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,
13 MatchEnv(..), matchList,
17 -- Side-effect free unification
18 tcUnifyTys, BindFlag(..),
19 niFixTvSubst, niSubstTvSet
23 #include "HsVersions.h"
38 import Control.Monad (guard)
42 %************************************************************************
46 %************************************************************************
49 Matching is much tricker than you might think.
51 1. The substitution we generate binds the *template type variables*
52 which are given to us explicitly.
54 2. We want to match in the presence of foralls;
55 e.g (forall a. t1) ~ (forall b. t2)
57 That is what the RnEnv2 is for; it does the alpha-renaming
58 that makes it as if a and b were the same variable.
59 Initialising the RnEnv2, so that it can generate a fresh
60 binder when necessary, entails knowing the free variables of
63 3. We must be careful not to bind a template type variable to a
64 locally bound variable. E.g.
65 (forall a. x) ~ (forall b. b)
66 where x is the template type variable. Then we do not want to
67 bind x to a/b! This is a kind of occurs check.
68 The necessary locals accumulate in the RnEnv2.
73 = ME { me_tmpls :: VarSet -- Template variables
74 , me_env :: RnEnv2 -- Renaming envt for nested foralls
75 } -- In-scope set includes template variables
76 -- Nota Bene: MatchEnv isn't specific to Types. It is used
77 -- for matching terms and coercions as well as types
79 tcMatchTy :: TyVarSet -- Template tyvars
82 -> Maybe TvSubst -- One-shot; in principle the template
83 -- variables could be free in the target
85 tcMatchTy tmpls ty1 ty2
86 = case match menv emptyTvSubstEnv ty1 ty2 of
87 Just subst_env -> Just (TvSubst in_scope subst_env)
90 menv = ME { me_tmpls = tmpls, me_env = mkRnEnv2 in_scope }
91 in_scope = mkInScopeSet (tmpls `unionVarSet` tyVarsOfType ty2)
92 -- We're assuming that all the interesting
93 -- tyvars in tys1 are in tmpls
95 tcMatchTys :: TyVarSet -- Template tyvars
98 -> Maybe TvSubst -- One-shot; in principle the template
99 -- variables could be free in the target
101 tcMatchTys tmpls tys1 tys2
102 = case match_tys menv emptyTvSubstEnv tys1 tys2 of
103 Just subst_env -> Just (TvSubst in_scope subst_env)
106 menv = ME { me_tmpls = tmpls, me_env = mkRnEnv2 in_scope }
107 in_scope = mkInScopeSet (tmpls `unionVarSet` tyVarsOfTypes tys2)
108 -- We're assuming that all the interesting
109 -- tyvars in tys1 are in tmpls
111 -- This is similar, but extends a substitution
112 tcMatchTyX :: TyVarSet -- Template tyvars
113 -> TvSubst -- Substitution to extend
117 tcMatchTyX tmpls (TvSubst in_scope subst_env) ty1 ty2
118 = case match menv subst_env ty1 ty2 of
119 Just subst_env -> Just (TvSubst in_scope subst_env)
122 menv = ME {me_tmpls = tmpls, me_env = mkRnEnv2 in_scope}
125 :: [TyVar] -- Bind these
126 -> [PredType] -> [PredType]
128 tcMatchPreds tmpls ps1 ps2
129 = matchList (match_pred menv) emptyTvSubstEnv ps1 ps2
131 menv = ME { me_tmpls = mkVarSet tmpls, me_env = mkRnEnv2 in_scope_tyvars }
132 in_scope_tyvars = mkInScopeSet (tyVarsOfTheta ps1 `unionVarSet` tyVarsOfTheta ps2)
134 -- This one is called from the expression matcher, which already has a MatchEnv in hand
135 ruleMatchTyX :: MatchEnv
136 -> TvSubstEnv -- Substitution to extend
141 ruleMatchTyX menv subst ty1 ty2 = match menv subst ty1 ty2 -- Rename for export
144 Now the internals of matching
147 match :: MatchEnv -- For the most part this is pushed downwards
148 -> TvSubstEnv -- Substitution so far:
149 -- Domain is subset of template tyvars
150 -- Free vars of range is subset of
151 -- in-scope set of the RnEnv2
152 -> Type -> Type -- Template and target respectively
154 -- This matcher works on core types; that is, it ignores PredTypes
155 -- Watch out if newtypes become transparent agin!
156 -- this matcher must respect newtypes
158 match menv subst ty1 ty2 | Just ty1' <- coreView ty1 = match menv subst ty1' ty2
159 | Just ty2' <- coreView ty2 = match menv subst ty1 ty2'
161 match menv subst (TyVarTy tv1) ty2
162 | Just ty1' <- lookupVarEnv subst tv1' -- tv1' is already bound
163 = if eqTypeX (nukeRnEnvL rn_env) ty1' ty2
164 -- ty1 has no locally-bound variables, hence nukeRnEnvL
166 else Nothing -- ty2 doesn't match
168 | tv1' `elemVarSet` me_tmpls menv
169 = if any (inRnEnvR rn_env) (varSetElems (tyVarsOfType ty2))
170 then Nothing -- Occurs check
171 else do { subst1 <- match_kind menv subst tv1 ty2
172 -- Note [Matching kinds]
173 ; return (extendVarEnv subst1 tv1' ty2) }
175 | otherwise -- tv1 is not a template tyvar
177 TyVarTy tv2 | tv1' == rnOccR rn_env tv2 -> Just subst
181 tv1' = rnOccL rn_env tv1
183 match menv subst (ForAllTy tv1 ty1) (ForAllTy tv2 ty2)
184 = match menv' subst ty1 ty2
185 where -- Use the magic of rnBndr2 to go under the binders
186 menv' = menv { me_env = rnBndr2 (me_env menv) tv1 tv2 }
188 match menv subst (PredTy p1) (PredTy p2)
189 = match_pred menv subst p1 p2
190 match menv subst (TyConApp tc1 tys1) (TyConApp tc2 tys2)
191 | tc1 == tc2 = match_tys menv subst tys1 tys2
192 match menv subst (FunTy ty1a ty1b) (FunTy ty2a ty2b)
193 = do { subst' <- match menv subst ty1a ty2a
194 ; match menv subst' ty1b ty2b }
195 match menv subst (AppTy ty1a ty1b) ty2
196 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
197 -- 'repSplit' used because the tcView stuff is done above
198 = do { subst' <- match menv subst ty1a ty2a
199 ; match menv subst' ty1b ty2b }
205 match_kind :: MatchEnv -> TvSubstEnv -> TyVar -> Type -> Maybe TvSubstEnv
206 -- Match the kind of the template tyvar with the kind of Type
207 -- Note [Matching kinds]
208 match_kind _ subst tv ty
209 = guard (typeKind ty `isSubKind` tyVarKind tv) >> return subst
211 -- Note [Matching kinds]
212 -- ~~~~~~~~~~~~~~~~~~~~~
213 -- For ordinary type variables, we don't want (m a) to match (n b)
214 -- if say (a::*) and (b::*->*). This is just a yes/no issue.
216 -- For coercion kinds matters are more complicated. If we have a
217 -- coercion template variable co::a~[b], where a,b are presumably also
218 -- template type variables, then we must match co's kind against the
219 -- kind of the actual argument, so as to give bindings to a,b.
221 -- In fact I have no example in mind that *requires* this kind-matching
222 -- to instantiate template type variables, but it seems like the right
223 -- thing to do. C.f. Note [Matching variable types] in Rules.lhs
226 match_tys :: MatchEnv -> TvSubstEnv -> [Type] -> [Type] -> Maybe TvSubstEnv
227 match_tys menv subst tys1 tys2 = matchList (match menv) subst tys1 tys2
230 matchList :: (env -> a -> b -> Maybe env)
231 -> env -> [a] -> [b] -> Maybe env
232 matchList _ subst [] [] = Just subst
233 matchList fn subst (a:as) (b:bs) = do { subst' <- fn subst a b
234 ; matchList fn subst' as bs }
235 matchList _ _ _ _ = Nothing
238 match_pred :: MatchEnv -> TvSubstEnv -> PredType -> PredType -> Maybe TvSubstEnv
239 match_pred menv subst (ClassP c1 tys1) (ClassP c2 tys2)
240 | c1 == c2 = match_tys menv subst tys1 tys2
241 match_pred menv subst (IParam n1 t1) (IParam n2 t2)
242 | n1 == n2 = match menv subst t1 t2
243 match_pred _ _ _ _ = Nothing
247 %************************************************************************
251 %************************************************************************
253 Note [Pruning dead case alternatives]
254 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
255 Consider data T a where
263 type instance F Bool = Int
265 Now consider case x of { T1 -> e1; T2 -> e2 }
267 The question before the house is this: if I know something about the type
268 of x, can I prune away the T1 alternative?
270 Suppose x::T Char. It's impossible to construct a (T Char) using T1,
271 Answer = YES (clearly)
273 Suppose x::T (F a), where 'a' is in scope. Then 'a' might be instantiated
274 to 'Bool', in which case x::T Int, so
275 ANSWER = NO (clearly)
277 Suppose x::T X. Then *in Haskell* it's impossible to construct a (non-bottom)
278 value of type (T X) using T1. But *in FC* it's quite possible. The newtype
281 So (T CoX) :: T X ~ T Int; hence (T1 `cast` sym (T CoX)) is a non-bottom value
282 of type (T X) constructed with T1. Hence
283 ANSWER = NO (surprisingly)
285 Furthermore, this can even happen; see Trac #1251. GHC's newtype-deriving
286 mechanism uses a cast, just as above, to move from one dictionary to another,
287 in effect giving the programmer access to CoX.
289 Finally, suppose x::T Y. Then *even in FC* we can't construct a
290 non-bottom value of type (T Y) using T1. That's because we can get
291 from Y to Char, but not to Int.
294 Here's a related question. data Eq a b where EQ :: Eq a a
296 case x of { EQ -> ... }
298 Suppose x::Eq Int Char. Is the alternative dead? Clearly yes.
300 What about x::Eq Int a, in a context where we have evidence that a~Char.
301 Then again the alternative is dead.
306 We are really doing a test for unsatisfiability of the type
307 constraints implied by the match. And that is clearly, in general, a
310 However, since we are simply dropping dead code, a conservative test
311 suffices. There is a continuum of tests, ranging from easy to hard, that
312 drop more and more dead code.
314 For now we implement a very simple test: type variables match
315 anything, type functions (incl newtypes) match anything, and only
316 distinct data types fail to match. We can elaborate later.
319 typesCantMatch :: [(Type,Type)] -> Bool
320 typesCantMatch prs = any (\(s,t) -> cant_match s t) prs
322 cant_match :: Type -> Type -> Bool
324 | Just t1' <- coreView t1 = cant_match t1' t2
325 | Just t2' <- coreView t2 = cant_match t1 t2'
327 cant_match (FunTy a1 r1) (FunTy a2 r2)
328 = cant_match a1 a2 || cant_match r1 r2
330 cant_match (TyConApp tc1 tys1) (TyConApp tc2 tys2)
331 | isDataTyCon tc1 && isDataTyCon tc2
332 = tc1 /= tc2 || typesCantMatch (zipEqual "typesCantMatch" tys1 tys2)
334 cant_match (FunTy {}) (TyConApp tc _) = isDataTyCon tc
335 cant_match (TyConApp tc _) (FunTy {}) = isDataTyCon tc
336 -- tc can't be FunTyCon by invariant
338 cant_match (AppTy f1 a1) ty2
339 | Just (f2, a2) <- repSplitAppTy_maybe ty2
340 = cant_match f1 f2 || cant_match a1 a2
341 cant_match ty1 (AppTy f2 a2)
342 | Just (f1, a1) <- repSplitAppTy_maybe ty1
343 = cant_match f1 f2 || cant_match a1 a2
345 cant_match _ _ = False -- Safe!
347 -- Things we could add;
349 -- look through newtypes
350 -- take account of tyvar bindings (EQ example above)
354 %************************************************************************
358 %************************************************************************
361 tcUnifyTys :: (TyVar -> BindFlag)
363 -> Maybe TvSubst -- A regular one-shot (idempotent) substitution
364 -- The two types may have common type variables, and indeed do so in the
365 -- second call to tcUnifyTys in FunDeps.checkClsFD
367 tcUnifyTys bind_fn tys1 tys2
368 = maybeErrToMaybe $ initUM bind_fn $
369 do { subst <- unifyList emptyTvSubstEnv tys1 tys2
371 -- Find the fixed point of the resulting non-idempotent substitution
372 ; return (niFixTvSubst subst) }
376 %************************************************************************
378 Non-idempotent substitution
380 %************************************************************************
382 Note [Non-idempotent substitution]
383 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
384 During unification we use a TvSubstEnv that is
386 (b) loop-free; ie repeatedly applying it yields a fixed point
389 niFixTvSubst :: TvSubstEnv -> TvSubst
390 -- Find the idempotent fixed point of the non-idempotent substitution
391 -- ToDo: use laziness instead of iteration?
392 niFixTvSubst env = f env
394 f e | not_fixpoint = f (mapVarEnv (substTy subst) e)
397 range_tvs = foldVarEnv (unionVarSet . tyVarsOfType) emptyVarSet e
398 subst = mkTvSubst (mkInScopeSet range_tvs) e
399 not_fixpoint = foldVarSet ((||) . in_domain) False range_tvs
400 in_domain tv = tv `elemVarEnv` e
402 niSubstTvSet :: TvSubstEnv -> TyVarSet -> TyVarSet
403 -- Apply the non-idempotent substitution to a set of type variables,
404 -- remembering that the substitution isn't necessarily idempotent
405 -- This is used in the occurs check, before extending the substitution
406 niSubstTvSet subst tvs
407 = foldVarSet (unionVarSet . get) emptyVarSet tvs
409 get tv = case lookupVarEnv subst tv of
410 Nothing -> unitVarSet tv
411 Just ty -> niSubstTvSet subst (tyVarsOfType ty)
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` niSubstTvSet 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 bindTv :: TvSubstEnv -> TyVar -> Type -> UM TvSubstEnv
557 bindTv subst tv ty -- ty is not a type variable
558 = do { b <- tvBindFlag tv
560 Skolem -> failWith (misMatch (TyVarTy tv) ty)
561 BindMe -> return $ extendVarEnv subst tv ty
565 %************************************************************************
569 %************************************************************************
573 = BindMe -- A regular type variable
575 | Skolem -- This type variable is a skolem constant
576 -- Don't bind it; it only matches itself
580 %************************************************************************
584 %************************************************************************
587 newtype UM a = UM { unUM :: (TyVar -> BindFlag)
588 -> MaybeErr Message a }
590 instance Monad UM where
591 return a = UM (\_tvs -> Succeeded a)
592 fail s = UM (\_tvs -> Failed (text s))
593 m >>= k = UM (\tvs -> case unUM m tvs of
594 Failed err -> Failed err
595 Succeeded v -> unUM (k v) tvs)
597 initUM :: (TyVar -> BindFlag) -> UM a -> MaybeErr Message a
598 initUM badtvs um = unUM um badtvs
600 tvBindFlag :: TyVar -> UM BindFlag
601 tvBindFlag tv = UM (\tv_fn -> Succeeded (tv_fn tv))
603 failWith :: Message -> UM a
604 failWith msg = UM (\_tv_fn -> Failed msg)
606 maybeErrToMaybe :: MaybeErr fail succ -> Maybe succ
607 maybeErrToMaybe (Succeeded a) = Just a
608 maybeErrToMaybe (Failed _) = Nothing
612 %************************************************************************
615 We go to a lot more trouble to tidy the types
616 in TcUnify. Maybe we'll end up having to do that
617 here too, but I'll leave it for now.
619 %************************************************************************
622 misMatch :: Type -> Type -> SDoc
624 = ptext (sLit "Can't match types") <+> quotes (ppr t1) <+>
625 ptext (sLit "and") <+> quotes (ppr t2)
627 lengthMisMatch :: [Type] -> [Type] -> SDoc
628 lengthMisMatch tys1 tys2
629 = sep [ptext (sLit "Can't match unequal length lists"),
630 nest 2 (ppr tys1), nest 2 (ppr tys2) ]
632 kindMisMatch :: TyVar -> Type -> SDoc
634 = vcat [ptext (sLit "Can't match kinds") <+> quotes (ppr (tyVarKind tv1)) <+>
635 ptext (sLit "and") <+> quotes (ppr (typeKind t2)),
636 ptext (sLit "when matching") <+> quotes (ppr tv1) <+>
637 ptext (sLit "with") <+> quotes (ppr t2)]
639 occursCheck :: TyVar -> Type -> SDoc
641 = hang (ptext (sLit "Can't construct the infinite type"))
642 2 (ppr tv <+> equals <+> ppr ty)