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
51 type InternalReft = TyVarEnv (Coercion, Type)
52 -- INVARIANT: a->(co,ty) then co :: (a:=:ty)
53 -- Not necessarily idemopotent
55 instance Outputable Refinement where
56 ppr (Reft in_scope env)
57 = ptext SLIT("Refinement") <+>
60 emptyRefinement :: Refinement
61 emptyRefinement = (Reft emptyInScopeSet emptyVarEnv)
64 refineType :: Refinement -> Type -> Maybe (Coercion, Type)
65 -- Apply the refinement to the type.
66 -- If (refineType r ty) = (co, ty')
67 -- Then co :: ty:=:ty'
68 -- Nothing => the refinement does nothing to this type
69 refineType (Reft in_scope env) ty
70 | not (isEmptyVarEnv env), -- Common case
71 any (`elemVarEnv` env) (varSetElems (tyVarsOfType ty))
72 = Just (substTy co_subst ty, substTy tv_subst ty)
74 = Nothing -- The type doesn't mention any refined type variables
76 tv_subst = mkTvSubst in_scope (mapVarEnv snd env)
77 co_subst = mkTvSubst in_scope (mapVarEnv fst env)
79 refineResType :: Refinement -> Type -> (HsWrapper, Type)
80 -- Like refineType, but returns the 'sym' coercion
81 -- If (refineResType r ty) = (co, ty')
82 -- Then co :: ty':=:ty
83 -- It's convenient to return a HsWrapper here
85 = case refineType reft ty of
86 Just (co, ty1) -> (WpCo (mkSymCoercion co), ty1)
87 Nothing -> (idHsWrapper, ty)
91 %************************************************************************
93 Generating a type refinement
95 %************************************************************************
98 gadtRefine :: Refinement
99 -> [TyVar] -- Bind these by preference
101 -> MaybeErr Message Refinement
104 (gadtRefine cvs) takes a list of coercion variables, and returns a
105 list of coercions, obtained by unifying the types equated by the
106 incoming coercions. The returned coercions all have kinds of form
107 (a:=:ty), where a is a rigid type variable.
110 gadtRefine [c :: (a,Int):=:(Bool,b)]
111 = [ right (left c) :: a:=:Bool,
112 sym (right c) :: b:=:Int ]
114 That is, given evidence 'c' that (a,Int)=(Bool,b), it returns derived
115 evidence in easy-to-use form. In particular, given any e::ty, we know
117 e `cast` ty[right (left c)/a, sym (right c)/b]
118 :: ty [Bool/a, Int/b]
122 - It can fail, if the coercion is unsatisfiable.
124 - It's biased, by being given a set of type variables to bind
125 when there is a choice. Example:
126 MkT :: forall a. a -> T [a]
127 f :: forall b. T [b] -> b
128 f x = let v = case x of { MkT y -> y }
130 Here we want to bind [a->b], not the other way round, because
131 in this example the return type is wobbly, and we want the
135 -- E.g. (a, Bool, right (left c))
136 -- INVARIANT: in the triple (tv, ty, co), we have (co :: tv:=:ty)
137 -- The result is idempotent: the
140 gadtRefine (Reft in_scope env1)
142 -- Precondition: fvs( co_vars ) # env1
143 -- That is, the kinds of the co_vars are a
144 -- fixed point of the incoming refinement
146 = ASSERT2( not $ any (`elemVarEnv` env1) (varSetElems $ tyVarsOfTypes $ map tyVarKind co_vars),
147 ppr env1 $$ ppr co_vars $$ ppr (map tyVarKind co_vars) )
148 initUM (tryToBind tv_set) $
149 do { -- Run the unifier, starting with an empty env
150 ; env2 <- foldM do_one emptyInternalReft co_vars
152 -- Find the fixed point of the resulting
153 -- non-idempotent substitution
154 ; let tmp_env = env1 `plusVarEnv` env2
155 out_env = fixTvCoEnv in_scope' tmp_env
156 ; WARN( not (null (badReftElts tmp_env)), ppr (badReftElts tmp_env) $$ ppr tmp_env )
157 WARN( not (null (badReftElts out_env)), ppr (badReftElts out_env) $$ ppr out_env )
158 return (Reft in_scope' out_env) }
160 tv_set = mkVarSet ex_tvs
161 in_scope' = foldr extend in_scope co_vars
163 -- For each co_var, add it *and* the tyvars it mentions, to in_scope
164 extend co_var in_scope
165 = extendInScopeSetSet in_scope $
166 extendVarSet (tyVarsOfType (tyVarKind co_var)) co_var
168 do_one reft co_var = unify reft (TyVarTy co_var) ty1 ty2
170 (ty1,ty2) = splitCoercionKind (tyVarKind co_var)
173 %************************************************************************
177 %************************************************************************
180 tcUnifyTys :: (TyVar -> BindFlag)
182 -> Maybe TvSubst -- A regular one-shot substitution
183 -- The two types may have common type variables, and indeed do so in the
184 -- second call to tcUnifyTys in FunDeps.checkClsFD
186 -- We implement tcUnifyTys using the evidence-generating 'unify' function
187 -- in this module, even though we don't need to generate any evidence.
188 -- This is simply to avoid replicating all all the code for unify
189 tcUnifyTys bind_fn tys1 tys2
190 = maybeErrToMaybe $ initUM bind_fn $
191 do { reft <- unifyList emptyInternalReft cos tys1 tys2
193 -- Find the fixed point of the resulting non-idempotent substitution
194 ; let in_scope = mkInScopeSet (tvs1 `unionVarSet` tvs2)
195 tv_env = fixTvSubstEnv in_scope (mapVarEnv snd reft)
197 ; return (mkTvSubst in_scope tv_env) }
199 tvs1 = tyVarsOfTypes tys1
200 tvs2 = tyVarsOfTypes tys2
201 cos = zipWith mkUnsafeCoercion tys1 tys2
204 ----------------------------
205 fixTvCoEnv :: InScopeSet -> InternalReft -> InternalReft
206 -- Find the fixed point of a Refinement
207 -- (assuming it has no loops!)
208 fixTvCoEnv in_scope env
211 fixpt = mapVarEnv step env
213 step (co, ty) = case refineType (Reft in_scope fixpt) ty of
215 Just (co', ty') -> (mkTransCoercion co co', ty')
216 -- Apply fixpt one step:
217 -- Use refineType to get a substituted type, ty', and a coercion, co_fn,
218 -- which justifies the substitution. If the coercion is not the identity
219 -- then use transitivity with the original coercion
221 -----------------------------
222 fixTvSubstEnv :: InScopeSet -> TvSubstEnv -> TvSubstEnv
223 fixTvSubstEnv in_scope env
226 fixpt = mapVarEnv (substTy (mkTvSubst in_scope fixpt)) env
228 ----------------------------
229 dataConCanMatch :: DataCon -> [Type] -> Bool
230 -- Returns True iff the data con can match a scrutinee of type (T tys)
231 -- where T is the type constructor for the data con
233 -- Instantiate the equations and try to unify them
234 dataConCanMatch con tys
235 = isJust (tcUnifyTys (\tv -> BindMe)
236 (map (substTyVar subst . fst) eq_spec)
239 dc_tvs = dataConUnivTyVars con
240 eq_spec = dataConEqSpec con
241 subst = zipTopTvSubst dc_tvs tys
243 ----------------------------
244 tryToBind :: TyVarSet -> TyVar -> BindFlag
245 tryToBind tv_set tv | tv `elemVarSet` tv_set = BindMe
246 | otherwise = AvoidMe
252 %************************************************************************
256 %************************************************************************
260 badReftElts :: InternalReft -> [(Unique, (Coercion,Type))]
261 -- Return the BAD elements of the refinement
262 -- Should be empty; used in asserions only
264 = filter (not . ok) (ufmToList env)
266 ok :: (Unique, (Coercion, Type)) -> Bool
267 ok (u, (co, ty)) | Just tv <- tcGetTyVar_maybe ty1
268 = varUnique tv == u && ty `tcEqType` ty2
271 (ty1,ty2) = coercionKind co
274 emptyInternalReft :: InternalReft
275 emptyInternalReft = emptyVarEnv
277 unify :: InternalReft -- An existing substitution to extend
278 -> Coercion -- Witness of their equality
279 -> Type -> Type -- Types to be unified, and witness of their equality
280 -> UM InternalReft -- Just the extended substitution,
281 -- Nothing if unification failed
282 -- We do not require the incoming substitution to be idempotent,
283 -- nor guarantee that the outgoing one is. That's fixed up by
286 -- PRE-CONDITION: in the call (unify r co ty1 ty2), we know that
289 -- Respects newtypes, PredTypes
291 unify subst co ty1 ty2 = -- pprTrace "unify" (ppr subst <+> pprParendType ty1 <+> pprParendType ty2) $
292 unify_ subst co ty1 ty2
294 -- in unify_, any NewTcApps/Preds should be taken at face value
295 unify_ subst co (TyVarTy tv1) ty2 = uVar False subst co tv1 ty2
296 unify_ subst co ty1 (TyVarTy tv2) = uVar True subst co tv2 ty1
298 unify_ subst co ty1 ty2 | Just ty1' <- tcView ty1 = unify subst co ty1' ty2
299 unify_ subst co ty1 ty2 | Just ty2' <- tcView ty2 = unify subst co ty1 ty2'
301 unify_ subst co (PredTy p1) (PredTy p2) = unify_pred subst co p1 p2
303 unify_ subst co t1@(TyConApp tyc1 tys1) t2@(TyConApp tyc2 tys2)
304 | tyc1 == tyc2 = unify_tys subst co tys1 tys2
306 unify_ subst co (FunTy ty1a ty1b) (FunTy ty2a ty2b)
307 = do { let [co1,co2] = decomposeCo 2 co
308 ; subst' <- unify subst co1 ty1a ty2a
309 ; unify subst' co2 ty1b ty2b }
311 -- Applications need a bit of care!
312 -- They can match FunTy and TyConApp, so use splitAppTy_maybe
313 -- NB: we've already dealt with type variables and Notes,
314 -- so if one type is an App the other one jolly well better be too
315 unify_ subst co (AppTy ty1a ty1b) ty2
316 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
317 = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
318 ; unify subst' (mkRightCoercion co) ty1b ty2b }
320 unify_ subst co ty1 (AppTy ty2a ty2b)
321 | Just (ty1a, ty1b) <- repSplitAppTy_maybe ty1
322 = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
323 ; unify subst' (mkRightCoercion co) ty1b ty2b }
325 unify_ subst co ty1 ty2 = failWith (misMatch ty1 ty2)
329 ------------------------------
330 unify_pred subst co (ClassP c1 tys1) (ClassP c2 tys2)
331 | c1 == c2 = unify_tys subst co tys1 tys2
332 unify_pred subst co (IParam n1 t1) (IParam n2 t2)
333 | n1 == n2 = unify subst co t1 t2
334 unify_pred subst co p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2))
336 ------------------------------
337 unify_tys :: InternalReft -> Coercion -> [Type] -> [Type] -> UM InternalReft
338 unify_tys subst co xs ys
339 = unifyList subst (decomposeCo (length xs) co) xs ys
341 unifyList :: InternalReft -> [Coercion] -> [Type] -> [Type] -> UM InternalReft
342 unifyList subst orig_cos orig_xs orig_ys
343 = go subst orig_cos orig_xs orig_ys
345 go subst _ [] [] = return subst
346 go subst (co:cos) (x:xs) (y:ys) = do { subst' <- unify subst co x y
347 ; go subst' cos xs ys }
348 go subst _ _ _ = failWith (lengthMisMatch orig_xs orig_ys)
350 ---------------------------------
351 uVar :: Bool -- Swapped
352 -> InternalReft -- An existing substitution to extend
354 -> TyVar -- Type variable to be unified
355 -> Type -- with this type
358 -- PRE-CONDITION: in the call (uVar swap r co tv1 ty), we know that
359 -- if swap=False co :: (tv1:=:ty)
360 -- if swap=True co :: (ty:=:tv1)
362 uVar swap subst co tv1 ty
363 = -- Check to see whether tv1 is refined by the substitution
364 case (lookupVarEnv subst tv1) of
366 -- Yes, call back into unify'
367 Just (co',ty') -- co' :: (tv1:=:ty')
368 | swap -- co :: (ty:=:tv1)
369 -> unify subst (mkTransCoercion co co') ty ty'
370 | otherwise -- co :: (tv1:=:ty)
371 -> unify subst (mkTransCoercion (mkSymCoercion co') co) ty' ty
374 Nothing -> uUnrefined swap subst co
378 uUnrefined :: Bool -- Whether the input is swapped
379 -> InternalReft -- An existing substitution to extend
381 -> TyVar -- Type variable to be unified
382 -> Type -- with this type
383 -> Type -- (de-noted version)
386 -- We know that tv1 isn't refined
387 -- PRE-CONDITION: in the call (uUnrefined False r co tv1 ty2 ty2'), we know that
389 -- and if the first argument is True instead, we know
392 uUnrefined swap subst co tv1 ty2 ty2'
393 | Just ty2'' <- tcView ty2'
394 = uUnrefined swap subst co tv1 ty2 ty2'' -- Unwrap synonyms
395 -- This is essential, in case we have
397 -- and then unify a :=: Foo a
399 uUnrefined swap subst co tv1 ty2 (TyVarTy tv2)
400 | tv1 == tv2 -- Same type variable
403 -- Check to see whether tv2 is refined
404 | Just (co',ty') <- lookupVarEnv subst tv2 -- co' :: tv2:=:ty'
405 = uUnrefined False subst (mkTransCoercion (doSwap swap co) co') tv1 ty' ty'
407 -- So both are unrefined; next, see if the kinds force the direction
408 | eqKind k1 k2 -- Can update either; so check the bind-flags
409 = do { b1 <- tvBindFlag tv1
410 ; b2 <- tvBindFlag tv2
412 (BindMe, _) -> bind swap tv1 ty2
414 (AvoidMe, BindMe) -> bind (not swap) tv2 ty1
415 (AvoidMe, _) -> bind swap tv1 ty2
417 (WildCard, WildCard) -> return subst
418 (WildCard, Skolem) -> return subst
419 (WildCard, _) -> bind (not swap) tv2 ty1
421 (Skolem, WildCard) -> return subst
422 (Skolem, Skolem) -> failWith (misMatch ty1 ty2)
423 (Skolem, _) -> bind (not swap) tv2 ty1
426 | k1 `isSubKind` k2 = bindTv (not swap) subst co tv2 ty1 -- Must update tv2
427 | k2 `isSubKind` k1 = bindTv swap subst co tv1 ty2 -- Must update tv1
429 | otherwise = failWith (kindMisMatch tv1 ty2)
434 bind swap tv ty = extendReft swap subst tv co ty
436 uUnrefined swap subst co tv1 ty2 ty2' -- ty2 is not a type variable
437 | tv1 `elemVarSet` substTvSet subst (tyVarsOfType ty2')
438 = failWith (occursCheck tv1 ty2) -- Occurs check
439 | not (k2 `isSubKind` k1)
440 = failWith (kindMisMatch tv1 ty2) -- Kind check
442 = bindTv swap subst co tv1 ty2 -- Bind tyvar to the synonym if poss
447 substTvSet :: InternalReft -> TyVarSet -> TyVarSet
448 -- Apply the non-idempotent substitution to a set of type variables,
449 -- remembering that the substitution isn't necessarily idempotent
451 = foldVarSet (unionVarSet . get) emptyVarSet tvs
453 get tv = case lookupVarEnv subst tv of
454 Nothing -> unitVarSet tv
455 Just (_,ty) -> substTvSet subst (tyVarsOfType ty)
457 bindTv swap subst co tv ty -- ty is not a type variable
458 = do { b <- tvBindFlag tv
460 Skolem -> failWith (misMatch (TyVarTy tv) ty)
461 WildCard -> return subst
462 other -> extendReft swap subst tv co ty
465 doSwap :: Bool -> Coercion -> Coercion
466 doSwap swap co = if swap then mkSymCoercion co else co
474 extendReft swap subst tv co ty
475 = ASSERT2( (coercionKindPredTy co1 `tcEqType` mkCoKind (mkTyVarTy tv) ty),
476 (text "Refinement invariant failure: co = " <+> ppr co1 <+> ppr (coercionKindPredTy co1) $$ text "subst = " <+> ppr tv <+> ppr (mkCoKind (mkTyVarTy tv) ty)) )
477 return (extendVarEnv subst tv (co1, ty))
483 %************************************************************************
487 %************************************************************************
491 = BindMe -- A regular type variable
492 | AvoidMe -- Like BindMe but, given the choice, avoid binding it
494 | Skolem -- This type variable is a skolem constant
495 -- Don't bind it; it only matches itself
497 | WildCard -- This type variable matches anything,
498 -- and does not affect the substitution
500 newtype UM a = UM { unUM :: (TyVar -> BindFlag)
501 -> MaybeErr Message a }
503 instance Monad UM where
504 return a = UM (\tvs -> Succeeded a)
505 fail s = UM (\tvs -> Failed (text s))
506 m >>= k = UM (\tvs -> case unUM m tvs of
507 Failed err -> Failed err
508 Succeeded v -> unUM (k v) tvs)
510 initUM :: (TyVar -> BindFlag) -> UM a -> MaybeErr Message a
511 initUM badtvs um = unUM um badtvs
513 tvBindFlag :: TyVar -> UM BindFlag
514 tvBindFlag tv = UM (\tv_fn -> Succeeded (tv_fn tv))
516 failWith :: Message -> UM a
517 failWith msg = UM (\tv_fn -> Failed msg)
519 maybeErrToMaybe :: MaybeErr fail succ -> Maybe succ
520 maybeErrToMaybe (Succeeded a) = Just a
521 maybeErrToMaybe (Failed m) = Nothing
525 %************************************************************************
528 We go to a lot more trouble to tidy the types
529 in TcUnify. Maybe we'll end up having to do that
530 here too, but I'll leave it for now.
532 %************************************************************************
536 = ptext SLIT("Can't match types") <+> quotes (ppr t1) <+>
537 ptext SLIT("and") <+> quotes (ppr t2)
539 lengthMisMatch tys1 tys2
540 = sep [ptext SLIT("Can't match unequal length lists"),
541 nest 2 (ppr tys1), nest 2 (ppr tys2) ]
544 = vcat [ptext SLIT("Can't match kinds") <+> quotes (ppr (tyVarKind tv1)) <+>
545 ptext SLIT("and") <+> quotes (ppr (typeKind t2)),
546 ptext SLIT("when matching") <+> quotes (ppr tv1) <+>
547 ptext SLIT("with") <+> quotes (ppr t2)]
550 = hang (ptext SLIT("Can't construct the infinite type"))
551 2 (ppr tv <+> equals <+> ppr ty)