    {-# LANGUAGE TypeFamilies #-}

    {-
    (c) The University of Glasgow 2006
    (c) The AQUA Project, Glasgow University, 1993-1998

    -}

    -- | Typechecking rewrite rules
    module GHC.Tc.Gen.Rule ( tcRules ) where

    import GHC.Prelude

    import GHC.Hs
    import GHC.Tc.Types
    import GHC.Tc.Utils.Monad
    import GHC.Tc.Solver
    import GHC.Tc.Solver.Monad ( runTcS )
    import GHC.Tc.Types.Constraint
    import GHC.Tc.Types.Origin
    import GHC.Tc.Utils.TcMType
    import GHC.Tc.Utils.TcType
    import GHC.Tc.Gen.HsType
    import GHC.Tc.Gen.Expr
    import GHC.Tc.Utils.Env
    import GHC.Tc.Utils.Unify( buildImplicationFor )
    import GHC.Tc.Zonk.TcType

    import GHC.Core.Type
    import GHC.Core.Coercion( mkCoVarCo )
    import GHC.Core.TyCon( isTypeFamilyTyCon )
    import GHC.Core.Predicate

    import GHC.Types.Id
    import GHC.Types.Var( EvVar, tyVarName )
    import GHC.Types.Var.Set
    import GHC.Types.Basic ( RuleName, NonStandardDefaultingStrategy(..) )
    import GHC.Types.SrcLoc
    import GHC.Utils.Outputable
    import GHC.Utils.Panic
    import GHC.Data.FastString
    import GHC.Data.Bag

    {-
    Note [Typechecking rules]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    We *infer* the typ of the LHS, and use that type to *check* the type of
    the RHS.  That means that higher-rank rules work reasonably well. Here's
    an example (test simplCore/should_compile/rule2.hs) produced by Roman:

       foo :: (forall m. m a -> m b) -> m a -> m b
       foo f = ...

       bar :: (forall m. m a -> m a) -> m a -> m a
       bar f = ...

       {-# RULES "foo/bar" foo = bar #-}

    He wanted the rule to typecheck.

    Note [TcLevel in type checking rules]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Bringing type variables into scope naturally bumps the TcLevel. Thus, we type
    check the term-level binders in a bumped level, and we must accordingly bump
    the level whenever these binders are in scope.

    Note [Re-quantify type variables in rules]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider this example from #17710:

      foo :: forall k (a :: k) (b :: k). Proxy a -> Proxy b
      foo x = Proxy
      {-# RULES "foo" forall (x :: Proxy (a :: k)). foo x = Proxy #-}

    Written out in more detail, the "foo" rewrite rule looks like this:

      forall k (a :: k). forall (x :: Proxy (a :: k)). foo @k @a @b0 x = Proxy @k @b0

    Where b0 is a unification variable. Where should b0 be quantified? We have to
    quantify it after k, since (b0 :: k). But generalization usually puts inferred
    type variables (such as b0) at the /front/ of the telescope! This creates a
    conflict.

    One option is to simply throw an error, per the principles of
    Note [Naughty quantification candidates] in GHC.Tc.Utils.TcMType. This is what would happen
    if we were generalising over a normal type signature. On the other hand, the
    types in a rewrite rule aren't quite "normal", since the notions of specified
    and inferred type variables aren't applicable.

    A more permissive design (and the design that GHC uses) is to simply requantify
    all of the type variables. That is, we would end up with this:

      forall k (a :: k) (b :: k). forall (x :: Proxy (a :: k)). foo @k @a @b x = Proxy @k @b

    It's a bit strange putting the generalized variable `b` after the user-written
    variables `k` and `a`. But again, the notion of specificity is not relevant to
    rewrite rules, since one cannot "visibly apply" a rewrite rule. This design not
    only makes "foo" typecheck, but it also makes the implementation simpler.

    See also Note [Generalising in tcTyFamInstEqnGuts] in GHC.Tc.TyCl, which
    explains a very similar design when generalising over a type family instance
    equation.
    -}

    tcRules :: [LRuleDecls GhcRn] -> TcM [LRuleDecls GhcTc]
    tcRules :: [LRuleDecls (GhcPass 'Renamed)] -> TcM [LRuleDecls GhcTc]
    tcRules [LRuleDecls (GhcPass 'Renamed)]
    decls = (GenLocated SrcSpanAnnA (RuleDecls (GhcPass 'Renamed))
     -> IOEnv
          (Env TcGblEnv TcLclEnv) (GenLocated SrcSpanAnnA (RuleDecls GhcTc)))
    -> [GenLocated SrcSpanAnnA (RuleDecls (GhcPass 'Renamed))]
    -> IOEnv
         (Env TcGblEnv TcLclEnv) [GenLocated SrcSpanAnnA (RuleDecls GhcTc)]
    forall (t :: * -> *) (m :: * -> *) a b.
    (Traversable t, Monad m) =>
    (a -> m b) -> t a -> m (t b)
    forall (m :: * -> *) a b. Monad m => (a -> m b) -> [a] -> m [b]
    mapM ((RuleDecls (GhcPass 'Renamed) -> TcM (RuleDecls GhcTc))
    -> GenLocated SrcSpanAnnA (RuleDecls (GhcPass 'Renamed))
    -> IOEnv
         (Env TcGblEnv TcLclEnv) (GenLocated SrcSpanAnnA (RuleDecls GhcTc))
    forall a b ann.
    (a -> TcM b)
    -> GenLocated (EpAnn ann) a -> TcRn (GenLocated (EpAnn ann) b)
    wrapLocMA RuleDecls (GhcPass 'Renamed) -> TcM (RuleDecls GhcTc)
    tcRuleDecls) [LRuleDecls (GhcPass 'Renamed)]
    [GenLocated SrcSpanAnnA (RuleDecls (GhcPass 'Renamed))]
    decls

    tcRuleDecls :: RuleDecls GhcRn -> TcM (RuleDecls GhcTc)
    tcRuleDecls :: RuleDecls (GhcPass 'Renamed) -> TcM (RuleDecls GhcTc)
    tcRuleDecls (HsRules { rds_ext :: forall pass. RuleDecls pass -> XCRuleDecls pass
    rds_ext = XCRuleDecls (GhcPass 'Renamed)
    src
                         , rds_rules :: forall pass. RuleDecls pass -> [LRuleDecl pass]
    rds_rules = [LRuleDecl (GhcPass 'Renamed)]
    decls })
       = do { tc_decls <- (GenLocated SrcSpanAnnA (RuleDecl (GhcPass 'Renamed))
     -> IOEnv
          (Env TcGblEnv TcLclEnv) (GenLocated SrcSpanAnnA (RuleDecl GhcTc)))
    -> [GenLocated SrcSpanAnnA (RuleDecl (GhcPass 'Renamed))]
    -> IOEnv
         (Env TcGblEnv TcLclEnv) [GenLocated SrcSpanAnnA (RuleDecl GhcTc)]
    forall (t :: * -> *) (m :: * -> *) a b.
    (Traversable t, Monad m) =>
    (a -> m b) -> t a -> m (t b)
    forall (m :: * -> *) a b. Monad m => (a -> m b) -> [a] -> m [b]
    mapM ((RuleDecl (GhcPass 'Renamed) -> TcM (RuleDecl GhcTc))
    -> GenLocated SrcSpanAnnA (RuleDecl (GhcPass 'Renamed))
    -> IOEnv
         (Env TcGblEnv TcLclEnv) (GenLocated SrcSpanAnnA (RuleDecl GhcTc))
    forall a b ann.
    (a -> TcM b)
    -> GenLocated (EpAnn ann) a -> TcRn (GenLocated (EpAnn ann) b)
    wrapLocMA RuleDecl (GhcPass 'Renamed) -> TcM (RuleDecl GhcTc)
    tcRule) [LRuleDecl (GhcPass 'Renamed)]
    [GenLocated SrcSpanAnnA (RuleDecl (GhcPass 'Renamed))]
    decls
            ; return $ HsRules { rds_ext   = src
                               , rds_rules = tc_decls } }

    tcRule :: RuleDecl GhcRn -> TcM (RuleDecl GhcTc)
    tcRule :: RuleDecl (GhcPass 'Renamed) -> TcM (RuleDecl GhcTc)
    tcRule (HsRule { rd_ext :: forall pass. RuleDecl pass -> XHsRule pass
    rd_ext  = XHsRule (GhcPass 'Renamed)
    ext
                   , rd_name :: forall pass. RuleDecl pass -> XRec pass RuleName
    rd_name = rname :: XRec (GhcPass 'Renamed) RuleName
    rname@(L EpAnnCO
    _ RuleName
    name)
                   , rd_act :: forall pass. RuleDecl pass -> Activation
    rd_act  = Activation
    act
                   , rd_tyvs :: forall pass.
    RuleDecl pass -> Maybe [LHsTyVarBndr () (NoGhcTc pass)]
    rd_tyvs = Maybe [LHsTyVarBndr () (NoGhcTc (GhcPass 'Renamed))]
    ty_bndrs
                   , rd_tmvs :: forall pass. RuleDecl pass -> [LRuleBndr pass]
    rd_tmvs = [LRuleBndr (GhcPass 'Renamed)]
    tm_bndrs
                   , rd_lhs :: forall pass. RuleDecl pass -> XRec pass (HsExpr pass)
    rd_lhs  = XRec (GhcPass 'Renamed) (HsExpr (GhcPass 'Renamed))
    lhs
                   , rd_rhs :: forall pass. RuleDecl pass -> XRec pass (HsExpr pass)
    rd_rhs  = XRec (GhcPass 'Renamed) (HsExpr (GhcPass 'Renamed))
    rhs })
      = SDoc -> TcM (RuleDecl GhcTc) -> TcM (RuleDecl GhcTc)
    forall a. SDoc -> TcM a -> TcM a
    addErrCtxt (RuleName -> SDoc
    ruleCtxt RuleName
    name)  (TcM (RuleDecl GhcTc) -> TcM (RuleDecl GhcTc))
    -> TcM (RuleDecl GhcTc) -> TcM (RuleDecl GhcTc)
    forall a b. (a -> b) -> a -> b
    $
        do { String -> SDoc -> TcRn ()
    traceTc String
    "---- Rule ------" (SourceText -> GenLocated EpAnnCO RuleName -> SDoc
    forall a. SourceText -> GenLocated a RuleName -> SDoc
    pprFullRuleName ((HsRuleRn, SourceText) -> SourceText
    forall a b. (a, b) -> b
    snd (HsRuleRn, SourceText)
    XHsRule (GhcPass 'Renamed)
    ext) XRec (GhcPass 'Renamed) RuleName
    GenLocated EpAnnCO RuleName
    rname)
           ; skol_info <- SkolemInfoAnon -> IOEnv (Env TcGblEnv TcLclEnv) SkolemInfo
    forall (m :: * -> *). MonadIO m => SkolemInfoAnon -> m SkolemInfo
    mkSkolemInfo (RuleName -> SkolemInfoAnon
    RuleSkol RuleName
    name)
            -- Note [Typechecking rules]
           ; (tc_lvl, stuff) <- pushTcLevelM $
                                generateRuleConstraints name ty_bndrs tm_bndrs lhs rhs

           ; let (id_bndrs, lhs', lhs_wanted
                          , rhs', rhs_wanted, rule_ty) = stuff

           ; traceTc "tcRule 1" (vcat [ pprFullRuleName (snd ext) rname
                                      , ppr lhs_wanted
                                      , ppr rhs_wanted ])

           ; (lhs_evs, residual_lhs_wanted, dont_default)
                <- simplifyRule name tc_lvl lhs_wanted rhs_wanted

           -- SimplifyRule Plan, step 4
           -- Now figure out what to quantify over
           -- c.f. GHC.Tc.Solver.simplifyInfer
           -- We quantify over any tyvars free in *either* the rule
           --  *or* the bound variables.  The latter is important.  Consider
           --      ss (x,(y,z)) = (x,z)
           --      RULE:  forall v. fst (ss v) = fst v
           -- The type of the rhs of the rule is just a, but v::(a,(b,c))
           --
           -- We also need to get the completely-unconstrained tyvars of
           -- the LHS, lest they otherwise get defaulted to Any; but we do that
           -- during zonking (see GHC.Tc.Zonk.Type.zonkRule)

           ; let tpl_ids = [TcTyVar]
    lhs_evs [TcTyVar] -> [TcTyVar] -> [TcTyVar]
    forall a. [a] -> [a] -> [a]
    ++ [TcTyVar]
    id_bndrs

           -- See Note [Re-quantify type variables in rules]
           ; forall_tkvs <- candidateQTyVarsOfTypes (rule_ty : map idType tpl_ids)
           ; let weed_out = (DVarSet -> TyCoVarSet -> DVarSet
    `dVarSetMinusVarSet` TyCoVarSet
    dont_default)
                 quant_cands = CandidatesQTvs
    forall_tkvs { dv_kvs = weed_out (dv_kvs forall_tkvs)
                                           , dv_tvs = weed_out (dv_tvs forall_tkvs) }
           ; qtkvs <- quantifyTyVars skol_info DefaultNonStandardTyVars quant_cands
           ; traceTc "tcRule" (vcat [ pprFullRuleName (snd ext) rname
                                    , text "forall_tkvs:" <+> ppr forall_tkvs
                                    , text "quant_cands:" <+> ppr quant_cands
                                    , text "dont_default:" <+> ppr dont_default
                                    , text "residual_lhs_wanted:" <+> ppr residual_lhs_wanted
                                    , text "qtkvs:" <+> ppr qtkvs
                                    , text "rule_ty:" <+> ppr rule_ty
                                    , text "ty_bndrs:" <+> ppr ty_bndrs
                                    , text "qtkvs ++ tpl_ids:" <+> ppr (qtkvs ++ tpl_ids)
                                    , text "tpl_id info:" <+>
                                      vcat [ ppr id <+> dcolon <+> ppr (idType id) | id <- tpl_ids ]
                      ])

           -- SimplfyRule Plan, step 5
           -- Simplify the LHS and RHS constraints:
           -- For the LHS constraints we must solve the remaining constraints
           -- (a) so that we report insoluble ones
           -- (b) so that we bind any soluble ones
           ; (lhs_implic, lhs_binds) <- buildImplicationFor tc_lvl (getSkolemInfo skol_info) qtkvs
                                             lhs_evs residual_lhs_wanted
           ; (rhs_implic, rhs_binds) <- buildImplicationFor tc_lvl (getSkolemInfo skol_info) qtkvs
                                             lhs_evs rhs_wanted
           ; emitImplications (lhs_implic `unionBags` rhs_implic)
           ; return $ HsRule { rd_ext = ext
                             , rd_name = rname
                             , rd_act = act
                             , rd_tyvs = ty_bndrs -- preserved for ppr-ing
                             , rd_tmvs = map (noLocA . RuleBndr noAnn . noLocA)
                                             (qtkvs ++ tpl_ids)
                             , rd_lhs  = mkHsDictLet lhs_binds lhs'
                             , rd_rhs  = mkHsDictLet rhs_binds rhs' } }

    generateRuleConstraints :: FastString
                            -> Maybe [LHsTyVarBndr () GhcRn] -> [LRuleBndr GhcRn]
                            -> LHsExpr GhcRn -> LHsExpr GhcRn
                            -> TcM ( [TcId]
                                   , LHsExpr GhcTc, WantedConstraints
                                   , LHsExpr GhcTc, WantedConstraints
                                   , TcType )
    generateRuleConstraints :: RuleName
    -> Maybe [LHsTyVarBndr () (GhcPass 'Renamed)]
    -> [LRuleBndr (GhcPass 'Renamed)]
    -> XRec (GhcPass 'Renamed) (HsExpr (GhcPass 'Renamed))
    -> XRec (GhcPass 'Renamed) (HsExpr (GhcPass 'Renamed))
    -> TcM
         ([TcTyVar], LHsExpr GhcTc, WantedConstraints, LHsExpr GhcTc,
          WantedConstraints, Type)
    generateRuleConstraints RuleName
    rule_name Maybe [LHsTyVarBndr () (GhcPass 'Renamed)]
    ty_bndrs [LRuleBndr (GhcPass 'Renamed)]
    tm_bndrs XRec (GhcPass 'Renamed) (HsExpr (GhcPass 'Renamed))
    lhs XRec (GhcPass 'Renamed) (HsExpr (GhcPass 'Renamed))
    rhs
      = do { ((tv_bndrs, id_bndrs), bndr_wanted) <- TcM ([TcTyVar], [TcTyVar])
    -> TcM (([TcTyVar], [TcTyVar]), WantedConstraints)
    forall a. TcM a -> TcM (a, WantedConstraints)
    captureConstraints (TcM ([TcTyVar], [TcTyVar])
     -> TcM (([TcTyVar], [TcTyVar]), WantedConstraints))
    -> TcM ([TcTyVar], [TcTyVar])
    -> TcM (([TcTyVar], [TcTyVar]), WantedConstraints)
    forall a b. (a -> b) -> a -> b
    $
                                                    RuleName
    -> Maybe [LHsTyVarBndr () (GhcPass 'Renamed)]
    -> [LRuleBndr (GhcPass 'Renamed)]
    -> TcM ([TcTyVar], [TcTyVar])
    tcRuleBndrs RuleName
    rule_name Maybe [LHsTyVarBndr () (GhcPass 'Renamed)]
    ty_bndrs [LRuleBndr (GhcPass 'Renamed)]
    tm_bndrs
                  -- bndr_wanted constraints can include wildcard hole
                  -- constraints, which we should not forget about.
                  -- It may mention the skolem type variables bound by
                  -- the RULE.  c.f. #10072
           ; tcExtendNameTyVarEnv [(tyVarName tv, tv) | tv <- tv_bndrs] $
             tcExtendIdEnv    id_bndrs $
        do { -- See Note [Solve order for RULES]
             ((lhs', rule_ty), lhs_wanted) <- captureConstraints (tcInferRho lhs)
           ; (rhs',            rhs_wanted) <- captureConstraints $
                                              tcCheckMonoExpr rhs rule_ty
           ; let all_lhs_wanted = WantedConstraints
    bndr_wanted WantedConstraints -> WantedConstraints -> WantedConstraints
    `andWC` WantedConstraints
    lhs_wanted
           ; return (id_bndrs, lhs', all_lhs_wanted, rhs', rhs_wanted, rule_ty) } }

    -- See Note [TcLevel in type checking rules]
    tcRuleBndrs :: FastString -> Maybe [LHsTyVarBndr () GhcRn] -> [LRuleBndr GhcRn]
                -> TcM ([TcTyVar], [Id])
    tcRuleBndrs :: RuleName
    -> Maybe [LHsTyVarBndr () (GhcPass 'Renamed)]
    -> [LRuleBndr (GhcPass 'Renamed)]
    -> TcM ([TcTyVar], [TcTyVar])
    tcRuleBndrs RuleName
    rule_name (Just [LHsTyVarBndr () (GhcPass 'Renamed)]
    bndrs) [LRuleBndr (GhcPass 'Renamed)]
    xs
      = do { skol_info <- SkolemInfoAnon -> IOEnv (Env TcGblEnv TcLclEnv) SkolemInfo
    forall (m :: * -> *). MonadIO m => SkolemInfoAnon -> m SkolemInfo
    mkSkolemInfo (RuleName -> SkolemInfoAnon
    RuleSkol RuleName
    rule_name)
           ; (tybndrs1,(tys2,tms)) <- bindExplicitTKBndrs_Skol skol_info bndrs $
                                      tcRuleTmBndrs rule_name xs
           ; let tys1 = [VarBndr TcTyVar ()] -> [TcTyVar]
    forall tv argf. [VarBndr tv argf] -> [tv]
    binderVars [VarBndr TcTyVar ()]
    tybndrs1
           ; return (tys1 ++ tys2, tms) }

    tcRuleBndrs RuleName
    rule_name Maybe [LHsTyVarBndr () (GhcPass 'Renamed)]
    Nothing [LRuleBndr (GhcPass 'Renamed)]
    xs
      = RuleName
    -> [LRuleBndr (GhcPass 'Renamed)] -> TcM ([TcTyVar], [TcTyVar])
    tcRuleTmBndrs RuleName
    rule_name [LRuleBndr (GhcPass 'Renamed)]
    xs

    -- See Note [TcLevel in type checking rules]
    tcRuleTmBndrs :: FastString -> [LRuleBndr GhcRn] -> TcM ([TcTyVar],[Id])
    tcRuleTmBndrs :: RuleName
    -> [LRuleBndr (GhcPass 'Renamed)] -> TcM ([TcTyVar], [TcTyVar])
    tcRuleTmBndrs RuleName
    _ [] = ([TcTyVar], [TcTyVar]) -> TcM ([TcTyVar], [TcTyVar])
    forall a. a -> IOEnv (Env TcGblEnv TcLclEnv) a
    forall (m :: * -> *) a. Monad m => a -> m a
    return ([],[])
    tcRuleTmBndrs RuleName
    rule_name (L EpAnnCO
    _ (RuleBndr XCRuleBndr (GhcPass 'Renamed)
    _ (L SrcSpanAnnN
    _ Name
    name)) : [LRuleBndr (GhcPass 'Renamed)]
    rule_bndrs)
      = do  { ty <- TcM Type
    newOpenFlexiTyVarTy
            ; (tyvars, tmvars) <- tcRuleTmBndrs rule_name rule_bndrs
            ; return (tyvars, mkLocalId name ManyTy ty : tmvars) }
    tcRuleTmBndrs RuleName
    rule_name (L EpAnnCO
    _ (RuleBndrSig XRuleBndrSig (GhcPass 'Renamed)
    _ (L SrcSpanAnnN
    _ Name
    name) HsPatSigType (GhcPass 'Renamed)
    rn_ty) : [LRuleBndr (GhcPass 'Renamed)]
    rule_bndrs)
    --  e.g         x :: a->a
    --  The tyvar 'a' is brought into scope first, just as if you'd written
    --              a::*, x :: a->a
    --  If there's an explicit forall, the renamer would have already reported an
    --   error for each out-of-scope type variable used
      = do  { let ctxt :: UserTypeCtxt
    ctxt = RuleName -> Name -> UserTypeCtxt
    RuleSigCtxt RuleName
    rule_name Name
    name
            ; (_ , tvs, id_ty) <- UserTypeCtxt
    -> HoleMode
    -> HsPatSigType (GhcPass 'Renamed)
    -> ContextKind
    -> TcM ([(Name, TcTyVar)], [(Name, TcTyVar)], Type)
    tcHsPatSigType UserTypeCtxt
    ctxt HoleMode
    HM_Sig HsPatSigType (GhcPass 'Renamed)
    rn_ty ContextKind
    OpenKind
            ; let id  = HasDebugCallStack => Name -> Type -> Type -> TcTyVar
    Name -> Type -> Type -> TcTyVar
    mkLocalId Name
    name Type
    ManyTy Type
    id_ty
                        -- See Note [Typechecking pattern signature binders] in GHC.Tc.Gen.HsType

                  -- The type variables scope over subsequent bindings; yuk
            ; (tyvars, tmvars) <- tcExtendNameTyVarEnv tvs $
                                       tcRuleTmBndrs rule_name rule_bndrs
            ; return (map snd tvs ++ tyvars, id : tmvars) }

    ruleCtxt :: FastString -> SDoc
    ruleCtxt :: RuleName -> SDoc
    ruleCtxt RuleName
    name = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "When checking the rewrite rule" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+>
                    SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    doubleQuotes (RuleName -> SDoc
    forall doc. IsLine doc => RuleName -> doc
    ftext RuleName
    name)

    {-
    *********************************************************************************
    *                                                                                 *
                  Constraint simplification for rules
    *                                                                                 *
    ***********************************************************************************

    Note [The SimplifyRule Plan]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Example.  Consider the following left-hand side of a rule
            f (x == y) (y > z) = ...
    If we typecheck this expression we get constraints
            d1 :: Ord a, d2 :: Eq a
    We do NOT want to "simplify" to the LHS
            forall x::a, y::a, z::a, d1::Ord a.
              f ((==) (eqFromOrd d1) x y) ((>) d1 y z) = ...
    Instead we want
            forall x::a, y::a, z::a, d1::Ord a, d2::Eq a.
              f ((==) d2 x y) ((>) d1 y z) = ...

    Here is another example:
            fromIntegral :: (Integral a, Num b) => a -> b
            {-# RULES "foo"  fromIntegral = id :: Int -> Int #-}
    In the rule, a=b=Int, and Num Int is a superclass of Integral Int. But
    we *dont* want to get
            forall dIntegralInt.
               fromIntegral Int Int dIntegralInt (scsel dIntegralInt) = id Int
    because the scsel will mess up RULE matching.  Instead we want
            forall dIntegralInt, dNumInt.
              fromIntegral Int Int dIntegralInt dNumInt = id Int

    Even if we have
            g (x == y) (y == z) = ..
    where the two dictionaries are *identical*, we do NOT WANT
            forall x::a, y::a, z::a, d1::Eq a
              f ((==) d1 x y) ((>) d1 y z) = ...
    because that will only match if the dict args are (visibly) equal.
    Instead we want to quantify over the dictionaries separately.

    In short, simplifyRuleLhs must *only* squash equalities, leaving
    all dicts unchanged, with absolutely no sharing.

    Also note that we can't solve the LHS constraints in isolation:
    Example   foo :: Ord a => a -> a
              foo_spec :: Int -> Int
              {-# RULE "foo"  foo = foo_spec #-}
    Here, it's the RHS that fixes the type variable

    HOWEVER, under a nested implication things are different
    Consider
      f :: (forall a. Eq a => a->a) -> Bool -> ...
      {-# RULES "foo" forall (v::forall b. Eq b => b->b).
           f b True = ...
        #-}
    Here we *must* solve the wanted (Eq a) from the given (Eq a)
    resulting from skolemising the argument type of g.  So we
    revert to SimplCheck when going under an implication.

    --------- So the SimplifyRule Plan is this -----------------------

    * Step 0: typecheck the LHS and RHS to get constraints from each

    * Step 1: Simplify the LHS and RHS constraints all together in one bag,
              but /discarding/ the simplified constraints. We do this only
              to discover all unification equalities.

    * Step 2: Zonk the ORIGINAL (unsimplified) LHS constraints, to take
              advantage of those unifications

    * Setp 3: Partition the LHS constraints into the ones we will
              quantify over, and the others.
              See Note [RULE quantification over equalities]

    * Step 4: Decide on the type variables to quantify over

    * Step 5: Simplify the LHS and RHS constraints separately, using the
              quantified constraints as givens

    Note [Solve order for RULES]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In step 1 above, we need to be a bit careful about solve order.
    Consider
       f :: Int -> T Int
       type instance T Int = Bool

       RULE f 3 = True

    From the RULE we get
       lhs-constraints:  T Int ~ alpha
       rhs-constraints:  Bool ~ alpha
    where 'alpha' is the type that connects the two.  If we glom them
    all together, and solve the RHS constraint first, we might solve
    with alpha := Bool.  But then we'd end up with a RULE like

        RULE: f 3 |> (co :: T Int ~ Bool) = True

    which is terrible.  We want

        RULE: f 3 = True |> (sym co :: Bool ~ T Int)

    So we are careful to solve the LHS constraints first, and *then* the
    RHS constraints.  Actually much of this is done by the on-the-fly
    constraint solving, so the same order must be observed in
    tcRule.

    Note [RULE quantification over equalities]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Deciding which equalities to quantify over is tricky:
     * We do not want to quantify over insoluble equalities (Int ~ Bool)
        (a) because we prefer to report a LHS type error
        (b) because if such things end up in 'givens' we get a bogus
            "inaccessible code" error

     * But we do want to quantify over things like (a ~ F b), where
       F is a type function.

    The difficulty is that it's hard to tell what is insoluble!
    So we see whether the simplification step yielded any type errors,
    and if so refrain from quantifying over *any* equalities.

    Note [Quantifying over coercion holes]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Equality constraints from the LHS will emit coercion hole Wanteds.
    These don't have a name, so we can't quantify over them directly.
    Instead, because we really do want to quantify here, invent a new
    EvVar for the coercion, fill the hole with the invented EvVar, and
    then quantify over the EvVar. Not too tricky -- just some
    impedance matching, really.

    Note [Simplify cloned constraints]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    At this stage, we're simplifying constraints only for insolubility
    and for unification. Note that all the evidence is quickly discarded.
    We use a clone of the real constraint. If we don't do this,
    then RHS coercion-hole constraints get filled in, only to get filled
    in *again* when solving the implications emitted from tcRule. That's
    terrible, so we avoid the problem by cloning the constraints.

    -}

    simplifyRule :: RuleName
                 -> TcLevel                 -- Level at which to solve the constraints
                 -> WantedConstraints       -- Constraints from LHS
                 -> WantedConstraints       -- Constraints from RHS
                 -> TcM ( [EvVar]               -- Quantify over these LHS vars
                        , WantedConstraints     -- Residual un-quantified LHS constraints
                        , TcTyVarSet )          -- Don't default these
    -- See Note [The SimplifyRule Plan]
    -- NB: This consumes all simple constraints on the LHS, but not
    -- any LHS implication constraints.
    simplifyRule :: RuleName
    -> TcLevel
    -> WantedConstraints
    -> WantedConstraints
    -> TcM ([TcTyVar], WantedConstraints, TyCoVarSet)
    simplifyRule RuleName
    name TcLevel
    tc_lvl WantedConstraints
    lhs_wanted WantedConstraints
    rhs_wanted
      = do {
           -- Note [The SimplifyRule Plan] step 1
           -- First solve the LHS and *then* solve the RHS
           -- Crucially, this performs unifications
           -- Why clone?  See Note [Simplify cloned constraints]
           ; lhs_clone <- WantedConstraints -> TcM WantedConstraints
    cloneWC WantedConstraints
    lhs_wanted
           ; rhs_clone <- cloneWC rhs_wanted
           ; (dont_default, _)
                <- setTcLevel tc_lvl $
                   runTcS            $
                   do { lhs_wc  <- solveWanteds lhs_clone
                      ; _rhs_wc <- solveWanteds rhs_clone
                            -- Why do them separately?
                            -- See Note [Solve order for RULES]

                      ; let dont_default = WantedConstraints -> TyCoVarSet
    nonDefaultableTyVarsOfWC WantedConstraints
    lhs_wc
                            -- If lhs_wanteds has
                            --   (a[sk] :: TYPE rr[sk]) ~ (b0[tau] :: TYPE r0[conc])
                            -- we want r0 to be non-defaultable;
                            -- see nonDefaultableTyVarsOfWC.  Simplest way to get
                            -- this is to look at the post-simplified lhs_wc, which
                            -- will contain (rr[sk] ~ r0[conc)].  An example is in
                            -- test rep-poly/RepPolyRule1
                      ; return dont_default }

           -- Note [The SimplifyRule Plan] step 2
           ; lhs_wanted <- liftZonkM $ zonkWC lhs_wanted
           ; let (quant_cts, residual_lhs_wanted) = getRuleQuantCts lhs_wanted

           -- Note [The SimplifyRule Plan] step 3
           ; quant_evs <- mapM mk_quant_ev (bagToList quant_cts)

           ; traceTc "simplifyRule" $
             vcat [ text "LHS of rule" <+> doubleQuotes (ftext name)
                  , text "lhs_wanted" <+> ppr lhs_wanted
                  , text "rhs_wanted" <+> ppr rhs_wanted
                  , text "quant_cts" <+> ppr quant_cts
                  , text "residual_lhs_wanted" <+> ppr residual_lhs_wanted
                  , text "dont_default" <+> ppr dont_default
                  ]

           ; return (quant_evs, residual_lhs_wanted, dont_default) }

      where
        mk_quant_ev :: Ct -> TcM EvVar
        mk_quant_ev :: Ct -> IOEnv (Env TcGblEnv TcLclEnv) TcTyVar
    mk_quant_ev Ct
    ct
          | CtWanted { ctev_dest :: CtEvidence -> TcEvDest
    ctev_dest = TcEvDest
    dest, ctev_pred :: CtEvidence -> Type
    ctev_pred = Type
    pred } <- Ct -> CtEvidence
    ctEvidence Ct
    ct
          = case TcEvDest
    dest of
              EvVarDest TcTyVar
    ev_id -> TcTyVar -> IOEnv (Env TcGblEnv TcLclEnv) TcTyVar
    forall a. a -> IOEnv (Env TcGblEnv TcLclEnv) a
    forall (m :: * -> *) a. Monad m => a -> m a
    return TcTyVar
    ev_id
              HoleDest CoercionHole
    hole   -> -- See Note [Quantifying over coercion holes]
                                 do { ev_id <- Type -> IOEnv (Env TcGblEnv TcLclEnv) TcTyVar
    forall gbl lcl. Type -> TcRnIf gbl lcl TcTyVar
    newEvVar Type
    pred
                                    ; fillCoercionHole hole (mkCoVarCo ev_id)
                                    ; return ev_id }
        mk_quant_ev Ct
    ct = String -> SDoc -> IOEnv (Env TcGblEnv TcLclEnv) TcTyVar
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "mk_quant_ev" (Ct -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Ct
    ct)

    getRuleQuantCts :: WantedConstraints -> (Cts, WantedConstraints)
    -- Extract all the constraints we can quantify over,
    --   also returning the depleted WantedConstraints
    --
    -- NB: we must look inside implications, because with
    --     -fdefer-type-errors we generate implications rather eagerly;
    --     see GHC.Tc.Utils.Unify.implicationNeeded. Not doing so caused #14732.
    --
    -- Unlike simplifyInfer, we don't leave the WantedConstraints unchanged,
    --   and attempt to solve them from the quantified constraints.  That
    --   nearly works, but fails for a constraint like (d :: Eq Int).
    --   We /do/ want to quantify over it, but the short-cut solver
    --   (see GHC.Tc.Solver.Dict Note [Shortcut solving]) ignores the quantified
    --   and instead solves from the top level.
    --
    --   So we must partition the WantedConstraints ourselves
    --   Not hard, but tiresome.

    getRuleQuantCts :: WantedConstraints -> (Cts, WantedConstraints)
    getRuleQuantCts WantedConstraints
    wc
      = TyCoVarSet -> WantedConstraints -> (Cts, WantedConstraints)
    float_wc TyCoVarSet
    emptyVarSet WantedConstraints
    wc
      where
        float_wc :: TcTyCoVarSet -> WantedConstraints -> (Cts, WantedConstraints)
        float_wc :: TyCoVarSet -> WantedConstraints -> (Cts, WantedConstraints)
    float_wc TyCoVarSet
    skol_tvs (WC { wc_simple :: WantedConstraints -> Cts
    wc_simple = Cts
    simples, wc_impl :: WantedConstraints -> Bag Implication
    wc_impl = Bag Implication
    implics, wc_errors :: WantedConstraints -> Bag DelayedError
    wc_errors = Bag DelayedError
    errs })
          = ( Cts
    simple_yes Cts -> Cts -> Cts
    `andCts` Cts
    implic_yes
            , WantedConstraints
    emptyWC { wc_simple = simple_no, wc_impl = implics_no, wc_errors = errs })
         where
            (Cts
    simple_yes, Cts
    simple_no) = (Ct -> Bool) -> Cts -> (Cts, Cts)
    forall a. (a -> Bool) -> Bag a -> (Bag a, Bag a)
    partitionBag (TyCoVarSet -> Ct -> Bool
    rule_quant_ct TyCoVarSet
    skol_tvs) Cts
    simples
            (Cts
    implic_yes, Bag Implication
    implics_no) = (Cts -> Implication -> (Cts, Implication))
    -> Cts -> Bag Implication -> (Cts, Bag Implication)
    forall acc x y.
    (acc -> x -> (acc, y)) -> acc -> Bag x -> (acc, Bag y)
    mapAccumBagL (TyCoVarSet -> Cts -> Implication -> (Cts, Implication)
    float_implic TyCoVarSet
    skol_tvs)
                                                    Cts
    forall a. Bag a
    emptyBag Bag Implication
    implics

        float_implic :: TcTyCoVarSet -> Cts -> Implication -> (Cts, Implication)
        float_implic :: TyCoVarSet -> Cts -> Implication -> (Cts, Implication)
    float_implic TyCoVarSet
    skol_tvs Cts
    yes1 Implication
    imp
          = (Cts
    yes1 Cts -> Cts -> Cts
    `andCts` Cts
    yes2, Implication
    imp { ic_wanted = no })
          where
            (Cts
    yes2, WantedConstraints
    no) = TyCoVarSet -> WantedConstraints -> (Cts, WantedConstraints)
    float_wc TyCoVarSet
    new_skol_tvs (Implication -> WantedConstraints
    ic_wanted Implication
    imp)
            new_skol_tvs :: TyCoVarSet
    new_skol_tvs = TyCoVarSet
    skol_tvs TyCoVarSet -> [TcTyVar] -> TyCoVarSet
    `extendVarSetList` Implication -> [TcTyVar]
    ic_skols Implication
    imp

        rule_quant_ct :: TcTyCoVarSet -> Ct -> Bool
        rule_quant_ct :: TyCoVarSet -> Ct -> Bool
    rule_quant_ct TyCoVarSet
    skol_tvs Ct
    ct = case Type -> Pred
    classifyPredType (Ct -> Type
    ctPred Ct
    ct) of
          EqPred EqRel
    _ Type
    t1 Type
    t2
            | Bool -> Bool
    not (Type -> Type -> Bool
    ok_eq Type
    t1 Type
    t2)
            -> Bool
    False        -- Note [RULE quantification over equalities]
          Pred
    _ -> Ct -> TyCoVarSet
    tyCoVarsOfCt Ct
    ct TyCoVarSet -> TyCoVarSet -> Bool
    `disjointVarSet` TyCoVarSet
    skol_tvs

        ok_eq :: Type -> Type -> Bool
    ok_eq Type
    t1 Type
    t2
           | Type
    t1 HasDebugCallStack => Type -> Type -> Bool
    Type -> Type -> Bool
    `tcEqType` Type
    t2 = Bool
    False
           | Bool
    otherwise        = Type -> Bool
    is_fun_app Type
    t1 Bool -> Bool -> Bool
    || Type -> Bool
    is_fun_app Type
    t2

        is_fun_app :: Type -> Bool
    is_fun_app Type
    ty   -- ty is of form (F tys) where F is a type function
          = case Type -> Maybe TyCon
    tyConAppTyCon_maybe Type
    ty of
              Just TyCon
    tc -> TyCon -> Bool
    isTypeFamilyTyCon TyCon
    tc
              Maybe TyCon
    Nothing -> Bool
    False