2 % (c) The University of Glasgow 2006
8 -- the "tc" prefix indicates that matching always
9 -- respects newtypes (rather than looking through them)
10 tcMatchTy, tcMatchTys, tcMatchTyX,
11 ruleMatchTyX, tcMatchPreds, MatchEnv(..),
15 -- Side-effect free unification
16 tcUnifyTys, BindFlag(..)
20 #include "HsVersions.h"
39 %************************************************************************
43 %************************************************************************
46 Matching is much tricker than you might think.
48 1. The substitution we generate binds the *template type variables*
49 which are given to us explicitly.
51 2. We want to match in the presence of foralls;
52 e.g (forall a. t1) ~ (forall b. t2)
54 That is what the RnEnv2 is for; it does the alpha-renaming
55 that makes it as if a and b were the same variable.
56 Initialising the RnEnv2, so that it can generate a fresh
57 binder when necessary, entails knowing the free variables of
60 3. We must be careful not to bind a template type variable to a
61 locally bound variable. E.g.
62 (forall a. x) ~ (forall b. b)
63 where x is the template type variable. Then we do not want to
64 bind x to a/b! This is a kind of occurs check.
65 The necessary locals accumulate in the RnEnv2.
70 = ME { me_tmpls :: VarSet -- Template tyvars
71 , me_env :: RnEnv2 -- Renaming envt for nested foralls
72 } -- In-scope set includes template tyvars
74 tcMatchTy :: TyVarSet -- Template tyvars
77 -> Maybe TvSubst -- One-shot; in principle the template
78 -- variables could be free in the target
80 tcMatchTy tmpls ty1 ty2
81 = case match menv emptyTvSubstEnv ty1 ty2 of
82 Just subst_env -> Just (TvSubst in_scope subst_env)
85 menv = ME { me_tmpls = tmpls, me_env = mkRnEnv2 in_scope }
86 in_scope = mkInScopeSet (tmpls `unionVarSet` tyVarsOfType ty2)
87 -- We're assuming that all the interesting
88 -- tyvars in tys1 are in tmpls
90 tcMatchTys :: TyVarSet -- Template tyvars
93 -> Maybe TvSubst -- One-shot; in principle the template
94 -- variables could be free in the target
96 tcMatchTys tmpls tys1 tys2
97 = case match_tys menv emptyTvSubstEnv tys1 tys2 of
98 Just subst_env -> Just (TvSubst in_scope subst_env)
101 menv = ME { me_tmpls = tmpls, me_env = mkRnEnv2 in_scope }
102 in_scope = mkInScopeSet (tmpls `unionVarSet` tyVarsOfTypes tys2)
103 -- We're assuming that all the interesting
104 -- tyvars in tys1 are in tmpls
106 -- This is similar, but extends a substitution
107 tcMatchTyX :: TyVarSet -- Template tyvars
108 -> TvSubst -- Substitution to extend
112 tcMatchTyX tmpls (TvSubst in_scope subst_env) ty1 ty2
113 = case match menv subst_env ty1 ty2 of
114 Just subst_env -> Just (TvSubst in_scope subst_env)
117 menv = ME {me_tmpls = tmpls, me_env = mkRnEnv2 in_scope}
120 :: [TyVar] -- Bind these
121 -> [PredType] -> [PredType]
123 tcMatchPreds tmpls ps1 ps2
124 = match_list (match_pred menv) emptyTvSubstEnv ps1 ps2
126 menv = ME { me_tmpls = mkVarSet tmpls, me_env = mkRnEnv2 in_scope_tyvars }
127 in_scope_tyvars = mkInScopeSet (tyVarsOfTheta ps1 `unionVarSet` tyVarsOfTheta ps2)
129 -- This one is called from the expression matcher, which already has a MatchEnv in hand
130 ruleMatchTyX :: MatchEnv
131 -> TvSubstEnv -- Substitution to extend
136 ruleMatchTyX menv subst ty1 ty2 = match menv subst ty1 ty2 -- Rename for export
139 Now the internals of matching
142 match :: MatchEnv -- For the most part this is pushed downwards
143 -> TvSubstEnv -- Substitution so far:
144 -- Domain is subset of template tyvars
145 -- Free vars of range is subset of
146 -- in-scope set of the RnEnv2
147 -> Type -> Type -- Template and target respectively
149 -- This matcher works on core types; that is, it ignores PredTypes
150 -- Watch out if newtypes become transparent agin!
151 -- this matcher must respect newtypes
153 match menv subst ty1 ty2 | Just ty1' <- coreView ty1 = match menv subst ty1' ty2
154 | Just ty2' <- coreView ty2 = match menv subst ty1 ty2'
156 match menv subst (TyVarTy tv1) ty2
157 | Just ty1' <- lookupVarEnv subst tv1' -- tv1' is already bound
158 = if tcEqTypeX (nukeRnEnvL rn_env) ty1' ty2
159 -- ty1 has no locally-bound variables, hence nukeRnEnvL
160 -- Note tcEqType...we are doing source-type matching here
162 else Nothing -- ty2 doesn't match
164 | tv1' `elemVarSet` me_tmpls menv
165 = if any (inRnEnvR rn_env) (varSetElems (tyVarsOfType ty2))
166 then Nothing -- Occurs check
167 else do { subst1 <- match_kind menv subst tv1 ty2
168 -- Note [Matching kinds]
169 ; return (extendVarEnv subst1 tv1' ty2) }
171 | otherwise -- tv1 is not a template tyvar
173 TyVarTy tv2 | tv1' == rnOccR rn_env tv2 -> Just subst
177 tv1' = rnOccL rn_env tv1
179 match menv subst (ForAllTy tv1 ty1) (ForAllTy tv2 ty2)
180 = match menv' subst ty1 ty2
181 where -- Use the magic of rnBndr2 to go under the binders
182 menv' = menv { me_env = rnBndr2 (me_env menv) tv1 tv2 }
184 match menv subst (PredTy p1) (PredTy p2)
185 = match_pred menv subst p1 p2
186 match menv subst (TyConApp tc1 tys1) (TyConApp tc2 tys2)
187 | tc1 == tc2 = match_tys menv subst tys1 tys2
188 match menv subst (FunTy ty1a ty1b) (FunTy ty2a ty2b)
189 = do { subst' <- match menv subst ty1a ty2a
190 ; match menv subst' ty1b ty2b }
191 match menv subst (AppTy ty1a ty1b) ty2
192 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
193 -- 'repSplit' used because the tcView stuff is done above
194 = do { subst' <- match menv subst ty1a ty2a
195 ; match menv subst' ty1b ty2b }
201 match_kind :: MatchEnv -> TvSubstEnv -> TyVar -> Type -> Maybe TvSubstEnv
202 -- Match the kind of the template tyvar with the kind of Type
203 -- Note [Matching kinds]
204 match_kind menv subst tv ty
205 | isCoVar tv = do { let (ty1,ty2) = coVarKind tv
206 (ty3,ty4) = coercionKind ty
207 ; subst1 <- match menv subst ty1 ty3
208 ; match menv subst1 ty2 ty4 }
209 | otherwise = if typeKind ty `isSubKind` tyVarKind tv
213 -- Note [Matching kinds]
214 -- ~~~~~~~~~~~~~~~~~~~~~
215 -- For ordinary type variables, we don't want (m a) to match (n b)
216 -- if say (a::*) and (b::*->*). This is just a yes/no issue.
218 -- For coercion kinds matters are more complicated. If we have a
219 -- coercion template variable co::a~[b], where a,b are presumably also
220 -- template type variables, then we must match co's kind against the
221 -- kind of the actual argument, so as to give bindings to a,b.
223 -- In fact I have no example in mind that *requires* this kind-matching
224 -- to instantiate template type variables, but it seems like the right
225 -- thing to do. C.f. Note [Matching variable types] in Rules.lhs
228 match_tys :: MatchEnv -> TvSubstEnv -> [Type] -> [Type] -> Maybe TvSubstEnv
229 match_tys menv subst tys1 tys2 = match_list (match menv) subst tys1 tys2
232 match_list :: (TvSubstEnv -> a -> a -> Maybe TvSubstEnv)
233 -> TvSubstEnv -> [a] -> [a] -> Maybe TvSubstEnv
234 match_list _ subst [] [] = Just subst
235 match_list fn subst (ty1:tys1) (ty2:tys2) = do { subst' <- fn subst ty1 ty2
236 ; match_list fn subst' tys1 tys2 }
237 match_list _ _ _ _ = Nothing
240 match_pred :: MatchEnv -> TvSubstEnv -> PredType -> PredType -> Maybe TvSubstEnv
241 match_pred menv subst (ClassP c1 tys1) (ClassP c2 tys2)
242 | c1 == c2 = match_tys menv subst tys1 tys2
243 match_pred menv subst (IParam n1 t1) (IParam n2 t2)
244 | n1 == n2 = match menv subst t1 t2
245 match_pred _ _ _ _ = Nothing
249 %************************************************************************
253 %************************************************************************
255 Note [Pruning dead case alternatives]
256 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
257 Consider data T a where
265 type instance F Bool = Int
267 Now consider case x of { T1 -> e1; T2 -> e2 }
269 The question before the house is this: if I know something about the type
270 of x, can I prune away the T1 alternative?
272 Suppose x::T Char. It's impossible to construct a (T Char) using T1,
273 Answer = YES (clearly)
275 Suppose x::T (F a), where 'a' is in scope. Then 'a' might be instantiated
276 to 'Bool', in which case x::T Int, so
277 ANSWER = NO (clearly)
279 Suppose x::T X. Then *in Haskell* it's impossible to construct a (non-bottom)
280 value of type (T X) using T1. But *in FC* it's quite possible. The newtype
283 So (T CoX) :: T X ~ T Int; hence (T1 `cast` sym (T CoX)) is a non-bottom value
284 of type (T X) constructed with T1. Hence
285 ANSWER = NO (surprisingly)
287 Furthermore, this can even happen; see Trac #1251. GHC's newtype-deriving
288 mechanism uses a cast, just as above, to move from one dictionary to another,
289 in effect giving the programmer access to CoX.
291 Finally, suppose x::T Y. Then *even in FC* we can't construct a
292 non-bottom value of type (T Y) using T1. That's because we can get
293 from Y to Char, but not to Int.
296 Here's a related question. data Eq a b where EQ :: Eq a a
298 case x of { EQ -> ... }
300 Suppose x::Eq Int Char. Is the alternative dead? Clearly yes.
302 What about x::Eq Int a, in a context where we have evidence that a~Char.
303 Then again the alternative is dead.
308 We are really doing a test for unsatisfiability of the type
309 constraints implied by the match. And that is clearly, in general, a
312 However, since we are simply dropping dead code, a conservative test
313 suffices. There is a continuum of tests, ranging from easy to hard, that
314 drop more and more dead code.
316 For now we implement a very simple test: type variables match
317 anything, type functions (incl newtypes) match anything, and only
318 distinct data types fail to match. We can elaborate later.
321 dataConCannotMatch :: [Type] -> DataCon -> Bool
322 -- Returns True iff the data con *definitely cannot* match a
323 -- scrutinee of type (T tys)
324 -- where T is the type constructor for the data con
326 dataConCannotMatch tys con
327 | null eq_spec = False -- Common
328 | all isTyVarTy tys = False -- Also common
330 = cant_match_s (map (substTyVar subst . fst) eq_spec)
333 dc_tvs = dataConUnivTyVars con
334 eq_spec = dataConEqSpec con
335 subst = zipTopTvSubst dc_tvs tys
337 cant_match_s :: [Type] -> [Type] -> Bool
338 cant_match_s tys1 tys2 = ASSERT( equalLength tys1 tys2 )
339 or (zipWith cant_match tys1 tys2)
341 cant_match :: Type -> Type -> Bool
343 | Just t1' <- coreView t1 = cant_match t1' t2
344 | Just t2' <- coreView t2 = cant_match t1 t2'
346 cant_match (FunTy a1 r1) (FunTy a2 r2)
347 = cant_match a1 a2 || cant_match r1 r2
349 cant_match (TyConApp tc1 tys1) (TyConApp tc2 tys2)
350 | isDataTyCon tc1 && isDataTyCon tc2
351 = tc1 /= tc2 || cant_match_s tys1 tys2
353 cant_match (FunTy {}) (TyConApp tc _) = isDataTyCon tc
354 cant_match (TyConApp tc _) (FunTy {}) = isDataTyCon tc
355 -- tc can't be FunTyCon by invariant
357 cant_match (AppTy f1 a1) ty2
358 | Just (f2, a2) <- repSplitAppTy_maybe ty2
359 = cant_match f1 f2 || cant_match a1 a2
360 cant_match ty1 (AppTy f2 a2)
361 | Just (f1, a1) <- repSplitAppTy_maybe ty1
362 = cant_match f1 f2 || cant_match a1 a2
364 cant_match _ _ = False -- Safe!
366 -- Things we could add;
368 -- look through newtypes
369 -- take account of tyvar bindings (EQ example above)
374 %************************************************************************
378 %************************************************************************
381 tcUnifyTys :: (TyVar -> BindFlag)
383 -> Maybe TvSubst -- A regular one-shot (idempotent) substitution
384 -- The two types may have common type variables, and indeed do so in the
385 -- second call to tcUnifyTys in FunDeps.checkClsFD
387 tcUnifyTys bind_fn tys1 tys2
388 = maybeErrToMaybe $ initUM bind_fn $
389 do { subst <- unifyList emptyTvSubstEnv tys1 tys2
391 -- Find the fixed point of the resulting non-idempotent substitution
392 ; let in_scope = mkInScopeSet (tvs1 `unionVarSet` tvs2)
393 tv_env = fixTvSubstEnv in_scope subst
395 ; return (mkTvSubst in_scope tv_env) }
397 tvs1 = tyVarsOfTypes tys1
398 tvs2 = tyVarsOfTypes tys2
400 ----------------------------
401 -- XXX Can we do this more nicely, by exploiting laziness?
402 -- Or avoid needing it in the first place?
403 fixTvSubstEnv :: InScopeSet -> TvSubstEnv -> TvSubstEnv
404 fixTvSubstEnv in_scope env = f env
406 f e = let e' = mapUFM (substTy (mkTvSubst in_scope e)) e
407 in if and $ eltsUFM $ intersectUFM_C tcEqType e e'
414 %************************************************************************
418 %************************************************************************
421 unify :: TvSubstEnv -- An existing substitution to extend
422 -> Type -> Type -- Types to be unified, and witness of their equality
423 -> UM TvSubstEnv -- Just the extended substitution,
424 -- Nothing if unification failed
425 -- We do not require the incoming substitution to be idempotent,
426 -- nor guarantee that the outgoing one is. That's fixed up by
429 -- Respects newtypes, PredTypes
431 -- in unify, any NewTcApps/Preds should be taken at face value
432 unify subst (TyVarTy tv1) ty2 = uVar subst tv1 ty2
433 unify subst ty1 (TyVarTy tv2) = uVar subst tv2 ty1
435 unify subst ty1 ty2 | Just ty1' <- tcView ty1 = unify subst ty1' ty2
436 unify subst ty1 ty2 | Just ty2' <- tcView ty2 = unify subst ty1 ty2'
438 unify subst (PredTy p1) (PredTy p2) = unify_pred subst p1 p2
440 unify subst (TyConApp tyc1 tys1) (TyConApp tyc2 tys2)
441 | tyc1 == tyc2 = unify_tys subst tys1 tys2
443 unify subst (FunTy ty1a ty1b) (FunTy ty2a ty2b)
444 = do { subst' <- unify subst ty1a ty2a
445 ; unify subst' ty1b ty2b }
447 -- Applications need a bit of care!
448 -- They can match FunTy and TyConApp, so use splitAppTy_maybe
449 -- NB: we've already dealt with type variables and Notes,
450 -- so if one type is an App the other one jolly well better be too
451 unify subst (AppTy ty1a ty1b) ty2
452 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
453 = do { subst' <- unify subst ty1a ty2a
454 ; unify subst' ty1b ty2b }
456 unify subst ty1 (AppTy ty2a ty2b)
457 | Just (ty1a, ty1b) <- repSplitAppTy_maybe ty1
458 = do { subst' <- unify subst ty1a ty2a
459 ; unify subst' ty1b ty2b }
461 unify _ ty1 ty2 = failWith (misMatch ty1 ty2)
464 ------------------------------
465 unify_pred :: TvSubstEnv -> PredType -> PredType -> UM TvSubstEnv
466 unify_pred subst (ClassP c1 tys1) (ClassP c2 tys2)
467 | c1 == c2 = unify_tys subst tys1 tys2
468 unify_pred subst (IParam n1 t1) (IParam n2 t2)
469 | n1 == n2 = unify subst t1 t2
470 unify_pred _ p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2))
472 ------------------------------
473 unify_tys :: TvSubstEnv -> [Type] -> [Type] -> UM TvSubstEnv
474 unify_tys subst xs ys = unifyList subst xs ys
476 unifyList :: TvSubstEnv -> [Type] -> [Type] -> UM TvSubstEnv
477 unifyList subst orig_xs orig_ys
478 = go subst orig_xs orig_ys
480 go subst [] [] = return subst
481 go subst (x:xs) (y:ys) = do { subst' <- unify subst x y
483 go _ _ _ = failWith (lengthMisMatch orig_xs orig_ys)
485 ---------------------------------
486 uVar :: TvSubstEnv -- An existing substitution to extend
487 -> TyVar -- Type variable to be unified
488 -> Type -- with this type
491 -- PRE-CONDITION: in the call (uVar swap r tv1 ty), we know that
492 -- if swap=False (tv1~ty)
493 -- if swap=True (ty~tv1)
496 = -- Check to see whether tv1 is refined by the substitution
497 case (lookupVarEnv subst tv1) of
498 Just ty' -> unify subst ty' ty -- Yes, call back into unify'
499 Nothing -> uUnrefined subst -- No, continue
502 uUnrefined :: TvSubstEnv -- An existing substitution to extend
503 -> TyVar -- Type variable to be unified
504 -> Type -- with this type
505 -> Type -- (version w/ expanded synonyms)
508 -- We know that tv1 isn't refined
510 uUnrefined subst tv1 ty2 ty2'
511 | Just ty2'' <- tcView ty2'
512 = uUnrefined subst tv1 ty2 ty2'' -- Unwrap synonyms
513 -- This is essential, in case we have
515 -- and then unify a ~ Foo a
517 uUnrefined subst tv1 ty2 (TyVarTy tv2)
518 | tv1 == tv2 -- Same type variable
521 -- Check to see whether tv2 is refined
522 | Just ty' <- lookupVarEnv subst tv2
523 = uUnrefined subst tv1 ty' ty'
525 -- So both are unrefined; next, see if the kinds force the direction
526 | eqKind k1 k2 -- Can update either; so check the bind-flags
527 = do { b1 <- tvBindFlag tv1
528 ; b2 <- tvBindFlag tv2
530 (BindMe, _) -> bind tv1 ty2
531 (Skolem, Skolem) -> failWith (misMatch ty1 ty2)
532 (Skolem, _) -> bind tv2 ty1
535 | k1 `isSubKind` k2 = bindTv subst tv2 ty1 -- Must update tv2
536 | k2 `isSubKind` k1 = bindTv subst tv1 ty2 -- Must update tv1
538 | otherwise = failWith (kindMisMatch tv1 ty2)
543 bind tv ty = return $ extendVarEnv subst tv ty
545 uUnrefined subst tv1 ty2 ty2' -- ty2 is not a type variable
546 | tv1 `elemVarSet` substTvSet subst (tyVarsOfType ty2')
547 = failWith (occursCheck tv1 ty2) -- Occurs check
548 | not (k2 `isSubKind` k1)
549 = failWith (kindMisMatch tv1 ty2) -- Kind check
551 = bindTv subst tv1 ty2 -- Bind tyvar to the synonym if poss
556 substTvSet :: TvSubstEnv -> TyVarSet -> TyVarSet
557 -- Apply the non-idempotent substitution to a set of type variables,
558 -- remembering that the substitution isn't necessarily idempotent
560 = foldVarSet (unionVarSet . get) emptyVarSet tvs
562 get tv = case lookupVarEnv subst tv of
563 Nothing -> unitVarSet tv
564 Just ty -> substTvSet subst (tyVarsOfType ty)
566 bindTv :: TvSubstEnv -> TyVar -> Type -> UM TvSubstEnv
567 bindTv subst tv ty -- ty is not a type variable
568 = do { b <- tvBindFlag tv
570 Skolem -> failWith (misMatch (TyVarTy tv) ty)
571 BindMe -> return $ extendVarEnv subst tv ty
575 %************************************************************************
579 %************************************************************************
583 = BindMe -- A regular type variable
585 | Skolem -- This type variable is a skolem constant
586 -- Don't bind it; it only matches itself
590 %************************************************************************
594 %************************************************************************
597 newtype UM a = UM { unUM :: (TyVar -> BindFlag)
598 -> MaybeErr Message a }
600 instance Monad UM where
601 return a = UM (\_tvs -> Succeeded a)
602 fail s = UM (\_tvs -> Failed (text s))
603 m >>= k = UM (\tvs -> case unUM m tvs of
604 Failed err -> Failed err
605 Succeeded v -> unUM (k v) tvs)
607 initUM :: (TyVar -> BindFlag) -> UM a -> MaybeErr Message a
608 initUM badtvs um = unUM um badtvs
610 tvBindFlag :: TyVar -> UM BindFlag
611 tvBindFlag tv = UM (\tv_fn -> Succeeded (tv_fn tv))
613 failWith :: Message -> UM a
614 failWith msg = UM (\_tv_fn -> Failed msg)
616 maybeErrToMaybe :: MaybeErr fail succ -> Maybe succ
617 maybeErrToMaybe (Succeeded a) = Just a
618 maybeErrToMaybe (Failed _) = Nothing
622 %************************************************************************
625 We go to a lot more trouble to tidy the types
626 in TcUnify. Maybe we'll end up having to do that
627 here too, but I'll leave it for now.
629 %************************************************************************
632 misMatch :: Type -> Type -> SDoc
634 = ptext (sLit "Can't match types") <+> quotes (ppr t1) <+>
635 ptext (sLit "and") <+> quotes (ppr t2)
637 lengthMisMatch :: [Type] -> [Type] -> SDoc
638 lengthMisMatch tys1 tys2
639 = sep [ptext (sLit "Can't match unequal length lists"),
640 nest 2 (ppr tys1), nest 2 (ppr tys2) ]
642 kindMisMatch :: TyVar -> Type -> SDoc
644 = vcat [ptext (sLit "Can't match kinds") <+> quotes (ppr (tyVarKind tv1)) <+>
645 ptext (sLit "and") <+> quotes (ppr (typeKind t2)),
646 ptext (sLit "when matching") <+> quotes (ppr tv1) <+>
647 ptext (sLit "with") <+> quotes (ppr t2)]
649 occursCheck :: TyVar -> Type -> SDoc
651 = hang (ptext (sLit "Can't construct the infinite type"))
652 2 (ppr tv <+> equals <+> ppr ty)