    {-
    (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 (
            FunDepEqn(..), pprEquation,
            improveFromInstEnv, improveFromAnother,
            checkInstCoverage, checkFunDeps,
            pprFundeps
        ) where

    #include "HsVersions.h"

    import Name
    import Var
    import Class
    import Type
    import TcType( transSuperClasses )
    import Unify
    import InstEnv
    import VarSet
    import VarEnv
    import Outputable
    import ErrUtils( Validity(..), allValid )
    import SrcLoc
    import Util

    import Pair             ( Pair(..) )
    import Data.List        ( nubBy )
    import Data.Maybe
    import Data.Foldable    ( fold )

    #if __GLASGOW_HASKELL__ < 709
    import Prelude hiding ( and )
    import Control.Applicative ( (<$>) )
    import Data.Foldable       ( and )
    #endif

    {-
    ************************************************************************
    *                                                                      *
    \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
    will generate the folloing FunDepEqn
         FDEqn { fd_qtvs = []
               , fd_eqs  = [Pair Bool alpha]
               , fd_pred1 = C Int Bool
               , fd_pred2 = C Int alpha
               , fd_loc = ... }
    However notice that a functional dependency may have more than one variable
    in the RHS which will create more than one pair of types in fd_eqs. Example:
         class C a b c | a -> b c
         [Wanted] C Int alpha alpha
         [Wanted] C Int Bool beta
    Will generate:
         FDEqn { fd_qtvs = []
               , fd_eqs  = [Pair Bool alpha, Pair alpha beta]
               , fd_pred1 = C Int Bool
               , fd_pred2 = C Int alpha
               , fd_loc = ... }

    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 FunDepEqn loc
      = FDEqn { fd_qtvs :: [TyVar]   -- Instantiate these type and kind vars
                                     --   to fresh unification vars,
                                     -- Non-empty only for FunDepEqns arising from instance decls

              , fd_eqs  :: [Pair Type]  -- Make these pairs of types equal
              , fd_pred1 :: PredType    -- The FunDepEqn arose from
              , fd_pred2 :: PredType    --  combining these two constraints
              , fd_loc :: loc  }

    {-
    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
    -- (instFD fd tvs tys) returns fd instantiated with (tvs -> tys)
    instFD (ls,rs) tvs tys
      = (map lookup ls, map lookup rs)
      where
        env       = zipVarEnv tvs tys
        lookup tv = lookupVarEnv_NF env tv

    zipAndComputeFDEqs :: (Type -> Type -> Bool) -- Discard this FDEq if true
                       -> [Type] -> [Type]
                       -> [Pair Type]
    -- Create a list of (Type,Type) pairs from two lists of types,
    -- making sure that the types are not already equal
    zipAndComputeFDEqs discard (ty1:tys1) (ty2:tys2)
     | discard ty1 ty2 = zipAndComputeFDEqs discard tys1 tys2
     | otherwise       = Pair ty1 ty2 : zipAndComputeFDEqs discard tys1 tys2
    zipAndComputeFDEqs _ _ _ = []

    -- Improve a class constraint from another class constraint
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    improveFromAnother :: loc
                       -> PredType -- Template item (usually given, or inert)
                       -> PredType -- Workitem [that can be improved]
                       -> [FunDepEqn loc]
    -- Post: FDEqs always oriented from the other to the workitem
    --       Equations have empty quantified variables
    improveFromAnother loc pred1 pred2
      | Just (cls1, tys1) <- getClassPredTys_maybe pred1
      , Just (cls2, tys2) <- getClassPredTys_maybe pred2
      , cls1 == cls2
      = [ FDEqn { fd_qtvs = [], fd_eqs = eqs, fd_pred1 = pred1, fd_pred2 = pred2, fd_loc = loc }
        | let (cls_tvs, cls_fds) = classTvsFds cls1
        , fd <- cls_fds
        , let (ltys1, rs1) = instFD fd cls_tvs tys1
              (ltys2, rs2) = instFD fd cls_tvs tys2
        , eqTypes ltys1 ltys2               -- The LHSs match
        , let eqs = zipAndComputeFDEqs eqType rs1 rs2
        , not (null eqs) ]

    improveFromAnother _ _ _ = []

    -- Improve a class constraint from instance declarations
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    pprEquation :: FunDepEqn a -> SDoc
    pprEquation (FDEqn { fd_qtvs = qtvs, fd_eqs = pairs })
      = vcat [text "forall" <+> braces (pprWithCommas ppr qtvs),
              nest 2 (vcat [ ppr t1 <+> text "~" <+> ppr t2
                           | Pair t1 t2 <- pairs])]

    improveFromInstEnv :: InstEnvs
                       -> (PredType -> SrcSpan -> loc)
                       -> PredType
                       -> [FunDepEqn loc] -- Needs to be a FunDepEqn 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 mk_loc pred
      | Just (cls, tys) <- getClassPredTys_maybe pred
      , 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 = mk_loc p_inst (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) <- improveClsFD cls_tvs fd ispec
                                          tys trimmed_tcs -- NB: orientation
        , let p_inst = mkClassPred cls (is_tys ispec)
        ]
    improveFromInstEnv _ _ _ = []

    improveClsFD :: [TyVar] -> FunDep TyVar    -- One functional dependency from the class
                 -> ClsInst                    -- An instance template
                 -> [Type] -> [Maybe Name]     -- Arguments of this (C tys) predicate
                 -> [([TyCoVar], [Pair Type])] -- Empty or singleton

    improveClsFD clas_tvs fd
                 (ClsInst { is_tvs = qtvs, is_tys = tys_inst, is_tcs = rough_tcs_inst })
                 tys_actual rough_tcs_actual

    -- Compare instance      {a,b}    C sx sp sy sq
    --         with wanted     [W] C tx tp ty tq
    --         for fundep (x,y -> p,q)  from class  (C x p y q)
    -- If (sx,sy) unifies with (tx,ty), take the subst S

    -- '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 a wanted constraint 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

      | 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 tcMatchTys ltys1 ltys2 of
            Nothing  -> []
            Just subst | isJust (tcMatchTysX subst 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 (substTyUnchecked subst) rtys1

                        fdeqs = zipAndComputeFDEqs (\_ _ -> False) rtys1' rtys2
                            -- 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 (substTyUnchecked subst (varType tv))
                                   | tv <- qtvs, tv `notElemTCvSubst` 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
        (ltys1, rtys1) = instFD fd clas_tvs tys_inst
        (ltys2, rtys2) = instFD 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
           | and (isEmptyVarSet <$> undetermined_tvs) = IsValid
           | otherwise                                = NotValid msg
           where
             (ls,rs) = instFD fd tyvars inst_taus
             ls_tvs = tyCoVarsOfTypes ls
             rs_tvs = splitVisVarsOfTypes rs

             undetermined_tvs | be_liberal = liberal_undet_tvs
                              | otherwise  = conserv_undet_tvs

             closed_ls_tvs = oclose theta ls_tvs
             liberal_undet_tvs = (`minusVarSet` closed_ls_tvs) <$> rs_tvs
             conserv_undet_tvs = (`minusVarSet` ls_tvs)        <$> rs_tvs

             undet_set = fold undetermined_tvs

             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 [ text "The"
                                <+> ppWhen be_liberal (text "liberal")
                                <+> text "coverage condition fails in class"
                                <+> quotes (ppr clas)
                              , nest 2 $ text "for functional dependency:"
                                <+> quotes (pprFunDep fd) ]
                        , sep [ text "Reason: lhs type"<>plural ls <+> pprQuotedList ls
                              , nest 2 $
                                (if isSingleton ls
                                 then text "does not"
                                 else text "do not jointly")
                                <+> text "determine rhs type"<>plural rs
                                <+> pprQuotedList rs ]
                        , text "Un-determined variable" <> pluralVarSet undet_set <> colon
                                <+> pprVarSet (pprWithCommas ppr) undet_set
                        , ppWhen (isEmptyVarSet $ pSnd undetermined_tvs) $
                          text "(Use -fprint-explicit-kinds to see the kind variables in the types)"
                        , ppWhen (not be_liberal &&
                                  and (isEmptyVarSet <$> liberal_undet_tvs)) $
                          text "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 (done automatically
        by tyCoVarsOfTypes 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] -> TyCoVarSet -> TyCoVarSet
    -- See Note [The liberal coverage condition]
    oclose preds fixed_tvs
      | null tv_fds = fixed_tvs -- Fast escape hatch for common case.
      | otherwise   = fixVarSet extend fixed_tvs
      where
        extend fixed_tvs = foldl add fixed_tvs tv_fds
           where
              add 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  :: [(TyCoVarSet,TyCoVarSet)]
        tv_fds  = [ (tyCoVarsOfTypes ls, tyCoVarsOfTypes rs)
                  | pred <- preds
                  , pred' <- pred : transSuperClasses pred
                       -- Look for fundeps in superclasses too
                  , (ls, rs) <- determined pred' ]

        determined :: PredType -> [([Type],[Type])]
        determined pred
           = case classifyPredType pred of
                EqPred NomEq t1 t2 -> [([t1],[t2]), ([t2],[t1])]
                ClassPred cls tys  -> [ instFD fd cls_tvs tys
                                      | let (cls_tvs, cls_fds) = classTvsFds cls
                                      , fd <- cls_fds ]
                _ -> []

    {-
    ************************************************************************
    *                                                                      *
            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

    Note [Bogus consistency check]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In checkFunDeps we check that a new ClsInst is consistent with all the
    ClsInsts in the environment.

    The bogus aspect is discussed in Trac #10675. Currenty it if the two
    types are *contradicatory*, using (isNothing . tcUnifyTys).  But all
    the papers say we should check if the two types are *equal* thus
       not (substTys subst rtys1 `eqTypes` substTys subst rtys2)
    For now I'm leaving the bogus form because that's the way it has
    been for years.
    -}

    checkFunDeps :: InstEnvs -> ClsInst -> [ClsInst]
    -- The Consistency Check.
    -- Check whether adding DFunId would break functional-dependency constraints
    -- Used only for instance decls defined in the module being compiled
    -- Returns a list of the ClsInst in InstEnvs that are inconsistent
    -- with the proposed new ClsInst
    checkFunDeps inst_envs (ClsInst { is_tvs = qtvs1, is_cls = cls
                                    , is_tys = tys1, is_tcs = rough_tcs1 })
      | null fds
      = []
      | otherwise
      = nubBy eq_inst $
        [ ispec | ispec <- cls_insts
                , fd    <- fds
                , is_inconsistent fd ispec ]
      where
        cls_insts      = classInstances inst_envs cls
        (cls_tvs, fds) = classTvsFds cls
        qtv_set1       = mkVarSet qtvs1

        is_inconsistent fd (ClsInst { is_tvs = qtvs2, is_tys = tys2, is_tcs = rough_tcs2 })
          | instanceCantMatch trimmed_tcs rough_tcs2
          = False
          | otherwise
          = case tcUnifyTys bind_fn ltys1 ltys2 of
              Nothing         -> False
              Just subst
                -> isNothing $   -- Bogus legacy test (Trac #10675)
                                 -- See Note [Bogus consistency check]
                   tcUnifyTys bind_fn (substTysUnchecked subst rtys1) (substTysUnchecked subst rtys2)

          where
            trimmed_tcs    = trimRoughMatchTcs cls_tvs fd rough_tcs1
            (ltys1, rtys1) = instFD fd cls_tvs tys1
            (ltys2, rtys2) = instFD fd cls_tvs tys2
            qtv_set2       = mkVarSet qtvs2
            bind_fn tv | tv `elemVarSet` qtv_set1 = BindMe
                       | tv `elemVarSet` qtv_set2 = BindMe
                       | otherwise                = Skolem

        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
    --
    -- Result list is same length as input list, just with more Nothings
    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