    {-
    (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 = tyVarsOfTypes ls
             rs_tvs = tyVarsOfTypes rs

             conservative_ok = rs_tvs `subVarSet` closeOverKinds ls_tvs
             liberal_ok      = rs_tvs `subVarSet` oclose theta (closeOverKinds ls_tvs)
                -- closeOverKinds: see Note [Closing over kinds in coverage]

             msg = vcat [ -- text "ls_tvs" <+> ppr ls_tvs
                          -- , text "closed ls_tvs" <+> ppr (closeOverKinds ls_tvs)
                          -- , text "theta" <+> ppr theta
                          -- , text "oclose" <+> ppr (oclose theta (closeOverKinds ls_tvs))
                          -- , text "rs_tvs" <+> ppr rs_tvs
                          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
          data Foo a = ...  -- Foo :: forall 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.  Trac #10109 is another example.

    Here is a more subtle example, from HList-0.4.0.0 (Trac #10564)

      class HasFieldM (l :: k) r (v :: Maybe *)
            | l r -> v where ...
      class HasFieldM1 (b :: Maybe [*]) (l :: k) r v
            | b l r -> v where ...
      class HMemberM (e1 :: k) (l :: [k]) (r :: Maybe [k])
            | e1 l -> r

      data Label :: k -> *
      type family LabelsOf (a :: [*]) ::  *

      instance (HMemberM (Label {k} (l::k)) (LabelsOf xs) b,
                HasFieldM1 b l (r xs) v)
             => HasFieldM l (r xs) v where

    Is the instance OK? Does {l,r,xs} determine v?  Well:

      * From the instance constraint HMemberM (Label k l) (LabelsOf xs) b,
        plus the fundep "| el l -> r" in class HMameberM,
        we get {l,k,xs} -> b

      * Note the 'k'!! We must call closeOverKinds on the seed set
        ls_tvs = {l,r,xs}, BEFORE doing oclose, else the {l,k,xs}->b
        fundep won't fire.  This was the reason for #10564.

      * So starting from seeds {l,r,xs,k} we do oclose to get
        first {l,r,xs,k,b}, via the HMemberM constraint, and then
        {l,r,xs,k,b,v}, via the HasFieldM1 constraint.

      * And that fixes v.

    However, we must closeOverKinds whenever augmenting the seed set
    in oclose!  Consider Trac #10109:

      data Succ a   -- Succ :: forall k. k -> *
      class Add (a :: k1) (b :: k2) (ab :: k3) | a b -> ab
      instance (Add a b ab) => Add (Succ {k1} (a :: k1))
                                   b
                                   (Succ {k3} (ab :: k3})

    We start with seed set {a:k1,b:k2} and closeOverKinds to {a,k1,b,k2}.
    Now use the fundep to extend to {a,k1,b,k2,ab}.  But we need to
    closeOverKinds *again* now to {a,k1,b,k2,ab,k3}, so that we fix all
    the variables free in (Succ {k3} ab).

    Bottom line:
      * closeOverKinds on initial seeds (in checkInstCoverage)
      * and closeOverKinds whenever extending those seeds (in oclose)

    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` closeOverKinds rs
            | otherwise                = fixed_tvs
            -- closeOverKinds: see Note [Closing over kinds in coverage]

        tv_fds  :: [(TyVarSet,TyVarSet)]
        tv_fds  = [ (tyVarsOfTypes ls, tyVarsOfTypes rs)
                  | pred <- preds
                  , (ls, rs) <- determined pred ]

        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