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"
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)
65 refineType :: Refinement -> Type -> Maybe (Coercion, Type)
66 -- Apply the refinement to the type.
67 -- If (refineType r ty) = (co, ty')
68 -- Then co :: ty:=:ty'
69 -- Nothing => the refinement does nothing to this type
70 refineType (Reft in_scope env) ty
71 | not (isEmptyVarEnv env), -- Common case
72 any (`elemVarEnv` env) (varSetElems (tyVarsOfType ty))
73 = Just (substTy co_subst ty, substTy tv_subst ty)
75 = Nothing -- The type doesn't mention any refined type variables
77 tv_subst = mkTvSubst in_scope (mapVarEnv snd env)
78 co_subst = mkTvSubst in_scope (mapVarEnv fst env)
80 refineResType :: Refinement -> Type -> (HsWrapper, Type)
81 -- Like refineType, but returns the 'sym' coercion
82 -- If (refineResType r ty) = (co, ty')
83 -- Then co :: ty':=:ty
84 -- It's convenient to return a HsWrapper here
86 = case refineType reft ty of
87 Just (co, ty1) -> (WpCo (mkSymCoercion co), ty1)
88 Nothing -> (idHsWrapper, ty)
92 %************************************************************************
94 Generating a type refinement
96 %************************************************************************
99 gadtRefine :: Refinement
100 -> [TyVar] -- Bind these by preference
102 -> MaybeErr Message Refinement
105 (gadtRefine cvs) takes a list of coercion variables, and returns a
106 list of coercions, obtained by unifying the types equated by the
107 incoming coercions. The returned coercions all have kinds of form
108 (a:=:ty), where a is a rigid type variable.
111 gadtRefine [c :: (a,Int):=:(Bool,b)]
112 = [ right (left c) :: a:=:Bool,
113 sym (right c) :: b:=:Int ]
115 That is, given evidence 'c' that (a,Int)=(Bool,b), it returns derived
116 evidence in easy-to-use form. In particular, given any e::ty, we know
118 e `cast` ty[right (left c)/a, sym (right c)/b]
119 :: ty [Bool/a, Int/b]
123 - It can fail, if the coercion is unsatisfiable.
125 - It's biased, by being given a set of type variables to bind
126 when there is a choice. Example:
127 MkT :: forall a. a -> T [a]
128 f :: forall b. T [b] -> b
129 f x = let v = case x of { MkT y -> y }
131 Here we want to bind [a->b], not the other way round, because
132 in this example the return type is wobbly, and we want the
136 -- E.g. (a, Bool, right (left c))
137 -- INVARIANT: in the triple (tv, ty, co), we have (co :: tv:=:ty)
138 -- The result is idempotent: the
141 gadtRefine (Reft in_scope env1)
143 -- Precondition: fvs( co_vars ) # env1
144 -- That is, the kinds of the co_vars are a
145 -- fixed point of the incoming refinement
147 = ASSERT2( not $ any (`elemVarEnv` env1) (varSetElems $ tyVarsOfTypes $ map tyVarKind co_vars),
148 ppr env1 $$ ppr co_vars $$ ppr (map tyVarKind co_vars) )
149 initUM (tryToBind tv_set) $
150 do { -- Run the unifier, starting with an empty env
151 ; env2 <- foldM do_one emptyInternalReft co_vars
153 -- Find the fixed point of the resulting
154 -- non-idempotent substitution
155 ; let tmp_env = env1 `plusVarEnv` env2
156 out_env = fixTvCoEnv in_scope' tmp_env
157 ; WARN( not (null (badReftElts tmp_env)), ppr (badReftElts tmp_env) $$ ppr tmp_env )
158 WARN( not (null (badReftElts out_env)), ppr (badReftElts out_env) $$ ppr out_env )
159 return (Reft in_scope' out_env) }
161 tv_set = mkVarSet ex_tvs
162 in_scope' = foldr extend in_scope co_vars
164 -- For each co_var, add it *and* the tyvars it mentions, to in_scope
165 extend co_var in_scope
166 = extendInScopeSetSet in_scope $
167 extendVarSet (tyVarsOfType (tyVarKind co_var)) co_var
169 do_one reft co_var = unify reft (TyVarTy co_var) ty1 ty2
171 (ty1,ty2) = splitCoercionKind (tyVarKind co_var)
174 %************************************************************************
178 %************************************************************************
181 tcUnifyTys :: (TyVar -> BindFlag)
183 -> Maybe TvSubst -- A regular one-shot substitution
184 -- The two types may have common type variables, and indeed do so in the
185 -- second call to tcUnifyTys in FunDeps.checkClsFD
187 -- We implement tcUnifyTys using the evidence-generating 'unify' function
188 -- in this module, even though we don't need to generate any evidence.
189 -- This is simply to avoid replicating all all the code for unify
190 tcUnifyTys bind_fn tys1 tys2
191 = maybeErrToMaybe $ initUM bind_fn $
192 do { reft <- unifyList emptyInternalReft cos tys1 tys2
194 -- Find the fixed point of the resulting non-idempotent substitution
195 ; let in_scope = mkInScopeSet (tvs1 `unionVarSet` tvs2)
196 tv_env = fixTvSubstEnv in_scope (mapVarEnv snd reft)
198 ; return (mkTvSubst in_scope tv_env) }
200 tvs1 = tyVarsOfTypes tys1
201 tvs2 = tyVarsOfTypes tys2
202 cos = zipWith mkUnsafeCoercion tys1 tys2
205 ----------------------------
206 fixTvCoEnv :: InScopeSet -> InternalReft -> InternalReft
207 -- Find the fixed point of a Refinement
208 -- (assuming it has no loops!)
209 fixTvCoEnv in_scope env
212 fixpt = mapVarEnv step env
214 step (co, ty) = case refineType (Reft in_scope fixpt) ty of
216 Just (co', ty') -> (mkTransCoercion co co', ty')
217 -- Apply fixpt one step:
218 -- Use refineType to get a substituted type, ty', and a coercion, co_fn,
219 -- which justifies the substitution. If the coercion is not the identity
220 -- then use transitivity with the original coercion
222 -----------------------------
223 fixTvSubstEnv :: InScopeSet -> TvSubstEnv -> TvSubstEnv
224 fixTvSubstEnv in_scope env
227 fixpt = mapVarEnv (substTy (mkTvSubst in_scope fixpt)) env
229 ----------------------------
230 dataConCanMatch :: [Type] -> DataCon -> Bool
231 -- Returns True iff the data con can match a scrutinee of type (T tys)
232 -- where T is the type constructor for the data con
234 -- Instantiate the equations and try to unify them
235 dataConCanMatch tys con
236 | null eq_spec = True -- Common
237 | all isTyVarTy tys = True -- Also common
239 = isJust (tcUnifyTys (\tv -> BindMe)
240 (map (substTyVar subst . fst) eq_spec)
243 dc_tvs = dataConUnivTyVars con
244 eq_spec = dataConEqSpec con
245 subst = zipTopTvSubst dc_tvs tys
247 ----------------------------
248 tryToBind :: TyVarSet -> TyVar -> BindFlag
249 tryToBind tv_set tv | tv `elemVarSet` tv_set = BindMe
250 | otherwise = AvoidMe
256 %************************************************************************
260 %************************************************************************
264 badReftElts :: InternalReft -> [(Unique, (Coercion,Type))]
265 -- Return the BAD elements of the refinement
266 -- Should be empty; used in asserions only
268 = filter (not . ok) (ufmToList env)
270 ok :: (Unique, (Coercion, Type)) -> Bool
271 ok (u, (co, ty)) | Just tv <- tcGetTyVar_maybe ty1
272 = varUnique tv == u && ty `tcEqType` ty2
275 (ty1,ty2) = coercionKind co
278 emptyInternalReft :: InternalReft
279 emptyInternalReft = emptyVarEnv
281 unify :: InternalReft -- An existing substitution to extend
282 -> Coercion -- Witness of their equality
283 -> Type -> Type -- Types to be unified, and witness of their equality
284 -> UM InternalReft -- Just the extended substitution,
285 -- Nothing if unification failed
286 -- We do not require the incoming substitution to be idempotent,
287 -- nor guarantee that the outgoing one is. That's fixed up by
290 -- PRE-CONDITION: in the call (unify r co ty1 ty2), we know that
293 -- Respects newtypes, PredTypes
295 unify subst co ty1 ty2 = -- pprTrace "unify" (ppr subst <+> pprParendType ty1 <+> pprParendType ty2) $
296 unify_ subst co ty1 ty2
298 -- in unify_, any NewTcApps/Preds should be taken at face value
299 unify_ subst co (TyVarTy tv1) ty2 = uVar False subst co tv1 ty2
300 unify_ subst co ty1 (TyVarTy tv2) = uVar True subst co tv2 ty1
302 unify_ subst co ty1 ty2 | Just ty1' <- tcView ty1 = unify subst co ty1' ty2
303 unify_ subst co ty1 ty2 | Just ty2' <- tcView ty2 = unify subst co ty1 ty2'
305 unify_ subst co (PredTy p1) (PredTy p2) = unify_pred subst co p1 p2
307 unify_ subst co t1@(TyConApp tyc1 tys1) t2@(TyConApp tyc2 tys2)
308 | tyc1 == tyc2 = unify_tys subst co tys1 tys2
310 unify_ subst co (FunTy ty1a ty1b) (FunTy ty2a ty2b)
311 = do { let [co1,co2] = decomposeCo 2 co
312 ; subst' <- unify subst co1 ty1a ty2a
313 ; unify subst' co2 ty1b ty2b }
315 -- Applications need a bit of care!
316 -- They can match FunTy and TyConApp, so use splitAppTy_maybe
317 -- NB: we've already dealt with type variables and Notes,
318 -- so if one type is an App the other one jolly well better be too
319 unify_ subst co (AppTy ty1a ty1b) ty2
320 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
321 = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
322 ; unify subst' (mkRightCoercion co) ty1b ty2b }
324 unify_ subst co ty1 (AppTy ty2a ty2b)
325 | Just (ty1a, ty1b) <- repSplitAppTy_maybe ty1
326 = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
327 ; unify subst' (mkRightCoercion co) ty1b ty2b }
329 unify_ subst co ty1 ty2 = failWith (misMatch ty1 ty2)
333 ------------------------------
334 unify_pred subst co (ClassP c1 tys1) (ClassP c2 tys2)
335 | c1 == c2 = unify_tys subst co tys1 tys2
336 unify_pred subst co (IParam n1 t1) (IParam n2 t2)
337 | n1 == n2 = unify subst co t1 t2
338 unify_pred subst co p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2))
340 ------------------------------
341 unify_tys :: InternalReft -> Coercion -> [Type] -> [Type] -> UM InternalReft
342 unify_tys subst co xs ys
343 = unifyList subst (decomposeCo (length xs) co) xs ys
345 unifyList :: InternalReft -> [Coercion] -> [Type] -> [Type] -> UM InternalReft
346 unifyList subst orig_cos orig_xs orig_ys
347 = go subst orig_cos orig_xs orig_ys
349 go subst _ [] [] = return subst
350 go subst (co:cos) (x:xs) (y:ys) = do { subst' <- unify subst co x y
351 ; go subst' cos xs ys }
352 go subst _ _ _ = failWith (lengthMisMatch orig_xs orig_ys)
354 ---------------------------------
355 uVar :: Bool -- Swapped
356 -> InternalReft -- An existing substitution to extend
358 -> TyVar -- Type variable to be unified
359 -> Type -- with this type
362 -- PRE-CONDITION: in the call (uVar swap r co tv1 ty), we know that
363 -- if swap=False co :: (tv1:=:ty)
364 -- if swap=True co :: (ty:=:tv1)
366 uVar swap subst co tv1 ty
367 = -- Check to see whether tv1 is refined by the substitution
368 case (lookupVarEnv subst tv1) of
370 -- Yes, call back into unify'
371 Just (co',ty') -- co' :: (tv1:=:ty')
372 | swap -- co :: (ty:=:tv1)
373 -> unify subst (mkTransCoercion co co') ty ty'
374 | otherwise -- co :: (tv1:=:ty)
375 -> unify subst (mkTransCoercion (mkSymCoercion co') co) ty' ty
378 Nothing -> uUnrefined swap subst co
382 uUnrefined :: Bool -- Whether the input is swapped
383 -> InternalReft -- An existing substitution to extend
385 -> TyVar -- Type variable to be unified
386 -> Type -- with this type
387 -> Type -- (de-noted version)
390 -- We know that tv1 isn't refined
391 -- PRE-CONDITION: in the call (uUnrefined False r co tv1 ty2 ty2'), we know that
393 -- and if the first argument is True instead, we know
396 uUnrefined swap subst co tv1 ty2 ty2'
397 | Just ty2'' <- tcView ty2'
398 = uUnrefined swap subst co tv1 ty2 ty2'' -- Unwrap synonyms
399 -- This is essential, in case we have
401 -- and then unify a :=: Foo a
403 uUnrefined swap subst co tv1 ty2 (TyVarTy tv2)
404 | tv1 == tv2 -- Same type variable
407 -- Check to see whether tv2 is refined
408 | Just (co',ty') <- lookupVarEnv subst tv2 -- co' :: tv2:=:ty'
409 = uUnrefined False subst (mkTransCoercion (doSwap swap co) co') tv1 ty' ty'
411 -- So both are unrefined; next, see if the kinds force the direction
412 | eqKind k1 k2 -- Can update either; so check the bind-flags
413 = do { b1 <- tvBindFlag tv1
414 ; b2 <- tvBindFlag tv2
416 (BindMe, _) -> bind swap tv1 ty2
418 (AvoidMe, BindMe) -> bind (not swap) tv2 ty1
419 (AvoidMe, _) -> bind swap tv1 ty2
421 (WildCard, WildCard) -> return subst
422 (WildCard, Skolem) -> return subst
423 (WildCard, _) -> bind (not swap) tv2 ty1
425 (Skolem, WildCard) -> return subst
426 (Skolem, Skolem) -> failWith (misMatch ty1 ty2)
427 (Skolem, _) -> bind (not swap) tv2 ty1
430 | k1 `isSubKind` k2 = bindTv (not swap) subst co tv2 ty1 -- Must update tv2
431 | k2 `isSubKind` k1 = bindTv swap subst co tv1 ty2 -- Must update tv1
433 | otherwise = failWith (kindMisMatch tv1 ty2)
438 bind swap tv ty = extendReft swap subst tv co ty
440 uUnrefined swap subst co tv1 ty2 ty2' -- ty2 is not a type variable
441 | tv1 `elemVarSet` substTvSet subst (tyVarsOfType ty2')
442 = failWith (occursCheck tv1 ty2) -- Occurs check
443 | not (k2 `isSubKind` k1)
444 = failWith (kindMisMatch tv1 ty2) -- Kind check
446 = bindTv swap subst co tv1 ty2 -- Bind tyvar to the synonym if poss
451 substTvSet :: InternalReft -> TyVarSet -> TyVarSet
452 -- Apply the non-idempotent substitution to a set of type variables,
453 -- remembering that the substitution isn't necessarily idempotent
455 = foldVarSet (unionVarSet . get) emptyVarSet tvs
457 get tv = case lookupVarEnv subst tv of
458 Nothing -> unitVarSet tv
459 Just (_,ty) -> substTvSet subst (tyVarsOfType ty)
461 bindTv swap subst co tv ty -- ty is not a type variable
462 = do { b <- tvBindFlag tv
464 Skolem -> failWith (misMatch (TyVarTy tv) ty)
465 WildCard -> return subst
466 other -> extendReft swap subst tv co ty
469 doSwap :: Bool -> Coercion -> Coercion
470 doSwap swap co = if swap then mkSymCoercion co else co
478 extendReft swap subst tv co ty
479 = ASSERT2( (coercionKindPredTy co1 `tcEqType` mkCoKind (mkTyVarTy tv) ty),
480 (text "Refinement invariant failure: co = " <+> ppr co1 <+> ppr (coercionKindPredTy co1) $$ text "subst = " <+> ppr tv <+> ppr (mkCoKind (mkTyVarTy tv) ty)) )
481 return (extendVarEnv subst tv (co1, ty))
487 %************************************************************************
491 %************************************************************************
495 = BindMe -- A regular type variable
496 | AvoidMe -- Like BindMe but, given the choice, avoid binding it
498 | Skolem -- This type variable is a skolem constant
499 -- Don't bind it; it only matches itself
501 | WildCard -- This type variable matches anything,
502 -- and does not affect the substitution
504 newtype UM a = UM { unUM :: (TyVar -> BindFlag)
505 -> MaybeErr Message a }
507 instance Monad UM where
508 return a = UM (\tvs -> Succeeded a)
509 fail s = UM (\tvs -> Failed (text s))
510 m >>= k = UM (\tvs -> case unUM m tvs of
511 Failed err -> Failed err
512 Succeeded v -> unUM (k v) tvs)
514 initUM :: (TyVar -> BindFlag) -> UM a -> MaybeErr Message a
515 initUM badtvs um = unUM um badtvs
517 tvBindFlag :: TyVar -> UM BindFlag
518 tvBindFlag tv = UM (\tv_fn -> Succeeded (tv_fn tv))
520 failWith :: Message -> UM a
521 failWith msg = UM (\tv_fn -> Failed msg)
523 maybeErrToMaybe :: MaybeErr fail succ -> Maybe succ
524 maybeErrToMaybe (Succeeded a) = Just a
525 maybeErrToMaybe (Failed m) = Nothing
529 %************************************************************************
532 We go to a lot more trouble to tidy the types
533 in TcUnify. Maybe we'll end up having to do that
534 here too, but I'll leave it for now.
536 %************************************************************************
540 = ptext SLIT("Can't match types") <+> quotes (ppr t1) <+>
541 ptext SLIT("and") <+> quotes (ppr t2)
543 lengthMisMatch tys1 tys2
544 = sep [ptext SLIT("Can't match unequal length lists"),
545 nest 2 (ppr tys1), nest 2 (ppr tys2) ]
548 = vcat [ptext SLIT("Can't match kinds") <+> quotes (ppr (tyVarKind tv1)) <+>
549 ptext SLIT("and") <+> quotes (ppr (typeKind t2)),
550 ptext SLIT("when matching") <+> quotes (ppr tv1) <+>
551 ptext SLIT("with") <+> quotes (ppr t2)]
554 = hang (ptext SLIT("Can't construct the infinite type"))
555 2 (ppr tv <+> equals <+> ppr ty)