{- (c) The University of Glasgow 2006 (c) The GRASP/AQUA Project, Glasgow University, 2000 FunDeps - functional dependencies It's better to read it as: "if we know these, then we're going to know these" -} {-# LANGUAGE CPP #-} module FunDeps ( FDEq (..), Equation(..), pprEquation, improveFromInstEnv, improveFromAnother, checkInstCoverage, checkFunDeps, pprFundeps ) where #include "HsVersions.h" import Name import Var import Class import Type import Unify import InstEnv import VarSet import VarEnv import Outputable import ErrUtils( Validity(..), allValid ) import SrcLoc import Util import FastString import Data.List ( nubBy ) import Data.Maybe ( isJust ) {- ************************************************************************ * * \subsection{Generate equations from functional dependencies} * * ************************************************************************ Each functional dependency with one variable in the RHS is responsible for generating a single equality. For instance: class C a b | a -> b The constraints ([Wanted] C Int Bool) and [Wanted] C Int alpha FDEq { fd_pos = 1 , fd_ty_left = Bool , fd_ty_right = alpha } However notice that a functional dependency may have more than one variable in the RHS which will create more than one FDEq. Example: class C a b c | a -> b c [Wanted] C Int alpha alpha [Wanted] C Int Bool beta Will generate: fd1 = FDEq { fd_pos = 1, fd_ty_left = alpha, fd_ty_right = Bool } and fd2 = FDEq { fd_pos = 2, fd_ty_left = alpha, fd_ty_right = beta } We record the paremeter position so that can immediately rewrite a constraint using the produced FDEqs and remove it from our worklist. INVARIANT: Corresponding types aren't already equal That is, there exists at least one non-identity equality in FDEqs. Assume: class C a b c | a -> b c instance C Int x x And: [Wanted] C Int Bool alpha We will /match/ the LHS of fundep equations, producing a matching substitution and create equations for the RHS sides. In our last example we'd have generated: ({x}, [fd1,fd2]) where fd1 = FDEq 1 Bool x fd2 = FDEq 2 alpha x 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 or generate a new constraint. In the above example we would generate a new unification variable 'beta' for x and produce the following constraints: [Wanted] (Bool ~ beta) [Wanted] (alpha ~ beta) Notice the subtle difference between the above class declaration and: class C a b c | a -> b, a -> c where we would generate: ({x},[fd1]),({x},[fd2]) This means that the template variable would be instantiated to different unification variables when producing the FD constraints. Finally, the position parameters will help us rewrite the wanted constraint ``on the spot'' -} data Equation loc = FDEqn { fd_qtvs :: [TyVar] -- Instantiate these type and kind vars to fresh unification vars , fd_eqs :: [FDEq] -- and then make these equal , fd_pred1, fd_pred2 :: PredType -- The Equation arose from combining these two constraints , fd_loc :: loc } data FDEq = FDEq { fd_pos :: Int -- We use '0' for the first position , fd_ty_left :: Type , fd_ty_right :: Type } instance Outputable FDEq where ppr (FDEq { fd_pos = p, fd_ty_left = tyl, fd_ty_right = tyr }) = parens (int p <> comma <+> ppr tyl <> comma <+> ppr tyr) {- 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 -} instFD :: FunDep TyVar -> [TyVar] -> [Type] -> FunDep Type -- A simpler version of instFD_WithPos to be used in checking instance coverage etc. instFD (ls,rs) tvs tys = (map lookup ls, map lookup rs) where env = zipVarEnv tvs tys lookup tv = lookupVarEnv_NF env tv instFD_WithPos :: FunDep TyVar -> [TyVar] -> [Type] -> ([Type], [(Int,Type)]) -- Returns a FunDep between the types accompanied along with their -- position (<=0) in the types argument list. instFD_WithPos (ls,rs) tvs tys = (map (snd . lookup) ls, map lookup rs) where ind_tys = zip [0..] tys env = zipVarEnv tvs ind_tys lookup tv = lookupVarEnv_NF env tv zipAndComputeFDEqs :: (Type -> Type -> Bool) -- Discard this FDEq if true -> [Type] -> [(Int,Type)] -> [FDEq] -- Create a list of FDEqs from two lists of types, making sure -- that the types are not equal. zipAndComputeFDEqs discard (ty1:tys1) ((i2,ty2):tys2) | discard ty1 ty2 = zipAndComputeFDEqs discard tys1 tys2 | otherwise = FDEq { fd_pos = i2 , fd_ty_left = ty1 , fd_ty_right = ty2 } : zipAndComputeFDEqs discard tys1 tys2 zipAndComputeFDEqs _ _ _ = [] -- Improve a class constraint from another class constraint -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ improveFromAnother :: PredType -- Template item (usually given, or inert) -> PredType -- Workitem [that can be improved] -> [Equation ()] -- Post: FDEqs always oriented from the other to the workitem -- Equations have empty quantified variables improveFromAnother pred1 pred2 | Just (cls1, tys1) <- getClassPredTys_maybe pred1 , Just (cls2, tys2) <- getClassPredTys_maybe pred2 , tys1 `lengthAtLeast` 2 && cls1 == cls2 = [ FDEqn { fd_qtvs = [], fd_eqs = eqs, fd_pred1 = pred1, fd_pred2 = pred2, fd_loc = () } | let (cls_tvs, cls_fds) = classTvsFds cls1 , fd <- cls_fds , let (ltys1, rs1) = instFD fd cls_tvs tys1 (ltys2, irs2) = instFD_WithPos fd cls_tvs tys2 , eqTypes ltys1 ltys2 -- The LHSs match , let eqs = zipAndComputeFDEqs eqType rs1 irs2 , not (null eqs) ] improveFromAnother _ _ = [] -- Improve a class constraint from instance declarations -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ pprEquation :: Equation a -> SDoc pprEquation (FDEqn { fd_qtvs = qtvs, fd_eqs = pairs }) = vcat [ptext (sLit "forall") <+> braces (pprWithCommas ppr qtvs), nest 2 (vcat [ ppr t1 <+> ptext (sLit "~") <+> ppr t2 | (FDEq _ t1 t2) <- pairs])] improveFromInstEnv :: InstEnvs -> PredType -> [Equation SrcSpan] -- Needs to be an Equation because -- of quantified variables -- Post: Equations oriented from the template (matching instance) to the workitem! improveFromInstEnv _inst_env pred | not (isClassPred pred) = panic "improveFromInstEnv: not a class predicate" improveFromInstEnv inst_env pred | Just (cls, tys) <- getClassPredTys_maybe pred , tys `lengthAtLeast` 2 , let (cls_tvs, cls_fds) = classTvsFds cls instances = classInstances inst_env cls rough_tcs = roughMatchTcs tys = [ FDEqn { fd_qtvs = meta_tvs, fd_eqs = eqs , fd_pred1 = p_inst, fd_pred2=pred , fd_loc = getSrcSpan (is_dfun ispec) } | fd <- cls_fds -- Iterate through the fundeps first, -- because there often are none! , let trimmed_tcs = trimRoughMatchTcs cls_tvs fd rough_tcs -- Trim the rough_tcs based on the head of the fundep. -- Remember that instanceCantMatch treats both argumnents -- symmetrically, so it's ok to trim the rough_tcs, -- rather than trimming each inst_tcs in turn , ispec <- instances , (meta_tvs, eqs) <- checkClsFD fd cls_tvs ispec emptyVarSet tys trimmed_tcs -- NB: orientation , let p_inst = mkClassPred cls (is_tys ispec) ] improveFromInstEnv _ _ = [] checkClsFD :: FunDep TyVar -> [TyVar] -- One functional dependency from the class -> ClsInst -- An instance template -> TyVarSet -> [Type] -> [Maybe Name] -- Arguments of this (C tys) predicate -- TyVarSet are extra tyvars that can be instantiated -> [([TyVar], [FDEq])] checkClsFD fd clas_tvs (ClsInst { is_tvs = qtvs, is_tys = tys_inst, is_tcs = rough_tcs_inst }) extra_qtvs tys_actual rough_tcs_actual -- '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 -- -- is_qtvs = {x}, is_tys = [Maybe x, Tree x] -- tys_actual = [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 | instanceCantMatch rough_tcs_inst rough_tcs_actual = [] -- Filter out ones that can't possibly match, | otherwise = ASSERT2( length tys_inst == length tys_actual && length tys_inst == length clas_tvs , ppr tys_inst <+> ppr tys_actual ) case tcUnifyTys bind_fn ltys1 ltys2 of Nothing -> [] Just subst | isJust (tcUnifyTys bind_fn rtys1' rtys2') -- 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 -- NB: We can't do this 'is-useful-equation' check element-wise -- because of: -- class C a b c | a -> b c -- instance C Int x x -- [Wanted] C Int alpha Int -- We would get that x -> alpha (isJust) and x -> Int (isJust) -- so we would produce no FDs, which is clearly wrong. -> [] | null fdeqs -> [] | otherwise -> [(meta_tvs, fdeqs)] -- 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 rtys1' = map (substTy subst) rtys1 irs2' = map (\(i,x) -> (i,substTy subst x)) irs2 rtys2' = map snd irs2' fdeqs = zipAndComputeFDEqs (\_ _ -> False) rtys1' irs2' -- Don't discard anything! -- We could discard equal types but it's an overkill to call -- eqType again, since we know for sure that /at least one/ -- equation in there is useful) meta_tvs = [ setVarType tv (substTy subst (varType tv)) | tv <- qtvs, tv `notElemTvSubst` subst ] -- meta_tvs 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) -- -- But note (a) we get them from the dfun_id, so they are *in order* -- because the kind variables may be mentioned in the -- type variabes' kinds -- (b) we must apply 'subst' to the kinds, in case we have -- matched out a kind variable, but not a type variable -- whose kind mentions that kind variable! -- Trac #6015, #6068 where qtv_set = mkVarSet qtvs bind_fn tv | tv `elemVarSet` qtv_set = BindMe | tv `elemVarSet` extra_qtvs = BindMe | otherwise = Skolem (ltys1, rtys1) = instFD fd clas_tvs tys_inst (ltys2, irs2) = instFD_WithPos fd clas_tvs tys_actual {- ************************************************************************ * * The Coverage condition for instance declarations * * ************************************************************************ Note [Coverage condition] ~~~~~~~~~~~~~~~~~~~~~~~~~ Example class C a b | a -> b instance theta => C t1 t2 For the coverage condition, we check (normal) fv(t2) `subset` fv(t1) (liberal) fv(t2) `subset` oclose(fv(t1), theta) The liberal version ensures the self-consistency of the instance, but it does not guarantee termination. 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 -} checkInstCoverage :: Bool -- Be liberal -> Class -> [PredType] -> [Type] -> Validity -- "be_liberal" flag says whether to use "liberal" coverage of -- See Note [Coverage Condition] below -- -- Return values -- Nothing => no problems -- Just msg => coverage problem described by msg checkInstCoverage be_liberal clas theta inst_taus = allValid (map fundep_ok fds) where (tyvars, fds) = classTvsFds clas fundep_ok fd | if be_liberal then liberal_ok else conservative_ok = IsValid | otherwise = NotValid msg where (ls,rs) = instFD fd tyvars inst_taus ls_tvs = closeOverKinds (tyVarsOfTypes ls) -- See Note [Closing over kinds in coverage] rs_tvs = tyVarsOfTypes rs conservative_ok = rs_tvs `subVarSet` ls_tvs liberal_ok = rs_tvs `subVarSet` oclose theta ls_tvs msg = vcat [ sep [ ptext (sLit "The") <+> ppWhen be_liberal (ptext (sLit "liberal")) <+> ptext (sLit "coverage condition fails in class") <+> quotes (ppr clas) , nest 2 $ ptext (sLit "for functional dependency:") <+> quotes (pprFunDep fd) ] , sep [ ptext (sLit "Reason: lhs type")<>plural ls <+> pprQuotedList ls , nest 2 $ (if isSingleton ls then ptext (sLit "does not") else ptext (sLit "do not jointly")) <+> ptext (sLit "determine rhs type")<>plural rs <+> pprQuotedList rs ] , ppWhen (not be_liberal && liberal_ok) $ ptext (sLit "Using UndecidableInstances might help") ] {- Note [Closing over kinds in coverage] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have a fundep (a::k) -> b Then if 'a' is instantiated to (x y), where x:k2->*, y:k2, then fixing x really fixes k2 as well, and so k2 should be added to the lhs tyvars in the fundep check. Example (Trac #8391), using liberal coverage type Foo a = a -- Foo :: forall k. k -> k class Bar a b | a -> b instance Bar a (Foo a) In the instance decl, (a:k) does fix (Foo k a), but only if we notice that (a:k) fixes k. Note [The liberal coverage condition] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (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. We also use equality predicates in the predicates; if we have an assumption `t1 ~ t2`, then we use the fact that if we know `t1` we also know `t2` and the other way. eg oclose [C (x,y) z, a ~ x] {a,y} = {a,y,z,x} oclose is used (only) when checking the coverage condition for an instance declaration -} oclose :: [PredType] -> TyVarSet -> TyVarSet -- See Note [The liberal coverage condition] 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)] tv_fds = [ (tyVarsOfTypes xs, tyVarsOfTypes ys) | (xs, ys) <- concatMap determined preds ] determined :: PredType -> [([Type],[Type])] determined pred = case classifyPredType pred of ClassPred cls tys -> do let (cls_tvs, cls_fds) = classTvsFds cls fd <- cls_fds return (instFD fd cls_tvs tys) EqPred NomEq t1 t2 -> [([t1],[t2]), ([t2],[t1])] TuplePred ts -> concatMap determined ts _ -> [] {- ************************************************************************ * * 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 -} checkFunDeps :: InstEnvs -> ClsInst -> Maybe [ClsInst] -- Nothing <=> ok -- Just dfs <=> conflict with dfs -- Check whether 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 :: [ClsInst] -> Class -> TyVarSet -> [Type] -- Proposed new instance type -> [ClsInst] badFunDeps cls_insts clas ins_tv_set ins_tys = nubBy eq_inst $ [ ispec | fd <- fds, -- fds is often empty, so do this first! let trimmed_tcs = trimRoughMatchTcs clas_tvs fd rough_tcs, ispec <- cls_insts, notNull (checkClsFD fd clas_tvs ispec ins_tv_set ins_tys trimmed_tcs) ] where (clas_tvs, fds) = classTvsFds clas rough_tcs = roughMatchTcs ins_tys eq_inst i1 i2 = instanceDFunId i1 == instanceDFunId i2 -- An single instance may appear twice in the un-nubbed conflict list -- because it may conflict with more than one fundep. E.g. -- class C a b c | a -> b, a -> c -- instance C Int Bool Bool -- instance C Int Char Char -- The second instance conflicts with the first by *both* fundeps trimRoughMatchTcs :: [TyVar] -> FunDep TyVar -> [Maybe Name] -> [Maybe Name] -- Computing rough_tcs for a particular fundep -- class C a b c | a -> b where ... -- For each instance .... => C ta tb tc -- we want to match only on the type ta; so our -- rough-match thing must similarly be filtered. -- Hence, we Nothing-ise the tb and tc types 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