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"
42 import Var hiding (isCoVar)
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
94 isCoVar :: Var -> Bool
95 isCoVar tv = isTyVar tv && isCoercionKind (tyVarKind tv)
98 type CoercionKind = Kind -- A CoercionKind is always of form (ty1 :=: ty2)
100 coercionKind :: Coercion -> (Type, Type)
102 -- Then (coercionKind c) = (t1,t2)
103 coercionKind ty@(TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind a)
104 | otherwise = (ty, ty)
105 coercionKind (AppTy ty1 ty2)
106 = let (t1, t2) = coercionKind ty1
107 (s1, s2) = coercionKind ty2 in
108 (mkAppTy t1 s1, mkAppTy t2 s2)
109 coercionKind (TyConApp tc args)
110 | Just (ar, rule) <- isCoercionTyCon_maybe tc
111 -- CoercionTyCons carry their kinding rule, so we use it here
112 = ASSERT( length args >= ar ) -- Always saturated
113 let (ty1,ty2) = rule (take ar args) -- Apply the rule to the right number of args
114 (tys1, tys2) = coercionKinds (drop ar args)
115 in (mkAppTys ty1 tys1, mkAppTys ty2 tys2)
118 = let (lArgs, rArgs) = coercionKinds args in
119 (TyConApp tc lArgs, TyConApp tc rArgs)
120 coercionKind (FunTy ty1 ty2)
121 = let (t1, t2) = coercionKind ty1
122 (s1, s2) = coercionKind ty2 in
123 (mkFunTy t1 s1, mkFunTy t2 s2)
124 coercionKind (ForAllTy tv ty)
125 = let (ty1, ty2) = coercionKind ty in
126 (ForAllTy tv ty1, ForAllTy tv ty2)
127 coercionKind (NoteTy _ ty) = coercionKind ty
128 coercionKind (PredTy (EqPred c1 c2))
129 = let k1 = coercionKindPredTy c1
130 k2 = coercionKindPredTy c2 in
132 coercionKind (PredTy (ClassP cl args))
133 = let (lArgs, rArgs) = coercionKinds args in
134 (PredTy (ClassP cl lArgs), PredTy (ClassP cl rArgs))
135 coercionKind (PredTy (IParam name ty))
136 = let (ty1, ty2) = coercionKind ty in
137 (PredTy (IParam name ty1), PredTy (IParam name ty2))
139 coercionKindPredTy :: Coercion -> CoercionKind
140 coercionKindPredTy c = let (t1, t2) = coercionKind c in mkCoKind t1 t2
142 coercionKinds :: [Coercion] -> ([Type], [Type])
143 coercionKinds tys = unzip $ map coercionKind tys
145 -------------------------------------
146 -- Coercion kind and type mk's
147 -- (make saturated TyConApp CoercionTyCon{...} args)
149 mkCoercion coCon args = ASSERT( tyConArity coCon == length args )
152 mkAppCoercion, mkFunCoercion, mkTransCoercion, mkInstCoercion :: Coercion -> Coercion -> Coercion
153 mkSymCoercion, mkLeftCoercion, mkRightCoercion :: Coercion -> Coercion
155 mkAppCoercion co1 co2 = mkAppTy co1 co2
156 mkAppsCoercion co1 tys = foldl mkAppTy co1 tys
157 -- note that a TyVar should be used here, not a CoVar (nor a TcTyVar)
158 mkForAllCoercion tv co = ASSERT ( isTyVar tv ) mkForAllTy tv co
159 mkFunCoercion co1 co2 = mkFunTy co1 co2
162 -- This smart constructor creates a sym'ed version its argument,
163 -- but tries to push the sym's down to the leaves. If we come to
164 -- sym tv or sym tycon then we can drop the sym because tv and tycon
165 -- are reflexive coercions
167 | Just co2 <- splitSymCoercion_maybe co = co2
168 -- sym (sym co) --> co
169 | Just (co1, arg_tys) <- splitTyConApp_maybe co
170 , not (isCoercionTyCon co1) = mkTyConApp co1 (map mkSymCoercion arg_tys)
171 -- we can drop the sym for a TyCon
172 -- sym (ty [t1, ..., tn]) --> ty [sym t1, ..., sym tn]
173 | (co1, arg_tys) <- splitAppTys co
174 , isTyVarTy co1 = mkAppTys (maybe_drop co1) (map mkSymCoercion arg_tys)
175 -- sym (tv [t1, ..., tn]) --> tv [sym t1, ..., sym tn]
176 -- if tv type variable
177 -- sym (cv [t1, ..., tn]) --> (sym cv) [sym t1, ..., sym tn]
178 -- if cv is a coercion variable
179 -- fall through if head is a CoercionTyCon
180 | Just (co1, co2) <- splitTransCoercion_maybe co
181 -- sym (co1 `trans` co2) --> (sym co2) `trans (sym co2)
182 = mkTransCoercion (mkSymCoercion co2) (mkSymCoercion co1)
183 | Just (co, ty) <- splitInstCoercion_maybe co
184 -- sym (co @ ty) --> (sym co) @ ty
185 = mkInstCoercion (mkSymCoercion co) ty
186 | Just co <- splitLeftCoercion_maybe co
187 -- sym (left co) --> left (sym co)
188 = mkLeftCoercion (mkSymCoercion co)
189 | Just co <- splitRightCoercion_maybe co
190 -- sym (right co) --> right (sym co)
191 = mkRightCoercion (mkSymCoercion co)
193 maybe_drop (TyVarTy tv)
194 | isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv]
195 | otherwise = TyVarTy tv
196 maybe_drop other = other
197 mkSymCoercion (ForAllTy tv ty) = ForAllTy tv (mkSymCoercion ty)
198 -- for atomic types and constructors, we can just ignore sym since these
199 -- are reflexive coercions
200 mkSymCoercion (TyVarTy tv)
201 | isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv]
202 | otherwise = TyVarTy tv
203 mkSymCoercion co = mkCoercion symCoercionTyCon [co]
205 -- Smart constructors for left and right
207 | Just (co', _) <- splitAppCoercion_maybe co = co'
208 | otherwise = mkCoercion leftCoercionTyCon [co]
211 | Just (co1, co2) <- splitAppCoercion_maybe co = co2
212 | otherwise = mkCoercion rightCoercionTyCon [co]
214 mkTransCoercion co1 co2 = mkCoercion transCoercionTyCon [co1, co2]
216 mkInstCoercion co ty = mkCoercion instCoercionTyCon [co, ty]
218 mkInstsCoercion co tys = foldl mkInstCoercion co tys
220 splitSymCoercion_maybe :: Coercion -> Maybe Coercion
221 splitSymCoercion_maybe (TyConApp tc [co]) =
222 if tc `hasKey` symCoercionTyConKey
225 splitSymCoercion_maybe co = Nothing
227 splitAppCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
228 -- Splits a coercion application, being careful *not* to split (left c), etc
229 -- which are really sytactic constructs, not applications
230 splitAppCoercion_maybe co | Just co' <- coreView co = splitAppCoercion_maybe co'
231 splitAppCoercion_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
232 splitAppCoercion_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
233 splitAppCoercion_maybe (TyConApp tc tys)
234 | not (isCoercionTyCon tc)
235 = case snocView tys of
236 Just (tys', ty') -> Just (TyConApp tc tys', ty')
238 splitAppCoercion_maybe co = Nothing
240 splitTransCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
241 splitTransCoercion_maybe (TyConApp tc [ty1, ty2])
242 = if tc `hasKey` transCoercionTyConKey then
246 splitTransCoercion_maybe other = Nothing
248 splitInstCoercion_maybe :: Coercion -> Maybe (Coercion, Type)
249 splitInstCoercion_maybe (TyConApp tc [ty1, ty2])
250 = if tc `hasKey` instCoercionTyConKey then
254 splitInstCoercion_maybe other = Nothing
256 splitLeftCoercion_maybe :: Coercion -> Maybe Coercion
257 splitLeftCoercion_maybe (TyConApp tc [co])
258 = if tc `hasKey` leftCoercionTyConKey then
262 splitLeftCoercion_maybe other = Nothing
264 splitRightCoercion_maybe :: Coercion -> Maybe Coercion
265 splitRightCoercion_maybe (TyConApp tc [co])
266 = if tc `hasKey` rightCoercionTyConKey then
270 splitRightCoercion_maybe other = Nothing
272 -- Unsafe coercion is not safe, it is used when we know we are dealing with
273 -- bottom, which is one case in which it is safe. It is also used to
274 -- implement the unsafeCoerce# primitive.
275 mkUnsafeCoercion :: Type -> Type -> Coercion
276 mkUnsafeCoercion ty1 ty2
277 = mkCoercion unsafeCoercionTyCon [ty1, ty2]
280 -- See note [Newtype coercions] in TyCon
281 mkNewTypeCoercion :: Name -> TyCon -> ([TyVar], Type) -> TyCon
282 mkNewTypeCoercion name tycon (tvs, rhs_ty)
283 = mkCoercionTyCon name co_con_arity rule
285 co_con_arity = length tvs
287 rule args = ASSERT( co_con_arity == length args )
288 (TyConApp tycon args, substTyWith tvs args rhs_ty)
290 -- Coercion identifying a data/newtype representation type and its family
291 -- instance. It has the form `Co tvs :: F ts :=: R tvs', where `Co' is the
292 -- coercion tycon built here, `F' the family tycon and `R' the (derived)
293 -- representation tycon.
295 mkDataInstCoercion :: Name -- unique name for the coercion tycon
296 -> [TyVar] -- type parameters of the coercion (`tvs')
297 -> TyCon -- family tycon (`F')
298 -> [Type] -- type instance (`ts')
299 -> TyCon -- representation tycon (`R')
300 -> TyCon -- => coercion tycon (`Co')
301 mkDataInstCoercion name tvs family instTys rep_tycon
302 = mkCoercionTyCon name coArity rule
305 rule args = (substTyWith tvs args $ -- with sigma = [tys/tvs],
306 TyConApp family instTys, -- sigma (F ts)
307 TyConApp rep_tycon args) -- :=: R tys
309 --------------------------------------
310 -- Coercion Type Constructors...
312 -- Example. The coercion ((sym c) (sym d) (sym e))
313 -- will be represented by (TyConApp sym [c, sym d, sym e])
317 -- then ((sym c) (sym d) (sym e)) :: (p1 p2 p3)=(q1 q2 q3)
319 symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, rightCoercionTyCon, instCoercionTyCon :: TyCon
320 -- Each coercion TyCon is built with the special CoercionTyCon record and
321 -- carries its own kinding rule. Such CoercionTyCons must be fully applied
322 -- by any TyConApp in which they are applied, however they may also be over
323 -- applied (see example above) and the kinding function must deal with this.
325 mkCoercionTyCon symCoercionTyConName 1 flipCoercionKindOf
327 flipCoercionKindOf (co:rest) = ASSERT( null rest ) (ty2, ty1)
329 (ty1, ty2) = coercionKind co
332 mkCoercionTyCon transCoercionTyConName 2 composeCoercionKindsOf
334 composeCoercionKindsOf (co1:co2:rest)
335 = ASSERT( null rest )
336 WARN( not (r1 `coreEqType` a2), text "Strange! Type mismatch in trans coercion, probably a bug")
339 (a1, r1) = coercionKind co1
340 (a2, r2) = coercionKind co2
343 mkCoercionTyCon leftCoercionTyConName 1 leftProjectCoercionKindOf
345 leftProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2)
347 (ty1,ty2) = fst (splitCoercionKindOf co)
350 mkCoercionTyCon rightCoercionTyConName 1 rightProjectCoercionKindOf
352 rightProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2)
354 (ty1,ty2) = snd (splitCoercionKindOf co)
356 splitCoercionKindOf :: Type -> ((Type,Type), (Type,Type))
357 -- Helper for left and right. Finds coercion kind of its input and
358 -- returns the left and right projections of the coercion...
360 -- if c :: t1 s1 :=: t2 s2 then splitCoercionKindOf c = ((t1, t2), (s1, s2))
361 splitCoercionKindOf co
362 | Just (ty1, ty2) <- splitCoercionKind_maybe (coercionKindPredTy co)
363 , Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1
364 , Just (ty_fun2, ty_arg2) <- splitAppTy_maybe ty2
365 = ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2))
368 = mkCoercionTyCon instCoercionTyConName 2 instCoercionKind
371 let Just (tv, ty) = splitForAllTy_maybe t in
372 substTyWith [tv] [s] ty
374 instCoercionKind (co1:ty:rest) = ASSERT( null rest )
375 (instantiateCo t1 ty, instantiateCo t2 ty)
376 where (t1, t2) = coercionKind co1
379 = mkCoercionTyCon unsafeCoercionTyConName 2 unsafeCoercionKind
381 unsafeCoercionKind (ty1:ty2:rest) = ASSERT( null rest ) (ty1,ty2)
383 --------------------------------------
384 -- ...and their names
386 mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkOccNameFS tcName occ)
387 key (ATyCon coCon) BuiltInSyntax
389 transCoercionTyConName = mkCoConName FSLIT("trans") transCoercionTyConKey transCoercionTyCon
390 symCoercionTyConName = mkCoConName FSLIT("sym") symCoercionTyConKey symCoercionTyCon
391 leftCoercionTyConName = mkCoConName FSLIT("left") leftCoercionTyConKey leftCoercionTyCon
392 rightCoercionTyConName = mkCoConName FSLIT("right") rightCoercionTyConKey rightCoercionTyCon
393 instCoercionTyConName = mkCoConName FSLIT("inst") instCoercionTyConKey instCoercionTyCon
394 unsafeCoercionTyConName = mkCoConName FSLIT("CoUnsafe") unsafeCoercionTyConKey unsafeCoercionTyCon
398 -- this is here to avoid module loops
399 splitNewTypeRepCo_maybe :: Type -> Maybe (Type, Coercion)
400 -- Sometimes we want to look through a newtype and get its associated coercion
401 -- It only strips *one layer* off, so the caller will usually call itself recursively
402 -- Only applied to types of kind *, hence the newtype is always saturated
403 splitNewTypeRepCo_maybe ty
404 | Just ty' <- coreView ty = splitNewTypeRepCo_maybe ty'
405 splitNewTypeRepCo_maybe (TyConApp tc tys)
406 | isClosedNewTyCon tc
407 = ASSERT( tys `lengthIs` tyConArity tc ) -- splitNewTypeRepCo_maybe only be applied
408 -- to *types* (of kind *)
409 case newTyConRhs tc of
411 ASSERT( length tvs == length tys )
412 Just (substTyWith tvs tys rep_ty, mkTyConApp co_con tys)
414 co_con = maybe (pprPanic "splitNewTypeRepCo_maybe" (ppr tc)) id (newTyConCo_maybe tc)
415 splitNewTypeRepCo_maybe other = Nothing