+++ /dev/null
-%
-% (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}
-
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