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/Commentary/CodingStyle#Warnings
21 Refinement, emptyRefinement, isEmptyRefinement,
23 refineType, refinePred, refineResType,
24 tcUnifyTys, BindFlag(..)
27 #include "HsVersions.h"
47 %************************************************************************
51 %************************************************************************
54 data Refinement = Reft InScopeSet InternalReft
56 type InternalReft = TyVarEnv (Coercion, Type)
57 -- INVARIANT: a->(co,ty) then co :: (a:=:ty)
58 -- Not necessarily idemopotent
60 instance Outputable Refinement where
61 ppr (Reft in_scope env)
62 = ptext SLIT("Refinement") <+>
65 emptyRefinement :: Refinement
66 emptyRefinement = (Reft emptyInScopeSet emptyVarEnv)
68 isEmptyRefinement :: Refinement -> Bool
69 isEmptyRefinement (Reft _ env) = isEmptyVarEnv env
71 refineType :: Refinement -> Type -> Maybe (Coercion, Type)
72 -- Apply the refinement to the type.
73 -- If (refineType r ty) = (co, ty')
74 -- Then co :: ty:=:ty'
75 -- Nothing => the refinement does nothing to this type
76 refineType (Reft in_scope env) ty
77 | not (isEmptyVarEnv env), -- Common case
78 any (`elemVarEnv` env) (varSetElems (tyVarsOfType ty))
79 = Just (substTy co_subst ty, substTy tv_subst ty)
81 = Nothing -- The type doesn't mention any refined type variables
83 tv_subst = mkTvSubst in_scope (mapVarEnv snd env)
84 co_subst = mkTvSubst in_scope (mapVarEnv fst env)
86 refinePred :: Refinement -> PredType -> Maybe (Coercion, PredType)
87 refinePred (Reft in_scope env) pred
88 | not (isEmptyVarEnv env), -- Common case
89 any (`elemVarEnv` env) (varSetElems (tyVarsOfPred pred))
90 = Just (mkPredTy (substPred co_subst pred), substPred tv_subst pred)
92 = Nothing -- The type doesn't mention any refined type variables
94 tv_subst = mkTvSubst in_scope (mapVarEnv snd env)
95 co_subst = mkTvSubst in_scope (mapVarEnv fst env)
97 refineResType :: Refinement -> Type -> (HsWrapper, Type)
98 -- Like refineType, but returns the 'sym' coercion
99 -- If (refineResType r ty) = (co, ty')
100 -- Then co :: ty':=:ty
101 -- It's convenient to return a HsWrapper here
102 refineResType reft ty
103 = case refineType reft ty of
104 Just (co, ty1) -> (WpCo (mkSymCoercion co), ty1)
105 Nothing -> (idHsWrapper, ty)
109 %************************************************************************
111 Generating a type refinement
113 %************************************************************************
116 gadtRefine :: Refinement
117 -> [TyVar] -- Bind these by preference
119 -> MaybeErr Message Refinement
122 (gadtRefine cvs) takes a list of coercion variables, and returns a
123 list of coercions, obtained by unifying the types equated by the
124 incoming coercions. The returned coercions all have kinds of form
125 (a:=:ty), where a is a rigid type variable.
128 gadtRefine [c :: (a,Int):=:(Bool,b)]
129 = [ right (left c) :: a:=:Bool,
130 sym (right c) :: b:=:Int ]
132 That is, given evidence 'c' that (a,Int)=(Bool,b), it returns derived
133 evidence in easy-to-use form. In particular, given any e::ty, we know
135 e `cast` ty[right (left c)/a, sym (right c)/b]
136 :: ty [Bool/a, Int/b]
140 - It can fail, if the coercion is unsatisfiable.
142 - It's biased, by being given a set of type variables to bind
143 when there is a choice. Example:
144 MkT :: forall a. a -> T [a]
145 f :: forall b. T [b] -> b
146 f x = let v = case x of { MkT y -> y }
148 Here we want to bind [a->b], not the other way round, because
149 in this example the return type is wobbly, and we want the
153 -- E.g. (a, Bool, right (left c))
154 -- INVARIANT: in the triple (tv, ty, co), we have (co :: tv:=:ty)
155 -- The result is idempotent: the
158 gadtRefine (Reft in_scope env1)
160 -- Precondition: fvs( co_vars ) # env1
161 -- That is, the kinds of the co_vars are a
162 -- fixed point of the incoming refinement
164 = ASSERT2( not $ any (`elemVarEnv` env1) (varSetElems $ tyVarsOfTypes $ map tyVarKind co_vars),
165 ppr env1 $$ ppr co_vars $$ ppr (map tyVarKind co_vars) )
166 initUM (tryToBind tv_set) $
167 do { -- Run the unifier, starting with an empty env
168 ; env2 <- foldM do_one emptyInternalReft co_vars
170 -- Find the fixed point of the resulting
171 -- non-idempotent substitution
172 ; let tmp_env = env1 `plusVarEnv` env2
173 out_env = fixTvCoEnv in_scope' tmp_env
174 ; WARN( not (null (badReftElts tmp_env)), ppr (badReftElts tmp_env) $$ ppr tmp_env )
175 WARN( not (null (badReftElts out_env)), ppr (badReftElts out_env) $$ ppr out_env )
176 return (Reft in_scope' out_env) }
178 tv_set = mkVarSet ex_tvs
179 in_scope' = foldr extend in_scope co_vars
181 -- For each co_var, add it *and* the tyvars it mentions, to in_scope
182 extend co_var in_scope
183 = extendInScopeSetSet in_scope $
184 extendVarSet (tyVarsOfType (tyVarKind co_var)) co_var
186 do_one reft co_var = unify reft (TyVarTy co_var) ty1 ty2
188 (ty1,ty2) = splitCoercionKind (tyVarKind co_var)
191 %************************************************************************
195 %************************************************************************
198 tcUnifyTys :: (TyVar -> BindFlag)
200 -> Maybe TvSubst -- A regular one-shot substitution
201 -- The two types may have common type variables, and indeed do so in the
202 -- second call to tcUnifyTys in FunDeps.checkClsFD
204 -- We implement tcUnifyTys using the evidence-generating 'unify' function
205 -- in this module, even though we don't need to generate any evidence.
206 -- This is simply to avoid replicating all all the code for unify
207 tcUnifyTys bind_fn tys1 tys2
208 = maybeErrToMaybe $ initUM bind_fn $
209 do { reft <- unifyList emptyInternalReft cos tys1 tys2
211 -- Find the fixed point of the resulting non-idempotent substitution
212 ; let in_scope = mkInScopeSet (tvs1 `unionVarSet` tvs2)
213 tv_env = fixTvSubstEnv in_scope (mapVarEnv snd reft)
215 ; return (mkTvSubst in_scope tv_env) }
217 tvs1 = tyVarsOfTypes tys1
218 tvs2 = tyVarsOfTypes tys2
219 cos = zipWith mkUnsafeCoercion tys1 tys2
222 ----------------------------
223 fixTvCoEnv :: InScopeSet -> InternalReft -> InternalReft
224 -- Find the fixed point of a Refinement
225 -- (assuming it has no loops!)
226 fixTvCoEnv in_scope env
229 fixpt = mapVarEnv step env
231 step (co, ty) = case refineType (Reft in_scope fixpt) ty of
233 Just (co', ty') -> (mkTransCoercion co co', ty')
234 -- Apply fixpt one step:
235 -- Use refineType to get a substituted type, ty', and a coercion, co_fn,
236 -- which justifies the substitution. If the coercion is not the identity
237 -- then use transitivity with the original coercion
239 -----------------------------
240 fixTvSubstEnv :: InScopeSet -> TvSubstEnv -> TvSubstEnv
241 fixTvSubstEnv in_scope env
244 fixpt = mapVarEnv (substTy (mkTvSubst in_scope fixpt)) env
246 ----------------------------
247 tryToBind :: TyVarSet -> TyVar -> BindFlag
248 tryToBind tv_set tv | tv `elemVarSet` tv_set = BindMe
249 | otherwise = AvoidMe
254 %************************************************************************
258 %************************************************************************
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
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)