2 % (c) The University of Glasgow 2006
3 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
6 %************************************************************************
8 Type refinement for GADTs
10 %************************************************************************
14 -- The above warning supression flag is a temporary kludge.
15 -- While working on this module you are encouraged to remove it and fix
16 -- any warnings in the module. See
17 -- http://hackage.haskell.org/trac/ghc/wiki/CodingStyle#Warnings
21 Refinement, emptyRefinement, isEmptyRefinement,
23 refineType, refinePred, refineResType,
24 tcUnifyTys, BindFlag(..)
27 #include "HsVersions.h"
50 %************************************************************************
54 %************************************************************************
57 data Refinement = Reft InScopeSet InternalReft
59 type InternalReft = TyVarEnv (Coercion, Type)
60 -- INVARIANT: a->(co,ty) then co :: (a:=:ty)
61 -- Not necessarily idemopotent
63 instance Outputable Refinement where
64 ppr (Reft in_scope env)
65 = ptext SLIT("Refinement") <+>
68 emptyRefinement :: Refinement
69 emptyRefinement = (Reft emptyInScopeSet emptyVarEnv)
71 isEmptyRefinement :: Refinement -> Bool
72 isEmptyRefinement (Reft _ env) = isEmptyVarEnv env
74 refineType :: Refinement -> Type -> Maybe (Coercion, Type)
75 -- Apply the refinement to the type.
76 -- If (refineType r ty) = (co, ty')
77 -- Then co :: ty:=:ty'
78 -- Nothing => the refinement does nothing to this type
79 refineType (Reft in_scope env) ty
80 | not (isEmptyVarEnv env), -- Common case
81 any (`elemVarEnv` env) (varSetElems (tyVarsOfType ty))
82 = Just (substTy co_subst ty, substTy tv_subst ty)
84 = Nothing -- The type doesn't mention any refined type variables
86 tv_subst = mkTvSubst in_scope (mapVarEnv snd env)
87 co_subst = mkTvSubst in_scope (mapVarEnv fst env)
89 refinePred :: Refinement -> PredType -> Maybe (Coercion, PredType)
90 refinePred (Reft in_scope env) pred
91 | not (isEmptyVarEnv env), -- Common case
92 any (`elemVarEnv` env) (varSetElems (tyVarsOfPred pred))
93 = Just (mkPredTy (substPred co_subst pred), substPred tv_subst pred)
95 = Nothing -- The type doesn't mention any refined type variables
97 tv_subst = mkTvSubst in_scope (mapVarEnv snd env)
98 co_subst = mkTvSubst in_scope (mapVarEnv fst env)
100 refineResType :: Refinement -> Type -> (HsWrapper, Type)
101 -- Like refineType, but returns the 'sym' coercion
102 -- If (refineResType r ty) = (co, ty')
103 -- Then co :: ty':=:ty
104 -- It's convenient to return a HsWrapper here
105 refineResType reft ty
106 = case refineType reft ty of
107 Just (co, ty1) -> (WpCo (mkSymCoercion co), ty1)
108 Nothing -> (idHsWrapper, ty)
112 %************************************************************************
114 Generating a type refinement
116 %************************************************************************
119 gadtRefine :: Refinement
120 -> [TyVar] -- Bind these by preference
122 -> MaybeErr Message Refinement
125 (gadtRefine cvs) takes a list of coercion variables, and returns a
126 list of coercions, obtained by unifying the types equated by the
127 incoming coercions. The returned coercions all have kinds of form
128 (a:=:ty), where a is a rigid type variable.
131 gadtRefine [c :: (a,Int):=:(Bool,b)]
132 = [ right (left c) :: a:=:Bool,
133 sym (right c) :: b:=:Int ]
135 That is, given evidence 'c' that (a,Int)=(Bool,b), it returns derived
136 evidence in easy-to-use form. In particular, given any e::ty, we know
138 e `cast` ty[right (left c)/a, sym (right c)/b]
139 :: ty [Bool/a, Int/b]
143 - It can fail, if the coercion is unsatisfiable.
145 - It's biased, by being given a set of type variables to bind
146 when there is a choice. Example:
147 MkT :: forall a. a -> T [a]
148 f :: forall b. T [b] -> b
149 f x = let v = case x of { MkT y -> y }
151 Here we want to bind [a->b], not the other way round, because
152 in this example the return type is wobbly, and we want the
156 -- E.g. (a, Bool, right (left c))
157 -- INVARIANT: in the triple (tv, ty, co), we have (co :: tv:=:ty)
158 -- The result is idempotent: the
161 gadtRefine (Reft in_scope env1)
163 -- Precondition: fvs( co_vars ) # env1
164 -- That is, the kinds of the co_vars are a
165 -- fixed point of the incoming refinement
167 = ASSERT2( not $ any (`elemVarEnv` env1) (varSetElems $ tyVarsOfTypes $ map tyVarKind co_vars),
168 ppr env1 $$ ppr co_vars $$ ppr (map tyVarKind co_vars) )
169 initUM (tryToBind tv_set) $
170 do { -- Run the unifier, starting with an empty env
171 ; env2 <- foldM do_one emptyInternalReft co_vars
173 -- Find the fixed point of the resulting
174 -- non-idempotent substitution
175 ; let tmp_env = env1 `plusVarEnv` env2
176 out_env = fixTvCoEnv in_scope' tmp_env
177 ; WARN( not (null (badReftElts tmp_env)), ppr (badReftElts tmp_env) $$ ppr tmp_env )
178 WARN( not (null (badReftElts out_env)), ppr (badReftElts out_env) $$ ppr out_env )
179 return (Reft in_scope' out_env) }
181 tv_set = mkVarSet ex_tvs
182 in_scope' = foldr extend in_scope co_vars
184 -- For each co_var, add it *and* the tyvars it mentions, to in_scope
185 extend co_var in_scope
186 = extendInScopeSetSet in_scope $
187 extendVarSet (tyVarsOfType (tyVarKind co_var)) co_var
189 do_one reft co_var = unify reft (TyVarTy co_var) ty1 ty2
191 (ty1,ty2) = splitCoercionKind (tyVarKind co_var)
194 %************************************************************************
198 %************************************************************************
201 tcUnifyTys :: (TyVar -> BindFlag)
203 -> Maybe TvSubst -- A regular one-shot substitution
204 -- The two types may have common type variables, and indeed do so in the
205 -- second call to tcUnifyTys in FunDeps.checkClsFD
207 -- We implement tcUnifyTys using the evidence-generating 'unify' function
208 -- in this module, even though we don't need to generate any evidence.
209 -- This is simply to avoid replicating all all the code for unify
210 tcUnifyTys bind_fn tys1 tys2
211 = maybeErrToMaybe $ initUM bind_fn $
212 do { reft <- unifyList emptyInternalReft cos tys1 tys2
214 -- Find the fixed point of the resulting non-idempotent substitution
215 ; let in_scope = mkInScopeSet (tvs1 `unionVarSet` tvs2)
216 tv_env = fixTvSubstEnv in_scope (mapVarEnv snd reft)
218 ; return (mkTvSubst in_scope tv_env) }
220 tvs1 = tyVarsOfTypes tys1
221 tvs2 = tyVarsOfTypes tys2
222 cos = zipWith mkUnsafeCoercion tys1 tys2
225 ----------------------------
226 fixTvCoEnv :: InScopeSet -> InternalReft -> InternalReft
227 -- Find the fixed point of a Refinement
228 -- (assuming it has no loops!)
229 fixTvCoEnv in_scope env
232 fixpt = mapVarEnv step env
234 step (co, ty) = case refineType (Reft in_scope fixpt) ty of
236 Just (co', ty') -> (mkTransCoercion co co', ty')
237 -- Apply fixpt one step:
238 -- Use refineType to get a substituted type, ty', and a coercion, co_fn,
239 -- which justifies the substitution. If the coercion is not the identity
240 -- then use transitivity with the original coercion
242 -----------------------------
243 fixTvSubstEnv :: InScopeSet -> TvSubstEnv -> TvSubstEnv
244 fixTvSubstEnv in_scope env
247 fixpt = mapVarEnv (substTy (mkTvSubst in_scope fixpt)) env
249 ----------------------------
250 tryToBind :: TyVarSet -> TyVar -> BindFlag
251 tryToBind tv_set tv | tv `elemVarSet` tv_set = BindMe
252 | otherwise = AvoidMe
257 %************************************************************************
261 %************************************************************************
265 badReftElts :: InternalReft -> [(Unique, (Coercion,Type))]
266 -- Return the BAD elements of the refinement
267 -- Should be empty; used in asserions only
269 = filter (not . ok) (ufmToList env)
271 ok :: (Unique, (Coercion, Type)) -> Bool
272 ok (u, (co, ty)) | Just tv <- tcGetTyVar_maybe ty1
273 = varUnique tv == u && ty `tcEqType` ty2
276 (ty1,ty2) = coercionKind co
279 emptyInternalReft :: InternalReft
280 emptyInternalReft = emptyVarEnv
282 unify :: InternalReft -- An existing substitution to extend
283 -> Coercion -- Witness of their equality
284 -> Type -> Type -- Types to be unified, and witness of their equality
285 -> UM InternalReft -- Just the extended substitution,
286 -- Nothing if unification failed
287 -- We do not require the incoming substitution to be idempotent,
288 -- nor guarantee that the outgoing one is. That's fixed up by
291 -- PRE-CONDITION: in the call (unify r co ty1 ty2), we know that
294 -- Respects newtypes, PredTypes
296 unify subst co ty1 ty2 = -- pprTrace "unify" (ppr subst <+> pprParendType ty1 <+> pprParendType ty2) $
297 unify_ subst co ty1 ty2
299 -- in unify_, any NewTcApps/Preds should be taken at face value
300 unify_ subst co (TyVarTy tv1) ty2 = uVar False subst co tv1 ty2
301 unify_ subst co ty1 (TyVarTy tv2) = uVar True subst co tv2 ty1
303 unify_ subst co ty1 ty2 | Just ty1' <- tcView ty1 = unify subst co ty1' ty2
304 unify_ subst co ty1 ty2 | Just ty2' <- tcView ty2 = unify subst co ty1 ty2'
306 unify_ subst co (PredTy p1) (PredTy p2) = unify_pred subst co p1 p2
308 unify_ subst co t1@(TyConApp tyc1 tys1) t2@(TyConApp tyc2 tys2)
309 | tyc1 == tyc2 = unify_tys subst co tys1 tys2
311 unify_ subst co (FunTy ty1a ty1b) (FunTy ty2a ty2b)
312 = do { let [co1,co2] = decomposeCo 2 co
313 ; subst' <- unify subst co1 ty1a ty2a
314 ; unify subst' co2 ty1b ty2b }
316 -- Applications need a bit of care!
317 -- They can match FunTy and TyConApp, so use splitAppTy_maybe
318 -- NB: we've already dealt with type variables and Notes,
319 -- so if one type is an App the other one jolly well better be too
320 unify_ subst co (AppTy ty1a ty1b) ty2
321 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
322 = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
323 ; unify subst' (mkRightCoercion co) ty1b ty2b }
325 unify_ subst co ty1 (AppTy ty2a ty2b)
326 | Just (ty1a, ty1b) <- repSplitAppTy_maybe ty1
327 = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
328 ; unify subst' (mkRightCoercion co) ty1b ty2b }
330 unify_ subst co ty1 ty2 = failWith (misMatch ty1 ty2)
334 ------------------------------
335 unify_pred subst co (ClassP c1 tys1) (ClassP c2 tys2)
336 | c1 == c2 = unify_tys subst co tys1 tys2
337 unify_pred subst co (IParam n1 t1) (IParam n2 t2)
338 | n1 == n2 = unify subst co t1 t2
339 unify_pred subst co p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2))
341 ------------------------------
342 unify_tys :: InternalReft -> Coercion -> [Type] -> [Type] -> UM InternalReft
343 unify_tys subst co xs ys
344 = unifyList subst (decomposeCo (length xs) co) xs ys
346 unifyList :: InternalReft -> [Coercion] -> [Type] -> [Type] -> UM InternalReft
347 unifyList subst orig_cos orig_xs orig_ys
348 = go subst orig_cos orig_xs orig_ys
350 go subst _ [] [] = return subst
351 go subst (co:cos) (x:xs) (y:ys) = do { subst' <- unify subst co x y
352 ; go subst' cos xs ys }
353 go subst _ _ _ = failWith (lengthMisMatch orig_xs orig_ys)
355 ---------------------------------
356 uVar :: Bool -- Swapped
357 -> InternalReft -- An existing substitution to extend
359 -> TyVar -- Type variable to be unified
360 -> Type -- with this type
363 -- PRE-CONDITION: in the call (uVar swap r co tv1 ty), we know that
364 -- if swap=False co :: (tv1:=:ty)
365 -- if swap=True co :: (ty:=:tv1)
367 uVar swap subst co tv1 ty
368 = -- Check to see whether tv1 is refined by the substitution
369 case (lookupVarEnv subst tv1) of
371 -- Yes, call back into unify'
372 Just (co',ty') -- co' :: (tv1:=:ty')
373 | swap -- co :: (ty:=:tv1)
374 -> unify subst (mkTransCoercion co co') ty ty'
375 | otherwise -- co :: (tv1:=:ty)
376 -> unify subst (mkTransCoercion (mkSymCoercion co') co) ty' ty
379 Nothing -> uUnrefined swap subst co
383 uUnrefined :: Bool -- Whether the input is swapped
384 -> InternalReft -- An existing substitution to extend
386 -> TyVar -- Type variable to be unified
387 -> Type -- with this type
388 -> Type -- (de-noted version)
391 -- We know that tv1 isn't refined
392 -- PRE-CONDITION: in the call (uUnrefined False r co tv1 ty2 ty2'), we know that
394 -- and if the first argument is True instead, we know
397 uUnrefined swap subst co tv1 ty2 ty2'
398 | Just ty2'' <- tcView ty2'
399 = uUnrefined swap subst co tv1 ty2 ty2'' -- Unwrap synonyms
400 -- This is essential, in case we have
402 -- and then unify a :=: Foo a
404 uUnrefined swap subst co tv1 ty2 (TyVarTy tv2)
405 | tv1 == tv2 -- Same type variable
408 -- Check to see whether tv2 is refined
409 | Just (co',ty') <- lookupVarEnv subst tv2 -- co' :: tv2:=:ty'
410 = uUnrefined False subst (mkTransCoercion (doSwap swap co) co') tv1 ty' ty'
412 -- So both are unrefined; next, see if the kinds force the direction
413 | eqKind k1 k2 -- Can update either; so check the bind-flags
414 = do { b1 <- tvBindFlag tv1
415 ; b2 <- tvBindFlag tv2
417 (BindMe, _) -> bind swap tv1 ty2
419 (AvoidMe, BindMe) -> bind (not swap) tv2 ty1
420 (AvoidMe, _) -> bind swap tv1 ty2
422 (WildCard, WildCard) -> return subst
423 (WildCard, Skolem) -> return subst
424 (WildCard, _) -> bind (not swap) tv2 ty1
426 (Skolem, WildCard) -> return subst
427 (Skolem, Skolem) -> failWith (misMatch ty1 ty2)
428 (Skolem, _) -> bind (not swap) tv2 ty1
431 | k1 `isSubKind` k2 = bindTv (not swap) subst co tv2 ty1 -- Must update tv2
432 | k2 `isSubKind` k1 = bindTv swap subst co tv1 ty2 -- Must update tv1
434 | otherwise = failWith (kindMisMatch tv1 ty2)
439 bind swap tv ty = extendReft swap subst tv co ty
441 uUnrefined swap subst co tv1 ty2 ty2' -- ty2 is not a type variable
442 | tv1 `elemVarSet` substTvSet subst (tyVarsOfType ty2')
443 = failWith (occursCheck tv1 ty2) -- Occurs check
444 | not (k2 `isSubKind` k1)
445 = failWith (kindMisMatch tv1 ty2) -- Kind check
447 = bindTv swap subst co tv1 ty2 -- Bind tyvar to the synonym if poss
452 substTvSet :: InternalReft -> TyVarSet -> TyVarSet
453 -- Apply the non-idempotent substitution to a set of type variables,
454 -- remembering that the substitution isn't necessarily idempotent
456 = foldVarSet (unionVarSet . get) emptyVarSet tvs
458 get tv = case lookupVarEnv subst tv of
459 Nothing -> unitVarSet tv
460 Just (_,ty) -> substTvSet subst (tyVarsOfType ty)
462 bindTv swap subst co tv ty -- ty is not a type variable
463 = do { b <- tvBindFlag tv
465 Skolem -> failWith (misMatch (TyVarTy tv) ty)
466 WildCard -> return subst
467 other -> extendReft swap subst tv co ty
470 doSwap :: Bool -> Coercion -> Coercion
471 doSwap swap co = if swap then mkSymCoercion co else co
479 extendReft swap subst tv co ty
480 = ASSERT2( (coercionKindPredTy co1 `tcEqType` mkCoKind (mkTyVarTy tv) ty),
481 (text "Refinement invariant failure: co = " <+> ppr co1 <+> ppr (coercionKindPredTy co1) $$ text "subst = " <+> ppr tv <+> ppr (mkCoKind (mkTyVarTy tv) ty)) )
482 return (extendVarEnv subst tv (co1, ty))
488 %************************************************************************
492 %************************************************************************
496 = BindMe -- A regular type variable
497 | AvoidMe -- Like BindMe but, given the choice, avoid binding it
499 | Skolem -- This type variable is a skolem constant
500 -- Don't bind it; it only matches itself
502 | WildCard -- This type variable matches anything,
503 -- and does not affect the substitution
505 newtype UM a = UM { unUM :: (TyVar -> BindFlag)
506 -> MaybeErr Message a }
508 instance Monad UM where
509 return a = UM (\tvs -> Succeeded a)
510 fail s = UM (\tvs -> Failed (text s))
511 m >>= k = UM (\tvs -> case unUM m tvs of
512 Failed err -> Failed err
513 Succeeded v -> unUM (k v) tvs)
515 initUM :: (TyVar -> BindFlag) -> UM a -> MaybeErr Message a
516 initUM badtvs um = unUM um badtvs
518 tvBindFlag :: TyVar -> UM BindFlag
519 tvBindFlag tv = UM (\tv_fn -> Succeeded (tv_fn tv))
521 failWith :: Message -> UM a
522 failWith msg = UM (\tv_fn -> Failed msg)
524 maybeErrToMaybe :: MaybeErr fail succ -> Maybe succ
525 maybeErrToMaybe (Succeeded a) = Just a
526 maybeErrToMaybe (Failed m) = Nothing
530 %************************************************************************
533 We go to a lot more trouble to tidy the types
534 in TcUnify. Maybe we'll end up having to do that
535 here too, but I'll leave it for now.
537 %************************************************************************
541 = ptext SLIT("Can't match types") <+> quotes (ppr t1) <+>
542 ptext SLIT("and") <+> quotes (ppr t2)
544 lengthMisMatch tys1 tys2
545 = sep [ptext SLIT("Can't match unequal length lists"),
546 nest 2 (ppr tys1), nest 2 (ppr tys2) ]
549 = vcat [ptext SLIT("Can't match kinds") <+> quotes (ppr (tyVarKind tv1)) <+>
550 ptext SLIT("and") <+> quotes (ppr (typeKind t2)),
551 ptext SLIT("when matching") <+> quotes (ppr tv1) <+>
552 ptext SLIT("with") <+> quotes (ppr t2)]
555 = hang (ptext SLIT("Can't construct the infinite type"))
556 2 (ppr tv <+> equals <+> ppr ty)