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, isEmptyRefinement,
16 refineType, refinePred, refineResType,
17 tcUnifyTys, BindFlag(..)
20 #include "HsVersions.h"
43 %************************************************************************
47 %************************************************************************
50 data Refinement = Reft InScopeSet InternalReft
52 type InternalReft = TyVarEnv (Coercion, Type)
53 -- INVARIANT: a->(co,ty) then co :: (a:=:ty)
54 -- Not necessarily idemopotent
56 instance Outputable Refinement where
57 ppr (Reft in_scope env)
58 = ptext SLIT("Refinement") <+>
61 emptyRefinement :: Refinement
62 emptyRefinement = (Reft emptyInScopeSet emptyVarEnv)
64 isEmptyRefinement :: Refinement -> Bool
65 isEmptyRefinement (Reft _ env) = isEmptyVarEnv env
67 refineType :: Refinement -> Type -> Maybe (Coercion, Type)
68 -- Apply the refinement to the type.
69 -- If (refineType r ty) = (co, ty')
70 -- Then co :: ty:=:ty'
71 -- Nothing => the refinement does nothing to this type
72 refineType (Reft in_scope env) ty
73 | not (isEmptyVarEnv env), -- Common case
74 any (`elemVarEnv` env) (varSetElems (tyVarsOfType ty))
75 = Just (substTy co_subst ty, substTy tv_subst ty)
77 = Nothing -- The type doesn't mention any refined type variables
79 tv_subst = mkTvSubst in_scope (mapVarEnv snd env)
80 co_subst = mkTvSubst in_scope (mapVarEnv fst env)
82 refinePred :: Refinement -> PredType -> Maybe (Coercion, PredType)
83 refinePred (Reft in_scope env) pred
84 | not (isEmptyVarEnv env), -- Common case
85 any (`elemVarEnv` env) (varSetElems (tyVarsOfPred pred))
86 = Just (mkPredTy (substPred co_subst pred), substPred tv_subst pred)
88 = Nothing -- The type doesn't mention any refined type variables
90 tv_subst = mkTvSubst in_scope (mapVarEnv snd env)
91 co_subst = mkTvSubst in_scope (mapVarEnv fst env)
93 refineResType :: Refinement -> Type -> (HsWrapper, Type)
94 -- Like refineType, but returns the 'sym' coercion
95 -- If (refineResType r ty) = (co, ty')
96 -- Then co :: ty':=:ty
97 -- It's convenient to return a HsWrapper here
99 = case refineType reft ty of
100 Just (co, ty1) -> (WpCo (mkSymCoercion co), ty1)
101 Nothing -> (idHsWrapper, ty)
105 %************************************************************************
107 Generating a type refinement
109 %************************************************************************
112 gadtRefine :: Refinement
113 -> [TyVar] -- Bind these by preference
115 -> MaybeErr Message Refinement
118 (gadtRefine cvs) takes a list of coercion variables, and returns a
119 list of coercions, obtained by unifying the types equated by the
120 incoming coercions. The returned coercions all have kinds of form
121 (a:=:ty), where a is a rigid type variable.
124 gadtRefine [c :: (a,Int):=:(Bool,b)]
125 = [ right (left c) :: a:=:Bool,
126 sym (right c) :: b:=:Int ]
128 That is, given evidence 'c' that (a,Int)=(Bool,b), it returns derived
129 evidence in easy-to-use form. In particular, given any e::ty, we know
131 e `cast` ty[right (left c)/a, sym (right c)/b]
132 :: ty [Bool/a, Int/b]
136 - It can fail, if the coercion is unsatisfiable.
138 - It's biased, by being given a set of type variables to bind
139 when there is a choice. Example:
140 MkT :: forall a. a -> T [a]
141 f :: forall b. T [b] -> b
142 f x = let v = case x of { MkT y -> y }
144 Here we want to bind [a->b], not the other way round, because
145 in this example the return type is wobbly, and we want the
149 -- E.g. (a, Bool, right (left c))
150 -- INVARIANT: in the triple (tv, ty, co), we have (co :: tv:=:ty)
151 -- The result is idempotent: the
154 gadtRefine (Reft in_scope env1)
156 -- Precondition: fvs( co_vars ) # env1
157 -- That is, the kinds of the co_vars are a
158 -- fixed point of the incoming refinement
160 = ASSERT2( not $ any (`elemVarEnv` env1) (varSetElems $ tyVarsOfTypes $ map tyVarKind co_vars),
161 ppr env1 $$ ppr co_vars $$ ppr (map tyVarKind co_vars) )
162 initUM (tryToBind tv_set) $
163 do { -- Run the unifier, starting with an empty env
164 ; env2 <- foldM do_one emptyInternalReft co_vars
166 -- Find the fixed point of the resulting
167 -- non-idempotent substitution
168 ; let tmp_env = env1 `plusVarEnv` env2
169 out_env = fixTvCoEnv in_scope' tmp_env
170 ; WARN( not (null (badReftElts tmp_env)), ppr (badReftElts tmp_env) $$ ppr tmp_env )
171 WARN( not (null (badReftElts out_env)), ppr (badReftElts out_env) $$ ppr out_env )
172 return (Reft in_scope' out_env) }
174 tv_set = mkVarSet ex_tvs
175 in_scope' = foldr extend in_scope co_vars
177 -- For each co_var, add it *and* the tyvars it mentions, to in_scope
178 extend co_var in_scope
179 = extendInScopeSetSet in_scope $
180 extendVarSet (tyVarsOfType (tyVarKind co_var)) co_var
182 do_one reft co_var = unify reft (TyVarTy co_var) ty1 ty2
184 (ty1,ty2) = splitCoercionKind (tyVarKind co_var)
187 %************************************************************************
191 %************************************************************************
194 tcUnifyTys :: (TyVar -> BindFlag)
196 -> Maybe TvSubst -- A regular one-shot substitution
197 -- The two types may have common type variables, and indeed do so in the
198 -- second call to tcUnifyTys in FunDeps.checkClsFD
200 -- We implement tcUnifyTys using the evidence-generating 'unify' function
201 -- in this module, even though we don't need to generate any evidence.
202 -- This is simply to avoid replicating all all the code for unify
203 tcUnifyTys bind_fn tys1 tys2
204 = maybeErrToMaybe $ initUM bind_fn $
205 do { reft <- unifyList emptyInternalReft cos tys1 tys2
207 -- Find the fixed point of the resulting non-idempotent substitution
208 ; let in_scope = mkInScopeSet (tvs1 `unionVarSet` tvs2)
209 tv_env = fixTvSubstEnv in_scope (mapVarEnv snd reft)
211 ; return (mkTvSubst in_scope tv_env) }
213 tvs1 = tyVarsOfTypes tys1
214 tvs2 = tyVarsOfTypes tys2
215 cos = zipWith mkUnsafeCoercion tys1 tys2
218 ----------------------------
219 fixTvCoEnv :: InScopeSet -> InternalReft -> InternalReft
220 -- Find the fixed point of a Refinement
221 -- (assuming it has no loops!)
222 fixTvCoEnv in_scope env
225 fixpt = mapVarEnv step env
227 step (co, ty) = case refineType (Reft in_scope fixpt) ty of
229 Just (co', ty') -> (mkTransCoercion co co', ty')
230 -- Apply fixpt one step:
231 -- Use refineType to get a substituted type, ty', and a coercion, co_fn,
232 -- which justifies the substitution. If the coercion is not the identity
233 -- then use transitivity with the original coercion
235 -----------------------------
236 fixTvSubstEnv :: InScopeSet -> TvSubstEnv -> TvSubstEnv
237 fixTvSubstEnv in_scope env
240 fixpt = mapVarEnv (substTy (mkTvSubst in_scope fixpt)) env
242 ----------------------------
243 tryToBind :: TyVarSet -> TyVar -> BindFlag
244 tryToBind tv_set tv | tv `elemVarSet` tv_set = BindMe
245 | otherwise = AvoidMe
250 %************************************************************************
254 %************************************************************************
258 badReftElts :: InternalReft -> [(Unique, (Coercion,Type))]
259 -- Return the BAD elements of the refinement
260 -- Should be empty; used in asserions only
262 = filter (not . ok) (ufmToList env)
264 ok :: (Unique, (Coercion, Type)) -> Bool
265 ok (u, (co, ty)) | Just tv <- tcGetTyVar_maybe ty1
266 = varUnique tv == u && ty `tcEqType` ty2
269 (ty1,ty2) = coercionKind co
272 emptyInternalReft :: InternalReft
273 emptyInternalReft = emptyVarEnv
275 unify :: InternalReft -- An existing substitution to extend
276 -> Coercion -- Witness of their equality
277 -> Type -> Type -- Types to be unified, and witness of their equality
278 -> UM InternalReft -- Just the extended substitution,
279 -- Nothing if unification failed
280 -- We do not require the incoming substitution to be idempotent,
281 -- nor guarantee that the outgoing one is. That's fixed up by
284 -- PRE-CONDITION: in the call (unify r co ty1 ty2), we know that
287 -- Respects newtypes, PredTypes
289 unify subst co ty1 ty2 = -- pprTrace "unify" (ppr subst <+> pprParendType ty1 <+> pprParendType ty2) $
290 unify_ subst co ty1 ty2
292 -- in unify_, any NewTcApps/Preds should be taken at face value
293 unify_ subst co (TyVarTy tv1) ty2 = uVar False subst co tv1 ty2
294 unify_ subst co ty1 (TyVarTy tv2) = uVar True subst co tv2 ty1
296 unify_ subst co ty1 ty2 | Just ty1' <- tcView ty1 = unify subst co ty1' ty2
297 unify_ subst co ty1 ty2 | Just ty2' <- tcView ty2 = unify subst co ty1 ty2'
299 unify_ subst co (PredTy p1) (PredTy p2) = unify_pred subst co p1 p2
301 unify_ subst co t1@(TyConApp tyc1 tys1) t2@(TyConApp tyc2 tys2)
302 | tyc1 == tyc2 = unify_tys subst co tys1 tys2
304 unify_ subst co (FunTy ty1a ty1b) (FunTy ty2a ty2b)
305 = do { let [co1,co2] = decomposeCo 2 co
306 ; subst' <- unify subst co1 ty1a ty2a
307 ; unify subst' co2 ty1b ty2b }
309 -- Applications need a bit of care!
310 -- They can match FunTy and TyConApp, so use splitAppTy_maybe
311 -- NB: we've already dealt with type variables and Notes,
312 -- so if one type is an App the other one jolly well better be too
313 unify_ subst co (AppTy ty1a ty1b) ty2
314 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
315 = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
316 ; unify subst' (mkRightCoercion co) ty1b ty2b }
318 unify_ subst co ty1 (AppTy ty2a ty2b)
319 | Just (ty1a, ty1b) <- repSplitAppTy_maybe ty1
320 = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
321 ; unify subst' (mkRightCoercion co) ty1b ty2b }
323 unify_ subst co ty1 ty2 = failWith (misMatch ty1 ty2)
327 ------------------------------
328 unify_pred subst co (ClassP c1 tys1) (ClassP c2 tys2)
329 | c1 == c2 = unify_tys subst co tys1 tys2
330 unify_pred subst co (IParam n1 t1) (IParam n2 t2)
331 | n1 == n2 = unify subst co t1 t2
332 unify_pred subst co p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2))
334 ------------------------------
335 unify_tys :: InternalReft -> Coercion -> [Type] -> [Type] -> UM InternalReft
336 unify_tys subst co xs ys
337 = unifyList subst (decomposeCo (length xs) co) xs ys
339 unifyList :: InternalReft -> [Coercion] -> [Type] -> [Type] -> UM InternalReft
340 unifyList subst orig_cos orig_xs orig_ys
341 = go subst orig_cos orig_xs orig_ys
343 go subst _ [] [] = return subst
344 go subst (co:cos) (x:xs) (y:ys) = do { subst' <- unify subst co x y
345 ; go subst' cos xs ys }
346 go subst _ _ _ = failWith (lengthMisMatch orig_xs orig_ys)
348 ---------------------------------
349 uVar :: Bool -- Swapped
350 -> InternalReft -- An existing substitution to extend
352 -> TyVar -- Type variable to be unified
353 -> Type -- with this type
356 -- PRE-CONDITION: in the call (uVar swap r co tv1 ty), we know that
357 -- if swap=False co :: (tv1:=:ty)
358 -- if swap=True co :: (ty:=:tv1)
360 uVar swap subst co tv1 ty
361 = -- Check to see whether tv1 is refined by the substitution
362 case (lookupVarEnv subst tv1) of
364 -- Yes, call back into unify'
365 Just (co',ty') -- co' :: (tv1:=:ty')
366 | swap -- co :: (ty:=:tv1)
367 -> unify subst (mkTransCoercion co co') ty ty'
368 | otherwise -- co :: (tv1:=:ty)
369 -> unify subst (mkTransCoercion (mkSymCoercion co') co) ty' ty
372 Nothing -> uUnrefined swap subst co
376 uUnrefined :: Bool -- Whether the input is swapped
377 -> InternalReft -- An existing substitution to extend
379 -> TyVar -- Type variable to be unified
380 -> Type -- with this type
381 -> Type -- (de-noted version)
384 -- We know that tv1 isn't refined
385 -- PRE-CONDITION: in the call (uUnrefined False r co tv1 ty2 ty2'), we know that
387 -- and if the first argument is True instead, we know
390 uUnrefined swap subst co tv1 ty2 ty2'
391 | Just ty2'' <- tcView ty2'
392 = uUnrefined swap subst co tv1 ty2 ty2'' -- Unwrap synonyms
393 -- This is essential, in case we have
395 -- and then unify a :=: Foo a
397 uUnrefined swap subst co tv1 ty2 (TyVarTy tv2)
398 | tv1 == tv2 -- Same type variable
401 -- Check to see whether tv2 is refined
402 | Just (co',ty') <- lookupVarEnv subst tv2 -- co' :: tv2:=:ty'
403 = uUnrefined False subst (mkTransCoercion (doSwap swap co) co') tv1 ty' ty'
405 -- So both are unrefined; next, see if the kinds force the direction
406 | eqKind k1 k2 -- Can update either; so check the bind-flags
407 = do { b1 <- tvBindFlag tv1
408 ; b2 <- tvBindFlag tv2
410 (BindMe, _) -> bind swap tv1 ty2
412 (AvoidMe, BindMe) -> bind (not swap) tv2 ty1
413 (AvoidMe, _) -> bind swap tv1 ty2
415 (WildCard, WildCard) -> return subst
416 (WildCard, Skolem) -> return subst
417 (WildCard, _) -> bind (not swap) tv2 ty1
419 (Skolem, WildCard) -> return subst
420 (Skolem, Skolem) -> failWith (misMatch ty1 ty2)
421 (Skolem, _) -> bind (not swap) tv2 ty1
424 | k1 `isSubKind` k2 = bindTv (not swap) subst co tv2 ty1 -- Must update tv2
425 | k2 `isSubKind` k1 = bindTv swap subst co tv1 ty2 -- Must update tv1
427 | otherwise = failWith (kindMisMatch tv1 ty2)
432 bind swap tv ty = extendReft swap subst tv co ty
434 uUnrefined swap subst co tv1 ty2 ty2' -- ty2 is not a type variable
435 | tv1 `elemVarSet` substTvSet subst (tyVarsOfType ty2')
436 = failWith (occursCheck tv1 ty2) -- Occurs check
437 | not (k2 `isSubKind` k1)
438 = failWith (kindMisMatch tv1 ty2) -- Kind check
440 = bindTv swap subst co tv1 ty2 -- Bind tyvar to the synonym if poss
445 substTvSet :: InternalReft -> TyVarSet -> TyVarSet
446 -- Apply the non-idempotent substitution to a set of type variables,
447 -- remembering that the substitution isn't necessarily idempotent
449 = foldVarSet (unionVarSet . get) emptyVarSet tvs
451 get tv = case lookupVarEnv subst tv of
452 Nothing -> unitVarSet tv
453 Just (_,ty) -> substTvSet subst (tyVarsOfType ty)
455 bindTv swap subst co tv ty -- ty is not a type variable
456 = do { b <- tvBindFlag tv
458 Skolem -> failWith (misMatch (TyVarTy tv) ty)
459 WildCard -> return subst
460 other -> extendReft swap subst tv co ty
463 doSwap :: Bool -> Coercion -> Coercion
464 doSwap swap co = if swap then mkSymCoercion co else co
472 extendReft swap subst tv co ty
473 = ASSERT2( (coercionKindPredTy co1 `tcEqType` mkCoKind (mkTyVarTy tv) ty),
474 (text "Refinement invariant failure: co = " <+> ppr co1 <+> ppr (coercionKindPredTy co1) $$ text "subst = " <+> ppr tv <+> ppr (mkCoKind (mkTyVarTy tv) ty)) )
475 return (extendVarEnv subst tv (co1, ty))
481 %************************************************************************
485 %************************************************************************
489 = BindMe -- A regular type variable
490 | AvoidMe -- Like BindMe but, given the choice, avoid binding it
492 | Skolem -- This type variable is a skolem constant
493 -- Don't bind it; it only matches itself
495 | WildCard -- This type variable matches anything,
496 -- and does not affect the substitution
498 newtype UM a = UM { unUM :: (TyVar -> BindFlag)
499 -> MaybeErr Message a }
501 instance Monad UM where
502 return a = UM (\tvs -> Succeeded a)
503 fail s = UM (\tvs -> Failed (text s))
504 m >>= k = UM (\tvs -> case unUM m tvs of
505 Failed err -> Failed err
506 Succeeded v -> unUM (k v) tvs)
508 initUM :: (TyVar -> BindFlag) -> UM a -> MaybeErr Message a
509 initUM badtvs um = unUM um badtvs
511 tvBindFlag :: TyVar -> UM BindFlag
512 tvBindFlag tv = UM (\tv_fn -> Succeeded (tv_fn tv))
514 failWith :: Message -> UM a
515 failWith msg = UM (\tv_fn -> Failed msg)
517 maybeErrToMaybe :: MaybeErr fail succ -> Maybe succ
518 maybeErrToMaybe (Succeeded a) = Just a
519 maybeErrToMaybe (Failed m) = Nothing
523 %************************************************************************
526 We go to a lot more trouble to tidy the types
527 in TcUnify. Maybe we'll end up having to do that
528 here too, but I'll leave it for now.
530 %************************************************************************
534 = ptext SLIT("Can't match types") <+> quotes (ppr t1) <+>
535 ptext SLIT("and") <+> quotes (ppr t2)
537 lengthMisMatch tys1 tys2
538 = sep [ptext SLIT("Can't match unequal length lists"),
539 nest 2 (ppr tys1), nest 2 (ppr tys2) ]
542 = vcat [ptext SLIT("Can't match kinds") <+> quotes (ppr (tyVarKind tv1)) <+>
543 ptext SLIT("and") <+> quotes (ppr (typeKind t2)),
544 ptext SLIT("when matching") <+> quotes (ppr tv1) <+>
545 ptext SLIT("with") <+> quotes (ppr t2)]
548 = hang (ptext SLIT("Can't construct the infinite type"))
549 2 (ppr tv <+> equals <+> ppr ty)