionTyCon, leftCoercionTyCon,
34 rightCoercionTyCon, instCoercionTyCon -- needed by TysWiredIn
37 #include "HsVersions.h"
52 ------------------------------
53 decomposeCo :: Arity -> Coercion -> [Coercion]
54 -- (decomposeCo 3 c) = [right (left (left c)), right (left c), right c]
55 -- So this breaks a coercion with kind T A B C :=: T D E F into
56 -- a list of coercions of kinds A :=: D, B :=: E and E :=: F
61 go n co cos = go (n-1) (mkLeftCoercion co)
62 (mkRightCoercion co : cos)
64 ------------------------------
66 -------------------------------------------------------
67 -- and some coercion kind stuff
69 isEqPredTy (PredTy pred) = isEqPred pred
70 isEqPredTy other = False
72 mkEqPred :: (Type, Type) -> PredType
73 mkEqPred (ty1, ty2) = EqPred ty1 ty2
75 getEqPredTys :: PredType -> (Type,Type)
76 getEqPredTys (EqPred ty1 ty2) = (ty1, ty2)
77 getEqPredTys other = pprPanic "getEqPredTys" (ppr other)
79 mkCoKind :: Type -> Type -> CoercionKind
80 mkCoKind ty1 ty2 = PredTy (EqPred ty1 ty2)
82 mkReflCoKind :: Type -> CoercionKind
83 mkReflCoKind ty = mkCoKind ty ty
85 splitCoercionKind :: CoercionKind -> (Type, Type)
86 splitCoercionKind co | Just co' <- kindView co = splitCoercionKind co'
87 splitCoercionKind (PredTy (EqPred ty1 ty2)) = (ty1, ty2)
89 splitCoercionKind_maybe :: Kind -> Maybe (Type, Type)
90 splitCoercionKind_maybe co | Just co' <- kindView co = splitCoercionKind_maybe co'
91 splitCoercionKind_maybe (PredTy (EqPred ty1 ty2)) = Just (ty1, ty2)
92 splitCoercionKind_maybe other = Nothing
95 type CoercionKind = Kind -- A CoercionKind is always of form (ty1 :=: ty2)
97 coercionKind :: Coercion -> (Type, Type)
99 -- Then (coercionKind c) = (t1,t2)
100 coercionKind ty@(TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind a)
101 | otherwise = (ty, ty)
102 coercionKind (AppTy ty1 ty2)
103 = let (t1, t2) = coercionKind ty1
104 (s1, s2) = coercionKind ty2 in
105 (mkAppTy t1 s1, mkAppTy t2 s2)
106 coercionKind (TyConApp tc args)
107 | Just (ar, rule) <- isCoercionTyCon_maybe tc
108 -- CoercionTyCons carry their kinding rule, so we use it here
109 = ASSERT( length args >= ar ) -- Always saturated
110 let (ty1,ty2) = rule (take ar args) -- Apply the rule to the right number of args
111 (tys1, tys2) = coercionKinds (drop ar args)
112 in (mkAppTys ty1 tys1, mkAppTys ty2 tys2)
115 = let (lArgs, rArgs) = coercionKinds args in
116 (TyConApp tc lArgs, TyConApp tc rArgs)
117 coercionKind (FunTy ty1 ty2)
118 = let (t1, t2) = coercionKind ty1
119 (s1, s2) = coercionKind ty2 in
120 (mkFunTy t1 s1, mkFunTy t2 s2)
121 coercionKind (ForAllTy tv ty)
122 = let (ty1, ty2) = coercionKind ty in
123 (ForAllTy tv ty1, ForAllTy tv ty2)
124 coercionKind (NoteTy _ ty) = coercionKind ty
125 coercionKind (PredTy (EqPred c1 c2))
126 = let k1 = coercionKindPredTy c1
127 k2 = coercionKindPredTy c2 in
129 coercionKind (PredTy (ClassP cl args))
130 = let (lArgs, rArgs) = coercionKinds args in
131 (PredTy (ClassP cl lArgs), PredTy (ClassP cl rArgs))
132 coercionKind (PredTy (IParam name ty))
133 = let (ty1, ty2) = coercionKind ty in
134 (PredTy (IParam name ty1), PredTy (IParam name ty2))
136 coercionKindPredTy :: Coercion -> CoercionKind
137 coercionKindPredTy c = let (t1, t2) = coercionKind c in mkCoKind t1 t2
139 coercionKinds :: [Coercion] -> ([Type], [Type])
140 coercionKinds tys = unzip $ map coercionKind tys
142 -------------------------------------
143 -- Coercion kind and type mk's
144 -- (make saturated TyConApp CoercionTyCon{...} args)
146 mkCoercion coCon args = ASSERT( tyConArity coCon == length args )
149 mkAppCoercion, mkFunCoercion, mkTransCoercion, mkInstCoercion :: Coercion -> Coercion -> Coercion
150 mkSymCoercion, mkLeftCoercion, mkRightCoercion :: Coercion -> Coercion
152 mkAppCoercion co1 co2 = mkAppTy co1 co2
153 mkAppsCoercion co1 tys = foldl mkAppTy co1 tys
154 -- note that a TyVar should be used here, not a CoVar (nor a TcTyVar)
155 mkForAllCoercion tv co = ASSERT ( isTyVar tv ) mkForAllTy tv co
156 mkFunCoercion co1 co2 = mkFunTy co1 co2
159 -------------------------------
160 -- This smart constructor creates a sym'ed version its argument,
161 -- but tries to push the sym's down to the leaves. If we come to
162 -- sym tv or sym tycon then we can drop the sym because tv and tycon
163 -- are reflexive coercions
165 | Just co' <- coreView co = mkSymCoercion co'
167 mkSymCoercion (ForAllTy tv ty) = ForAllTy tv (mkSymCoercion ty)
168 mkSymCoercion (AppTy co1 co2) = AppTy (mkSymCoercion co1) (mkSymCoercion co2)
169 mkSymCoercion (FunTy co1 co2) = FunTy (mkSymCoercion co1) (mkSymCoercion co2)
171 mkSymCoercion (TyConApp tc cos)
172 | not (isCoercionTyCon tc) = mkTyConApp tc (map mkSymCoercion cos)
174 mkSymCoercion (TyConApp tc [co])
175 | tc `hasKey` symCoercionTyConKey = co -- sym (sym co) --> co
176 | tc `hasKey` leftCoercionTyConKey = mkLeftCoercion (mkSymCoercion co)
177 | tc `hasKey` rightCoercionTyConKey = mkRightCoercion (mkSymCoercion co)
179 mkSymCoercion (TyConApp tc [co1,co2])
180 | tc `hasKey` transCoercionTyConKey
181 -- sym (co1 `trans` co2) --> (sym co2) `trans (sym co2)
182 -- Note reversal of arguments!
183 = mkTransCoercion (mkSymCoercion co2) (mkSymCoercion co1)
185 | tc `hasKey` instCoercionTyConKey
186 -- sym (co @ ty) --> (sym co) @ ty
187 -- Note: sym is not applied to 'ty'
188 = mkInstCoercion (mkSymCoercion co1) co2
190 mkSymCoercion (TyConApp tc cos) -- Other coercion tycons, such as those
191 = mkCoercion symCoercionTyCon [TyConApp tc cos] -- arising from newtypes
193 mkSymCoercion (TyVarTy tv)
194 | isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv]
195 | otherwise = TyVarTy tv -- Reflexive
197 -------------------------------
198 -- ToDo: we should be cleverer about transitivity
199 mkTransCoercion g1 g2 -- sym g `trans` g = id
200 | (t1,_) <- coercionKind g1
201 , (_,t2) <- coercionKind g2
206 = mkCoercion transCoercionTyCon [g1, g2]
209 -------------------------------
210 -- Smart constructors for left and right
212 | Just (co', _) <- splitAppCoercion_maybe co = co'
213 | otherwise = mkCoercion leftCoercionTyCon [co]
216 | Just (co1, co2) <- splitAppCoercion_maybe co = co2
217 | otherwise = mkCoercion rightCoercionTyCon [co]
220 | Just (tv,co') <- splitForAllTy_maybe co
221 = substTyWith [tv] [ty] co' -- (forall a.co) @ ty --> co[ty/a]
223 = mkCoercion instCoercionTyCon [co, ty]
225 mkInstsCoercion co tys = foldl mkInstCoercion co tys
227 splitSymCoercion_maybe :: Coercion -> Maybe Coercion
228 splitSymCoercion_maybe (TyConApp tc [co]) =
229 if tc `hasKey` symCoercionTyConKey
232 splitSymCoercion_maybe co = Nothing
234 splitAppCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
235 -- Splits a coercion application, being careful *not* to split (left c), etc
236 -- which are really sytactic constructs, not applications
237 splitAppCoercion_maybe co | Just co' <- coreView co = splitAppCoercion_maybe co'
238 splitAppCoercion_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
239 splitAppCoercion_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
240 splitAppCoercion_maybe (TyConApp tc tys)
241 | not (isCoercionTyCon tc)
242 = case snocView tys of
243 Just (tys', ty') -> Just (TyConApp tc tys', ty')
245 splitAppCoercion_maybe co = Nothing
247 splitTransCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
248 splitTransCoercion_maybe (TyConApp tc [ty1, ty2])
249 = if tc `hasKey` transCoercionTyConKey then
253 splitTransCoercion_maybe other = Nothing
255 splitInstCoercion_maybe :: Coercion -> Maybe (Coercion, Type)
256 splitInstCoercion_maybe (TyConApp tc [ty1, ty2])
257 = if tc `hasKey` instCoercionTyConKey then
261 splitInstCoercion_maybe other = Nothing
263 splitLeftCoercion_maybe :: Coercion -> Maybe Coercion
264 splitLeftCoercion_maybe (TyConApp tc [co])
265 = if tc `hasKey` leftCoercionTyConKey then
269 splitLeftCoercion_maybe other = Nothing
271 splitRightCoercion_maybe :: Coercion -> Maybe Coercion
272 splitRightCoercion_maybe (TyConApp tc [co])
273 = if tc `hasKey` rightCoercionTyConKey then
277 splitRightCoercion_maybe other = Nothing
279 -- Unsafe coercion is not safe, it is used when we know we are dealing with
280 -- bottom, which is one case in which it is safe. It is also used to
281 -- implement the unsafeCoerce# primitive.
282 mkUnsafeCoercion :: Type -> Type -> Coercion
283 mkUnsafeCoercion ty1 ty2
284 = mkCoercion unsafeCoercionTyCon [ty1, ty2]
287 -- See note [Newtype coercions] in TyCon
288 mkNewTypeCoercion :: Name -> TyCon -> [TyVar] -> Type -> TyCon
289 mkNewTypeCoercion name tycon tvs rhs_ty
290 = mkCoercionTyCon name co_con_arity rule
292 co_con_arity = length tvs
294 rule args = ASSERT( co_con_arity == length args )
295 (TyConApp tycon args, substTyWith tvs args rhs_ty)
297 -- Coercion identifying a data/newtype representation type and its family
298 -- instance. It has the form `Co tvs :: F ts :=: R tvs', where `Co' is the
299 -- coercion tycon built here, `F' the family tycon and `R' the (derived)
300 -- representation tycon.
302 mkDataInstCoercion :: Name -- unique name for the coercion tycon
303 -> [TyVar] -- type parameters of the coercion (`tvs')
304 -> TyCon -- family tycon (`F')
305 -> [Type] -- type instance (`ts')
306 -> TyCon -- representation tycon (`R')
307 -> TyCon -- => coercion tycon (`Co')
308 mkDataInstCoercion name tvs family instTys rep_tycon
309 = mkCoercionTyCon name coArity rule
312 rule args = (substTyWith tvs args $ -- with sigma = [tys/tvs],
313 TyConApp family instTys, -- sigma (F ts)
314 TyConApp rep_tycon args) -- :=: R tys
316 --------------------------------------
317 -- Coercion Type Constructors...
319 -- Example. The coercion ((sym c) (sym d) (sym e))
320 -- will be represented by (TyConApp sym [c, sym d, sym e])
324 -- then ((sym c) (sym d) (sym e)) :: (p1 p2 p3)=(q1 q2 q3)
326 symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, rightCoercionTyCon, instCoercionTyCon :: TyCon
327 -- Each coercion TyCon is built with the special CoercionTyCon record and
328 -- carries its own kinding rule. Such CoercionTyCons must be fully applied
329 -- by any TyConApp in which they are applied, however they may also be over
330 -- applied (see example above) and the kinding function must deal with this.
332 mkCoercionTyCon symCoercionTyConName 1 flipCoercionKindOf
334 flipCoercionKindOf (co:rest) = ASSERT( null rest ) (ty2, ty1)
336 (ty1, ty2) = coercionKind co
339 mkCoercionTyCon transCoercionTyConName 2 composeCoercionKindsOf
341 composeCoercionKindsOf (co1:co2:rest)
342 = ASSERT( null rest )
343 WARN( not (r1 `coreEqType` a2), text "Strange! Type mismatch in trans coercion, probably a bug")
346 (a1, r1) = coercionKind co1
347 (a2, r2) = coercionKind co2
350 mkCoercionTyCon leftCoercionTyConName 1 leftProjectCoercionKindOf
352 leftProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2)
354 (ty1,ty2) = fst (splitCoercionKindOf co)
357 mkCoercionTyCon rightCoercionTyConName 1 rightProjectCoercionKindOf
359 rightProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2)
361 (ty1,ty2) = snd (splitCoercionKindOf co)
363 splitCoercionKindOf :: Type -> ((Type,Type), (Type,Type))
364 -- Helper for left and right. Finds coercion kind of its input and
365 -- returns the left and right projections of the coercion...
367 -- if c :: t1 s1 :=: t2 s2 then splitCoercionKindOf c = ((t1, t2), (s1, s2))
368 splitCoercionKindOf co
369 | Just (ty1, ty2) <- splitCoercionKind_maybe (coercionKindPredTy co)
370 , Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1
371 , Just (ty_fun2, ty_arg2) <- splitAppTy_maybe ty2
372 = ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2))
375 = mkCoercionTyCon instCoercionTyConName 2 instCoercionKind
378 let Just (tv, ty) = splitForAllTy_maybe t in
379 substTyWith [tv] [s] ty
381 instCoercionKind (co1:ty:rest) = ASSERT( null rest )
382 (instantiateCo t1 ty, instantiateCo t2 ty)
383 where (t1, t2) = coercionKind co1
386 = mkCoercionTyCon unsafeCoercionTyConName 2 unsafeCoercionKind
388 unsafeCoercionKind (ty1:ty2:rest) = ASSERT( null rest ) (ty1,ty2)
390 --------------------------------------
391 -- ...and their names
393 mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkOccNameFS tcName occ)
394 key (ATyCon coCon) BuiltInSyntax
396 transCoercionTyConName = mkCoConName FSLIT("trans") transCoercionTyConKey transCoercionTyCon
397 symCoercionTyConName = mkCoConName FSLIT("sym") symCoercionTyConKey symCoercionTyCon
398 leftCoercionTyConName = mkCoConName FSLIT("left") leftCoercionTyConKey leftCoercionTyCon
399 rightCoercionTyConName = mkCoConName FSLIT("right") rightCoercionTyConKey rightCoercionTyCon
400 instCoercionTyConName = mkCoConName FSLIT("inst") instCoercionTyConKey instCoercionTyCon
401 unsafeCoercionTyConName = mkCoConName FSLIT("CoUnsafe") unsafeCoercionTyConKey unsafeCoercionTyCon
405 -- this is here to avoid module loops
406 splitNewTypeRepCo_maybe :: Type -> Maybe (Type, Coercion)
407 -- Sometimes we want to look through a newtype and get its associated coercion
408 -- It only strips *one layer* off, so the caller will usually call itself recursively
409 -- Only applied to types of kind *, hence the newtype is always saturated
410 splitNewTypeRepCo_maybe ty
411 | Just ty' <- coreView ty = splitNewTypeRepCo_maybe ty'
412 splitNewTypeRepCo_maybe (TyConApp tc tys)
413 | isClosedNewTyCon tc
414 = ASSERT( tys `lengthIs` tyConArity tc ) -- splitNewTypeRepCo_maybe only be applied
415 -- to *types* (of kind *)
416 case newTyConRhs tc of
418 ASSERT( length tvs == length tys )
419 Just (substTyWith tvs tys rep_ty, mkTyConApp co_con tys)
421 co_con = maybe (pprPanic "splitNewTypeRepCo_maybe" (ppr tc)) id (newTyConCo_maybe tc)
422 splitNewTypeRepCo_maybe other = Nothing