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 Refinement, emptyRefinement, gadtRefine,
15 refineType, refineResType,
17 tcUnifyTys, BindFlag(..)
20 #include "HsVersions.h"
42 %************************************************************************
46 %************************************************************************
49 data Refinement = Reft InScopeSet InternalReft
50 -- INVARIANT: a->(co,ty) then co :: (a:=:ty)
51 -- Not necessarily idemopotent
53 instance Outputable Refinement where
54 ppr (Reft in_scope env)
55 = ptext SLIT("Refinement") <+>
58 emptyRefinement :: Refinement
59 emptyRefinement = (Reft emptyInScopeSet emptyVarEnv)
62 refineType :: Refinement -> Type -> Maybe (Coercion, Type)
63 -- Apply the refinement to the type.
64 -- If (refineType r ty) = (co, ty')
65 -- Then co :: ty:=:ty'
66 -- Nothing => the refinement does nothing to this type
67 refineType (Reft in_scope env) ty
68 | not (isEmptyVarEnv env), -- Common case
69 any (`elemVarEnv` env) (varSetElems (tyVarsOfType ty))
70 = Just (substTy co_subst ty, substTy tv_subst ty)
72 = Nothing -- The type doesn't mention any refined type variables
74 tv_subst = mkTvSubst in_scope (mapVarEnv snd env)
75 co_subst = mkTvSubst in_scope (mapVarEnv fst env)
77 refineResType :: Refinement -> Type -> (HsWrapper, Type)
78 -- Like refineType, but returns the 'sym' coercion
79 -- If (refineResType r ty) = (co, ty')
80 -- Then co :: ty':=:ty
81 -- It's convenient to return a HsWrapper here
83 = case refineType reft ty of
84 Just (co, ty1) -> (WpCo (mkSymCoercion co), ty1)
85 Nothing -> (idHsWrapper, ty)
89 %************************************************************************
91 Generating a type refinement
93 %************************************************************************
96 gadtRefine :: Refinement
97 -> [TyVar] -- Bind these by preference
99 -> MaybeErr Message Refinement
102 (gadtRefine cvs) takes a list of coercion variables, and returns a
103 list of coercions, obtained by unifying the types equated by the
104 incoming coercions. The returned coercions all have kinds of form
105 (a:=:ty), where a is a rigid type variable.
108 gadtRefine [c :: (a,Int):=:(Bool,b)]
109 = [ right (left c) :: a:=:Bool,
110 sym (right c) :: b:=:Int ]
112 That is, given evidence 'c' that (a,Int)=(Bool,b), it returns derived
113 evidence in easy-to-use form. In particular, given any e::ty, we know
115 e `cast` ty[right (left c)/a, sym (right c)/b]
116 :: ty [Bool/a, Int/b]
120 - It can fail, if the coercion is unsatisfiable.
122 - It's biased, by being given a set of type variables to bind
123 when there is a choice. Example:
124 MkT :: forall a. a -> T [a]
125 f :: forall b. T [b] -> b
126 f x = let v = case x of { MkT y -> y }
128 Here we want to bind [a->b], not the other way round, because
129 in this example the return type is wobbly, and we want the
133 -- E.g. (a, Bool, right (left c))
134 -- INVARIANT: in the triple (tv, ty, co), we have (co :: tv:=:ty)
135 -- The result is idempotent: the
138 gadtRefine (Reft in_scope env1)
140 -- Precondition: fvs( co_vars ) # env1
141 -- That is, the kinds of the co_vars are a
142 -- fixed point of the incoming refinement
144 = ASSERT2( not $ any (`elemVarEnv` env1) (varSetElems $ tyVarsOfTypes $ map tyVarKind co_vars),
145 ppr env1 $$ ppr co_vars $$ ppr (map tyVarKind co_vars) )
146 initUM (tryToBind tv_set) $
147 do { -- Run the unifier, starting with an empty env
148 ; env2 <- foldM do_one emptyInternalReft co_vars
150 -- Find the fixed point of the resulting
151 -- non-idempotent substitution
152 ; let tmp_env = env1 `plusVarEnv` env2
153 out_env = fixTvCoEnv in_scope' tmp_env
154 ; WARN( not (null (badReftElts tmp_env)), ppr (badReftElts tmp_env) $$ ppr tmp_env )
155 WARN( not (null (badReftElts out_env)), ppr (badReftElts out_env) $$ ppr out_env )
156 return (Reft in_scope' out_env) }
158 tv_set = mkVarSet ex_tvs
159 in_scope' = foldr extend in_scope co_vars
160 extend co_var in_scope
161 = extendInScopeSetSet (extendInScopeSet in_scope co_var)
162 (tyVarsOfType (tyVarKind co_var))
164 do_one reft co_var = unify reft (TyVarTy co_var) ty1 ty2
166 (ty1,ty2) = splitCoercionKind (tyVarKind co_var)
169 %************************************************************************
173 %************************************************************************
176 tcUnifyTys :: (TyVar -> BindFlag)
178 -> Maybe TvSubst -- A regular one-shot substitution
179 -- The two types may have common type variables, and indeed do so in the
180 -- second call to tcUnifyTys in FunDeps.checkClsFD
182 -- We implement tcUnifyTys using the evidence-generating 'unify' function
183 -- in this module, even though we don't need to generate any evidence.
184 -- This is simply to avoid replicating all all the code for unify
185 tcUnifyTys bind_fn tys1 tys2
186 = maybeErrToMaybe $ initUM bind_fn $
187 do { reft <- unifyList emptyInternalReft cos tys1 tys2
189 -- Find the fixed point of the resulting non-idempotent substitution
190 ; let in_scope = mkInScopeSet (tvs1 `unionVarSet` tvs2)
191 tv_env = fixTvSubstEnv in_scope (mapVarEnv snd reft)
193 ; return (mkTvSubst in_scope tv_env) }
195 tvs1 = tyVarsOfTypes tys1
196 tvs2 = tyVarsOfTypes tys2
197 cos = zipWith mkUnsafeCoercion tys1 tys2
200 ----------------------------
201 fixTvCoEnv :: InScopeSet -> InternalReft -> InternalReft
202 -- Find the fixed point of a Refinement
203 -- (assuming it has no loops!)
204 fixTvCoEnv in_scope env
207 fixpt = mapVarEnv step env
209 step (co, ty) = case refineType (Reft in_scope fixpt) ty of
211 Just (co', ty') -> (mkTransCoercion co co', ty')
212 -- Apply fixpt one step:
213 -- Use refineType to get a substituted type, ty', and a coercion, co_fn,
214 -- which justifies the substitution. If the coercion is not the identity
215 -- then use transitivity with the original coercion
217 -----------------------------
218 fixTvSubstEnv :: InScopeSet -> TvSubstEnv -> TvSubstEnv
219 fixTvSubstEnv in_scope env
222 fixpt = mapVarEnv (substTy (mkTvSubst in_scope fixpt)) env
224 ----------------------------
225 dataConCanMatch :: DataCon -> [Type] -> Bool
226 -- Returns True iff the data con can match a scrutinee of type (T tys)
227 -- where T is the type constructor for the data con
229 -- Instantiate the equations and try to unify them
230 dataConCanMatch con tys
231 = isJust (tcUnifyTys (\tv -> BindMe)
232 (map (substTyVar subst . fst) eq_spec)
235 dc_tvs = dataConUnivTyVars con
236 eq_spec = dataConEqSpec con
237 subst = zipTopTvSubst dc_tvs tys
239 ----------------------------
240 tryToBind :: TyVarSet -> TyVar -> BindFlag
241 tryToBind tv_set tv | tv `elemVarSet` tv_set = BindMe
242 | otherwise = AvoidMe
248 %************************************************************************
252 %************************************************************************
255 type InternalReft = TyVarEnv (Coercion, Type)
257 -- INVARIANT: a->(co,ty) then co :: (a:=:ty)
258 -- Not necessarily idemopotent
261 badReftElts :: InternalReft -> [(Unique, (Coercion,Type))]
262 -- Return the BAD elements of the refinement
263 -- Should be empty; used in asserions only
265 = filter (not . ok) (ufmToList env)
267 ok :: (Unique, (Coercion, Type)) -> Bool
268 ok (u, (co, ty)) | Just tv <- tcGetTyVar_maybe ty1
269 = varUnique tv == u && ty `tcEqType` ty2
272 (ty1,ty2) = coercionKind co
275 emptyInternalReft :: InternalReft
276 emptyInternalReft = emptyVarEnv
278 unify :: InternalReft -- An existing substitution to extend
279 -> Coercion -- Witness of their equality
280 -> Type -> Type -- Types to be unified, and witness of their equality
281 -> UM InternalReft -- Just the extended substitution,
282 -- Nothing if unification failed
283 -- We do not require the incoming substitution to be idempotent,
284 -- nor guarantee that the outgoing one is. That's fixed up by
287 -- PRE-CONDITION: in the call (unify r co ty1 ty2), we know that
290 -- Respects newtypes, PredTypes
292 unify subst co ty1 ty2 = -- pprTrace "unify" (ppr subst <+> pprParendType ty1 <+> pprParendType ty2) $
293 unify_ subst co ty1 ty2
295 -- in unify_, any NewTcApps/Preds should be taken at face value
296 unify_ subst co (TyVarTy tv1) ty2 = uVar False subst co tv1 ty2
297 unify_ subst co ty1 (TyVarTy tv2) = uVar True subst co tv2 ty1
299 unify_ subst co ty1 ty2 | Just ty1' <- tcView ty1 = unify subst co ty1' ty2
300 unify_ subst co ty1 ty2 | Just ty2' <- tcView ty2 = unify subst co ty1 ty2'
302 unify_ subst co (PredTy p1) (PredTy p2) = unify_pred subst co p1 p2
304 unify_ subst co t1@(TyConApp tyc1 tys1) t2@(TyConApp tyc2 tys2)
305 | tyc1 == tyc2 = unify_tys subst co tys1 tys2
307 unify_ subst co (FunTy ty1a ty1b) (FunTy ty2a ty2b)
308 = do { let [co1,co2] = decomposeCo 2 co
309 ; subst' <- unify subst co1 ty1a ty2a
310 ; unify subst' co2 ty1b ty2b }
312 -- Applications need a bit of care!
313 -- They can match FunTy and TyConApp, so use splitAppTy_maybe
314 -- NB: we've already dealt with type variables and Notes,
315 -- so if one type is an App the other one jolly well better be too
316 unify_ subst co (AppTy ty1a ty1b) ty2
317 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
318 = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
319 ; unify subst' (mkRightCoercion co) ty1b ty2b }
321 unify_ subst co ty1 (AppTy ty2a ty2b)
322 | Just (ty1a, ty1b) <- repSplitAppTy_maybe ty1
323 = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
324 ; unify subst' (mkRightCoercion co) ty1b ty2b }
326 unify_ subst co ty1 ty2 = failWith (misMatch ty1 ty2)
330 ------------------------------
331 unify_pred subst co (ClassP c1 tys1) (ClassP c2 tys2)
332 | c1 == c2 = unify_tys subst co tys1 tys2
333 unify_pred subst co (IParam n1 t1) (IParam n2 t2)
334 | n1 == n2 = unify subst co t1 t2
335 unify_pred subst co p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2))
337 ------------------------------
338 unify_tys :: InternalReft -> Coercion -> [Type] -> [Type] -> UM InternalReft
339 unify_tys subst co xs ys
340 = unifyList subst (decomposeCo (length xs) co) xs ys
342 unifyList :: InternalReft -> [Coercion] -> [Type] -> [Type] -> UM InternalReft
343 unifyList subst orig_cos orig_xs orig_ys
344 = go subst orig_cos orig_xs orig_ys
346 go subst _ [] [] = return subst
347 go subst (co:cos) (x:xs) (y:ys) = do { subst' <- unify subst co x y
348 ; go subst' cos xs ys }
349 go subst _ _ _ = failWith (lengthMisMatch orig_xs orig_ys)
351 ---------------------------------
352 uVar :: Bool -- Swapped
353 -> InternalReft -- An existing substitution to extend
355 -> TyVar -- Type variable to be unified
356 -> Type -- with this type
359 -- PRE-CONDITION: in the call (uVar swap r co tv1 ty), we know that
360 -- if swap=False co :: (tv1:=:ty)
361 -- if swap=True co :: (ty:=:tv1)
363 uVar swap subst co tv1 ty
364 = -- Check to see whether tv1 is refined by the substitution
365 case (lookupVarEnv subst tv1) of
367 -- Yes, call back into unify'
368 Just (co',ty') -- co' :: (tv1:=:ty')
369 | swap -- co :: (ty:=:tv1)
370 -> unify subst (mkTransCoercion co co') ty ty'
371 | otherwise -- co :: (tv1:=:ty)
372 -> unify subst (mkTransCoercion (mkSymCoercion co') co) ty' ty
375 Nothing -> uUnrefined swap subst co
379 uUnrefined :: Bool -- Whether the input is swapped
380 -> InternalReft -- An existing substitution to extend
382 -> TyVar -- Type variable to be unified
383 -> Type -- with this type
384 -> Type -- (de-noted version)
387 -- We know that tv1 isn't refined
388 -- PRE-CONDITION: in the call (uUnrefined False r co tv1 ty2 ty2'), we know that
390 -- and if the first argument is True instead, we know
393 uUnrefined swap subst co tv1 ty2 ty2'
394 | Just ty2'' <- tcView ty2'
395 = uUnrefined swap subst co tv1 ty2 ty2'' -- Unwrap synonyms
396 -- This is essential, in case we have
398 -- and then unify a :=: Foo a
400 uUnrefined swap subst co tv1 ty2 (TyVarTy tv2)
401 | tv1 == tv2 -- Same type variable
404 -- Check to see whether tv2 is refined
405 | Just (co',ty') <- lookupVarEnv subst tv2 -- co' :: tv2:=:ty'
406 = uUnrefined False subst (mkTransCoercion (doSwap swap co) co') tv1 ty' ty'
408 -- So both are unrefined; next, see if the kinds force the direction
409 | eqKind k1 k2 -- Can update either; so check the bind-flags
410 = do { b1 <- tvBindFlag tv1
411 ; b2 <- tvBindFlag tv2
413 (BindMe, _) -> bind swap tv1 ty2
415 (AvoidMe, BindMe) -> bind (not swap) tv2 ty1
416 (AvoidMe, _) -> bind swap tv1 ty2
418 (WildCard, WildCard) -> return subst
419 (WildCard, Skolem) -> return subst
420 (WildCard, _) -> bind (not swap) tv2 ty1
422 (Skolem, WildCard) -> return subst
423 (Skolem, Skolem) -> failWith (misMatch ty1 ty2)
424 (Skolem, _) -> bind (not swap) tv2 ty1
427 | k1 `isSubKind` k2 = bindTv (not swap) subst co tv2 ty1 -- Must update tv2
428 | k2 `isSubKind` k1 = bindTv swap subst co tv1 ty2 -- Must update tv1
430 | otherwise = failWith (kindMisMatch tv1 ty2)
435 bind swap tv ty = extendReft swap subst tv co ty
437 uUnrefined swap subst co tv1 ty2 ty2' -- ty2 is not a type variable
438 | tv1 `elemVarSet` substTvSet subst (tyVarsOfType ty2')
439 = failWith (occursCheck tv1 ty2) -- Occurs check
440 | not (k2 `isSubKind` k1)
441 = failWith (kindMisMatch tv1 ty2) -- Kind check
443 = bindTv swap subst co tv1 ty2 -- Bind tyvar to the synonym if poss
448 substTvSet :: InternalReft -> TyVarSet -> TyVarSet
449 -- Apply the non-idempotent substitution to a set of type variables,
450 -- remembering that the substitution isn't necessarily idempotent
452 = foldVarSet (unionVarSet . get) emptyVarSet tvs
454 get tv = case lookupVarEnv subst tv of
455 Nothing -> unitVarSet tv
456 Just (_,ty) -> substTvSet subst (tyVarsOfType ty)
458 bindTv swap subst co tv ty -- ty is not a type variable
459 = do { b <- tvBindFlag tv
461 Skolem -> failWith (misMatch (TyVarTy tv) ty)
462 WildCard -> return subst
463 other -> extendReft swap subst tv co ty
466 doSwap :: Bool -> Coercion -> Coercion
467 doSwap swap co = if swap then mkSymCoercion co else co
475 extendReft swap subst tv co ty
476 = ASSERT2( (coercionKindPredTy co1 `tcEqType` mkCoKind (mkTyVarTy tv) ty),
477 (text "Refinement invariant failure: co = " <+> ppr co1 <+> ppr (coercionKindPredTy co1) $$ text "subst = " <+> ppr tv <+> ppr (mkCoKind (mkTyVarTy tv) ty)) )
478 return (extendVarEnv subst tv (co1, ty))
484 %************************************************************************
488 %************************************************************************
492 = BindMe -- A regular type variable
493 | AvoidMe -- Like BindMe but, given the choice, avoid binding it
495 | Skolem -- This type variable is a skolem constant
496 -- Don't bind it; it only matches itself
498 | WildCard -- This type variable matches anything,
499 -- and does not affect the substitution
501 newtype UM a = UM { unUM :: (TyVar -> BindFlag)
502 -> MaybeErr Message a }
504 instance Monad UM where
505 return a = UM (\tvs -> Succeeded a)
506 fail s = UM (\tvs -> Failed (text s))
507 m >>= k = UM (\tvs -> case unUM m tvs of
508 Failed err -> Failed err
509 Succeeded v -> unUM (k v) tvs)
511 initUM :: (TyVar -> BindFlag) -> UM a -> MaybeErr Message a
512 initUM badtvs um = unUM um badtvs
514 tvBindFlag :: TyVar -> UM BindFlag
515 tvBindFlag tv = UM (\tv_fn -> Succeeded (tv_fn tv))
517 failWith :: Message -> UM a
518 failWith msg = UM (\tv_fn -> Failed msg)
520 maybeErrToMaybe :: MaybeErr fail succ -> Maybe succ
521 maybeErrToMaybe (Succeeded a) = Just a
522 maybeErrToMaybe (Failed m) = Nothing
526 %************************************************************************
529 We go to a lot more trouble to tidy the types
530 in TcUnify. Maybe we'll end up having to do that
531 here too, but I'll leave it for now.
533 %************************************************************************
537 = ptext SLIT("Can't match types") <+> quotes (ppr t1) <+>
538 ptext SLIT("and") <+> quotes (ppr t2)
540 lengthMisMatch tys1 tys2
541 = sep [ptext SLIT("Can't match unequal length lists"),
542 nest 2 (ppr tys1), nest 2 (ppr tys2) ]
545 = vcat [ptext SLIT("Can't match kinds") <+> quotes (ppr (tyVarKind tv1)) <+>
546 ptext SLIT("and") <+> quotes (ppr (typeKind t2)),
547 ptext SLIT("when matching") <+> quotes (ppr tv1) <+>
548 ptext SLIT("with") <+> quotes (ppr t2)]
551 = hang (ptext SLIT("Can't construct the infinite type"))
552 2 (ppr tv <+> equals <+> ppr ty)