2 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
5 %************************************************************************
7 Type refinement for GADTs
9 %************************************************************************
13 Refinement, emptyRefinement, gadtRefine,
14 refineType, refineResType,
16 tcUnifyTys, BindFlag(..)
19 import HsSyn ( ExprCoFn(..), idCoercion, isIdCoercion )
20 import Coercion ( Coercion, mkSymCoercion, mkTransCoercion, mkUnsafeCoercion,
21 mkLeftCoercion, mkRightCoercion, mkCoKind, coercionKindPredTy,
22 splitCoercionKind, decomposeCo, coercionKind )
23 import TcType ( TvSubst(..), TvSubstEnv, substTy, mkTvSubst,
24 substTyVar, zipTopTvSubst, typeKind,
25 eqKind, isSubKind, repSplitAppTy_maybe,
26 tcView, tcGetTyVar_maybe
28 import Type ( Type, tyVarsOfType, tyVarsOfTypes, tcEqType, mkTyVarTy )
29 import TypeRep ( Type(..), PredType(..) )
30 import DataCon ( DataCon, dataConUnivTyVars, dataConEqSpec )
31 import Var ( CoVar, TyVar, tyVarKind, varUnique )
34 import ErrUtils ( Message )
35 import Maybes ( MaybeErr(..), isJust )
36 import Control.Monad ( foldM )
38 import Unique ( Unique )
39 import UniqFM ( ufmToList )
41 #include "HsVersions.h"
45 %************************************************************************
49 %************************************************************************
52 data Refinement = Reft InScopeSet InternalReft
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 -> (ExprCoFn, Type)
66 -- Apply the refinement to the type.
67 -- If (refineType r ty) = (co, ty')
68 -- Then co :: ty:=:ty'
69 refineType (Reft in_scope env) ty
70 | not (isEmptyVarEnv env), -- Common case
71 any (`elemVarEnv` env) (varSetElems (tyVarsOfType ty))
72 = (ExprCoFn (substTy co_subst ty), substTy tv_subst ty)
74 = (idCoercion, ty) -- The type doesn't mention any refined type variables
76 tv_subst = mkTvSubst in_scope (mapVarEnv snd env)
77 co_subst = mkTvSubst in_scope (mapVarEnv fst env)
79 refineResType :: Refinement -> Type -> (ExprCoFn, Type)
80 -- Like refineType, but returns the 'sym' coercion
81 -- If (refineResType r ty) = (co, ty')
82 -- Then co :: ty':=:ty
84 = case refineType reft ty of
85 (ExprCoFn co, ty1) -> (ExprCoFn (mkSymCoercion co), ty1)
86 (id_co, ty1) -> ASSERT( isIdCoercion id_co )
91 %************************************************************************
93 Generating a type refinement
95 %************************************************************************
98 gadtRefine :: Refinement
99 -> [TyVar] -- Bind these by preference
101 -> MaybeErr Message Refinement
104 (gadtRefine cvs) takes a list of coercion variables, and returns a
105 list of coercions, obtained by unifying the types equated by the
106 incoming coercions. The returned coercions all have kinds of form
107 (a:=:ty), where a is a rigid type variable.
110 gadtRefine [c :: (a,Int):=:(Bool,b)]
111 = [ right (left c) :: a:=:Bool,
112 sym (right c) :: b:=:Int ]
114 That is, given evidence 'c' that (a,Int)=(Bool,b), it returns derived
115 evidence in easy-to-use form. In particular, given any e::ty, we know
117 e `cast` ty[right (left c)/a, sym (right c)/b]
118 :: ty [Bool/a, Int/b]
122 - It can fail, if the coercion is unsatisfiable.
124 - It's biased, by being given a set of type variables to bind
125 when there is a choice. Example:
126 MkT :: forall a. a -> T [a]
127 f :: forall b. T [b] -> b
128 f x = let v = case x of { MkT y -> y }
130 Here we want to bind [a->b], not the other way round, because
131 in this example the return type is wobbly, and we want the
135 -- E.g. (a, Bool, right (left c))
136 -- INVARIANT: in the triple (tv, ty, co), we have (co :: tv:=:ty)
137 -- The result is idempotent: the
140 gadtRefine (Reft in_scope env1)
142 -- Precondition: fvs( co_vars ) # env1
143 -- That is, the kinds of the co_vars are a
144 -- fixed point of the incoming refinement
146 = ASSERT2( not $ any (`elemVarEnv` env1) (varSetElems $ tyVarsOfTypes $ map tyVarKind co_vars),
147 ppr env1 $$ ppr co_vars $$ ppr (map tyVarKind co_vars) )
148 initUM (tryToBind tv_set) $
149 do { -- Run the unifier, starting with an empty env
150 ; env2 <- foldM do_one emptyInternalReft co_vars
152 -- Find the fixed point of the resulting
153 -- non-idempotent substitution
154 ; let tmp_env = env1 `plusVarEnv` env2
155 out_env = fixTvCoEnv in_scope' tmp_env
156 ; WARN( not (null (badReftElts tmp_env)), ppr (badReftElts tmp_env) $$ ppr tmp_env )
157 WARN( not (null (badReftElts out_env)), ppr (badReftElts out_env) $$ ppr out_env )
158 return (Reft in_scope' out_env) }
160 tv_set = mkVarSet ex_tvs
161 in_scope' = foldr extend in_scope co_vars
162 extend co_var in_scope
163 = extendInScopeSetSet (extendInScopeSet in_scope co_var)
164 (tyVarsOfType (tyVarKind co_var))
166 do_one reft co_var = unify reft (TyVarTy co_var) ty1 ty2
168 (ty1,ty2) = splitCoercionKind (tyVarKind co_var)
171 %************************************************************************
175 %************************************************************************
178 tcUnifyTys :: (TyVar -> BindFlag)
180 -> Maybe TvSubst -- A regular one-shot substitution
181 -- The two types may have common type variables, and indeed do so in the
182 -- second call to tcUnifyTys in FunDeps.checkClsFD
184 -- We implement tcUnifyTys using the evidence-generating 'unify' function
185 -- in this module, even though we don't need to generate any evidence.
186 -- This is simply to avoid replicating all all the code for unify
187 tcUnifyTys bind_fn tys1 tys2
188 = maybeErrToMaybe $ initUM bind_fn $
189 do { reft <- unifyList emptyInternalReft cos tys1 tys2
191 -- Find the fixed point of the resulting non-idempotent substitution
192 ; let in_scope = mkInScopeSet (tvs1 `unionVarSet` tvs2)
193 tv_env = fixTvSubstEnv in_scope (mapVarEnv snd reft)
195 ; return (mkTvSubst in_scope tv_env) }
197 tvs1 = tyVarsOfTypes tys1
198 tvs2 = tyVarsOfTypes tys2
199 cos = zipWith mkUnsafeCoercion tys1 tys2
202 ----------------------------
203 fixTvCoEnv :: InScopeSet -> InternalReft -> InternalReft
204 -- Find the fixed point of a Refinement
205 -- (assuming it has no loops!)
206 fixTvCoEnv in_scope env
209 fixpt = mapVarEnv step env
211 step (co, ty) = (co1, ty')
212 -- Apply fixpt one step:
213 -- Use refineType to get a substituted type, ty', and a coercion, co_fn,
214 -- which justifies the substitution. If the coercion is not the identity
215 -- then use transitivity with the original coercion
217 (co_fn, ty') = refineType (Reft in_scope fixpt) ty
218 co1 | ExprCoFn co'' <- co_fn = mkTransCoercion co co''
219 | otherwise = ASSERT( isIdCoercion co_fn ) co
221 -----------------------------
222 fixTvSubstEnv :: InScopeSet -> TvSubstEnv -> TvSubstEnv
223 fixTvSubstEnv in_scope env
226 fixpt = mapVarEnv (substTy (mkTvSubst in_scope fixpt)) env
228 ----------------------------
229 dataConCanMatch :: DataCon -> [Type] -> Bool
230 -- Returns True iff the data con can match a scrutinee of type (T tys)
231 -- where T is the type constructor for the data con
233 -- Instantiate the equations and try to unify them
234 dataConCanMatch con tys
235 = isJust (tcUnifyTys (\tv -> BindMe)
236 (map (substTyVar subst . fst) eq_spec)
239 dc_tvs = dataConUnivTyVars con
240 eq_spec = dataConEqSpec con
241 subst = zipTopTvSubst dc_tvs tys
243 ----------------------------
244 tryToBind :: TyVarSet -> TyVar -> BindFlag
245 tryToBind tv_set tv | tv `elemVarSet` tv_set = BindMe
246 | otherwise = AvoidMe
252 %************************************************************************
256 %************************************************************************
259 type InternalReft = TyVarEnv (Coercion, Type)
261 -- INVARIANT: a->(co,ty) then co :: (a:=:ty)
262 -- Not necessarily idemopotent
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
277 emptyInternalReft :: InternalReft
278 emptyInternalReft = emptyVarEnv
280 unify :: InternalReft -- An existing substitution to extend
281 -> Coercion -- Witness of their equality
282 -> Type -> Type -- Types to be unified, and witness of their equality
283 -> UM InternalReft -- 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 -- PRE-CONDITION: in the call (unify r co ty1 ty2), we know that
292 -- Respects newtypes, PredTypes
294 unify subst co ty1 ty2 = -- pprTrace "unify" (ppr subst <+> pprParendType ty1 <+> pprParendType ty2) $
295 unify_ subst co ty1 ty2
297 -- in unify_, any NewTcApps/Preds should be taken at face value
298 unify_ subst co (TyVarTy tv1) ty2 = uVar False subst co tv1 ty2
299 unify_ subst co ty1 (TyVarTy tv2) = uVar True subst co tv2 ty1
301 unify_ subst co ty1 ty2 | Just ty1' <- tcView ty1 = unify subst co ty1' ty2
302 unify_ subst co ty1 ty2 | Just ty2' <- tcView ty2 = unify subst co ty1 ty2'
304 unify_ subst co (PredTy p1) (PredTy p2) = unify_pred subst co p1 p2
306 unify_ subst co t1@(TyConApp tyc1 tys1) t2@(TyConApp tyc2 tys2)
307 | tyc1 == tyc2 = unify_tys subst co tys1 tys2
309 unify_ subst co (FunTy ty1a ty1b) (FunTy ty2a ty2b)
310 = do { let [co1,co2] = decomposeCo 2 co
311 ; subst' <- unify subst co1 ty1a ty2a
312 ; unify subst' co2 ty1b ty2b }
314 -- Applications need a bit of care!
315 -- They can match FunTy and TyConApp, so use splitAppTy_maybe
316 -- NB: we've already dealt with type variables and Notes,
317 -- so if one type is an App the other one jolly well better be too
318 unify_ subst co (AppTy ty1a ty1b) ty2
319 | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
320 = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
321 ; unify subst' (mkRightCoercion co) ty1b ty2b }
323 unify_ subst co ty1 (AppTy ty2a ty2b)
324 | Just (ty1a, ty1b) <- repSplitAppTy_maybe ty1
325 = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
326 ; unify subst' (mkRightCoercion co) ty1b ty2b }
328 unify_ subst co ty1 ty2 = failWith (misMatch ty1 ty2)
332 ------------------------------
333 unify_pred subst co (ClassP c1 tys1) (ClassP c2 tys2)
334 | c1 == c2 = unify_tys subst co tys1 tys2
335 unify_pred subst co (IParam n1 t1) (IParam n2 t2)
336 | n1 == n2 = unify subst co t1 t2
337 unify_pred subst co p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2))
339 ------------------------------
340 unify_tys :: InternalReft -> Coercion -> [Type] -> [Type] -> UM InternalReft
341 unify_tys subst co xs ys
342 = unifyList subst (decomposeCo (length xs) co) xs ys
344 unifyList :: InternalReft -> [Coercion] -> [Type] -> [Type] -> UM InternalReft
345 unifyList subst orig_cos orig_xs orig_ys
346 = go subst orig_cos orig_xs orig_ys
348 go subst _ [] [] = return subst
349 go subst (co:cos) (x:xs) (y:ys) = do { subst' <- unify subst co x y
350 ; go subst' cos xs ys }
351 go subst _ _ _ = failWith (lengthMisMatch orig_xs orig_ys)
353 ---------------------------------
354 uVar :: Bool -- Swapped
355 -> InternalReft -- An existing substitution to extend
357 -> TyVar -- Type variable to be unified
358 -> Type -- with this type
361 -- PRE-CONDITION: in the call (uVar swap r co tv1 ty), we know that
362 -- if swap=False co :: (tv1:=:ty)
363 -- if swap=True co :: (ty:=:tv1)
365 uVar swap subst co tv1 ty
366 = -- Check to see whether tv1 is refined by the substitution
367 case (lookupVarEnv subst tv1) of
369 -- Yes, call back into unify'
370 Just (co',ty') -- co' :: (tv1:=:ty')
371 | swap -- co :: (ty:=:tv1)
372 -> unify subst (mkTransCoercion co co') ty ty'
373 | otherwise -- co :: (tv1:=:ty)
374 -> unify subst (mkTransCoercion (mkSymCoercion co') co) ty' ty
377 Nothing -> uUnrefined swap subst co
381 uUnrefined :: Bool -- Whether the input is swapped
382 -> InternalReft -- An existing substitution to extend
384 -> TyVar -- Type variable to be unified
385 -> Type -- with this type
386 -> Type -- (de-noted version)
389 -- We know that tv1 isn't refined
390 -- PRE-CONDITION: in the call (uUnrefined False r co tv1 ty2 ty2'), we know that
392 -- and if the first argument is True instead, we know
395 uUnrefined swap subst co tv1 ty2 ty2'
396 | Just ty2'' <- tcView ty2'
397 = uUnrefined swap subst co tv1 ty2 ty2'' -- Unwrap synonyms
398 -- This is essential, in case we have
400 -- and then unify a :=: Foo a
402 uUnrefined swap subst co tv1 ty2 (TyVarTy tv2)
403 | tv1 == tv2 -- Same type variable
406 -- Check to see whether tv2 is refined
407 | Just (co',ty') <- lookupVarEnv subst tv2 -- co' :: tv2:=:ty'
408 = uUnrefined False subst (mkTransCoercion (doSwap swap co) co') tv1 ty' ty'
410 -- So both are unrefined; next, see if the kinds force the direction
411 | eqKind k1 k2 -- Can update either; so check the bind-flags
412 = do { b1 <- tvBindFlag tv1
413 ; b2 <- tvBindFlag tv2
415 (BindMe, _) -> bind swap tv1 ty2
417 (AvoidMe, BindMe) -> bind (not swap) tv2 ty1
418 (AvoidMe, _) -> bind swap tv1 ty2
420 (WildCard, WildCard) -> return subst
421 (WildCard, Skolem) -> return subst
422 (WildCard, _) -> bind (not swap) tv2 ty1
424 (Skolem, WildCard) -> return subst
425 (Skolem, Skolem) -> failWith (misMatch ty1 ty2)
426 (Skolem, _) -> bind (not swap) tv2 ty1
429 | k1 `isSubKind` k2 = bindTv (not swap) subst co tv2 ty1 -- Must update tv2
430 | k2 `isSubKind` k1 = bindTv swap subst co tv1 ty2 -- Must update tv1
432 | otherwise = failWith (kindMisMatch tv1 ty2)
437 bind swap tv ty = extendReft swap subst tv co ty
439 uUnrefined swap subst co tv1 ty2 ty2' -- ty2 is not a type variable
440 | tv1 `elemVarSet` substTvSet subst (tyVarsOfType ty2')
441 = failWith (occursCheck tv1 ty2) -- Occurs check
442 | not (k2 `isSubKind` k1)
443 = failWith (kindMisMatch tv1 ty2) -- Kind check
445 = bindTv swap subst co tv1 ty2 -- Bind tyvar to the synonym if poss
450 substTvSet :: InternalReft -> TyVarSet -> TyVarSet
451 -- Apply the non-idempotent substitution to a set of type variables,
452 -- remembering that the substitution isn't necessarily idempotent
454 = foldVarSet (unionVarSet . get) emptyVarSet tvs
456 get tv = case lookupVarEnv subst tv of
457 Nothing -> unitVarSet tv
458 Just (_,ty) -> substTvSet subst (tyVarsOfType ty)
460 bindTv swap subst co tv ty -- ty is not a type variable
461 = do { b <- tvBindFlag tv
463 Skolem -> failWith (misMatch (TyVarTy tv) ty)
464 WildCard -> return subst
465 other -> extendReft swap subst tv co ty
468 doSwap :: Bool -> Coercion -> Coercion
469 doSwap swap co = if swap then mkSymCoercion co else co
477 extendReft swap subst tv co ty
478 = ASSERT2( (coercionKindPredTy co1 `tcEqType` mkCoKind (mkTyVarTy tv) ty),
479 (text "Refinement invariant failure: co = " <+> ppr co1 <+> ppr (coercionKindPredTy co1) $$ text "subst = " <+> ppr tv <+> ppr (mkCoKind (mkTyVarTy tv) ty)) )
480 return (extendVarEnv subst tv (co1, ty))
486 %************************************************************************
490 %************************************************************************
494 = BindMe -- A regular type variable
495 | AvoidMe -- Like BindMe but, given the choice, avoid binding it
497 | Skolem -- This type variable is a skolem constant
498 -- Don't bind it; it only matches itself
500 | WildCard -- This type variable matches anything,
501 -- and does not affect the substitution
503 newtype UM a = UM { unUM :: (TyVar -> BindFlag)
504 -> MaybeErr Message a }
506 instance Monad UM where
507 return a = UM (\tvs -> Succeeded a)
508 fail s = UM (\tvs -> Failed (text s))
509 m >>= k = UM (\tvs -> case unUM m tvs of
510 Failed err -> Failed err
511 Succeeded v -> unUM (k v) tvs)
513 initUM :: (TyVar -> BindFlag) -> UM a -> MaybeErr Message a
514 initUM badtvs um = unUM um badtvs
516 tvBindFlag :: TyVar -> UM BindFlag
517 tvBindFlag tv = UM (\tv_fn -> Succeeded (tv_fn tv))
519 failWith :: Message -> UM a
520 failWith msg = UM (\tv_fn -> Failed msg)
522 maybeErrToMaybe :: MaybeErr fail succ -> Maybe succ
523 maybeErrToMaybe (Succeeded a) = Just a
524 maybeErrToMaybe (Failed m) = Nothing
528 %************************************************************************
531 We go to a lot more trouble to tidy the types
532 in TcUnify. Maybe we'll end up having to do that
533 here too, but I'll leave it for now.
535 %************************************************************************
539 = ptext SLIT("Can't match types") <+> quotes (ppr t1) <+>
540 ptext SLIT("and") <+> quotes (ppr t2)
542 lengthMisMatch tys1 tys2
543 = sep [ptext SLIT("Can't match unequal length lists"),
544 nest 2 (ppr tys1), nest 2 (ppr tys2) ]
547 = vcat [ptext SLIT("Can't match kinds") <+> quotes (ppr (tyVarKind tv1)) <+>
548 ptext SLIT("and") <+> quotes (ppr (typeKind t2)),
549 ptext SLIT("when matching") <+> quotes (ppr tv1) <+>
550 ptext SLIT("with") <+> quotes (ppr t2)]
553 = hang (ptext SLIT("Can't construct the infinite type"))
554 2 (ppr tv <+> equals <+> ppr ty)