3 -- Matching and unification
4 matchTys, matchTyX, tcMatchPreds, MatchEnv(..),
8 tcRefineTys, tcMatchTys, coreRefineTys,
14 #include "HsVersions.h"
16 import Var ( Var, TyVar, tyVarKind )
19 import Kind ( isSubKind )
20 import Type ( typeKind, tyVarsOfType, tyVarsOfTypes, tyVarsOfTheta,
21 TvSubstEnv, TvSubst(..), substTy, tcEqTypeX )
22 import TypeRep ( Type(..), PredType(..), funTyCon )
23 import Util ( snocView )
24 import ErrUtils ( Message )
30 %************************************************************************
34 %************************************************************************
37 Matching is much tricker than you might think.
39 1. The substitution we generate binds the *template type variables*
40 which are given to us explicitly.
42 2. We want to match in the presence of foralls;
43 e.g (forall a. t1) ~ (forall b. t2)
45 That is what the RnEnv2 is for; it does the alpha-renaming
46 that makes it as if a and b were the same variable.
47 Initialising the RnEnv2, so that it can generate a fresh
48 binder when necessary, entails knowing the free variables of
51 3. We must be careful not to bind a template type variable to a
52 locally bound variable. E.g.
53 (forall a. x) ~ (forall b. b)
54 where x is the template type variable. Then we do not want to
55 bind x to a/b! This is a kind of occurs check.
56 The necessary locals accumulate in the RnEnv2.
61 = ME { me_tmpls :: VarSet -- Template tyvars
62 , me_env :: RnEnv2 -- Renaming envt for nested foralls
63 } -- In-scope set includes template tyvars
65 matchTys :: TyVarSet -- Template tyvars
68 -> Maybe TvSubstEnv -- One-shot; in principle the template
69 -- variables could be free in the target
71 matchTys tmpls tys1 tys2
72 = match_tys (ME { me_tmpls = tmpls, me_env = mkRnEnv2 in_scope_tyvars})
76 in_scope_tyvars = mkInScopeSet (tmpls `unionVarSet` tyVarsOfTypes tys2)
77 -- We're assuming that all the interesting
78 -- tyvars in tys1 are in tmpls
81 :: [TyVar] -- Bind these
82 -> [PredType] -> [PredType]
84 tcMatchPreds tmpls ps1 ps2
85 = match_list (match_pred menv) emptyTvSubstEnv ps1 ps2
87 menv = ME { me_tmpls = mkVarSet tmpls, me_env = mkRnEnv2 in_scope_tyvars }
88 in_scope_tyvars = mkInScopeSet (tyVarsOfTheta ps1 `unionVarSet` tyVarsOfTheta ps2)
91 -> TvSubstEnv -- Substitution to extend
96 matchTyX menv subst ty1 ty2 = match menv subst ty1 ty2 -- Rename for export
99 Now the internals of matching
102 match :: MatchEnv -- For the ost part this is pushed downwards
103 -> TvSubstEnv -- Substitution so far:
104 -- Domain is subset of template tyvars
105 -- Free vars of range is subset of
106 -- in-scope set of the RnEnv2
107 -> Type -> Type -- Template and target respectively
109 -- This matcher works on source types; that is,
110 -- it respects NewTypes and PredType
112 match menv subst (NoteTy _ ty1) ty2 = match menv subst ty1 ty2
113 match menv subst ty1 (NoteTy _ ty2) = match menv subst ty1 ty2
115 match menv subst (TyVarTy tv1) ty2
116 | tv1 `elemVarSet` me_tmpls menv
117 = case lookupVarEnv subst tv1' of
118 Nothing | any (inRnEnvR rn_env) (varSetElems (tyVarsOfType ty2))
119 -> Nothing -- Occurs check
121 -> Just (extendVarEnv subst tv1 ty2)
123 Just ty1' | tcEqTypeX (nukeRnEnvL rn_env) ty1' ty2
124 -- ty1 has no locally-bound variables, hence nukeRnEnvL
125 -- Note tcEqType...we are doing source-type matching here
130 | otherwise -- tv1 is not a template tyvar
132 TyVarTy tv2 | tv1' == rnOccR rn_env tv2 -> Just subst
136 tv1' = rnOccL rn_env tv1
138 match menv subst (ForAllTy tv1 ty1) (ForAllTy tv2 ty2)
139 = match menv' subst ty1 ty2
140 where -- Use the magic of rnBndr2 to go under the binders
141 menv' = menv { me_env = rnBndr2 (me_env menv) tv1 tv2 }
143 match menv subst (PredTy p1) (PredTy p2)
144 = match_pred menv subst p1 p2
145 match menv subst (TyConApp tc1 tys1) (TyConApp tc2 tys2)
146 | tc1 == tc2 = match_tys menv subst tys1 tys2
147 match menv subst (FunTy ty1a ty1b) (FunTy ty2a ty2b)
148 = do { subst' <- match menv subst ty1a ty2a
149 ; match menv subst' ty1b ty2b }
150 match menv subst (AppTy ty1a ty1b) ty2
151 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
152 = do { subst' <- match menv subst ty1a ty2a
153 ; match menv subst' ty1b ty2b }
155 match menv subst ty1 ty2
159 match_tys menv subst tys1 tys2 = match_list (match menv) subst tys1 tys2
162 match_list :: (TvSubstEnv -> a -> a -> Maybe TvSubstEnv)
163 -> TvSubstEnv -> [a] -> [a] -> Maybe TvSubstEnv
164 match_list fn subst [] [] = Just subst
165 match_list fn subst (ty1:tys1) (ty2:tys2) = do { subst' <- fn subst ty1 ty2
166 ; match_list fn subst' tys1 tys2 }
167 match_list fn subst tys1 tys2 = Nothing
170 match_pred menv subst (ClassP c1 tys1) (ClassP c2 tys2)
171 | c1 == c2 = match_tys menv subst tys1 tys2
172 match_pred menv subst (IParam n1 t1) (IParam n2 t2)
173 | n1 == n2 = match menv subst t1 t2
174 match_pred menv subst p1 p2 = Nothing
178 %************************************************************************
182 %************************************************************************
185 tcRefineTys, tcMatchTys
186 :: [TyVar] -- Try to unify these
187 -> TvSubstEnv -- Not idempotent
189 -> MaybeErr Message TvSubstEnv -- Not idempotent
190 -- This one is used by the type checker. Neither the input nor result
191 -- substitition is idempotent
192 tcRefineTys ex_tvs subst tys1 tys2
193 = initUM (tryToBind (mkVarSet ex_tvs)) (unify_tys subst tys1 tys2)
195 tcMatchTys ex_tvs subst tys1 tys2
196 = initUM (bindOnly (mkVarSet ex_tvs)) (unify_tys subst tys1 tys2)
198 ----------------------------
199 coreRefineTys :: [TyVar] -- Try to unify these
200 -> TvSubst -- A full-blown apply-once substitition
201 -> Type -- A fixed point of the incoming substitution
203 -> Maybe TvSubstEnv -- In-scope set is unaffected
204 -- Used by Core Lint and the simplifier. Takes a full apply-once substitution.
205 -- The incoming substitution's in-scope set should mention all the variables free
206 -- in the incoming types
207 coreRefineTys ex_tvs subst@(TvSubst in_scope orig_env) ty1 ty2
208 = maybeErrToMaybe $ initUM (tryToBind (mkVarSet ex_tvs)) $
209 do { -- Apply the input substitution; nothing int ty2
210 let ty1' = substTy subst ty1
211 -- Run the unifier, starting with an empty env
212 ; extra_env <- unify emptyTvSubstEnv ty1' ty2
214 -- Find the fixed point of the resulting non-idempotent
215 -- substitution, and apply it to the
216 ; let extra_subst = TvSubst in_scope extra_env_fixpt
217 extra_env_fixpt = mapVarEnv (substTy extra_subst) extra_env
218 orig_env' = mapVarEnv (substTy extra_subst) orig_env
219 ; return (orig_env' `plusVarEnv` extra_env_fixpt) }
222 ----------------------------
223 unifyTys :: TyVarSet -> [Type] -> [Type] -> Maybe TvSubstEnv
224 unifyTys bind_these tys1 tys2
225 = maybeErrToMaybe $ initUM (bindOnly bind_these) $
226 unify_tys emptyTvSubstEnv tys1 tys2
228 unifyTysX :: TyVarSet -> TvSubstEnv -> [Type] -> [Type] -> Maybe TvSubstEnv
229 unifyTysX bind_these subst tys1 tys2
230 = maybeErrToMaybe $ initUM (bindOnly bind_these) $
231 unify_tys subst tys1 tys2
233 ----------------------------
234 tryToBind, bindOnly :: TyVarSet -> TyVar -> BindFlag
235 tryToBind tv_set tv | tv `elemVarSet` tv_set = BindMe
236 | otherwise = AvoidMe
238 bindOnly tv_set tv | tv `elemVarSet` tv_set = BindMe
239 | otherwise = DontBindMe
241 emptyTvSubstEnv :: TvSubstEnv
242 emptyTvSubstEnv = emptyVarEnv
246 %************************************************************************
250 %************************************************************************
253 unify :: TvSubstEnv -- An existing substitution to extend
254 -> Type -> Type -- Types to be unified
255 -> UM TvSubstEnv -- Just the extended substitution,
256 -- Nothing if unification failed
257 -- We do not require the incoming substitution to be idempotent,
258 -- nor guarantee that the outgoing one is. That's fixed up by
261 unify subst ty1 ty2 = -- pprTrace "unify" (ppr subst <+> pprParendType ty1 <+> pprParendType ty2) $
264 -- in unify_, any NewTcApps/Preds should be taken at face value
265 unify_ subst (TyVarTy tv1) ty2 = uVar False subst tv1 ty2
266 unify_ subst ty1 (TyVarTy tv2) = uVar True subst tv2 ty1
268 unify_ subst (NoteTy _ ty1) ty2 = unify subst ty1 ty2
269 unify_ subst ty1 (NoteTy _ ty2) = unify subst ty1 ty2
271 unify_ subst (PredTy p1) (PredTy p2) = unify_pred subst p1 p2
273 unify_ subst t1@(TyConApp tyc1 tys1) t2@(TyConApp tyc2 tys2)
274 | tyc1 == tyc2 = unify_tys subst tys1 tys2
276 unify_ subst (FunTy ty1a ty1b) (FunTy ty2a ty2b)
277 = do { subst' <- unify subst ty1a ty2a
278 ; unify subst' ty1b ty2b }
280 -- Applications need a bit of care!
281 -- They can match FunTy and TyConApp, so use splitAppTy_maybe
282 -- NB: we've already dealt with type variables and Notes,
283 -- so if one type is an App the other one jolly well better be too
284 unify_ subst (AppTy ty1a ty1b) ty2
285 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
286 = do { subst' <- unify subst ty1a ty2a
287 ; unify subst' ty1b ty2b }
289 unify_ subst ty1 (AppTy ty2a ty2b)
290 | Just (ty1a, ty1b) <- repSplitAppTy_maybe ty1
291 = do { subst' <- unify subst ty1a ty2a
292 ; unify subst' ty1b ty2b }
294 unify_ subst ty1 ty2 = failWith (misMatch ty1 ty2)
296 ------------------------------
297 unify_pred subst (ClassP c1 tys1) (ClassP c2 tys2)
298 | c1 == c2 = unify_tys subst tys1 tys2
299 unify_pred subst (IParam n1 t1) (IParam n2 t2)
300 | n1 == n2 = unify subst t1 t2
301 unify_pred subst p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2))
303 ------------------------------
304 unify_tys = unifyList unify
306 unifyList :: Outputable a
307 => (TvSubstEnv -> a -> a -> UM TvSubstEnv)
308 -> TvSubstEnv -> [a] -> [a] -> UM TvSubstEnv
309 unifyList unifier subst orig_xs orig_ys
310 = go subst orig_xs orig_ys
312 go subst [] [] = return subst
313 go subst (x:xs) (y:ys) = do { subst' <- unifier subst x y
315 go subst _ _ = failWith (lengthMisMatch orig_xs orig_ys)
317 ------------------------------
318 uVar :: Bool -- Swapped
319 -> TvSubstEnv -- An existing substitution to extend
320 -> TyVar -- Type variable to be unified
321 -> Type -- with this type
324 uVar swap subst tv1 ty
325 = -- check to see whether tv1 is refined
326 case (lookupVarEnv subst tv1) of
327 -- yes, call back into unify'
328 Just ty' | swap -> unify subst ty ty'
329 | otherwise -> unify subst ty' ty
331 Nothing -> uUnrefined subst tv1 ty
334 uUnrefined :: TvSubstEnv -- An existing substitution to extend
335 -> TyVar -- Type variable to be unified
336 -> Type -- with this type
339 -- We know that tv1 isn't refined
340 uUnrefined subst tv1 ty2@(TyVarTy tv2)
341 | tv1 == tv2 -- Same, do nothing
344 -- Check to see whether tv2 is refined
345 | Just ty' <- lookupVarEnv subst tv2
346 = uUnrefined subst tv1 ty'
348 -- So both are unrefined; next, see if the kinds force the direction
349 | k1 == k2 -- Can update either; so check the bind-flags
350 = do { b1 <- tvBindFlag tv1
351 ; b2 <- tvBindFlag tv2
353 (DontBindMe, DontBindMe) -> failWith (misMatch ty1 ty2)
354 (DontBindMe, _) -> bindTv subst tv2 ty1
355 (BindMe, _) -> bindTv subst tv1 ty2
356 (AvoidMe, BindMe) -> bindTv subst tv2 ty1
357 (AvoidMe, _) -> bindTv subst tv1 ty2
360 | k1 `isSubKind` k2 -- Must update tv2
361 = do { b2 <- tvBindFlag tv2
363 DontBindMe -> failWith (misMatch ty1 ty2)
364 other -> bindTv subst tv2 ty1
367 | k2 `isSubKind` k1 -- Must update tv1
368 = do { b1 <- tvBindFlag tv1
370 DontBindMe -> failWith (misMatch ty1 ty2)
371 other -> bindTv subst tv1 ty2
374 | otherwise = failWith (kindMisMatch tv1 ty2)
380 uUnrefined subst tv1 ty2 -- ty2 is not a type variable
381 -- Do occurs check...
382 | tv1 `elemVarSet` substTvSet subst (tyVarsOfType ty2)
383 = failWith (occursCheck tv1 ty2)
384 -- And a kind check...
386 = do { b1 <- tvBindFlag tv1
387 ; case b1 of -- And check that tv1 is bindable
388 DontBindMe -> failWith (misMatch ty1 ty2)
389 other -> bindTv subst tv1 ty2
392 = pprTrace "kind" (ppr tv1 <+> ppr k1 $$ ppr ty2 <+> ppr k2) $
393 failWith (kindMisMatch tv1 ty2)
399 substTvSet :: TvSubstEnv -> TyVarSet -> TyVarSet
400 -- Apply the non-idempotent substitution to a set of type variables,
401 -- remembering that the substitution isn't necessarily idempotent
403 = foldVarSet (unionVarSet . get) emptyVarSet tvs
405 get tv = case lookupVarEnv subst tv of
406 Nothing -> unitVarSet tv
407 Just ty -> substTvSet subst (tyVarsOfType ty)
409 bindTv subst tv ty = return (extendVarEnv subst tv ty)
412 %************************************************************************
416 %************************************************************************
419 data BindFlag = BindMe | AvoidMe | DontBindMe
421 newtype UM a = UM { unUM :: (TyVar -> BindFlag)
422 -> MaybeErr Message a }
424 instance Monad UM where
425 return a = UM (\tvs -> Succeeded a)
426 fail s = UM (\tvs -> Failed (text s))
427 m >>= k = UM (\tvs -> case unUM m tvs of
428 Failed err -> Failed err
429 Succeeded v -> unUM (k v) tvs)
431 initUM :: (TyVar -> BindFlag) -> UM a -> MaybeErr Message a
432 initUM badtvs um = unUM um badtvs
434 tvBindFlag :: TyVar -> UM BindFlag
435 tvBindFlag tv = UM (\tv_fn -> Succeeded (tv_fn tv))
437 failWith :: Message -> UM a
438 failWith msg = UM (\tv_fn -> Failed msg)
440 maybeErrToMaybe :: MaybeErr fail succ -> Maybe succ
441 maybeErrToMaybe (Succeeded a) = Just a
442 maybeErrToMaybe (Failed m) = Nothing
444 ------------------------------
445 repSplitAppTy_maybe :: Type -> Maybe (Type,Type)
446 -- Like Type.splitAppTy_maybe, but any coreView stuff is already done
447 repSplitAppTy_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
448 repSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
449 repSplitAppTy_maybe (TyConApp tc tys) = case snocView tys of
450 Just (tys', ty') -> Just (TyConApp tc tys', ty')
452 repSplitAppTy_maybe other = Nothing
456 %************************************************************************
459 We go to a lot more trouble to tidy the types
460 in TcUnify. Maybe we'll end up having to do that
461 here too, but I'll leave it for now.
463 %************************************************************************
467 = ptext SLIT("Can't match types") <+> quotes (ppr t1) <+>
468 ptext SLIT("and") <+> quotes (ppr t2)
470 lengthMisMatch tys1 tys2
471 = sep [ptext SLIT("Can't match unequal length lists"),
472 nest 2 (ppr tys1), nest 2 (ppr tys2) ]
475 = vcat [ptext SLIT("Can't match kinds") <+> quotes (ppr (tyVarKind tv1)) <+>
476 ptext SLIT("and") <+> quotes (ppr (typeKind t2)),
477 ptext SLIT("when matching") <+> quotes (ppr tv1) <+>
478 ptext SLIT("with") <+> quotes (ppr t2)]
481 = hang (ptext SLIT("Can't construct the infinite type"))
482 2 (ppr tv <+> equals <+> ppr ty)