2 % (c) The GRASP/AQUA Project, Glasgow University, 2000
4 \section[FunDeps]{FunDeps - functional dependencies}
6 It's better to read it as: "if we know these, then we're going to know these"
10 Equation, pprEquation,
11 oclose, grow, improve,
12 checkInstCoverage, checkFunDeps,
16 #include "HsVersions.h"
18 import Name ( Name, getSrcLoc )
20 import Class ( Class, FunDep, pprFundeps, classTvsFds )
21 import TcGadt ( tcUnifyTys, BindFlag(..) )
22 import Type ( substTys, notElemTvSubst )
23 import Coercion ( isEqPred )
24 import TcType ( Type, PredType(..), tcEqType,
25 predTyUnique, mkClassPred, tyVarsOfTypes, tyVarsOfPred )
26 import InstEnv ( Instance(..), InstEnv, instanceHead, classInstances,
27 instanceCantMatch, roughMatchTcs )
31 import Util ( notNull )
33 import Maybe ( isJust )
34 import ListSetOps ( equivClassesByUniq )
38 %************************************************************************
40 \subsection{Close type variables}
42 %************************************************************************
44 (oclose preds tvs) closes the set of type variables tvs,
45 wrt functional dependencies in preds. The result is a superset
46 of the argument set. For example, if we have
47 class C a b | a->b where ...
49 oclose [C (x,y) z, C (x,p) q] {x,y} = {x,y,z}
50 because if we know x and y then that fixes z.
56 a) When determining ambiguity. The type
57 forall a,b. C a b => a
58 is not ambiguous (given the above class decl for C) because
61 b) When generalising a type T. Usually we take FV(T) \ FV(Env),
64 where the '+' is the oclosure operation. Notice that we do not
65 take FV(T)+. This puzzled me for a bit. Consider
69 and suppose e have that E :: C a b => a, and suppose that b is
70 free in the environment. Then we quantify over 'a' only, giving
71 the type forall a. C a b => a. Since a->b but we don't have b->a,
72 we might have instance decls like
73 instance C Bool Int where ...
74 instance C Char Int where ...
75 so knowing that b=Int doesn't fix 'a'; so we quantify over it.
80 If we have class C a b => D a b where ....
81 class D a b | a -> b where ...
82 and the preds are [C (x,y) z], then we want to see the fd in D,
83 even though it is not explicit in C, giving [({x,y},{z})]
85 Similarly for instance decls? E.g. Suppose we have
86 instance C a b => Eq (T a b) where ...
87 and we infer a type t with constraints Eq (T a b) for a particular
88 expression, and suppose that 'a' is free in the environment.
89 We could generalise to
90 forall b. Eq (T a b) => t
91 but if we reduced the constraint, to C a b, we'd see that 'a' determines
92 b, so that a better type might be
93 t (with free constraint C a b)
94 Perhaps it doesn't matter, because we'll still force b to be a
95 particular type at the call sites. Generalising over too many
96 variables (provided we don't shadow anything by quantifying over a
97 variable that is actually free in the envt) may postpone errors; it
98 won't hide them altogether.
102 oclose :: [PredType] -> TyVarSet -> TyVarSet
103 oclose preds fixed_tvs
104 | null tv_fds = fixed_tvs -- Fast escape hatch for common case
105 | otherwise = loop fixed_tvs
108 | new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs
109 | otherwise = loop new_fixed_tvs
111 new_fixed_tvs = foldl extend fixed_tvs tv_fds
113 extend fixed_tvs (ls,rs) | ls `subVarSet` fixed_tvs = fixed_tvs `unionVarSet` rs
114 | otherwise = fixed_tvs
116 tv_fds :: [(TyVarSet,TyVarSet)]
117 -- In our example, tv_fds will be [ ({x,y}, {z}), ({x,p},{q}) ]
118 -- Meaning "knowing x,y fixes z, knowing x,p fixes q"
119 tv_fds = [ (tyVarsOfTypes xs, tyVarsOfTypes ys)
120 | ClassP cls tys <- preds, -- Ignore implicit params
121 let (cls_tvs, cls_fds) = classTvsFds cls,
123 let (xs,ys) = instFD fd cls_tvs tys
128 grow :: [PredType] -> TyVarSet -> TyVarSet
129 -- See Note [Ambiguity] in TcSimplify
131 | null preds = fixed_tvs
132 | otherwise = loop fixed_tvs
135 | new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs
136 | otherwise = loop new_fixed_tvs
138 new_fixed_tvs = foldl extend fixed_tvs pred_sets
140 extend fixed_tvs pred_tvs
141 | fixed_tvs `intersectsVarSet` pred_tvs = fixed_tvs `unionVarSet` pred_tvs
142 | otherwise = fixed_tvs
144 pred_sets = [tyVarsOfPred pred | pred <- preds]
147 %************************************************************************
149 \subsection{Generate equations from functional dependencies}
151 %************************************************************************
156 type Equation = (TyVarSet, [(Type, Type)])
157 -- These pairs of types should be equal, for some
158 -- substitution of the tyvars in the tyvar set
159 -- INVARIANT: corresponding types aren't already equal
161 -- It's important that we have a *list* of pairs of types. Consider
162 -- class C a b c | a -> b c where ...
163 -- instance C Int x x where ...
164 -- Then, given the constraint (C Int Bool v) we should improve v to Bool,
165 -- via the equation ({x}, [(Bool,x), (v,x)])
166 -- This would not happen if the class had looked like
167 -- class C a b c | a -> b, a -> c
169 -- To "execute" the equation, make fresh type variable for each tyvar in the set,
170 -- instantiate the two types with these fresh variables, and then unify.
172 -- For example, ({a,b}, (a,Int,b), (Int,z,Bool))
173 -- We unify z with Int, but since a and b are quantified we do nothing to them
174 -- We usually act on an equation by instantiating the quantified type varaibles
175 -- to fresh type variables, and then calling the standard unifier.
177 pprEquation (qtvs, pairs)
178 = vcat [ptext SLIT("forall") <+> braces (pprWithCommas ppr (varSetElems qtvs)),
179 nest 2 (vcat [ ppr t1 <+> ptext SLIT(":=:") <+> ppr t2 | (t1,t2) <- pairs])]
182 type Pred_Loc = (PredType, SDoc) -- SDoc says where the Pred comes from
184 improve :: (Class -> [Instance]) -- Gives instances for given class
185 -> [Pred_Loc] -- Current constraints;
186 -> [(Equation,Pred_Loc,Pred_Loc)] -- Derived equalities that must also hold
187 -- (NB the above INVARIANT for type Equation)
188 -- The Pred_Locs explain which two predicates were
189 -- combined (for error messages)
192 Given a bunch of predicates that must hold, such as
194 C Int t1, C Int t2, C Bool t3, ?x::t4, ?x::t5
196 improve figures out what extra equations must hold.
197 For example, if we have
199 class C a b | a->b where ...
201 then improve will return
207 * improve does not iterate. It's possible that when we make
208 t1=t2, for example, that will in turn trigger a new equation.
209 This would happen if we also had
211 If t1=t2, we also get t7=t8.
213 improve does *not* do this extra step. It relies on the caller
216 * The equations unify types that are not already equal. So there
217 is no effect iff the result of improve is empty
222 improve inst_env preds
223 = [ eqn | group <- equivClassesByUniq (predTyUnique . fst) (filterEqPreds preds),
224 eqn <- checkGroup inst_env group ]
226 filterEqPreds = filter (not . isEqPred . fst)
227 -- Equality predicates don't have uniques
228 -- In any case, improvement *generates*, rather than
229 -- *consumes*, equality constraints
232 checkGroup :: (Class -> [Instance])
234 -> [(Equation, Pred_Loc, Pred_Loc)]
235 -- The preds are all for the same class or implicit param
237 checkGroup inst_env (p1@(IParam _ ty, _) : ips)
238 = -- For implicit parameters, all the types must match
239 [ ((emptyVarSet, [(ty,ty')]), p1, p2)
240 | p2@(IParam _ ty', _) <- ips, not (ty `tcEqType` ty')]
242 checkGroup inst_env clss@((ClassP cls _, _) : _)
243 = -- For classes life is more complicated
244 -- Suppose the class is like
245 -- classs C as | (l1 -> r1), (l2 -> r2), ... where ...
246 -- Then FOR EACH PAIR (ClassP c tys1, ClassP c tys2) in the list clss
248 -- U l1[tys1/as] = U l2[tys2/as]
249 -- (where U is a unifier)
251 -- If so, we return the pair
252 -- U r1[tys1/as] = U l2[tys2/as]
254 -- We need to do something very similar comparing each predicate
255 -- with relevant instance decls
257 instance_eqns ++ pairwise_eqns
258 -- NB: we put the instance equations first. This biases the
259 -- order so that we first improve individual constraints against the
260 -- instances (which are perhaps in a library and less likely to be
261 -- wrong; and THEN perform the pairwise checks.
262 -- The other way round, it's possible for the pairwise check to succeed
263 -- and cause a subsequent, misleading failure of one of the pair with an
264 -- instance declaration. See tcfail143.hs for an exmample
267 (cls_tvs, cls_fds) = classTvsFds cls
268 instances = inst_env cls
270 -- NOTE that we iterate over the fds first; they are typically
271 -- empty, which aborts the rest of the loop.
272 pairwise_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
273 pairwise_eqns -- This group comes from pairwise comparison
276 p1@(ClassP _ tys1, _) : rest <- tails clss,
277 p2@(ClassP _ tys2, _) <- rest,
278 eqn <- checkClsFD emptyVarSet fd cls_tvs tys1 tys2
281 instance_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
282 instance_eqns -- This group comes from comparing with instance decls
284 | fd <- cls_fds, -- Iterate through the fundeps first,
285 -- because there often are none!
286 p2@(ClassP _ tys2, _) <- clss,
287 let rough_tcs2 = trimRoughMatchTcs cls_tvs fd (roughMatchTcs tys2),
288 ispec@(Instance { is_tvs = qtvs, is_tys = tys1,
289 is_tcs = mb_tcs1 }) <- instances,
290 not (instanceCantMatch mb_tcs1 rough_tcs2),
291 eqn <- checkClsFD qtvs fd cls_tvs tys1 tys2,
292 let p1 = (mkClassPred cls tys1,
293 ptext SLIT("arising from the instance declaration at") <+>
294 ppr (getSrcLoc ispec))
297 checkClsFD :: TyVarSet -- Quantified type variables; see note below
298 -> FunDep TyVar -> [TyVar] -- One functional dependency from the class
302 checkClsFD qtvs fd clas_tvs tys1 tys2
303 -- 'qtvs' are the quantified type variables, the ones which an be instantiated
304 -- to make the types match. For example, given
305 -- class C a b | a->b where ...
306 -- instance C (Maybe x) (Tree x) where ..
308 -- and an Inst of form (C (Maybe t1) t2),
309 -- then we will call checkClsFD with
311 -- qtvs = {x}, tys1 = [Maybe x, Tree x]
312 -- tys2 = [Maybe t1, t2]
314 -- We can instantiate x to t1, and then we want to force
315 -- (Tree x) [t1/x] :=: t2
317 -- This function is also used when matching two Insts (rather than an Inst
318 -- against an instance decl. In that case, qtvs is empty, and we are doing
321 -- This function is also used by InstEnv.badFunDeps, which needs to *unify*
322 -- For the one-sided matching case, the qtvs are just from the template,
323 -- so we get matching
325 = ASSERT2( length tys1 == length tys2 &&
326 length tys1 == length clas_tvs
327 , ppr tys1 <+> ppr tys2 )
329 case tcUnifyTys bind_fn ls1 ls2 of
331 Just subst | isJust (tcUnifyTys bind_fn rs1' rs2')
332 -- Don't include any equations that already hold.
333 -- Reason: then we know if any actual improvement has happened,
334 -- in which case we need to iterate the solver
335 -- In making this check we must taking account of the fact that any
336 -- qtvs that aren't already instantiated can be instantiated to anything
340 | otherwise -- Aha! A useful equation
341 -> [ (qtvs', zip rs1' rs2')]
342 -- We could avoid this substTy stuff by producing the eqn
343 -- (qtvs, ls1++rs1, ls2++rs2)
344 -- which will re-do the ls1/ls2 unification when the equation is
345 -- executed. What we're doing instead is recording the partial
346 -- work of the ls1/ls2 unification leaving a smaller unification problem
348 rs1' = substTys subst rs1
349 rs2' = substTys subst rs2
350 qtvs' = filterVarSet (`notElemTvSubst` subst) qtvs
351 -- qtvs' are the quantified type variables
352 -- that have not been substituted out
354 -- Eg. class C a b | a -> b
355 -- instance C Int [y]
356 -- Given constraint C Int z
357 -- we generate the equation
360 bind_fn tv | tv `elemVarSet` qtvs = BindMe
363 (ls1, rs1) = instFD fd clas_tvs tys1
364 (ls2, rs2) = instFD fd clas_tvs tys2
366 instFD :: FunDep TyVar -> [TyVar] -> [Type] -> FunDep Type
367 instFD (ls,rs) tvs tys
368 = (map lookup ls, map lookup rs)
370 env = zipVarEnv tvs tys
371 lookup tv = lookupVarEnv_NF env tv
375 checkInstCoverage :: Class -> [Type] -> Bool
376 -- Check that the Coverage Condition is obeyed in an instance decl
377 -- For example, if we have
378 -- class theta => C a b | a -> b
380 -- Then we require fv(t2) `subset` fv(t1)
381 -- See Note [Coverage Condition] below
383 checkInstCoverage clas inst_taus
386 (tyvars, fds) = classTvsFds clas
387 fundep_ok fd = tyVarsOfTypes rs `subVarSet` tyVarsOfTypes ls
389 (ls,rs) = instFD fd tyvars inst_taus
392 Note [Coverage condition]
393 ~~~~~~~~~~~~~~~~~~~~~~~~~
394 For the coverage condition, we used to require only that
395 fv(t2) `subset` oclose(fv(t1), theta)
398 class Mul a b c | a b -> c where
401 instance Mul Int Int Int where (.*.) = (*)
402 instance Mul Int Float Float where x .*. y = fromIntegral x * y
403 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
405 In the third instance, it's not the case that fv([c]) `subset` fv(a,[b]).
406 But it is the case that fv([c]) `subset` oclose( theta, fv(a,[b]) )
408 But it is a mistake to accept the instance because then this defn:
409 f = \ b x y -> if b then x .*. [y] else y
410 makes instance inference go into a loop, because it requires the constraint
414 %************************************************************************
416 Check that a new instance decl is OK wrt fundeps
418 %************************************************************************
420 Here is the bad case:
421 class C a b | a->b where ...
422 instance C Int Bool where ...
423 instance C Int Char where ...
425 The point is that a->b, so Int in the first parameter must uniquely
426 determine the second. In general, given the same class decl, and given
428 instance C s1 s2 where ...
429 instance C t1 t2 where ...
431 Then the criterion is: if U=unify(s1,t1) then U(s2) = U(t2).
433 Matters are a little more complicated if there are free variables in
436 class D a b c | a -> b
437 instance D a b => D [(a,a)] [b] Int
438 instance D a b => D [a] [b] Bool
440 The instance decls don't overlap, because the third parameter keeps
441 them separate. But we want to make sure that given any constraint
447 checkFunDeps :: (InstEnv, InstEnv) -> Instance
448 -> Maybe [Instance] -- Nothing <=> ok
449 -- Just dfs <=> conflict with dfs
450 -- Check wheher adding DFunId would break functional-dependency constraints
451 -- Used only for instance decls defined in the module being compiled
452 checkFunDeps inst_envs ispec
453 | null bad_fundeps = Nothing
454 | otherwise = Just bad_fundeps
456 (ins_tvs, _, clas, ins_tys) = instanceHead ispec
457 ins_tv_set = mkVarSet ins_tvs
458 cls_inst_env = classInstances inst_envs clas
459 bad_fundeps = badFunDeps cls_inst_env clas ins_tv_set ins_tys
461 badFunDeps :: [Instance] -> Class
462 -> TyVarSet -> [Type] -- Proposed new instance type
464 badFunDeps cls_insts clas ins_tv_set ins_tys
465 = [ ispec | fd <- fds, -- fds is often empty
466 let trimmed_tcs = trimRoughMatchTcs clas_tvs fd rough_tcs,
467 ispec@(Instance { is_tcs = mb_tcs, is_tvs = tvs,
468 is_tys = tys }) <- cls_insts,
469 -- Filter out ones that can't possibly match,
470 -- based on the head of the fundep
471 not (instanceCantMatch trimmed_tcs mb_tcs),
472 notNull (checkClsFD (tvs `unionVarSet` ins_tv_set)
473 fd clas_tvs tys ins_tys)
476 (clas_tvs, fds) = classTvsFds clas
477 rough_tcs = roughMatchTcs ins_tys
479 trimRoughMatchTcs :: [TyVar] -> FunDep TyVar -> [Maybe Name] -> [Maybe Name]
480 -- Computing rough_tcs for a particular fundep
481 -- class C a b c | a c -> b where ...
482 -- For each instance .... => C ta tb tc
483 -- we want to match only on the types ta, tb; so our
484 -- rough-match thing must similarly be filtered.
485 -- Hence, we Nothing-ise the tb type right here
486 trimRoughMatchTcs clas_tvs (ltvs,_) mb_tcs
487 = zipWith select clas_tvs mb_tcs
489 select clas_tv mb_tc | clas_tv `elem` ltvs = mb_tc
490 | otherwise = Nothing