3 -- Matching and unification
4 tcMatchTys, tcMatchTyX, ruleMatchTyX, tcMatchPreds, MatchEnv(..),
8 gadtRefineTys, BindFlag(..),
10 coreRefineTys, TypeRefinement,
16 #include "HsVersions.h"
18 import Var ( Var, TyVar, tyVarKind )
21 import Kind ( isSubKind )
22 import Type ( typeKind, tyVarsOfType, tyVarsOfTypes, tyVarsOfTheta, mkTyVarTys,
23 TvSubstEnv, emptyTvSubstEnv, TvSubst(..), substTy, tcEqTypeX,
25 import TypeRep ( Type(..), PredType(..), funTyCon )
26 import DataCon ( DataCon, dataConInstResTy )
27 import Util ( snocView )
28 import ErrUtils ( Message )
34 %************************************************************************
38 %************************************************************************
41 Matching is much tricker than you might think.
43 1. The substitution we generate binds the *template type variables*
44 which are given to us explicitly.
46 2. We want to match in the presence of foralls;
47 e.g (forall a. t1) ~ (forall b. t2)
49 That is what the RnEnv2 is for; it does the alpha-renaming
50 that makes it as if a and b were the same variable.
51 Initialising the RnEnv2, so that it can generate a fresh
52 binder when necessary, entails knowing the free variables of
55 3. We must be careful not to bind a template type variable to a
56 locally bound variable. E.g.
57 (forall a. x) ~ (forall b. b)
58 where x is the template type variable. Then we do not want to
59 bind x to a/b! This is a kind of occurs check.
60 The necessary locals accumulate in the RnEnv2.
65 = ME { me_tmpls :: VarSet -- Template tyvars
66 , me_env :: RnEnv2 -- Renaming envt for nested foralls
67 } -- In-scope set includes template tyvars
69 tcMatchTys :: TyVarSet -- Template tyvars
72 -> Maybe TvSubst -- One-shot; in principle the template
73 -- variables could be free in the target
75 tcMatchTys tmpls tys1 tys2
76 = case match_tys menv emptyTvSubstEnv tys1 tys2 of
77 Just subst_env -> Just (TvSubst in_scope subst_env)
80 menv = ME { me_tmpls = tmpls, me_env = mkRnEnv2 in_scope }
81 in_scope = mkInScopeSet (tmpls `unionVarSet` tyVarsOfTypes tys2)
82 -- We're assuming that all the interesting
83 -- tyvars in tys1 are in tmpls
85 -- This is similar, but extends a substitution
86 tcMatchTyX :: TyVarSet -- Template tyvars
87 -> TvSubst -- Substitution to extend
91 tcMatchTyX tmpls (TvSubst in_scope subst_env) ty1 ty2
92 = case match menv subst_env ty1 ty2 of
93 Just subst_env -> Just (TvSubst in_scope subst_env)
96 menv = ME {me_tmpls = tmpls, me_env = mkRnEnv2 in_scope}
99 :: [TyVar] -- Bind these
100 -> [PredType] -> [PredType]
102 tcMatchPreds tmpls ps1 ps2
103 = match_list (match_pred menv) emptyTvSubstEnv ps1 ps2
105 menv = ME { me_tmpls = mkVarSet tmpls, me_env = mkRnEnv2 in_scope_tyvars }
106 in_scope_tyvars = mkInScopeSet (tyVarsOfTheta ps1 `unionVarSet` tyVarsOfTheta ps2)
108 -- This one is called from the expression matcher, which already has a MatchEnv in hand
109 ruleMatchTyX :: MatchEnv
110 -> TvSubstEnv -- Substitution to extend
115 ruleMatchTyX menv subst ty1 ty2 = match menv subst ty1 ty2 -- Rename for export
118 Now the internals of matching
121 match :: MatchEnv -- For the most part this is pushed downwards
122 -> TvSubstEnv -- Substitution so far:
123 -- Domain is subset of template tyvars
124 -- Free vars of range is subset of
125 -- in-scope set of the RnEnv2
126 -> Type -> Type -- Template and target respectively
128 -- This matcher works on source types; that is,
129 -- it respects NewTypes and PredType
131 match menv subst ty1 ty2 | Just ty1' <- tcView ty1 = match menv subst ty1' ty2
132 match menv subst ty1 ty2 | Just ty2' <- tcView ty2 = match menv subst ty1 ty2'
134 match menv subst (TyVarTy tv1) ty2
135 | tv1 `elemVarSet` me_tmpls menv
136 = case lookupVarEnv subst tv1' of
137 Nothing | any (inRnEnvR rn_env) (varSetElems (tyVarsOfType ty2))
138 -> Nothing -- Occurs check
139 | not (typeKind ty2 `isSubKind` tyVarKind tv1)
140 -> Nothing -- Kind mis-match
142 -> Just (extendVarEnv subst tv1 ty2)
144 Just ty1' | tcEqTypeX (nukeRnEnvL rn_env) ty1' ty2
145 -- ty1 has no locally-bound variables, hence nukeRnEnvL
146 -- Note tcEqType...we are doing source-type matching here
151 | otherwise -- tv1 is not a template tyvar
153 TyVarTy tv2 | tv1' == rnOccR rn_env tv2 -> Just subst
157 tv1' = rnOccL rn_env tv1
159 match menv subst (ForAllTy tv1 ty1) (ForAllTy tv2 ty2)
160 = match menv' subst ty1 ty2
161 where -- Use the magic of rnBndr2 to go under the binders
162 menv' = menv { me_env = rnBndr2 (me_env menv) tv1 tv2 }
164 match menv subst (PredTy p1) (PredTy p2)
165 = match_pred menv subst p1 p2
166 match menv subst (TyConApp tc1 tys1) (TyConApp tc2 tys2)
167 | tc1 == tc2 = match_tys menv subst tys1 tys2
168 match menv subst (FunTy ty1a ty1b) (FunTy ty2a ty2b)
169 = do { subst' <- match menv subst ty1a ty2a
170 ; match menv subst' ty1b ty2b }
171 match menv subst (AppTy ty1a ty1b) ty2
172 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
173 = do { subst' <- match menv subst ty1a ty2a
174 ; match menv subst' ty1b ty2b }
176 match menv subst ty1 ty2
180 match_tys menv subst tys1 tys2 = match_list (match menv) subst tys1 tys2
183 match_list :: (TvSubstEnv -> a -> a -> Maybe TvSubstEnv)
184 -> TvSubstEnv -> [a] -> [a] -> Maybe TvSubstEnv
185 match_list fn subst [] [] = Just subst
186 match_list fn subst (ty1:tys1) (ty2:tys2) = do { subst' <- fn subst ty1 ty2
187 ; match_list fn subst' tys1 tys2 }
188 match_list fn subst tys1 tys2 = Nothing
191 match_pred menv subst (ClassP c1 tys1) (ClassP c2 tys2)
192 | c1 == c2 = match_tys menv subst tys1 tys2
193 match_pred menv subst (IParam n1 t1) (IParam n2 t2)
194 | n1 == n2 = match menv subst t1 t2
195 match_pred menv subst p1 p2 = Nothing
199 %************************************************************************
203 %************************************************************************
206 tcUnifyTys :: (TyVar -> BindFlag)
208 -> Maybe TvSubst -- A regular one-shot substitution
209 -- The two types may have common type variables, and indeed do so in the
210 -- second call to tcUnifyTys in FunDeps.checkClsFD
211 tcUnifyTys bind_fn tys1 tys2
212 = maybeErrToMaybe $ initUM bind_fn $
213 do { subst_env <- unify_tys emptyTvSubstEnv tys1 tys2
215 -- Find the fixed point of the resulting non-idempotent substitution
216 ; let in_scope = mkInScopeSet (tvs1 `unionVarSet` tvs2)
217 subst = TvSubst in_scope subst_env_fixpt
218 subst_env_fixpt = mapVarEnv (substTy subst) subst_env
221 tvs1 = tyVarsOfTypes tys1
222 tvs2 = tyVarsOfTypes tys2
224 ----------------------------
225 coreRefineTys :: InScopeSet -- Superset of free vars of either type
226 -> DataCon -> [TyVar] -- Case pattern (con tv1 .. tvn ...)
227 -> Type -- Type of scrutinee
228 -> Maybe TypeRefinement
230 type TypeRefinement = (TvSubstEnv, Bool)
231 -- The Bool is True iff all the bindings in the
232 -- env are for the pattern type variables
233 -- In this case, there is no type refinement
234 -- for already-in-scope type variables
236 -- Used by Core Lint and the simplifier.
237 coreRefineTys in_scope con tvs scrut_ty
238 = maybeErrToMaybe $ initUM (tryToBind tv_set) $
239 do { -- Run the unifier, starting with an empty env
240 ; subst_env <- unify emptyTvSubstEnv pat_res_ty scrut_ty
242 -- Find the fixed point of the resulting non-idempotent substitution
243 ; let subst = TvSubst in_scope subst_env_fixpt
244 subst_env_fixpt = mapVarEnv (substTy subst) subst_env
246 ; return (subst_env_fixpt, all_bound_here subst_env) }
248 pat_res_ty = dataConInstResTy con (mkTyVarTys tvs)
250 -- 'tvs' are the tyvars bound by the pattern
251 tv_set = mkVarSet tvs
252 all_bound_here env = all bound_here (varEnvKeys env)
253 bound_here uniq = elemVarSetByKey uniq tv_set
256 ----------------------------
258 :: (TyVar -> BindFlag) -- Try to unify these
259 -> TvSubstEnv -- Not idempotent
261 -> MaybeErr Message TvSubstEnv -- Not idempotent
262 -- This one is used by the type checker. Neither the input nor result
263 -- substitition is idempotent
264 gadtRefineTys bind_fn subst tys1 tys2
265 = initUM bind_fn (unify_tys subst tys1 tys2)
267 ----------------------------
268 tryToBind :: TyVarSet -> TyVar -> BindFlag
269 tryToBind tv_set tv | tv `elemVarSet` tv_set = BindMe
270 | otherwise = AvoidMe
274 %************************************************************************
278 %************************************************************************
281 unify :: TvSubstEnv -- An existing substitution to extend
282 -> Type -> Type -- Types to be unified
283 -> UM TvSubstEnv -- Just the extended substitution,
284 -- Nothing if unification failed
285 -- We do not require the incoming substitution to be idempotent,
286 -- nor guarantee that the outgoing one is. That's fixed up by
289 -- Respects newtypes, PredTypes
291 unify subst ty1 ty2 = -- pprTrace "unify" (ppr subst <+> pprParendType ty1 <+> pprParendType ty2) $
294 -- in unify_, any NewTcApps/Preds should be taken at face value
295 unify_ subst (TyVarTy tv1) ty2 = uVar False subst tv1 ty2
296 unify_ subst ty1 (TyVarTy tv2) = uVar True subst tv2 ty1
298 unify_ subst ty1 ty2 | Just ty1' <- tcView ty1 = unify subst ty1' ty2
299 unify_ subst ty1 ty2 | Just ty2' <- tcView ty2 = unify subst ty1 ty2'
301 unify_ subst (PredTy p1) (PredTy p2) = unify_pred subst p1 p2
303 unify_ subst t1@(TyConApp tyc1 tys1) t2@(TyConApp tyc2 tys2)
304 | tyc1 == tyc2 = unify_tys subst tys1 tys2
306 unify_ subst (FunTy ty1a ty1b) (FunTy ty2a ty2b)
307 = do { subst' <- unify subst ty1a ty2a
308 ; unify subst' ty1b ty2b }
310 -- Applications need a bit of care!
311 -- They can match FunTy and TyConApp, so use splitAppTy_maybe
312 -- NB: we've already dealt with type variables and Notes,
313 -- so if one type is an App the other one jolly well better be too
314 unify_ subst (AppTy ty1a ty1b) ty2
315 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
316 = do { subst' <- unify subst ty1a ty2a
317 ; unify subst' ty1b ty2b }
319 unify_ subst ty1 (AppTy ty2a ty2b)
320 | Just (ty1a, ty1b) <- repSplitAppTy_maybe ty1
321 = do { subst' <- unify subst ty1a ty2a
322 ; unify subst' ty1b ty2b }
324 unify_ subst ty1 ty2 = failWith (misMatch ty1 ty2)
326 ------------------------------
327 unify_pred subst (ClassP c1 tys1) (ClassP c2 tys2)
328 | c1 == c2 = unify_tys subst tys1 tys2
329 unify_pred subst (IParam n1 t1) (IParam n2 t2)
330 | n1 == n2 = unify subst t1 t2
331 unify_pred subst p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2))
333 ------------------------------
334 unify_tys = unifyList unify
336 unifyList :: Outputable a
337 => (TvSubstEnv -> a -> a -> UM TvSubstEnv)
338 -> TvSubstEnv -> [a] -> [a] -> UM TvSubstEnv
339 unifyList unifier subst orig_xs orig_ys
340 = go subst orig_xs orig_ys
342 go subst [] [] = return subst
343 go subst (x:xs) (y:ys) = do { subst' <- unifier subst x y
345 go subst _ _ = failWith (lengthMisMatch orig_xs orig_ys)
347 ------------------------------
348 uVar :: Bool -- Swapped
349 -> TvSubstEnv -- An existing substitution to extend
350 -> TyVar -- Type variable to be unified
351 -> Type -- with this type
354 uVar swap subst tv1 ty
355 = -- Check to see whether tv1 is refined by the substitution
356 case (lookupVarEnv subst tv1) of
357 -- Yes, call back into unify'
358 Just ty' | swap -> unify subst ty ty'
359 | otherwise -> unify subst ty' ty
361 Nothing -> uUnrefined subst tv1 ty ty
364 uUnrefined :: TvSubstEnv -- An existing substitution to extend
365 -> TyVar -- Type variable to be unified
366 -> Type -- with this type
367 -> Type -- (de-noted version)
370 -- We know that tv1 isn't refined
372 uUnrefined subst tv1 ty2 ty2'
373 | Just ty2'' <- tcView ty2'
374 = uUnrefined subst tv1 ty2 ty2'' -- Unwrap synonyms
375 -- This is essential, in case we have
377 -- and then unify a :=: Foo a
379 uUnrefined subst tv1 ty2 (TyVarTy tv2)
380 | tv1 == tv2 -- Same type variable
383 -- Check to see whether tv2 is refined
384 | Just ty' <- lookupVarEnv subst tv2
385 = uUnrefined subst tv1 ty' ty'
387 -- So both are unrefined; next, see if the kinds force the direction
388 | k1 == k2 -- Can update either; so check the bind-flags
389 = do { b1 <- tvBindFlag tv1
390 ; b2 <- tvBindFlag tv2
392 (BindMe, _) -> bind tv1 ty2
394 (AvoidMe, BindMe) -> bind tv2 ty1
395 (AvoidMe, _) -> bind tv1 ty2
397 (WildCard, WildCard) -> return subst
398 (WildCard, Skolem) -> return subst
399 (WildCard, _) -> bind tv2 ty1
401 (Skolem, WildCard) -> return subst
402 (Skolem, Skolem) -> failWith (misMatch ty1 ty2)
403 (Skolem, _) -> bind tv2 ty1
406 | k1 `isSubKind` k2 = bindTv subst tv2 ty1 -- Must update tv2
407 | k2 `isSubKind` k1 = bindTv subst tv1 ty2 -- Must update tv1
409 | otherwise = failWith (kindMisMatch tv1 ty2)
414 bind tv ty = return (extendVarEnv subst tv ty)
416 uUnrefined subst tv1 ty2 ty2' -- ty2 is not a type variable
417 | tv1 `elemVarSet` substTvSet subst (tyVarsOfType ty2')
418 = failWith (occursCheck tv1 ty2) -- Occurs check
419 | not (k2 `isSubKind` k1)
420 = failWith (kindMisMatch tv1 ty2) -- Kind check
422 = bindTv subst tv1 ty2 -- Bind tyvar to the synonym if poss
427 substTvSet :: TvSubstEnv -> TyVarSet -> TyVarSet
428 -- Apply the non-idempotent substitution to a set of type variables,
429 -- remembering that the substitution isn't necessarily idempotent
431 = foldVarSet (unionVarSet . get) emptyVarSet tvs
433 get tv = case lookupVarEnv subst tv of
434 Nothing -> unitVarSet tv
435 Just ty -> substTvSet subst (tyVarsOfType ty)
437 bindTv subst tv ty -- ty is not a type variable
438 = do { b <- tvBindFlag tv
440 Skolem -> failWith (misMatch (TyVarTy tv) ty)
441 WildCard -> return subst
442 other -> return (extendVarEnv subst tv ty)
446 %************************************************************************
450 %************************************************************************
454 = BindMe -- A regular type variable
455 | AvoidMe -- Like BindMe but, given the choice, avoid binding it
457 | Skolem -- This type variable is a skolem constant
458 -- Don't bind it; it only matches itself
460 | WildCard -- This type variable matches anything,
461 -- and does not affect the substitution
463 newtype UM a = UM { unUM :: (TyVar -> BindFlag)
464 -> MaybeErr Message a }
466 instance Monad UM where
467 return a = UM (\tvs -> Succeeded a)
468 fail s = UM (\tvs -> Failed (text s))
469 m >>= k = UM (\tvs -> case unUM m tvs of
470 Failed err -> Failed err
471 Succeeded v -> unUM (k v) tvs)
473 initUM :: (TyVar -> BindFlag) -> UM a -> MaybeErr Message a
474 initUM badtvs um = unUM um badtvs
476 tvBindFlag :: TyVar -> UM BindFlag
477 tvBindFlag tv = UM (\tv_fn -> Succeeded (tv_fn tv))
479 failWith :: Message -> UM a
480 failWith msg = UM (\tv_fn -> Failed msg)
482 maybeErrToMaybe :: MaybeErr fail succ -> Maybe succ
483 maybeErrToMaybe (Succeeded a) = Just a
484 maybeErrToMaybe (Failed m) = Nothing
486 ------------------------------
487 repSplitAppTy_maybe :: Type -> Maybe (Type,Type)
488 -- Like Type.splitAppTy_maybe, but any coreView stuff is already done
489 repSplitAppTy_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
490 repSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
491 repSplitAppTy_maybe (TyConApp tc tys) = case snocView tys of
492 Just (tys', ty') -> Just (TyConApp tc tys', ty')
494 repSplitAppTy_maybe other = Nothing
498 %************************************************************************
501 We go to a lot more trouble to tidy the types
502 in TcUnify. Maybe we'll end up having to do that
503 here too, but I'll leave it for now.
505 %************************************************************************
509 = ptext SLIT("Can't match types") <+> quotes (ppr t1) <+>
510 ptext SLIT("and") <+> quotes (ppr t2)
512 lengthMisMatch tys1 tys2
513 = sep [ptext SLIT("Can't match unequal length lists"),
514 nest 2 (ppr tys1), nest 2 (ppr tys2) ]
517 = vcat [ptext SLIT("Can't match kinds") <+> quotes (ppr (tyVarKind tv1)) <+>
518 ptext SLIT("and") <+> quotes (ppr (typeKind t2)),
519 ptext SLIT("when matching") <+> quotes (ppr tv1) <+>
520 ptext SLIT("with") <+> quotes (ppr t2)]
523 = hang (ptext SLIT("Can't construct the infinite type"))
524 2 (ppr tv <+> equals <+> ppr ty)