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,
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
233 checkGroup :: (Class -> [Instance])
235 -> [(Equation, Pred_Loc, Pred_Loc)]
236 -- The preds are all for the same class or implicit param
238 checkGroup inst_env (p1@(IParam _ ty, _) : ips)
239 = -- For implicit parameters, all the types must match
240 [ ((emptyVarSet, [(ty,ty')]), p1, p2)
241 | p2@(IParam _ ty', _) <- ips, not (ty `tcEqType` ty')]
243 checkGroup inst_env clss@((ClassP cls _, _) : _)
244 = -- For classes life is more complicated
245 -- Suppose the class is like
246 -- classs C as | (l1 -> r1), (l2 -> r2), ... where ...
247 -- Then FOR EACH PAIR (ClassP c tys1, ClassP c tys2) in the list clss
249 -- U l1[tys1/as] = U l2[tys2/as]
250 -- (where U is a unifier)
252 -- If so, we return the pair
253 -- U r1[tys1/as] = U l2[tys2/as]
255 -- We need to do something very similar comparing each predicate
256 -- with relevant instance decls
258 instance_eqns ++ pairwise_eqns
259 -- NB: we put the instance equations first. This biases the
260 -- order so that we first improve individual constraints against the
261 -- instances (which are perhaps in a library and less likely to be
262 -- wrong; and THEN perform the pairwise checks.
263 -- The other way round, it's possible for the pairwise check to succeed
264 -- and cause a subsequent, misleading failure of one of the pair with an
265 -- instance declaration. See tcfail143.hs for an exmample
268 (cls_tvs, cls_fds) = classTvsFds cls
269 instances = inst_env cls
271 -- NOTE that we iterate over the fds first; they are typically
272 -- empty, which aborts the rest of the loop.
273 pairwise_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
274 pairwise_eqns -- This group comes from pairwise comparison
277 p1@(ClassP _ tys1, _) : rest <- tails clss,
278 p2@(ClassP _ tys2, _) <- rest,
279 eqn <- checkClsFD emptyVarSet fd cls_tvs tys1 tys2
282 instance_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
283 instance_eqns -- This group comes from comparing with instance decls
285 | fd <- cls_fds, -- Iterate through the fundeps first,
286 -- because there often are none!
287 p2@(ClassP _ tys2, _) <- clss,
288 let rough_tcs2 = trimRoughMatchTcs cls_tvs fd (roughMatchTcs tys2),
289 ispec@(Instance { is_tvs = qtvs, is_tys = tys1,
290 is_tcs = mb_tcs1 }) <- instances,
291 not (instanceCantMatch mb_tcs1 rough_tcs2),
292 eqn <- checkClsFD qtvs fd cls_tvs tys1 tys2,
293 let p1 = (mkClassPred cls tys1,
294 ptext SLIT("arising from the instance declaration at") <+>
295 ppr (getSrcLoc ispec))
298 checkClsFD :: TyVarSet -- Quantified type variables; see note below
299 -> FunDep TyVar -> [TyVar] -- One functional dependency from the class
303 checkClsFD qtvs fd clas_tvs tys1 tys2
304 -- 'qtvs' are the quantified type variables, the ones which an be instantiated
305 -- to make the types match. For example, given
306 -- class C a b | a->b where ...
307 -- instance C (Maybe x) (Tree x) where ..
309 -- and an Inst of form (C (Maybe t1) t2),
310 -- then we will call checkClsFD with
312 -- qtvs = {x}, tys1 = [Maybe x, Tree x]
313 -- tys2 = [Maybe t1, t2]
315 -- We can instantiate x to t1, and then we want to force
316 -- (Tree x) [t1/x] :=: t2
318 -- This function is also used when matching two Insts (rather than an Inst
319 -- against an instance decl. In that case, qtvs is empty, and we are doing
322 -- This function is also used by InstEnv.badFunDeps, which needs to *unify*
323 -- For the one-sided matching case, the qtvs are just from the template,
324 -- so we get matching
326 = ASSERT2( length tys1 == length tys2 &&
327 length tys1 == length clas_tvs
328 , ppr tys1 <+> ppr tys2 )
330 case tcUnifyTys bind_fn ls1 ls2 of
332 Just subst | isJust (tcUnifyTys bind_fn rs1' rs2')
333 -- Don't include any equations that already hold.
334 -- Reason: then we know if any actual improvement has happened,
335 -- in which case we need to iterate the solver
336 -- In making this check we must taking account of the fact that any
337 -- qtvs that aren't already instantiated can be instantiated to anything
341 | otherwise -- Aha! A useful equation
342 -> [ (qtvs', zip rs1' rs2')]
343 -- We could avoid this substTy stuff by producing the eqn
344 -- (qtvs, ls1++rs1, ls2++rs2)
345 -- which will re-do the ls1/ls2 unification when the equation is
346 -- executed. What we're doing instead is recording the partial
347 -- work of the ls1/ls2 unification leaving a smaller unification problem
349 rs1' = substTys subst rs1
350 rs2' = substTys subst rs2
351 qtvs' = filterVarSet (`notElemTvSubst` subst) qtvs
352 -- qtvs' are the quantified type variables
353 -- that have not been substituted out
355 -- Eg. class C a b | a -> b
356 -- instance C Int [y]
357 -- Given constraint C Int z
358 -- we generate the equation
361 bind_fn tv | tv `elemVarSet` qtvs = BindMe
364 (ls1, rs1) = instFD fd clas_tvs tys1
365 (ls2, rs2) = instFD fd clas_tvs tys2
367 instFD :: FunDep TyVar -> [TyVar] -> [Type] -> FunDep Type
368 instFD (ls,rs) tvs tys
369 = (map lookup ls, map lookup rs)
371 env = zipVarEnv tvs tys
372 lookup tv = lookupVarEnv_NF env tv
376 checkInstCoverage :: Class -> [Type] -> Bool
377 -- Check that the Coverage Condition is obeyed in an instance decl
378 -- For example, if we have
379 -- class theta => C a b | a -> b
381 -- Then we require fv(t2) `subset` fv(t1)
382 -- See Note [Coverage Condition] below
384 checkInstCoverage clas inst_taus
387 (tyvars, fds) = classTvsFds clas
388 fundep_ok fd = tyVarsOfTypes rs `subVarSet` tyVarsOfTypes ls
390 (ls,rs) = instFD fd tyvars inst_taus
393 Note [Coverage condition]
394 ~~~~~~~~~~~~~~~~~~~~~~~~~
395 For the coverage condition, we used to require only that
396 fv(t2) `subset` oclose(fv(t1), theta)
399 class Mul a b c | a b -> c where
402 instance Mul Int Int Int where (.*.) = (*)
403 instance Mul Int Float Float where x .*. y = fromIntegral x * y
404 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
406 In the third instance, it's not the case that fv([c]) `subset` fv(a,[b]).
407 But it is the case that fv([c]) `subset` oclose( theta, fv(a,[b]) )
409 But it is a mistake to accept the instance because then this defn:
410 f = \ b x y -> if b then x .*. [y] else y
411 makes instance inference go into a loop, because it requires the constraint
415 %************************************************************************
417 Check that a new instance decl is OK wrt fundeps
419 %************************************************************************
421 Here is the bad case:
422 class C a b | a->b where ...
423 instance C Int Bool where ...
424 instance C Int Char where ...
426 The point is that a->b, so Int in the first parameter must uniquely
427 determine the second. In general, given the same class decl, and given
429 instance C s1 s2 where ...
430 instance C t1 t2 where ...
432 Then the criterion is: if U=unify(s1,t1) then U(s2) = U(t2).
434 Matters are a little more complicated if there are free variables in
437 class D a b c | a -> b
438 instance D a b => D [(a,a)] [b] Int
439 instance D a b => D [a] [b] Bool
441 The instance decls don't overlap, because the third parameter keeps
442 them separate. But we want to make sure that given any constraint
448 checkFunDeps :: (InstEnv, InstEnv) -> Instance
449 -> Maybe [Instance] -- Nothing <=> ok
450 -- Just dfs <=> conflict with dfs
451 -- Check wheher adding DFunId would break functional-dependency constraints
452 -- Used only for instance decls defined in the module being compiled
453 checkFunDeps inst_envs ispec
454 | null bad_fundeps = Nothing
455 | otherwise = Just bad_fundeps
457 (ins_tvs, _, clas, ins_tys) = instanceHead ispec
458 ins_tv_set = mkVarSet ins_tvs
459 cls_inst_env = classInstances inst_envs clas
460 bad_fundeps = badFunDeps cls_inst_env clas ins_tv_set ins_tys
462 badFunDeps :: [Instance] -> Class
463 -> TyVarSet -> [Type] -- Proposed new instance type
465 badFunDeps cls_insts clas ins_tv_set ins_tys
466 = [ ispec | fd <- fds, -- fds is often empty
467 let trimmed_tcs = trimRoughMatchTcs clas_tvs fd rough_tcs,
468 ispec@(Instance { is_tcs = mb_tcs, is_tvs = tvs,
469 is_tys = tys }) <- cls_insts,
470 -- Filter out ones that can't possibly match,
471 -- based on the head of the fundep
472 not (instanceCantMatch trimmed_tcs mb_tcs),
473 notNull (checkClsFD (tvs `unionVarSet` ins_tv_set)
474 fd clas_tvs tys ins_tys)
477 (clas_tvs, fds) = classTvsFds clas
478 rough_tcs = roughMatchTcs ins_tys
480 trimRoughMatchTcs :: [TyVar] -> FunDep TyVar -> [Maybe Name] -> [Maybe Name]
481 -- Computing rough_tcs for a particular fundep
482 -- class C a b c | a c -> b where ...
483 -- For each instance .... => C ta tb tc
484 -- we want to match only on the types ta, tb; so our
485 -- rough-match thing must similarly be filtered.
486 -- Hence, we Nothing-ise the tb type right here
487 trimRoughMatchTcs clas_tvs (ltvs,_) mb_tcs
488 = zipWith select clas_tvs mb_tcs
490 select clas_tv mb_tc | clas_tv `elem` ltvs = mb_tc
491 | otherwise = Nothing