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, improveOne,
14 checkInstCoverage, checkFunDeps,
18 #include "HsVersions.h"
30 import Data.Maybe ( isJust )
34 %************************************************************************
36 \subsection{Close type variables}
38 %************************************************************************
40 oclose(vs,C) The result of extending the set of tyvars vs
41 using the functional dependencies from C
43 grow(vs,C) The result of extend the set of tyvars vs
44 using all conceivable links from C.
46 E.g. vs = {a}, C = {H [a] b, K (b,Int) c, Eq e}
47 Then grow(vs,C) = {a,b,c}
49 Note that grow(vs,C) `superset` grow(vs,simplify(C))
50 That is, simplfication can only shrink the result of grow.
53 oclose is conservative v `elem` oclose(vs,C)
54 one way: => v is definitely fixed by vs
56 grow is conservative if v might be fixed by vs
57 the other way: => v `elem` grow(vs,C)
59 ----------------------------------------------------------
60 (oclose preds tvs) closes the set of type variables tvs,
61 wrt functional dependencies in preds. The result is a superset
62 of the argument set. For example, if we have
63 class C a b | a->b where ...
65 oclose [C (x,y) z, C (x,p) q] {x,y} = {x,y,z}
66 because if we know x and y then that fixes z.
68 oclose is used (only) when generalising a type T; see extensive
71 Note [Important subtlety in oclose]
72 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
73 Consider (oclose (C Int t) {}), where class C a b | a->b
74 Then, since a->b, 't' is fully determined by Int, and the
75 uniform thing is to return {t}.
79 f x = e -- Generates constraint (D s Int t)
81 Then, if (oclose (D s Int t) {}) = {t}, we'll make the function
82 monomorphic in 't', thus
83 f :: forall s. D s Int t => s -> s
85 But if this function is never called, t will never be instantiated;
86 the functional dependencies that fix t may well be instance decls in
87 some importing module. But the top-level defaulting of unconstrained
88 type variales will fix t=GHC.Prim.Any, and that's simply a bug.
90 Conclusion: oclose only returns a type variable as "fixed" if it
91 depends on at least one type variable in the input fixed_tvs.
93 Remember, it's always sound for oclose to return a smaller set.
96 oclose :: [PredType] -> TyVarSet -> TyVarSet
97 oclose preds fixed_tvs
98 | null tv_fds = fixed_tvs -- Fast escape hatch for common case
99 | isEmptyVarSet fixed_tvs = emptyVarSet -- Note [Important subtlety in oclose]
100 | otherwise = loop fixed_tvs
103 | new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs
104 | otherwise = loop new_fixed_tvs
106 new_fixed_tvs = foldl extend fixed_tvs tv_fds
108 extend fixed_tvs (ls,rs)
109 | not (isEmptyVarSet ls) -- Note [Important subtlety in oclose]
110 , ls `subVarSet` fixed_tvs = fixed_tvs `unionVarSet` rs
111 | otherwise = fixed_tvs
113 tv_fds :: [(TyVarSet,TyVarSet)]
114 -- In our example, tv_fds will be [ ({x,y}, {z}), ({x,p},{q}) ]
115 -- Meaning "knowing x,y fixes z, knowing x,p fixes q"
116 tv_fds = [ (tyVarsOfTypes xs, tyVarsOfTypes ys)
117 | ClassP cls tys <- preds, -- Ignore implicit params
118 let (cls_tvs, cls_fds) = classTvsFds cls,
120 let (xs,ys) = instFD fd cls_tvs tys
124 Note [Growing the tau-tvs using constraints]
125 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
126 (grow preds tvs) is the result of extend the set of tyvars tvs
127 using all conceivable links from pred
129 E.g. tvs = {a}, preds = {H [a] b, K (b,Int) c, Eq e}
130 Then grow precs tvs = {a,b,c}
132 All the type variables from an implicit parameter are added, whether or
133 not they are mentioned in tvs; see Note [Implicit parameters and ambiguity]
136 See also Note [Ambiguity] in TcSimplify
139 grow :: [PredType] -> TyVarSet -> TyVarSet
141 | null preds = real_fixed_tvs
142 | otherwise = loop real_fixed_tvs
144 -- Add the implicit parameters;
145 -- see Note [Implicit parameters and ambiguity] in TcSimplify
146 real_fixed_tvs = foldr unionVarSet fixed_tvs ip_tvs
149 | new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs
150 | otherwise = loop new_fixed_tvs
152 new_fixed_tvs = foldl extend fixed_tvs non_ip_tvs
154 extend fixed_tvs pred_tvs
155 | fixed_tvs `intersectsVarSet` pred_tvs = fixed_tvs `unionVarSet` pred_tvs
156 | otherwise = fixed_tvs
158 (ip_tvs, non_ip_tvs) = partitionWith get_ip preds
159 get_ip (IParam _ ty) = Left (tyVarsOfType ty)
160 get_ip other = Right (tyVarsOfPred other)
163 %************************************************************************
165 \subsection{Generate equations from functional dependencies}
167 %************************************************************************
171 type Equation = (TyVarSet, [(Type, Type)])
172 -- These pairs of types should be equal, for some
173 -- substitution of the tyvars in the tyvar set
174 -- INVARIANT: corresponding types aren't already equal
176 -- It's important that we have a *list* of pairs of types. Consider
177 -- class C a b c | a -> b c where ...
178 -- instance C Int x x where ...
179 -- Then, given the constraint (C Int Bool v) we should improve v to Bool,
180 -- via the equation ({x}, [(Bool,x), (v,x)])
181 -- This would not happen if the class had looked like
182 -- class C a b c | a -> b, a -> c
184 -- To "execute" the equation, make fresh type variable for each tyvar in the set,
185 -- instantiate the two types with these fresh variables, and then unify.
187 -- For example, ({a,b}, (a,Int,b), (Int,z,Bool))
188 -- We unify z with Int, but since a and b are quantified we do nothing to them
189 -- We usually act on an equation by instantiating the quantified type varaibles
190 -- to fresh type variables, and then calling the standard unifier.
192 pprEquation (qtvs, pairs)
193 = vcat [ptext SLIT("forall") <+> braces (pprWithCommas ppr (varSetElems qtvs)),
194 nest 2 (vcat [ ppr t1 <+> ptext SLIT(":=:") <+> ppr t2 | (t1,t2) <- pairs])]
197 Given a bunch of predicates that must hold, such as
199 C Int t1, C Int t2, C Bool t3, ?x::t4, ?x::t5
201 improve figures out what extra equations must hold.
202 For example, if we have
204 class C a b | a->b where ...
206 then improve will return
212 * improve does not iterate. It's possible that when we make
213 t1=t2, for example, that will in turn trigger a new equation.
214 This would happen if we also had
216 If t1=t2, we also get t7=t8.
218 improve does *not* do this extra step. It relies on the caller
221 * The equations unify types that are not already equal. So there
222 is no effect iff the result of improve is empty
227 type Pred_Loc = (PredType, SDoc) -- SDoc says where the Pred comes from
229 improveOne :: (Class -> [Instance]) -- Gives instances for given class
230 -> Pred_Loc -- Do improvement triggered by this
231 -> [Pred_Loc] -- Current constraints
232 -> [(Equation,Pred_Loc,Pred_Loc)] -- Derived equalities that must also hold
233 -- (NB the above INVARIANT for type Equation)
234 -- The Pred_Locs explain which two predicates were
235 -- combined (for error messages)
236 -- Just do improvement triggered by a single, distinguised predicate
238 improveOne inst_env pred@(IParam ip ty, _) preds
239 = [ ((emptyVarSet, [(ty,ty2)]), pred, p2)
240 | p2@(IParam ip2 ty2, _) <- preds
242 , not (ty `tcEqType` ty2)]
244 improveOne inst_env pred@(ClassP cls tys, _) preds
245 | tys `lengthAtLeast` 2
246 = instance_eqns ++ pairwise_eqns
247 -- NB: we put the instance equations first. This biases the
248 -- order so that we first improve individual constraints against the
249 -- instances (which are perhaps in a library and less likely to be
250 -- wrong; and THEN perform the pairwise checks.
251 -- The other way round, it's possible for the pairwise check to succeed
252 -- and cause a subsequent, misleading failure of one of the pair with an
253 -- instance declaration. See tcfail143.hs for an example
255 (cls_tvs, cls_fds) = classTvsFds cls
256 instances = inst_env cls
257 rough_tcs = roughMatchTcs tys
259 -- NOTE that we iterate over the fds first; they are typically
260 -- empty, which aborts the rest of the loop.
261 pairwise_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
262 pairwise_eqns -- This group comes from pairwise comparison
265 , p2@(ClassP cls2 tys2, _) <- preds
267 , eqn <- checkClsFD emptyVarSet fd cls_tvs tys tys2
270 instance_eqns :: [(Equation,Pred_Loc,Pred_Loc)]
271 instance_eqns -- This group comes from comparing with instance decls
272 = [ (eqn, p_inst, pred)
273 | fd <- cls_fds -- Iterate through the fundeps first,
274 -- because there often are none!
275 , let trimmed_tcs = trimRoughMatchTcs cls_tvs fd rough_tcs
276 -- Trim the rough_tcs based on the head of the fundep.
277 -- Remember that instanceCantMatch treats both argumnents
278 -- symmetrically, so it's ok to trim the rough_tcs,
279 -- rather than trimming each inst_tcs in turn
280 , ispec@(Instance { is_tvs = qtvs, is_tys = tys_inst,
281 is_tcs = inst_tcs }) <- instances
282 , not (instanceCantMatch inst_tcs trimmed_tcs)
283 , eqn <- checkClsFD qtvs fd cls_tvs tys_inst tys
284 , let p_inst = (mkClassPred cls tys_inst,
285 ptext SLIT("arising from the instance declaration at")
286 <+> ppr (getSrcLoc ispec))
289 improveOne inst_env eq_pred preds
293 checkClsFD :: TyVarSet -- Quantified type variables; see note below
294 -> FunDep TyVar -> [TyVar] -- One functional dependency from the class
298 checkClsFD qtvs fd clas_tvs tys1 tys2
299 -- 'qtvs' are the quantified type variables, the ones which an be instantiated
300 -- to make the types match. For example, given
301 -- class C a b | a->b where ...
302 -- instance C (Maybe x) (Tree x) where ..
304 -- and an Inst of form (C (Maybe t1) t2),
305 -- then we will call checkClsFD with
307 -- qtvs = {x}, tys1 = [Maybe x, Tree x]
308 -- tys2 = [Maybe t1, t2]
310 -- We can instantiate x to t1, and then we want to force
311 -- (Tree x) [t1/x] :=: t2
313 -- This function is also used when matching two Insts (rather than an Inst
314 -- against an instance decl. In that case, qtvs is empty, and we are doing
317 -- This function is also used by InstEnv.badFunDeps, which needs to *unify*
318 -- For the one-sided matching case, the qtvs are just from the template,
319 -- so we get matching
321 = ASSERT2( length tys1 == length tys2 &&
322 length tys1 == length clas_tvs
323 , ppr tys1 <+> ppr tys2 )
325 case tcUnifyTys bind_fn ls1 ls2 of
327 Just subst | isJust (tcUnifyTys bind_fn rs1' rs2')
328 -- Don't include any equations that already hold.
329 -- Reason: then we know if any actual improvement has happened,
330 -- in which case we need to iterate the solver
331 -- In making this check we must taking account of the fact that any
332 -- qtvs that aren't already instantiated can be instantiated to anything
336 | otherwise -- Aha! A useful equation
337 -> [ (qtvs', zip rs1' rs2')]
338 -- We could avoid this substTy stuff by producing the eqn
339 -- (qtvs, ls1++rs1, ls2++rs2)
340 -- which will re-do the ls1/ls2 unification when the equation is
341 -- executed. What we're doing instead is recording the partial
342 -- work of the ls1/ls2 unification leaving a smaller unification problem
344 rs1' = substTys subst rs1
345 rs2' = substTys subst rs2
346 qtvs' = filterVarSet (`notElemTvSubst` subst) qtvs
347 -- qtvs' are the quantified type variables
348 -- that have not been substituted out
350 -- Eg. class C a b | a -> b
351 -- instance C Int [y]
352 -- Given constraint C Int z
353 -- we generate the equation
356 bind_fn tv | tv `elemVarSet` qtvs = BindMe
359 (ls1, rs1) = instFD fd clas_tvs tys1
360 (ls2, rs2) = instFD fd clas_tvs tys2
362 instFD :: FunDep TyVar -> [TyVar] -> [Type] -> FunDep Type
363 instFD (ls,rs) tvs tys
364 = (map lookup ls, map lookup rs)
366 env = zipVarEnv tvs tys
367 lookup tv = lookupVarEnv_NF env tv
371 checkInstCoverage :: Class -> [Type] -> Bool
372 -- Check that the Coverage Condition is obeyed in an instance decl
373 -- For example, if we have
374 -- class theta => C a b | a -> b
376 -- Then we require fv(t2) `subset` fv(t1)
377 -- See Note [Coverage Condition] below
379 checkInstCoverage clas inst_taus
382 (tyvars, fds) = classTvsFds clas
383 fundep_ok fd = tyVarsOfTypes rs `subVarSet` tyVarsOfTypes ls
385 (ls,rs) = instFD fd tyvars inst_taus
388 Note [Coverage condition]
389 ~~~~~~~~~~~~~~~~~~~~~~~~~
390 For the coverage condition, we used to require only that
391 fv(t2) `subset` oclose(fv(t1), theta)
394 class Mul a b c | a b -> c where
397 instance Mul Int Int Int where (.*.) = (*)
398 instance Mul Int Float Float where x .*. y = fromIntegral x * y
399 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
401 In the third instance, it's not the case that fv([c]) `subset` fv(a,[b]).
402 But it is the case that fv([c]) `subset` oclose( theta, fv(a,[b]) )
404 But it is a mistake to accept the instance because then this defn:
405 f = \ b x y -> if b then x .*. [y] else y
406 makes instance inference go into a loop, because it requires the constraint
410 %************************************************************************
412 Check that a new instance decl is OK wrt fundeps
414 %************************************************************************
416 Here is the bad case:
417 class C a b | a->b where ...
418 instance C Int Bool where ...
419 instance C Int Char where ...
421 The point is that a->b, so Int in the first parameter must uniquely
422 determine the second. In general, given the same class decl, and given
424 instance C s1 s2 where ...
425 instance C t1 t2 where ...
427 Then the criterion is: if U=unify(s1,t1) then U(s2) = U(t2).
429 Matters are a little more complicated if there are free variables in
432 class D a b c | a -> b
433 instance D a b => D [(a,a)] [b] Int
434 instance D a b => D [a] [b] Bool
436 The instance decls don't overlap, because the third parameter keeps
437 them separate. But we want to make sure that given any constraint
443 checkFunDeps :: (InstEnv, InstEnv) -> Instance
444 -> Maybe [Instance] -- Nothing <=> ok
445 -- Just dfs <=> conflict with dfs
446 -- Check wheher adding DFunId would break functional-dependency constraints
447 -- Used only for instance decls defined in the module being compiled
448 checkFunDeps inst_envs ispec
449 | null bad_fundeps = Nothing
450 | otherwise = Just bad_fundeps
452 (ins_tvs, _, clas, ins_tys) = instanceHead ispec
453 ins_tv_set = mkVarSet ins_tvs
454 cls_inst_env = classInstances inst_envs clas
455 bad_fundeps = badFunDeps cls_inst_env clas ins_tv_set ins_tys
457 badFunDeps :: [Instance] -> Class
458 -> TyVarSet -> [Type] -- Proposed new instance type
460 badFunDeps cls_insts clas ins_tv_set ins_tys
461 = [ ispec | fd <- fds, -- fds is often empty
462 let trimmed_tcs = trimRoughMatchTcs clas_tvs fd rough_tcs,
463 ispec@(Instance { is_tcs = inst_tcs, is_tvs = tvs,
464 is_tys = tys }) <- cls_insts,
465 -- Filter out ones that can't possibly match,
466 -- based on the head of the fundep
467 not (instanceCantMatch inst_tcs trimmed_tcs),
468 notNull (checkClsFD (tvs `unionVarSet` ins_tv_set)
469 fd clas_tvs tys ins_tys)
472 (clas_tvs, fds) = classTvsFds clas
473 rough_tcs = roughMatchTcs ins_tys
475 trimRoughMatchTcs :: [TyVar] -> FunDep TyVar -> [Maybe Name] -> [Maybe Name]
476 -- Computing rough_tcs for a particular fundep
477 -- class C a b c | a -> b where ...
478 -- For each instance .... => C ta tb tc
479 -- we want to match only on the types ta, tc; so our
480 -- rough-match thing must similarly be filtered.
481 -- Hence, we Nothing-ise the tb type right here
482 trimRoughMatchTcs clas_tvs (_,rtvs) mb_tcs
483 = zipWith select clas_tvs mb_tcs
485 select clas_tv mb_tc | clas_tv `elem` rtvs = Nothing