2 % (c) The University of Glasgow 2006
3 % (c) The GRASP/AQUA Project, Glasgow University, 2000
6 FunDeps - functional dependencies
8 It's better to read it as: "if we know these, then we're going to know these"
12 Equation, pprEquation,
13 oclose, grow, improve, improveOne,
14 checkInstCoverage, checkFunDeps,
18 #include "HsVersions.h"
32 import Data.List ( tails )
33 import Data.Maybe ( isJust )
37 %************************************************************************
39 \subsection{Close type variables}
41 %************************************************************************
43 (oclose preds tvs) closes the set of type variables tvs,
44 wrt functional dependencies in preds. The result is a superset
45 of the argument set. For example, if we have
46 class C a b | a->b where ...
48 oclose [C (x,y) z, C (x,p) q] {x,y} = {x,y,z}
49 because if we know x and y then that fixes z.
55 a) When determining ambiguity. The type
56 forall a,b. C a b => a
57 is not ambiguous (given the above class decl for C) because
60 b) When generalising a type T. Usually we take FV(T) \ FV(Env),
63 where the '+' is the oclosure operation. Notice that we do not
64 take FV(T)+. This puzzled me for a bit. Consider
68 and suppose e have that E :: C a b => a, and suppose that b is
69 free in the environment. Then we quantify over 'a' only, giving
70 the type forall a. C a b => a. Since a->b but we don't have b->a,
71 we might have instance decls like
72 instance C Bool Int where ...
73 instance C Char Int where ...
74 so knowing that b=Int doesn't fix 'a'; so we quantify over it.
79 If we have class C a b => D a b where ....
80 class D a b | a -> b where ...
81 and the preds are [C (x,y) z], then we want to see the fd in D,
82 even though it is not explicit in C, giving [({x,y},{z})]
84 Similarly for instance decls? E.g. Suppose we have
85 instance C a b => Eq (T a b) where ...
86 and we infer a type t with constraints Eq (T a b) for a particular
87 expression, and suppose that 'a' is free in the environment.
88 We could generalise to
89 forall b. Eq (T a b) => t
90 but if we reduced the constraint, to C a b, we'd see that 'a' determines
91 b, so that a better type might be
92 t (with free constraint C a b)
93 Perhaps it doesn't matter, because we'll still force b to be a
94 particular type at the call sites. Generalising over too many
95 variables (provided we don't shadow anything by quantifying over a
96 variable that is actually free in the envt) may postpone errors; it
97 won't hide them altogether.
101 oclose :: [PredType] -> TyVarSet -> TyVarSet
102 oclose preds fixed_tvs
103 | null tv_fds = fixed_tvs -- Fast escape hatch for common case
104 | otherwise = loop fixed_tvs
107 | new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs
108 | otherwise = loop new_fixed_tvs
110 new_fixed_tvs = foldl extend fixed_tvs tv_fds
112 extend fixed_tvs (ls,rs) | ls `subVarSet` fixed_tvs = fixed_tvs `unionVarSet` rs
113 | otherwise = fixed_tvs
115 tv_fds :: [(TyVarSet,TyVarSet)]
116 -- In our example, tv_fds will be [ ({x,y}, {z}), ({x,p},{q}) ]
117 -- Meaning "knowing x,y fixes z, knowing x,p fixes q"
118 tv_fds = [ (tyVarsOfTypes xs, tyVarsOfTypes ys)
119 | ClassP cls tys <- preds, -- Ignore implicit params
120 let (cls_tvs, cls_fds) = classTvsFds cls,
122 let (xs,ys) = instFD fd cls_tvs tys
126 Note [Growing the tau-tvs using constraints]
127 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
128 (grow preds tvs) is the result of extend the set of tyvars tvs
129 using all conceivable links from pred
131 E.g. tvs = {a}, preds = {H [a] b, K (b,Int) c, Eq e}
132 Then grow precs tvs = {a,b,c}
134 All the type variables from an implicit parameter are added, whether or
135 not they are mentioned in tvs; see Note [Implicit parameters and ambiguity]
138 See also Note [Ambiguity] in TcSimplify
141 grow :: [PredType] -> TyVarSet -> TyVarSet
143 | null preds = real_fixed_tvs
144 | otherwise = loop real_fixed_tvs
146 -- Add the implicit parameters;
147 -- see Note [Implicit parameters and ambiguity] in TcSimplify
148 real_fixed_tvs = foldr unionVarSet fixed_tvs ip_tvs
151 | new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs
152 | otherwise = loop new_fixed_tvs
154 new_fixed_tvs = foldl extend fixed_tvs non_ip_tvs
156 extend fixed_tvs pred_tvs
157 | fixed_tvs `intersectsVarSet` pred_tvs = fixed_tvs `unionVarSet` pred_tvs
158 | otherwise = fixed_tvs
160 (ip_tvs, non_ip_tvs) = partitionWith get_ip preds
161 get_ip (IParam _ ty) = Left (tyVarsOfType ty)
162 get_ip other = Right (tyVarsOfPred other)
165 %************************************************************************
167 \subsection{Generate equations from functional dependencies}
169 %************************************************************************
174 type Equation = (TyVarSet, [(Type, Type)])
175 -- These pairs of types should be equal, for some
176 -- substitution of the tyvars in the tyvar set
177 -- INVARIANT: corresponding types aren't already equal
179 -- It's important that we have a *list* of pairs of types. Consider
180 -- class C a b c | a -> b c where ...
181 -- instance C Int x x where ...
182 -- Then, given the constraint (C Int Bool v) we should improve v to Bool,
183 -- via the equation ({x}, [(Bool,x), (v,x)])
184 -- This would not happen if the class had looked like
185 -- class C a b c | a -> b, a -> c
187 -- To "execute" the equation, make fresh type variable for each tyvar in the set,
188 -- instantiate the two types with these fresh variables, and then unify.
190 -- For example, ({a,b}, (a,Int,b), (Int,z,Bool))
191 -- We unify z with Int, but since a and b are quantified we do nothing to them
192 -- We usually act on an equation by instantiating the quantified type varaibles
193 -- to fresh type variables, and then calling the standard unifier.
195 pprEquation (qtvs, pairs)
196 = vcat [ptext SLIT("forall") <+> braces (pprWithCommas ppr (varSetElems qtvs)),
197 nest 2 (vcat [ ppr t1 <+> ptext SLIT(":=:") <+> ppr t2 | (t1,t2) <- pairs])]
200 type Pred_Loc = (PredType, SDoc) -- SDoc says where the Pred comes from
202 improve :: (Class -> [Instance]) -- Gives instances for given class
203 -> [Pred_Loc] -- Current constraints;
204 -> [(Equation,Pred_Loc,Pred_Loc)] -- Derived equalities that must also hold
205 -- (NB the above INVARIANT for type Equation)
206 -- The Pred_Locs explain which two predicates were
207 -- combined (for error messages)
210 Given a bunch of predicates that must hold, such as
212 C Int t1, C Int t2, C Bool t3, ?x::t4, ?x::t5
214 improve figures out what extra equations must hold.
215 For example, if we have
217 class C a b | a->b where ...
219 then improve will return
225 * improve does not iterate. It's possible that when we make
226 t1=t2, for example, that will in turn trigger a new equation.
227 This would happen if we also had
229 If t1=t2, we also get t7=t8.
231 improve does *not* do this extra step. It relies on the caller
234 * The equations unify types that are not already equal. So there
235 is no effect iff the result of improve is empty
240 improve inst_env preds
241 = [ eqn | group <- equivClassesByUniq (predTyUnique . fst) (filterEqPreds preds),
242 eqn <- checkGroup inst_env group ]
244 filterEqPreds = filter (not . isEqPred . fst)
245 -- Equality predicates don't have uniques
246 -- In any case, improvement *generates*, rather than
247 -- *consumes*, equality constraints
249 improveOne :: (Class -> [Instance])
252 -> [(Equation,Pred_Loc,Pred_Loc)]
254 -- Just do improvement triggered by a single, distinguised predicate
256 improveOne inst_env pred@(IParam ip ty, _) preds
257 = [ ((emptyVarSet, [(ty,ty2)]), pred, p2)
258 | p2@(IParam ip2 ty2, _) <- preds
260 , not (ty `tcEqType` ty2)]
262 improveOne inst_env pred@(ClassP cls tys, _) preds
263 | tys `lengthAtLeast` 2
264 = instance_eqns ++ pairwise_eqns
265 -- NB: we put the instance equations first. This biases the
266 -- order so that we first improve individual constraints against the
267 -- instances (which are perhaps in a library and less likely to be
268 -- wrong; and THEN perform the pairwise checks.
269 -- The other way round, it's possible for the pairwise check to succeed
270 -- and cause a subsequent, misleading failure of one of the pair with an
271 -- instance declaration. See tcfail143.hs for an example
273 (cls_tvs, cls_fds) = classTvsFds cls
274 instances = inst_env cls
275 rough_tcs = roughMatchTcs tys
277 -- NOTE that we iterate over the fds first; they are typically
278 -- empty, which aborts the rest of the loop.
279 pairwise_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
280 pairwise_eqns -- This group comes from pairwise comparison
283 , p2@(ClassP cls2 tys2, _) <- preds
285 , eqn <- checkClsFD emptyVarSet fd cls_tvs tys tys2
288 instance_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
289 instance_eqns -- This group comes from comparing with instance decls
290 = [ (eqn, p_inst, pred)
291 | fd <- cls_fds -- Iterate through the fundeps first,
292 -- because there often are none!
293 , let rough_fd_tcs = trimRoughMatchTcs cls_tvs fd rough_tcs
294 , ispec@(Instance { is_tvs = qtvs, is_tys = tys_inst,
295 is_tcs = mb_tcs_inst }) <- instances
296 , not (instanceCantMatch mb_tcs_inst rough_fd_tcs)
297 , eqn <- checkClsFD qtvs fd cls_tvs tys_inst tys
298 , let p_inst = (mkClassPred cls tys_inst,
299 ptext SLIT("arising from the instance declaration at")
300 <+> ppr (getSrcLoc ispec))
303 improveOne inst_env eq_pred preds
307 checkGroup :: (Class -> [Instance])
309 -> [(Equation, Pred_Loc, Pred_Loc)]
310 -- The preds are all for the same class or implicit param
312 checkGroup inst_env (p1@(IParam _ ty, _) : ips)
313 = -- For implicit parameters, all the types must match
314 [ ((emptyVarSet, [(ty,ty')]), p1, p2)
315 | p2@(IParam _ ty', _) <- ips, not (ty `tcEqType` ty')]
317 checkGroup inst_env clss@((ClassP cls _, _) : _)
318 = -- For classes life is more complicated
319 -- Suppose the class is like
320 -- classs C as | (l1 -> r1), (l2 -> r2), ... where ...
321 -- Then FOR EACH PAIR (ClassP c tys1, ClassP c tys2) in the list clss
323 -- U l1[tys1/as] = U l2[tys2/as]
324 -- (where U is a unifier)
326 -- If so, we return the pair
327 -- U r1[tys1/as] = U l2[tys2/as]
329 -- We need to do something very similar comparing each predicate
330 -- with relevant instance decls
332 instance_eqns ++ pairwise_eqns
333 -- NB: we put the instance equations first. This biases the
334 -- order so that we first improve individual constraints against the
335 -- instances (which are perhaps in a library and less likely to be
336 -- wrong; and THEN perform the pairwise checks.
337 -- The other way round, it's possible for the pairwise check to succeed
338 -- and cause a subsequent, misleading failure of one of the pair with an
339 -- instance declaration. See tcfail143.hs for an exmample
342 (cls_tvs, cls_fds) = classTvsFds cls
343 instances = inst_env cls
345 -- NOTE that we iterate over the fds first; they are typically
346 -- empty, which aborts the rest of the loop.
347 pairwise_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
348 pairwise_eqns -- This group comes from pairwise comparison
351 p1@(ClassP _ tys1, _) : rest <- tails clss,
352 p2@(ClassP _ tys2, _) <- rest,
353 eqn <- checkClsFD emptyVarSet fd cls_tvs tys1 tys2
356 instance_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
357 instance_eqns -- This group comes from comparing with instance decls
359 | fd <- cls_fds, -- Iterate through the fundeps first,
360 -- because there often are none!
361 p2@(ClassP _ tys2, _) <- clss,
362 let rough_tcs2 = trimRoughMatchTcs cls_tvs fd (roughMatchTcs tys2),
363 ispec@(Instance { is_tvs = qtvs, is_tys = tys1,
364 is_tcs = mb_tcs1 }) <- instances,
365 not (instanceCantMatch mb_tcs1 rough_tcs2),
366 eqn <- checkClsFD qtvs fd cls_tvs tys1 tys2,
367 let p1 = (mkClassPred cls tys1,
368 ptext SLIT("arising from the instance declaration at") <+>
369 ppr (getSrcLoc ispec))
372 checkClsFD :: TyVarSet -- Quantified type variables; see note below
373 -> FunDep TyVar -> [TyVar] -- One functional dependency from the class
377 checkClsFD qtvs fd clas_tvs tys1 tys2
378 -- 'qtvs' are the quantified type variables, the ones which an be instantiated
379 -- to make the types match. For example, given
380 -- class C a b | a->b where ...
381 -- instance C (Maybe x) (Tree x) where ..
383 -- and an Inst of form (C (Maybe t1) t2),
384 -- then we will call checkClsFD with
386 -- qtvs = {x}, tys1 = [Maybe x, Tree x]
387 -- tys2 = [Maybe t1, t2]
389 -- We can instantiate x to t1, and then we want to force
390 -- (Tree x) [t1/x] :=: t2
392 -- This function is also used when matching two Insts (rather than an Inst
393 -- against an instance decl. In that case, qtvs is empty, and we are doing
396 -- This function is also used by InstEnv.badFunDeps, which needs to *unify*
397 -- For the one-sided matching case, the qtvs are just from the template,
398 -- so we get matching
400 = ASSERT2( length tys1 == length tys2 &&
401 length tys1 == length clas_tvs
402 , ppr tys1 <+> ppr tys2 )
404 case tcUnifyTys bind_fn ls1 ls2 of
406 Just subst | isJust (tcUnifyTys bind_fn rs1' rs2')
407 -- Don't include any equations that already hold.
408 -- Reason: then we know if any actual improvement has happened,
409 -- in which case we need to iterate the solver
410 -- In making this check we must taking account of the fact that any
411 -- qtvs that aren't already instantiated can be instantiated to anything
415 | otherwise -- Aha! A useful equation
416 -> [ (qtvs', zip rs1' rs2')]
417 -- We could avoid this substTy stuff by producing the eqn
418 -- (qtvs, ls1++rs1, ls2++rs2)
419 -- which will re-do the ls1/ls2 unification when the equation is
420 -- executed. What we're doing instead is recording the partial
421 -- work of the ls1/ls2 unification leaving a smaller unification problem
423 rs1' = substTys subst rs1
424 rs2' = substTys subst rs2
425 qtvs' = filterVarSet (`notElemTvSubst` subst) qtvs
426 -- qtvs' are the quantified type variables
427 -- that have not been substituted out
429 -- Eg. class C a b | a -> b
430 -- instance C Int [y]
431 -- Given constraint C Int z
432 -- we generate the equation
435 bind_fn tv | tv `elemVarSet` qtvs = BindMe
438 (ls1, rs1) = instFD fd clas_tvs tys1
439 (ls2, rs2) = instFD fd clas_tvs tys2
441 instFD :: FunDep TyVar -> [TyVar] -> [Type] -> FunDep Type
442 instFD (ls,rs) tvs tys
443 = (map lookup ls, map lookup rs)
445 env = zipVarEnv tvs tys
446 lookup tv = lookupVarEnv_NF env tv
450 checkInstCoverage :: Class -> [Type] -> Bool
451 -- Check that the Coverage Condition is obeyed in an instance decl
452 -- For example, if we have
453 -- class theta => C a b | a -> b
455 -- Then we require fv(t2) `subset` fv(t1)
456 -- See Note [Coverage Condition] below
458 checkInstCoverage clas inst_taus
461 (tyvars, fds) = classTvsFds clas
462 fundep_ok fd = tyVarsOfTypes rs `subVarSet` tyVarsOfTypes ls
464 (ls,rs) = instFD fd tyvars inst_taus
467 Note [Coverage condition]
468 ~~~~~~~~~~~~~~~~~~~~~~~~~
469 For the coverage condition, we used to require only that
470 fv(t2) `subset` oclose(fv(t1), theta)
473 class Mul a b c | a b -> c where
476 instance Mul Int Int Int where (.*.) = (*)
477 instance Mul Int Float Float where x .*. y = fromIntegral x * y
478 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
480 In the third instance, it's not the case that fv([c]) `subset` fv(a,[b]).
481 But it is the case that fv([c]) `subset` oclose( theta, fv(a,[b]) )
483 But it is a mistake to accept the instance because then this defn:
484 f = \ b x y -> if b then x .*. [y] else y
485 makes instance inference go into a loop, because it requires the constraint
489 %************************************************************************
491 Check that a new instance decl is OK wrt fundeps
493 %************************************************************************
495 Here is the bad case:
496 class C a b | a->b where ...
497 instance C Int Bool where ...
498 instance C Int Char where ...
500 The point is that a->b, so Int in the first parameter must uniquely
501 determine the second. In general, given the same class decl, and given
503 instance C s1 s2 where ...
504 instance C t1 t2 where ...
506 Then the criterion is: if U=unify(s1,t1) then U(s2) = U(t2).
508 Matters are a little more complicated if there are free variables in
511 class D a b c | a -> b
512 instance D a b => D [(a,a)] [b] Int
513 instance D a b => D [a] [b] Bool
515 The instance decls don't overlap, because the third parameter keeps
516 them separate. But we want to make sure that given any constraint
522 checkFunDeps :: (InstEnv, InstEnv) -> Instance
523 -> Maybe [Instance] -- Nothing <=> ok
524 -- Just dfs <=> conflict with dfs
525 -- Check wheher adding DFunId would break functional-dependency constraints
526 -- Used only for instance decls defined in the module being compiled
527 checkFunDeps inst_envs ispec
528 | null bad_fundeps = Nothing
529 | otherwise = Just bad_fundeps
531 (ins_tvs, _, clas, ins_tys) = instanceHead ispec
532 ins_tv_set = mkVarSet ins_tvs
533 cls_inst_env = classInstances inst_envs clas
534 bad_fundeps = badFunDeps cls_inst_env clas ins_tv_set ins_tys
536 badFunDeps :: [Instance] -> Class
537 -> TyVarSet -> [Type] -- Proposed new instance type
539 badFunDeps cls_insts clas ins_tv_set ins_tys
540 = [ ispec | fd <- fds, -- fds is often empty
541 let trimmed_tcs = trimRoughMatchTcs clas_tvs fd rough_tcs,
542 ispec@(Instance { is_tcs = mb_tcs, is_tvs = tvs,
543 is_tys = tys }) <- cls_insts,
544 -- Filter out ones that can't possibly match,
545 -- based on the head of the fundep
546 not (instanceCantMatch trimmed_tcs mb_tcs),
547 notNull (checkClsFD (tvs `unionVarSet` ins_tv_set)
548 fd clas_tvs tys ins_tys)
551 (clas_tvs, fds) = classTvsFds clas
552 rough_tcs = roughMatchTcs ins_tys
554 trimRoughMatchTcs :: [TyVar] -> FunDep TyVar -> [Maybe Name] -> [Maybe Name]
555 -- Computing rough_tcs for a particular fundep
556 -- class C a b c | a c -> b where ...
557 -- For each instance .... => C ta tb tc
558 -- we want to match only on the types ta, tb; so our
559 -- rough-match thing must similarly be filtered.
560 -- Hence, we Nothing-ise the tb type right here
561 trimRoughMatchTcs clas_tvs (ltvs,_) mb_tcs
562 = zipWith select clas_tvs mb_tcs
564 select clas_tv mb_tc | clas_tv `elem` ltvs = mb_tc
565 | otherwise = Nothing