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, pprEquationDoc,
11 oclose, grow, improve, checkInstFDs, checkClsFD, pprFundeps
14 #include "HsVersions.h"
16 import Name ( getSrcLoc )
17 import Var ( Id, TyVar )
18 import Class ( Class, FunDep, classTvsFds )
19 import Subst ( mkSubst, emptyInScopeSet, substTy )
20 import TcType ( Type, ThetaType, SourceType(..), PredType,
21 predTyUnique, mkClassPred, tyVarsOfTypes, tyVarsOfPred,
22 unifyTyListsX, unifyExtendTysX, tcEqType
29 import Maybes ( maybeToBool )
30 import ListSetOps ( equivClassesByUniq )
34 %************************************************************************
36 \subsection{Close type variables}
38 %************************************************************************
40 (oclose preds tvs) closes the set of type variables tvs,
41 wrt functional dependencies in preds. The result is a superset
42 of the argument set. For example, if we have
43 class C a b | a->b where ...
45 oclose [C (x,y) z, C (x,p) q] {x,y} = {x,y,z}
46 because if we know x and y then that fixes z.
52 a) When determining ambiguity. The type
53 forall a,b. C a b => a
54 is not ambiguous (given the above class decl for C) because
57 b) When generalising a type T. Usually we take FV(T) \ FV(Env),
60 where the '+' is the oclosure operation. Notice that we do not
61 take FV(T)+. This puzzled me for a bit. Consider
65 and suppose e have that E :: C a b => a, and suppose that b is
66 free in the environment. Then we quantify over 'a' only, giving
67 the type forall a. C a b => a. Since a->b but we don't have b->a,
68 we might have instance decls like
69 instance C Bool Int where ...
70 instance C Char Int where ...
71 so knowing that b=Int doesn't fix 'a'; so we quantify over it.
76 If we have class C a b => D a b where ....
77 class D a b | a -> b where ...
78 and the preds are [C (x,y) z], then we want to see the fd in D,
79 even though it is not explicit in C, giving [({x,y},{z})]
81 Similarly for instance decls? E.g. Suppose we have
82 instance C a b => Eq (T a b) where ...
83 and we infer a type t with constraints Eq (T a b) for a particular
84 expression, and suppose that 'a' is free in the environment.
85 We could generalise to
86 forall b. Eq (T a b) => t
87 but if we reduced the constraint, to C a b, we'd see that 'a' determines
88 b, so that a better type might be
89 t (with free constraint C a b)
90 Perhaps it doesn't matter, because we'll still force b to be a
91 particular type at the call sites. Generalising over too many
92 variables (provided we don't shadow anything by quantifying over a
93 variable that is actually free in the envt) may postpone errors; it
94 won't hide them altogether.
98 oclose :: [PredType] -> TyVarSet -> TyVarSet
99 oclose preds fixed_tvs
100 | null tv_fds = fixed_tvs -- Fast escape hatch for common case
101 | otherwise = loop fixed_tvs
104 | new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs
105 | otherwise = loop new_fixed_tvs
107 new_fixed_tvs = foldl extend fixed_tvs tv_fds
109 extend fixed_tvs (ls,rs) | ls `subVarSet` fixed_tvs = fixed_tvs `unionVarSet` rs
110 | otherwise = fixed_tvs
112 tv_fds :: [(TyVarSet,TyVarSet)]
113 -- In our example, tv_fds will be [ ({x,y}, {z}), ({x,p},{q}) ]
114 -- Meaning "knowing x,y fixes z, knowing x,p fixes q"
115 tv_fds = [ (tyVarsOfTypes xs, tyVarsOfTypes ys)
116 | ClassP cls tys <- preds, -- Ignore implicit params
117 let (cls_tvs, cls_fds) = classTvsFds cls,
119 let (xs,ys) = instFD fd cls_tvs tys
124 grow :: [PredType] -> TyVarSet -> TyVarSet
126 | null pred_sets = fixed_tvs
127 | otherwise = loop fixed_tvs
130 | new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs
131 | otherwise = loop new_fixed_tvs
133 new_fixed_tvs = foldl extend fixed_tvs pred_sets
135 extend fixed_tvs pred_tvs
136 | fixed_tvs `intersectsVarSet` pred_tvs = fixed_tvs `unionVarSet` pred_tvs
137 | otherwise = fixed_tvs
139 pred_sets = [tyVarsOfPred pred | pred <- preds]
142 %************************************************************************
144 \subsection{Generate equations from functional dependencies}
146 %************************************************************************
151 type Equation = (TyVarSet, Type, Type) -- These two types should be equal, for some
152 -- substitution of the tyvars in the tyvar set
153 -- For example, ({a,b}, (a,Int,b), (Int,z,Bool))
154 -- We unify z with Int, but since a and b are quantified we do nothing to them
155 -- We usually act on an equation by instantiating the quantified type varaibles
156 -- to fresh type variables, and then calling the standard unifier.
158 -- INVARIANT: they aren't already equal
162 pprEquationDoc (eqn, doc) = vcat [pprEquation eqn, nest 2 doc]
164 pprEquation (qtvs, t1, t2) = ptext SLIT("forall") <+> braces (pprWithCommas ppr (varSetElems qtvs))
165 <+> ppr t1 <+> ptext SLIT(":=:") <+> ppr t2
168 improve :: InstEnv Id -- Gives instances for given class
169 -> [(PredType,SDoc)] -- Current constraints; doc says where they come from
170 -> [(Equation,SDoc)] -- Derived equalities that must also hold
171 -- (NB the above INVARIANT for type Equation)
172 -- The SDoc explains why the equation holds (for error messages)
174 type InstEnv a = Class -> [(TyVarSet, [Type], a)]
175 -- This is a bit clumsy, because InstEnv is really
176 -- defined in module InstEnv. However, we don't want
177 -- to define it (and ClsInstEnv) here because InstEnv
178 -- is their home. Nor do we want to make a recursive
179 -- module group (InstEnv imports stuff from FunDeps).
182 Given a bunch of predicates that must hold, such as
184 C Int t1, C Int t2, C Bool t3, ?x::t4, ?x::t5
186 improve figures out what extra equations must hold.
187 For example, if we have
189 class C a b | a->b where ...
191 then improve will return
197 * improve does not iterate. It's possible that when we make
198 t1=t2, for example, that will in turn trigger a new equation.
199 This would happen if we also had
201 If t1=t2, we also get t7=t8.
203 improve does *not* do this extra step. It relies on the caller
206 * The equations unify types that are not already equal. So there
207 is no effect iff the result of improve is empty
212 improve inst_env preds
213 = [ eqn | group <- equivClassesByUniq (predTyUnique . fst) preds,
214 eqn <- checkGroup inst_env group ]
217 checkGroup :: InstEnv Id -> [(PredType,SDoc)] -> [(Equation, SDoc)]
218 -- The preds are all for the same class or implicit param
220 checkGroup inst_env (p1@(IParam _ ty, _) : ips)
221 = -- For implicit parameters, all the types must match
222 [ ((emptyVarSet, ty, ty'), mkEqnMsg p1 p2)
223 | p2@(IParam _ ty', _) <- ips, not (ty `tcEqType` ty')]
225 checkGroup inst_env clss@((ClassP cls _, _) : _)
226 = -- For classes life is more complicated
227 -- Suppose the class is like
228 -- classs C as | (l1 -> r1), (l2 -> r2), ... where ...
229 -- Then FOR EACH PAIR (ClassP c tys1, ClassP c tys2) in the list clss
231 -- U l1[tys1/as] = U l2[tys2/as]
232 -- (where U is a unifier)
234 -- If so, we return the pair
235 -- U r1[tys1/as] = U l2[tys2/as]
237 -- We need to do something very similar comparing each predicate
238 -- with relevant instance decls
239 pairwise_eqns ++ instance_eqns
242 (cls_tvs, cls_fds) = classTvsFds cls
243 cls_inst_env = inst_env cls
245 -- NOTE that we iterate over the fds first; they are typically
246 -- empty, which aborts the rest of the loop.
247 pairwise_eqns :: [(Equation,SDoc)]
248 pairwise_eqns -- This group comes from pairwise comparison
249 = [ (eqn, mkEqnMsg p1 p2)
251 p1@(ClassP _ tys1, _) : rest <- tails clss,
252 p2@(ClassP _ tys2, _) <- rest,
253 eqn <- checkClsFD emptyVarSet fd cls_tvs tys1 tys2
256 instance_eqns :: [(Equation,SDoc)]
257 instance_eqns -- This group comes from comparing with instance decls
258 = [ (eqn, mkEqnMsg p1 p2)
260 (qtvs, tys1, dfun_id) <- cls_inst_env,
261 let p1 = (mkClassPred cls tys1,
262 ptext SLIT("arising from the instance declaration at") <+> ppr (getSrcLoc dfun_id)),
263 p2@(ClassP _ tys2, _) <- clss,
264 eqn <- checkClsFD qtvs fd cls_tvs tys1 tys2
267 mkEqnMsg (pred1,from1) (pred2,from2)
268 = vcat [ptext SLIT("When using functional dependencies to combine"),
269 nest 2 (sep [ppr pred1 <> comma, nest 2 from1]),
270 nest 2 (sep [ppr pred2 <> comma, nest 2 from2])]
273 checkClsFD :: TyVarSet -- Quantified type variables; see note below
274 -> FunDep TyVar -> [TyVar] -- One functional dependency from the class
278 checkClsFD qtvs fd clas_tvs tys1 tys2
279 -- 'qtvs' are the quantified type variables, the ones which an be instantiated
280 -- to make the types match. For example, given
281 -- class C a b | a->b where ...
282 -- instance C (Maybe x) (Tree x) where ..
283 -- and an Inst of form (C (Maybe t1 t2),
284 -- then we will call checkClsFD with
286 -- qtvs = {x}, tys1 = [Maybe x, Tree x]
287 -- tys2 = [Maybe t1, t2]
289 -- We can instantiate x to t1, and then we want to force
290 -- Tree x [t1/x] :=: t2
292 -- We use 'unify' even though we are often only matching
293 -- unifyTyListsX will only bind variables in qtvs, so it's OK!
294 = case unifyTyListsX qtvs ls1 ls2 of
296 Just unif -> -- pprTrace "checkFD" (vcat [ppr_fd fd,
297 -- ppr (varSetElems qtvs) <+> (ppr ls1 $$ ppr ls2),
299 [ (qtvs', substTy full_unif r1, substTy full_unif r2)
300 | (r1,r2) <- rs1 `zip` rs2,
301 not (maybeToBool (unifyExtendTysX qtvs unif r1 r2))]
302 -- Don't include any equations that already hold
303 -- taking account of the fact that any qtvs that aren't
304 -- already instantiated can be instantiated to anything at all
305 -- NB: qtvs, not qtvs' because unifyExtendTysX only tries to
306 -- look template tyvars up in the substitution
308 full_unif = mkSubst emptyInScopeSet unif
309 -- No for-alls in sight; hmm
311 qtvs' = filterVarSet (\v -> not (v `elemSubstEnv` unif)) qtvs
312 -- qtvs' are the quantified type variables
313 -- that have not been substituted out
315 (ls1, rs1) = instFD fd clas_tvs tys1
316 (ls2, rs2) = instFD fd clas_tvs tys2
318 instFD :: FunDep TyVar -> [TyVar] -> [Type] -> FunDep Type
319 instFD (ls,rs) tvs tys
320 = (map lookup ls, map lookup rs)
322 env = zipVarEnv tvs tys
323 lookup tv = lookupVarEnv_NF env tv
327 checkInstFDs :: ThetaType -> Class -> [Type] -> Bool
328 -- Check that functional dependencies are obeyed in an instance decl
329 -- For example, if we have
330 -- class theta => C a b | a -> b
332 -- Then we require fv(t2) `subset` oclose(fv(t1), theta)
334 checkInstFDs theta clas inst_taus
337 (tyvars, fds) = classTvsFds clas
338 fundep_ok fd = tyVarsOfTypes rs `subVarSet` oclose theta (tyVarsOfTypes ls)
340 (ls,rs) = instFD fd tyvars inst_taus
343 %************************************************************************
345 \subsection{Miscellaneous}
347 %************************************************************************
350 pprFundeps :: Outputable a => [FunDep a] -> SDoc
351 pprFundeps [] = empty
352 pprFundeps fds = hsep (ptext SLIT("|") : punctuate comma (map ppr_fd fds))
354 ppr_fd (us, vs) = hsep [interppSP us, ptext SLIT("->"), interppSP vs]