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"
34 import Data.List ( tails )
35 import Data.Maybe ( isJust )
39 %************************************************************************
41 \subsection{Close type variables}
43 %************************************************************************
45 (oclose preds tvs) closes the set of type variables tvs,
46 wrt functional dependencies in preds. The result is a superset
47 of the argument set. For example, if we have
48 class C a b | a->b where ...
50 oclose [C (x,y) z, C (x,p) q] {x,y} = {x,y,z}
51 because if we know x and y then that fixes z.
57 a) When determining ambiguity. The type
58 forall a,b. C a b => a
59 is not ambiguous (given the above class decl for C) because
62 b) When generalising a type T. Usually we take FV(T) \ FV(Env),
65 where the '+' is the oclosure operation. Notice that we do not
66 take FV(T)+. This puzzled me for a bit. Consider
70 and suppose e have that E :: C a b => a, and suppose that b is
71 free in the environment. Then we quantify over 'a' only, giving
72 the type forall a. C a b => a. Since a->b but we don't have b->a,
73 we might have instance decls like
74 instance C Bool Int where ...
75 instance C Char Int where ...
76 so knowing that b=Int doesn't fix 'a'; so we quantify over it.
81 If we have class C a b => D a b where ....
82 class D a b | a -> b where ...
83 and the preds are [C (x,y) z], then we want to see the fd in D,
84 even though it is not explicit in C, giving [({x,y},{z})]
86 Similarly for instance decls? E.g. Suppose we have
87 instance C a b => Eq (T a b) where ...
88 and we infer a type t with constraints Eq (T a b) for a particular
89 expression, and suppose that 'a' is free in the environment.
90 We could generalise to
91 forall b. Eq (T a b) => t
92 but if we reduced the constraint, to C a b, we'd see that 'a' determines
93 b, so that a better type might be
94 t (with free constraint C a b)
95 Perhaps it doesn't matter, because we'll still force b to be a
96 particular type at the call sites. Generalising over too many
97 variables (provided we don't shadow anything by quantifying over a
98 variable that is actually free in the envt) may postpone errors; it
99 won't hide them altogether.
103 oclose :: [PredType] -> TyVarSet -> TyVarSet
104 oclose preds fixed_tvs
105 | null tv_fds = fixed_tvs -- Fast escape hatch for common case
106 | otherwise = loop fixed_tvs
109 | new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs
110 | otherwise = loop new_fixed_tvs
112 new_fixed_tvs = foldl extend fixed_tvs tv_fds
114 extend fixed_tvs (ls,rs) | ls `subVarSet` fixed_tvs = fixed_tvs `unionVarSet` rs
115 | otherwise = fixed_tvs
117 tv_fds :: [(TyVarSet,TyVarSet)]
118 -- In our example, tv_fds will be [ ({x,y}, {z}), ({x,p},{q}) ]
119 -- Meaning "knowing x,y fixes z, knowing x,p fixes q"
120 tv_fds = [ (tyVarsOfTypes xs, tyVarsOfTypes ys)
121 | ClassP cls tys <- preds, -- Ignore implicit params
122 let (cls_tvs, cls_fds) = classTvsFds cls,
124 let (xs,ys) = instFD fd cls_tvs tys
129 grow :: [PredType] -> TyVarSet -> TyVarSet
130 -- See Note [Ambiguity] in TcSimplify
132 | null preds = fixed_tvs
133 | otherwise = loop fixed_tvs
136 | new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs
137 | otherwise = loop new_fixed_tvs
139 new_fixed_tvs = foldl extend fixed_tvs pred_sets
141 extend fixed_tvs pred_tvs
142 | fixed_tvs `intersectsVarSet` pred_tvs = fixed_tvs `unionVarSet` pred_tvs
143 | otherwise = fixed_tvs
145 pred_sets = [tyVarsOfPred pred | pred <- preds]
148 %************************************************************************
150 \subsection{Generate equations from functional dependencies}
152 %************************************************************************
157 type Equation = (TyVarSet, [(Type, Type)])
158 -- These pairs of types should be equal, for some
159 -- substitution of the tyvars in the tyvar set
160 -- INVARIANT: corresponding types aren't already equal
162 -- It's important that we have a *list* of pairs of types. Consider
163 -- class C a b c | a -> b c where ...
164 -- instance C Int x x where ...
165 -- Then, given the constraint (C Int Bool v) we should improve v to Bool,
166 -- via the equation ({x}, [(Bool,x), (v,x)])
167 -- This would not happen if the class had looked like
168 -- class C a b c | a -> b, a -> c
170 -- To "execute" the equation, make fresh type variable for each tyvar in the set,
171 -- instantiate the two types with these fresh variables, and then unify.
173 -- For example, ({a,b}, (a,Int,b), (Int,z,Bool))
174 -- We unify z with Int, but since a and b are quantified we do nothing to them
175 -- We usually act on an equation by instantiating the quantified type varaibles
176 -- to fresh type variables, and then calling the standard unifier.
178 pprEquation (qtvs, pairs)
179 = vcat [ptext SLIT("forall") <+> braces (pprWithCommas ppr (varSetElems qtvs)),
180 nest 2 (vcat [ ppr t1 <+> ptext SLIT(":=:") <+> ppr t2 | (t1,t2) <- pairs])]
183 type Pred_Loc = (PredType, SDoc) -- SDoc says where the Pred comes from
185 improve :: (Class -> [Instance]) -- Gives instances for given class
186 -> [Pred_Loc] -- Current constraints;
187 -> [(Equation,Pred_Loc,Pred_Loc)] -- Derived equalities that must also hold
188 -- (NB the above INVARIANT for type Equation)
189 -- The Pred_Locs explain which two predicates were
190 -- combined (for error messages)
193 Given a bunch of predicates that must hold, such as
195 C Int t1, C Int t2, C Bool t3, ?x::t4, ?x::t5
197 improve figures out what extra equations must hold.
198 For example, if we have
200 class C a b | a->b where ...
202 then improve will return
208 * improve does not iterate. It's possible that when we make
209 t1=t2, for example, that will in turn trigger a new equation.
210 This would happen if we also had
212 If t1=t2, we also get t7=t8.
214 improve does *not* do this extra step. It relies on the caller
217 * The equations unify types that are not already equal. So there
218 is no effect iff the result of improve is empty
223 improve inst_env preds
224 = [ eqn | group <- equivClassesByUniq (predTyUnique . fst) (filterEqPreds preds),
225 eqn <- checkGroup inst_env group ]
227 filterEqPreds = filter (not . isEqPred . fst)
228 -- Equality predicates don't have uniques
229 -- In any case, improvement *generates*, rather than
230 -- *consumes*, equality constraints
232 improveOne :: (Class -> [Instance])
235 -> [(Equation,Pred_Loc,Pred_Loc)]
237 -- Just do improvement triggered by a single, distinguised predicate
239 improveOne inst_env pred@(IParam ip ty, _) preds
240 = [ ((emptyVarSet, [(ty,ty2)]), pred, p2)
241 | p2@(IParam ip2 ty2, _) <- preds
243 , not (ty `tcEqType` ty2)]
245 improveOne inst_env pred@(ClassP cls tys, _) preds
246 | tys `lengthAtLeast` 2
247 = instance_eqns ++ pairwise_eqns
248 -- NB: we put the instance equations first. This biases the
249 -- order so that we first improve individual constraints against the
250 -- instances (which are perhaps in a library and less likely to be
251 -- wrong; and THEN perform the pairwise checks.
252 -- The other way round, it's possible for the pairwise check to succeed
253 -- and cause a subsequent, misleading failure of one of the pair with an
254 -- instance declaration. See tcfail143.hs for an example
256 (cls_tvs, cls_fds) = classTvsFds cls
257 instances = inst_env cls
258 rough_tcs = roughMatchTcs tys
260 -- NOTE that we iterate over the fds first; they are typically
261 -- empty, which aborts the rest of the loop.
262 pairwise_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
263 pairwise_eqns -- This group comes from pairwise comparison
266 , p2@(ClassP cls2 tys2, _) <- preds
268 , eqn <- checkClsFD emptyVarSet fd cls_tvs tys tys2
271 instance_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
272 instance_eqns -- This group comes from comparing with instance decls
273 = [ (eqn, p_inst, pred)
274 | fd <- cls_fds -- Iterate through the fundeps first,
275 -- because there often are none!
276 , let rough_fd_tcs = trimRoughMatchTcs cls_tvs fd rough_tcs
277 , ispec@(Instance { is_tvs = qtvs, is_tys = tys_inst,
278 is_tcs = mb_tcs_inst }) <- instances
279 , not (instanceCantMatch mb_tcs_inst rough_tcs)
280 , eqn <- checkClsFD qtvs fd cls_tvs tys_inst tys
281 , let p_inst = (mkClassPred cls tys_inst,
282 ptext SLIT("arising from the instance declaration at")
283 <+> ppr (getSrcLoc ispec))
286 improveOne inst_env eq_pred preds
290 checkGroup :: (Class -> [Instance])
292 -> [(Equation, Pred_Loc, Pred_Loc)]
293 -- The preds are all for the same class or implicit param
295 checkGroup inst_env (p1@(IParam _ ty, _) : ips)
296 = -- For implicit parameters, all the types must match
297 [ ((emptyVarSet, [(ty,ty')]), p1, p2)
298 | p2@(IParam _ ty', _) <- ips, not (ty `tcEqType` ty')]
300 checkGroup inst_env clss@((ClassP cls _, _) : _)
301 = -- For classes life is more complicated
302 -- Suppose the class is like
303 -- classs C as | (l1 -> r1), (l2 -> r2), ... where ...
304 -- Then FOR EACH PAIR (ClassP c tys1, ClassP c tys2) in the list clss
306 -- U l1[tys1/as] = U l2[tys2/as]
307 -- (where U is a unifier)
309 -- If so, we return the pair
310 -- U r1[tys1/as] = U l2[tys2/as]
312 -- We need to do something very similar comparing each predicate
313 -- with relevant instance decls
315 instance_eqns ++ pairwise_eqns
316 -- NB: we put the instance equations first. This biases the
317 -- order so that we first improve individual constraints against the
318 -- instances (which are perhaps in a library and less likely to be
319 -- wrong; and THEN perform the pairwise checks.
320 -- The other way round, it's possible for the pairwise check to succeed
321 -- and cause a subsequent, misleading failure of one of the pair with an
322 -- instance declaration. See tcfail143.hs for an exmample
325 (cls_tvs, cls_fds) = classTvsFds cls
326 instances = inst_env cls
328 -- NOTE that we iterate over the fds first; they are typically
329 -- empty, which aborts the rest of the loop.
330 pairwise_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
331 pairwise_eqns -- This group comes from pairwise comparison
334 p1@(ClassP _ tys1, _) : rest <- tails clss,
335 p2@(ClassP _ tys2, _) <- rest,
336 eqn <- checkClsFD emptyVarSet fd cls_tvs tys1 tys2
339 instance_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
340 instance_eqns -- This group comes from comparing with instance decls
342 | fd <- cls_fds, -- Iterate through the fundeps first,
343 -- because there often are none!
344 p2@(ClassP _ tys2, _) <- clss,
345 let rough_tcs2 = trimRoughMatchTcs cls_tvs fd (roughMatchTcs tys2),
346 ispec@(Instance { is_tvs = qtvs, is_tys = tys1,
347 is_tcs = mb_tcs1 }) <- instances,
348 not (instanceCantMatch mb_tcs1 rough_tcs2),
349 eqn <- checkClsFD qtvs fd cls_tvs tys1 tys2,
350 let p1 = (mkClassPred cls tys1,
351 ptext SLIT("arising from the instance declaration at") <+>
352 ppr (getSrcLoc ispec))
355 checkClsFD :: TyVarSet -- Quantified type variables; see note below
356 -> FunDep TyVar -> [TyVar] -- One functional dependency from the class
360 checkClsFD qtvs fd clas_tvs tys1 tys2
361 -- 'qtvs' are the quantified type variables, the ones which an be instantiated
362 -- to make the types match. For example, given
363 -- class C a b | a->b where ...
364 -- instance C (Maybe x) (Tree x) where ..
366 -- and an Inst of form (C (Maybe t1) t2),
367 -- then we will call checkClsFD with
369 -- qtvs = {x}, tys1 = [Maybe x, Tree x]
370 -- tys2 = [Maybe t1, t2]
372 -- We can instantiate x to t1, and then we want to force
373 -- (Tree x) [t1/x] :=: t2
375 -- This function is also used when matching two Insts (rather than an Inst
376 -- against an instance decl. In that case, qtvs is empty, and we are doing
379 -- This function is also used by InstEnv.badFunDeps, which needs to *unify*
380 -- For the one-sided matching case, the qtvs are just from the template,
381 -- so we get matching
383 = ASSERT2( length tys1 == length tys2 &&
384 length tys1 == length clas_tvs
385 , ppr tys1 <+> ppr tys2 )
387 case tcUnifyTys bind_fn ls1 ls2 of
389 Just subst | isJust (tcUnifyTys bind_fn rs1' rs2')
390 -- Don't include any equations that already hold.
391 -- Reason: then we know if any actual improvement has happened,
392 -- in which case we need to iterate the solver
393 -- In making this check we must taking account of the fact that any
394 -- qtvs that aren't already instantiated can be instantiated to anything
398 | otherwise -- Aha! A useful equation
399 -> [ (qtvs', zip rs1' rs2')]
400 -- We could avoid this substTy stuff by producing the eqn
401 -- (qtvs, ls1++rs1, ls2++rs2)
402 -- which will re-do the ls1/ls2 unification when the equation is
403 -- executed. What we're doing instead is recording the partial
404 -- work of the ls1/ls2 unification leaving a smaller unification problem
406 rs1' = substTys subst rs1
407 rs2' = substTys subst rs2
408 qtvs' = filterVarSet (`notElemTvSubst` subst) qtvs
409 -- qtvs' are the quantified type variables
410 -- that have not been substituted out
412 -- Eg. class C a b | a -> b
413 -- instance C Int [y]
414 -- Given constraint C Int z
415 -- we generate the equation
418 bind_fn tv | tv `elemVarSet` qtvs = BindMe
421 (ls1, rs1) = instFD fd clas_tvs tys1
422 (ls2, rs2) = instFD fd clas_tvs tys2
424 instFD :: FunDep TyVar -> [TyVar] -> [Type] -> FunDep Type
425 instFD (ls,rs) tvs tys
426 = (map lookup ls, map lookup rs)
428 env = zipVarEnv tvs tys
429 lookup tv = lookupVarEnv_NF env tv
433 checkInstCoverage :: Class -> [Type] -> Bool
434 -- Check that the Coverage Condition is obeyed in an instance decl
435 -- For example, if we have
436 -- class theta => C a b | a -> b
438 -- Then we require fv(t2) `subset` fv(t1)
439 -- See Note [Coverage Condition] below
441 checkInstCoverage clas inst_taus
444 (tyvars, fds) = classTvsFds clas
445 fundep_ok fd = tyVarsOfTypes rs `subVarSet` tyVarsOfTypes ls
447 (ls,rs) = instFD fd tyvars inst_taus
450 Note [Coverage condition]
451 ~~~~~~~~~~~~~~~~~~~~~~~~~
452 For the coverage condition, we used to require only that
453 fv(t2) `subset` oclose(fv(t1), theta)
456 class Mul a b c | a b -> c where
459 instance Mul Int Int Int where (.*.) = (*)
460 instance Mul Int Float Float where x .*. y = fromIntegral x * y
461 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
463 In the third instance, it's not the case that fv([c]) `subset` fv(a,[b]).
464 But it is the case that fv([c]) `subset` oclose( theta, fv(a,[b]) )
466 But it is a mistake to accept the instance because then this defn:
467 f = \ b x y -> if b then x .*. [y] else y
468 makes instance inference go into a loop, because it requires the constraint
472 %************************************************************************
474 Check that a new instance decl is OK wrt fundeps
476 %************************************************************************
478 Here is the bad case:
479 class C a b | a->b where ...
480 instance C Int Bool where ...
481 instance C Int Char where ...
483 The point is that a->b, so Int in the first parameter must uniquely
484 determine the second. In general, given the same class decl, and given
486 instance C s1 s2 where ...
487 instance C t1 t2 where ...
489 Then the criterion is: if U=unify(s1,t1) then U(s2) = U(t2).
491 Matters are a little more complicated if there are free variables in
494 class D a b c | a -> b
495 instance D a b => D [(a,a)] [b] Int
496 instance D a b => D [a] [b] Bool
498 The instance decls don't overlap, because the third parameter keeps
499 them separate. But we want to make sure that given any constraint
505 checkFunDeps :: (InstEnv, InstEnv) -> Instance
506 -> Maybe [Instance] -- Nothing <=> ok
507 -- Just dfs <=> conflict with dfs
508 -- Check wheher adding DFunId would break functional-dependency constraints
509 -- Used only for instance decls defined in the module being compiled
510 checkFunDeps inst_envs ispec
511 | null bad_fundeps = Nothing
512 | otherwise = Just bad_fundeps
514 (ins_tvs, _, clas, ins_tys) = instanceHead ispec
515 ins_tv_set = mkVarSet ins_tvs
516 cls_inst_env = classInstances inst_envs clas
517 bad_fundeps = badFunDeps cls_inst_env clas ins_tv_set ins_tys
519 badFunDeps :: [Instance] -> Class
520 -> TyVarSet -> [Type] -- Proposed new instance type
522 badFunDeps cls_insts clas ins_tv_set ins_tys
523 = [ ispec | fd <- fds, -- fds is often empty
524 let trimmed_tcs = trimRoughMatchTcs clas_tvs fd rough_tcs,
525 ispec@(Instance { is_tcs = mb_tcs, is_tvs = tvs,
526 is_tys = tys }) <- cls_insts,
527 -- Filter out ones that can't possibly match,
528 -- based on the head of the fundep
529 not (instanceCantMatch trimmed_tcs mb_tcs),
530 notNull (checkClsFD (tvs `unionVarSet` ins_tv_set)
531 fd clas_tvs tys ins_tys)
534 (clas_tvs, fds) = classTvsFds clas
535 rough_tcs = roughMatchTcs ins_tys
537 trimRoughMatchTcs :: [TyVar] -> FunDep TyVar -> [Maybe Name] -> [Maybe Name]
538 -- Computing rough_tcs for a particular fundep
539 -- class C a b c | a c -> b where ...
540 -- For each instance .... => C ta tb tc
541 -- we want to match only on the types ta, tb; so our
542 -- rough-match thing must similarly be filtered.
543 -- Hence, we Nothing-ise the tb type right here
544 trimRoughMatchTcs clas_tvs (ltvs,_) mb_tcs
545 = zipWith select clas_tvs mb_tcs
547 select clas_tv mb_tc | clas_tv `elem` ltvs = mb_tc
548 | otherwise = Nothing