+%
+% (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(oclose, instantiateFdClassTys, pprFundeps) where
+module FunDeps (
+ Equation, pprEquation,
+ oclose, grow, improve,
+ checkInstCoverage, checkFunDeps,
+ pprFundeps
+ ) where
#include "HsVersions.h"
-import Class (classTvsFds)
-import Outputable (interppSP, ptext, empty, hsep, punctuate, comma)
-import UniqSet (elementOfUniqSet, addOneToUniqSet )
-import List (elemIndex)
-
-oclose fds vs =
- case oclose1 fds vs of
- (vs', False) -> vs'
- (vs', True) -> oclose fds vs'
-
-oclose1 [] vs = (vs, False)
-oclose1 (fd@(ls, rs):fds) vs =
- if osubset ls vs then
- (vs'', b1 || b2)
- else
- vs'b1
- where
- vs'b1@(vs', b1) = oclose1 fds vs
- (vs'', b2) = ounion rs vs'
-
-osubset [] vs = True
-osubset (u:us) vs = if u `elementOfUniqSet` vs then osubset us vs else False
-
-ounion [] ys = (ys, False)
-ounion (x:xs) ys =
- if x `elementOfUniqSet` ys then (ys', b) else (addOneToUniqSet ys' x, True)
- where
- (ys', b) = ounion xs ys
-
-instantiateFdClassTys clas ts =
- map (lookupInstFundep tyvars ts) fundeps
- where
- (tyvars, fundeps) = classTvsFds clas
- lookupInstFundep tyvars ts (us, vs) =
- (lookupInstTys tyvars ts us, lookupInstTys tyvars ts vs)
-lookupInstTys tyvars ts = map (lookupInstTy tyvars ts)
-lookupInstTy tyvars ts u = ts !! i
- where Just i = elemIndex u tyvars
+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}
+
projects / ghc-hetmet.git / blobdiff