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Diffstat (limited to 'compiler/types/FunDeps.lhs')
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diff --git a/compiler/types/FunDeps.lhs b/compiler/types/FunDeps.lhs new file mode 100644 index 0000000000..9347f5f665 --- /dev/null +++ b/compiler/types/FunDeps.lhs @@ -0,0 +1,500 @@ +% +% (c) The GRASP/AQUA Project, Glasgow University, 2000 +% +\section[FunDeps]{FunDeps - functional dependencies} + +It's better to read it as: "if we know these, then we're going to know these" + +\begin{code} +module FunDeps ( + Equation, pprEquation, + oclose, grow, improve, + checkInstCoverage, checkFunDeps, + pprFundeps + ) where + +#include "HsVersions.h" + +import Name ( Name, getSrcLoc ) +import Var ( TyVar ) +import Class ( Class, FunDep, classTvsFds ) +import Unify ( tcUnifyTys, BindFlag(..) ) +import Type ( substTys, notElemTvSubst ) +import TcType ( Type, PredType(..), tcEqType, + predTyUnique, mkClassPred, tyVarsOfTypes, tyVarsOfPred ) +import InstEnv ( Instance(..), InstEnv, instanceHead, classInstances, + instanceCantMatch, roughMatchTcs ) +import VarSet +import VarEnv +import Outputable +import Util ( notNull ) +import List ( tails ) +import Maybe ( isJust ) +import ListSetOps ( equivClassesByUniq ) +\end{code} + + +%************************************************************************ +%* * +\subsection{Close type variables} +%* * +%************************************************************************ + +(oclose preds tvs) closes the set of type variables tvs, +wrt functional dependencies in preds. The result is a superset +of the argument set. For example, if we have + class C a b | a->b where ... +then + oclose [C (x,y) z, C (x,p) q] {x,y} = {x,y,z} +because if we know x and y then that fixes z. + +Using oclose +~~~~~~~~~~~~ +oclose is used + +a) When determining ambiguity. The type + forall a,b. C a b => a +is not ambiguous (given the above class decl for C) because +a determines b. + +b) When generalising a type T. Usually we take FV(T) \ FV(Env), +but in fact we need + FV(T) \ (FV(Env)+) +where the '+' is the oclosure operation. Notice that we do not +take FV(T)+. This puzzled me for a bit. Consider + + f = E + +and suppose e have that E :: C a b => a, and suppose that b is +free in the environment. Then we quantify over 'a' only, giving +the type forall a. C a b => a. Since a->b but we don't have b->a, +we might have instance decls like + instance C Bool Int where ... + instance C Char Int where ... +so knowing that b=Int doesn't fix 'a'; so we quantify over it. + + --------------- + A WORRY: ToDo! + --------------- +If we have class C a b => D a b where .... + class D a b | a -> b where ... +and the preds are [C (x,y) z], then we want to see the fd in D, +even though it is not explicit in C, giving [({x,y},{z})] + +Similarly for instance decls? E.g. Suppose we have + instance C a b => Eq (T a b) where ... +and we infer a type t with constraints Eq (T a b) for a particular +expression, and suppose that 'a' is free in the environment. +We could generalise to + forall b. Eq (T a b) => t +but if we reduced the constraint, to C a b, we'd see that 'a' determines +b, so that a better type might be + t (with free constraint C a b) +Perhaps it doesn't matter, because we'll still force b to be a +particular type at the call sites. Generalising over too many +variables (provided we don't shadow anything by quantifying over a +variable that is actually free in the envt) may postpone errors; it +won't hide them altogether. + + +\begin{code} +oclose :: [PredType] -> TyVarSet -> TyVarSet +oclose preds fixed_tvs + | null tv_fds = fixed_tvs -- Fast escape hatch for common case + | otherwise = loop fixed_tvs + where + loop fixed_tvs + | new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs + | otherwise = loop new_fixed_tvs + where + new_fixed_tvs = foldl extend fixed_tvs tv_fds + + extend fixed_tvs (ls,rs) | ls `subVarSet` fixed_tvs = fixed_tvs `unionVarSet` rs + | otherwise = fixed_tvs + + tv_fds :: [(TyVarSet,TyVarSet)] + -- In our example, tv_fds will be [ ({x,y}, {z}), ({x,p},{q}) ] + -- Meaning "knowing x,y fixes z, knowing x,p fixes q" + tv_fds = [ (tyVarsOfTypes xs, tyVarsOfTypes ys) + | ClassP cls tys <- preds, -- Ignore implicit params + let (cls_tvs, cls_fds) = classTvsFds cls, + fd <- cls_fds, + let (xs,ys) = instFD fd cls_tvs tys + ] +\end{code} + +\begin{code} +grow :: [PredType] -> TyVarSet -> TyVarSet +grow preds fixed_tvs + | null preds = fixed_tvs + | otherwise = loop fixed_tvs + where + loop fixed_tvs + | new_fixed_tvs `subVarSet` fixed_tvs = fixed_tvs + | otherwise = loop new_fixed_tvs + where + new_fixed_tvs = foldl extend fixed_tvs pred_sets + + extend fixed_tvs pred_tvs + | fixed_tvs `intersectsVarSet` pred_tvs = fixed_tvs `unionVarSet` pred_tvs + | otherwise = fixed_tvs + + pred_sets = [tyVarsOfPred pred | pred <- preds] +\end{code} + +%************************************************************************ +%* * +\subsection{Generate equations from functional dependencies} +%* * +%************************************************************************ + + +\begin{code} +---------- +type Equation = (TyVarSet, [(Type, Type)]) +-- These pairs of types should be equal, for some +-- substitution of the tyvars in the tyvar set +-- INVARIANT: corresponding types aren't already equal + +-- It's important that we have a *list* of pairs of types. Consider +-- class C a b c | a -> b c where ... +-- instance C Int x x where ... +-- Then, given the constraint (C Int Bool v) we should improve v to Bool, +-- via the equation ({x}, [(Bool,x), (v,x)]) +-- This would not happen if the class had looked like +-- class C a b c | a -> b, a -> c + +-- To "execute" the equation, make fresh type variable for each tyvar in the set, +-- instantiate the two types with these fresh variables, and then unify. +-- +-- For example, ({a,b}, (a,Int,b), (Int,z,Bool)) +-- We unify z with Int, but since a and b are quantified we do nothing to them +-- We usually act on an equation by instantiating the quantified type varaibles +-- to fresh type variables, and then calling the standard unifier. + +pprEquation (qtvs, pairs) + = vcat [ptext SLIT("forall") <+> braces (pprWithCommas ppr (varSetElems qtvs)), + nest 2 (vcat [ ppr t1 <+> ptext SLIT(":=:") <+> ppr t2 | (t1,t2) <- pairs])] + +---------- +type Pred_Loc = (PredType, SDoc) -- SDoc says where the Pred comes from + +improve :: (Class -> [Instance]) -- Gives instances for given class + -> [Pred_Loc] -- Current constraints; + -> [(Equation,Pred_Loc,Pred_Loc)] -- Derived equalities that must also hold + -- (NB the above INVARIANT for type Equation) + -- The Pred_Locs explain which two predicates were + -- combined (for error messages) +\end{code} + +Given a bunch of predicates that must hold, such as + + C Int t1, C Int t2, C Bool t3, ?x::t4, ?x::t5 + +improve figures out what extra equations must hold. +For example, if we have + + class C a b | a->b where ... + +then improve will return + + [(t1,t2), (t4,t5)] + +NOTA BENE: + + * improve does not iterate. It's possible that when we make + t1=t2, for example, that will in turn trigger a new equation. + This would happen if we also had + C t1 t7, C t2 t8 + If t1=t2, we also get t7=t8. + + improve does *not* do this extra step. It relies on the caller + doing so. + + * The equations unify types that are not already equal. So there + is no effect iff the result of improve is empty + + + +\begin{code} +improve inst_env preds + = [ eqn | group <- equivClassesByUniq (predTyUnique . fst) preds, + eqn <- checkGroup inst_env group ] + +---------- +checkGroup :: (Class -> [Instance]) + -> [Pred_Loc] + -> [(Equation, Pred_Loc, Pred_Loc)] + -- The preds are all for the same class or implicit param + +checkGroup inst_env (p1@(IParam _ ty, _) : ips) + = -- For implicit parameters, all the types must match + [ ((emptyVarSet, [(ty,ty')]), p1, p2) + | p2@(IParam _ ty', _) <- ips, not (ty `tcEqType` ty')] + +checkGroup inst_env clss@((ClassP cls _, _) : _) + = -- For classes life is more complicated + -- Suppose the class is like + -- classs C as | (l1 -> r1), (l2 -> r2), ... where ... + -- Then FOR EACH PAIR (ClassP c tys1, ClassP c tys2) in the list clss + -- we check whether + -- U l1[tys1/as] = U l2[tys2/as] + -- (where U is a unifier) + -- + -- If so, we return the pair + -- U r1[tys1/as] = U l2[tys2/as] + -- + -- We need to do something very similar comparing each predicate + -- with relevant instance decls + + instance_eqns ++ pairwise_eqns + -- NB: we put the instance equations first. This biases the + -- order so that we first improve individual constraints against the + -- instances (which are perhaps in a library and less likely to be + -- wrong; and THEN perform the pairwise checks. + -- The other way round, it's possible for the pairwise check to succeed + -- and cause a subsequent, misleading failure of one of the pair with an + -- instance declaration. See tcfail143.hs for an exmample + + where + (cls_tvs, cls_fds) = classTvsFds cls + instances = inst_env cls + + -- NOTE that we iterate over the fds first; they are typically + -- empty, which aborts the rest of the loop. + pairwise_eqns :: [(Equation,Pred_Loc,Pred_Loc)] + pairwise_eqns -- This group comes from pairwise comparison + = [ (eqn, p1, p2) + | fd <- cls_fds, + p1@(ClassP _ tys1, _) : rest <- tails clss, + p2@(ClassP _ tys2, _) <- rest, + eqn <- checkClsFD emptyVarSet fd cls_tvs tys1 tys2 + ] + + instance_eqns :: [(Equation,Pred_Loc,Pred_Loc)] + instance_eqns -- This group comes from comparing with instance decls + = [ (eqn, p1, p2) + | fd <- cls_fds, -- Iterate through the fundeps first, + -- because there often are none! + p2@(ClassP _ tys2, _) <- clss, + let rough_tcs2 = trimRoughMatchTcs cls_tvs fd (roughMatchTcs tys2), + ispec@(Instance { is_tvs = qtvs, is_tys = tys1, + is_tcs = mb_tcs1 }) <- instances, + not (instanceCantMatch mb_tcs1 rough_tcs2), + eqn <- checkClsFD qtvs fd cls_tvs tys1 tys2, + let p1 = (mkClassPred cls tys1, + ptext SLIT("arising from the instance declaration at") <+> + ppr (getSrcLoc ispec)) + ] +---------- +checkClsFD :: TyVarSet -- Quantified type variables; see note below + -> FunDep TyVar -> [TyVar] -- One functional dependency from the class + -> [Type] -> [Type] + -> [Equation] + +checkClsFD qtvs fd clas_tvs tys1 tys2 +-- 'qtvs' are the quantified type variables, the ones which an be instantiated +-- to make the types match. For example, given +-- class C a b | a->b where ... +-- instance C (Maybe x) (Tree x) where .. +-- +-- and an Inst of form (C (Maybe t1) t2), +-- then we will call checkClsFD with +-- +-- qtvs = {x}, tys1 = [Maybe x, Tree x] +-- tys2 = [Maybe t1, t2] +-- +-- We can instantiate x to t1, and then we want to force +-- (Tree x) [t1/x] :=: t2 +-- +-- This function is also used when matching two Insts (rather than an Inst +-- against an instance decl. In that case, qtvs is empty, and we are doing +-- an equality check +-- +-- This function is also used by InstEnv.badFunDeps, which needs to *unify* +-- For the one-sided matching case, the qtvs are just from the template, +-- so we get matching +-- + = ASSERT2( length tys1 == length tys2 && + length tys1 == length clas_tvs + , ppr tys1 <+> ppr tys2 ) + + case tcUnifyTys bind_fn ls1 ls2 of + Nothing -> [] + Just subst | isJust (tcUnifyTys bind_fn rs1' rs2') + -- Don't include any equations that already hold. + -- Reason: then we know if any actual improvement has happened, + -- in which case we need to iterate the solver + -- In making this check we must taking account of the fact that any + -- qtvs that aren't already instantiated can be instantiated to anything + -- at all + -> [] + + | otherwise -- Aha! A useful equation + -> [ (qtvs', zip rs1' rs2')] + -- We could avoid this substTy stuff by producing the eqn + -- (qtvs, ls1++rs1, ls2++rs2) + -- which will re-do the ls1/ls2 unification when the equation is + -- executed. What we're doing instead is recording the partial + -- work of the ls1/ls2 unification leaving a smaller unification problem + where + rs1' = substTys subst rs1 + rs2' = substTys subst rs2 + qtvs' = filterVarSet (`notElemTvSubst` subst) qtvs + -- qtvs' are the quantified type variables + -- that have not been substituted out + -- + -- Eg. class C a b | a -> b + -- instance C Int [y] + -- Given constraint C Int z + -- we generate the equation + -- ({y}, [y], z) + where + bind_fn tv | tv `elemVarSet` qtvs = BindMe + | otherwise = Skolem + + (ls1, rs1) = instFD fd clas_tvs tys1 + (ls2, rs2) = instFD fd clas_tvs tys2 + +instFD :: FunDep TyVar -> [TyVar] -> [Type] -> FunDep Type +instFD (ls,rs) tvs tys + = (map lookup ls, map lookup rs) + where + env = zipVarEnv tvs tys + lookup tv = lookupVarEnv_NF env tv +\end{code} + +\begin{code} +checkInstCoverage :: Class -> [Type] -> Bool +-- Check that the Coverage Condition is obeyed in an instance decl +-- For example, if we have +-- class theta => C a b | a -> b +-- instance C t1 t2 +-- Then we require fv(t2) `subset` fv(t1) +-- See Note [Coverage Condition] below + +checkInstCoverage clas inst_taus + = all fundep_ok fds + where + (tyvars, fds) = classTvsFds clas + fundep_ok fd = tyVarsOfTypes rs `subVarSet` tyVarsOfTypes ls + where + (ls,rs) = instFD fd tyvars inst_taus +\end{code} + +Note [Coverage condition] +~~~~~~~~~~~~~~~~~~~~~~~~~ +For the coverage condition, we used to require only that + fv(t2) `subset` oclose(fv(t1), theta) + +Example: + class Mul a b c | a b -> c where + (.*.) :: a -> b -> c + + instance Mul Int Int Int where (.*.) = (*) + instance Mul Int Float Float where x .*. y = fromIntegral x * y + instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v + +In the third instance, it's not the case that fv([c]) `subset` fv(a,[b]). +But it is the case that fv([c]) `subset` oclose( theta, fv(a,[b]) ) + +But it is a mistake to accept the instance because then this defn: + f = \ b x y -> if b then x .*. [y] else y +makes instance inference go into a loop, because it requires the constraint + Mul a [b] b + + +%************************************************************************ +%* * + Check that a new instance decl is OK wrt fundeps +%* * +%************************************************************************ + +Here is the bad case: + class C a b | a->b where ... + instance C Int Bool where ... + instance C Int Char where ... + +The point is that a->b, so Int in the first parameter must uniquely +determine the second. In general, given the same class decl, and given + + instance C s1 s2 where ... + instance C t1 t2 where ... + +Then the criterion is: if U=unify(s1,t1) then U(s2) = U(t2). + +Matters are a little more complicated if there are free variables in +the s2/t2. + + class D a b c | a -> b + instance D a b => D [(a,a)] [b] Int + instance D a b => D [a] [b] Bool + +The instance decls don't overlap, because the third parameter keeps +them separate. But we want to make sure that given any constraint + D s1 s2 s3 +if s1 matches + + +\begin{code} +checkFunDeps :: (InstEnv, InstEnv) -> Instance + -> Maybe [Instance] -- Nothing <=> ok + -- Just dfs <=> conflict with dfs +-- Check wheher adding DFunId would break functional-dependency constraints +-- Used only for instance decls defined in the module being compiled +checkFunDeps inst_envs ispec + | null bad_fundeps = Nothing + | otherwise = Just bad_fundeps + where + (ins_tvs, _, clas, ins_tys) = instanceHead ispec + ins_tv_set = mkVarSet ins_tvs + cls_inst_env = classInstances inst_envs clas + bad_fundeps = badFunDeps cls_inst_env clas ins_tv_set ins_tys + +badFunDeps :: [Instance] -> Class + -> TyVarSet -> [Type] -- Proposed new instance type + -> [Instance] +badFunDeps cls_insts clas ins_tv_set ins_tys + = [ ispec | fd <- fds, -- fds is often empty + let trimmed_tcs = trimRoughMatchTcs clas_tvs fd rough_tcs, + ispec@(Instance { is_tcs = mb_tcs, is_tvs = tvs, + is_tys = tys }) <- cls_insts, + -- Filter out ones that can't possibly match, + -- based on the head of the fundep + not (instanceCantMatch trimmed_tcs mb_tcs), + notNull (checkClsFD (tvs `unionVarSet` ins_tv_set) + fd clas_tvs tys ins_tys) + ] + where + (clas_tvs, fds) = classTvsFds clas + rough_tcs = roughMatchTcs ins_tys + +trimRoughMatchTcs :: [TyVar] -> FunDep TyVar -> [Maybe Name] -> [Maybe Name] +-- Computing rough_tcs for a particular fundep +-- class C a b c | a c -> b where ... +-- For each instance .... => C ta tb tc +-- we want to match only on the types ta, tb; so our +-- rough-match thing must similarly be filtered. +-- Hence, we Nothing-ise the tb type right here +trimRoughMatchTcs clas_tvs (ltvs,_) mb_tcs + = zipWith select clas_tvs mb_tcs + where + select clas_tv mb_tc | clas_tv `elem` ltvs = mb_tc + | otherwise = Nothing +\end{code} + + +%************************************************************************ +%* * +\subsection{Miscellaneous} +%* * +%************************************************************************ + +\begin{code} +pprFundeps :: Outputable a => [FunDep a] -> SDoc +pprFundeps [] = empty +pprFundeps fds = hsep (ptext SLIT("|") : punctuate comma (map ppr_fd fds)) + +ppr_fd (us, vs) = hsep [interppSP us, ptext SLIT("->"), interppSP vs] +\end{code} + |