content: {-# LANGUAGE CPP #-}
  module Eta.TypeCheck.TcCanonical(
       canonicalize,
       unifyDerived,
  
       StopOrContinue(..), stopWith, continueWith
    ) where
  
  import Eta.TypeCheck.TcRnTypes
  import Eta.TypeCheck.TcType
  import Eta.Types.Type
  import Eta.Types.Kind
  import Eta.TypeCheck.TcFlatten
  import Eta.TypeCheck.TcSMonad
  import Eta.TypeCheck.TcEvidence
  import Eta.Types.Class
  import Eta.Types.TyCon
  import Eta.Types.TypeRep
  import Eta.Types.Coercion
  import Eta.Types.FamInstEnv ( FamInstEnvs )
  import Eta.TypeCheck.FamInst ( tcTopNormaliseNewTypeTF_maybe )
  import Eta.BasicTypes.Var
  import qualified Eta.BasicTypes.Var as Var
  import Eta.BasicTypes.DataCon ( dataConName )
  import Eta.BasicTypes.Name( isSystemName, nameOccName )
  import Eta.BasicTypes.OccName( OccName )
  import Eta.Utils.Outputable
  import Control.Monad
  import Eta.Main.DynFlags( DynFlags )
  import Eta.BasicTypes.VarSet
  import Eta.BasicTypes.RdrName
  
  import Eta.Utils.Pair
  import Eta.Utils.Util
  import Eta.Utils.MonadUtils ( zipWith3M, zipWith3M_ )
  import Data.List  ( zip4 )
  import Eta.BasicTypes.BasicTypes
  import Data.Maybe ( isJust )
  import Eta.Utils.FastString
  
  #include "HsVersions.h"
  
  {-
  ************************************************************************
  *                                                                      *
  *                      The Canonicaliser                               *
  *                                                                      *
  ************************************************************************
  
  Note [Canonicalization]
  ~~~~~~~~~~~~~~~~~~~~~~~
  
  Canonicalization converts a simple constraint to a canonical form. It is
  unary (i.e. treats individual constraints one at a time), does not do
  any zonking, but lives in TcS monad because it needs to create fresh
  variables (for flattening) and consult the inerts (for efficiency).
  
  The execution plan for canonicalization is the following:
  
    1) Decomposition of equalities happens as necessary until we reach a
       variable or type family in one side. There is no decomposition step
       for other forms of constraints.
  
    2) If, when we decompose, we discover a variable on the head then we
       look at inert_eqs from the current inert for a substitution for this
       variable and contine decomposing. Hence we lazily apply the inert
       substitution if it is needed.
  
    3) If no more decomposition is possible, we deeply apply the substitution
       from the inert_eqs and continue with flattening.
  
    4) During flattening, we examine whether we have already flattened some
       function application by looking at all the CTyFunEqs with the same
       function in the inert set. The reason for deeply applying the inert
       substitution at step (3) is to maximise our chances of matching an
       already flattened family application in the inert.
  
  The net result is that a constraint coming out of the canonicalization
  phase cannot be rewritten any further from the inerts (but maybe /it/ can
  rewrite an inert or still interact with an inert in a further phase in the
  simplifier.
  
  Note [Caching for canonicals]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Our plan with pre-canonicalization is to be able to solve a constraint
  really fast from existing bindings in TcEvBinds. So one may think that
  the condition (isCNonCanonical) is not necessary.  However consider
  the following setup:
  
  InertSet = { [W] d1 : Num t }
  WorkList = { [W] d2 : Num t, [W] c : t ~ Int}
  
  Now, we prioritize equalities, but in our concrete example
  (should_run/mc17.hs) the first (d2) constraint is dealt with first,
  because (t ~ Int) is an equality that only later appears in the
  worklist since it is pulled out from a nested implication
  constraint. So, let's examine what happens:
  
     - We encounter work item (d2 : Num t)
  
     - Nothing is yet in EvBinds, so we reach the interaction with inerts
       and set:
                d2 := d1
      and we discard d2 from the worklist. The inert set remains unaffected.
  
     - Now the equation ([W] c : t ~ Int) is encountered and kicks-out
       (d1 : Num t) from the inerts.  Then that equation gets
       spontaneously solved, perhaps. We end up with:
          InertSet : { [G] c : t ~ Int }
          WorkList : { [W] d1 : Num t}
  
     - Now we examine (d1), we observe that there is a binding for (Num
       t) in the evidence binds and we set:
               d1 := d2
       and end up in a loop!
  
  Now, the constraints that get kicked out from the inert set are always
  Canonical, so by restricting the use of the pre-canonicalizer to
  NonCanonical constraints we eliminate this danger. Moreover, for
  canonical constraints we already have good caching mechanisms
  (effectively the interaction solver) and we are interested in reducing
  things like superclasses of the same non-canonical constraint being
  generated hence I don't expect us to lose a lot by introducing the
  (isCNonCanonical) restriction.
  
  A similar situation can arise in TcSimplify, at the end of the
  solve_wanteds function, where constraints from the inert set are
  returned as new work -- our substCt ensures however that if they are
  not rewritten by subst, they remain canonical and hence we will not
  attempt to solve them from the EvBinds. If on the other hand they did
  get rewritten and are now non-canonical they will still not match the
  EvBinds, so we are again good.
  -}
  
  -- Top-level canonicalization
  -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  
  canonicalize :: Ct -> TcS (StopOrContinue Ct)
  canonicalize ct@(CNonCanonical { cc_ev = ev })
    = do { traceTcS "canonicalize (non-canonical)" (ppr ct)
         ; {-# SCC "canEvVar" #-}
           canEvNC ev }
  
  canonicalize (CDictCan { cc_ev = ev
                         , cc_class  = cls
                         , cc_tyargs = xis })
    = {-# SCC "canClass" #-}
      canClass ev cls xis -- Do not add any superclasses
  canonicalize (CTyEqCan { cc_ev = ev
                         , cc_tyvar  = tv
                         , cc_rhs    = xi
                         , cc_eq_rel = eq_rel })
    = {-# SCC "canEqLeafTyVarEq" #-}
      canEqTyVar ev eq_rel NotSwapped tv xi xi
  
  canonicalize (CFunEqCan { cc_ev = ev
                          , cc_fun    = fn
                          , cc_tyargs = xis1
                          , cc_fsk    = fsk })
    = {-# SCC "canEqLeafFunEq" #-}
      canCFunEqCan ev fn xis1 fsk
  
  canonicalize (CIrredEvCan { cc_ev = ev })
    = canIrred ev
  canonicalize (CHoleCan { cc_ev = ev, cc_occ = occ, cc_hole = hole })
    = canHole ev occ hole
  
  canEvNC :: CtEvidence -> TcS (StopOrContinue Ct)
  -- Called only for non-canonical EvVars
  canEvNC ev
    = case classifyPredType (ctEvPred ev) of
        ClassPred cls tys     -> do traceTcS "canEvNC:cls" (ppr cls <+> ppr tys)
                                    canClassNC ev cls tys
        EqPred eq_rel ty1 ty2 -> do traceTcS "canEvNC:eq" (ppr ty1 $$ ppr ty2)
                                    canEqNC    ev eq_rel ty1 ty2
        TuplePred tys         -> do traceTcS "canEvNC:tup" (ppr tys)
                                    canTuple   ev tys
        IrredPred {}          -> do traceTcS "canEvNC:irred" (ppr (ctEvPred ev))
                                    canIrred   ev
  {-
  ************************************************************************
  *                                                                      *
  *                      Tuple Canonicalization
  *                                                                      *
  ************************************************************************
  -}
  
  canTuple :: CtEvidence -> [PredType] -> TcS (StopOrContinue Ct)
  canTuple ev tys
    = do { traceTcS "can_pred" (text "TuplePred!")
         ; let xcomp = EvTupleMk
               xdecomp x = zipWith (\_ i -> EvTupleSel x i) tys [0..]
         ; xCtEvidence ev (XEvTerm tys xcomp xdecomp)
         ; stopWith ev "Decomposed tuple constraint" }
  
  {-
  ************************************************************************
  *                                                                      *
  *                      Class Canonicalization
  *                                                                      *
  ************************************************************************
  -}
  
  canClass, canClassNC
     :: CtEvidence
     -> Class -> [Type] -> TcS (StopOrContinue Ct)
  -- Precondition: EvVar is class evidence
  
  -- The canClassNC version is used on non-canonical constraints
  -- and adds superclasses.  The plain canClass version is used
  -- for already-canonical class constraints (but which might have
  -- been subsituted or somthing), and hence do not need superclasses
  
  canClassNC ev cls tys
    = canClass ev cls tys
      `andWhenContinue` emitSuperclasses
  
  canClass ev cls tys
    =   -- all classes do *nominal* matching
      ASSERT2( ctEvRole ev == Nominal, ppr ev $$ ppr cls $$ ppr tys )
      do { (xis, cos) <- flattenMany FM_FlattenAll ev (repeat Nominal) tys
         ; let co = mkTcTyConAppCo Nominal (classTyCon cls) cos
               xi = mkClassPred cls xis
               mk_ct new_ev = CDictCan { cc_ev = new_ev
                                       , cc_tyargs = xis, cc_class = cls }
         ; mb <- rewriteEvidence ev xi co
         ; traceTcS "canClass" (vcat [ ppr ev <+> ppr cls <+> ppr tys
                                     , ppr xi, ppr mb ])
         ; return (fmap mk_ct mb) }
  
  emitSuperclasses :: Ct -> TcS (StopOrContinue Ct)
  emitSuperclasses ct@(CDictCan { cc_ev = ev , cc_tyargs = xis_new, cc_class = cls })
              -- Add superclasses of this one here, See Note [Adding superclasses].
              -- But only if we are not simplifying the LHS of a rule.
   = do { newSCWorkFromFlavored ev cls xis_new
        -- Arguably we should "seq" the coercions if they are derived,
        -- as we do below for emit_kind_constraint, to allow errors in
        -- superclasses to be executed if deferred to runtime!
        ; continueWith ct }
  emitSuperclasses _ = panic "emit_superclasses of non-class!"
  
  {-
  Note [Adding superclasses]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~
  Since dictionaries are canonicalized only once in their lifetime, the
  place to add their superclasses is canonicalisation (The alternative
  would be to do it during constraint solving, but we'd have to be
  extremely careful to not repeatedly introduced the same superclass in
  our worklist). Here is what we do:
  
  For Givens:
         We add all their superclasses as Givens.
  
  For Wanteds:
         Generally speaking we want to be able to add superclasses of
         wanteds for two reasons:
  
         (1) Oportunities for improvement. Example:
                    class (a ~ b) => C a b
             Wanted constraint is: C alpha beta
             We'd like to simply have C alpha alpha. Similar
             situations arise in relation to functional dependencies.
  
         (2) To have minimal constraints to quantify over:
             For instance, if our wanted constraint is (Eq a, Ord a)
             we'd only like to quantify over Ord a.
  
         To deal with (1) above we only add the superclasses of wanteds
         which may lead to improvement, that is: equality superclasses or
         superclasses with functional dependencies.
  
         We deal with (2) completely independently in TcSimplify. See
         Note [Minimize by SuperClasses] in TcSimplify.
  
  
         Moreover, in all cases the extra improvement constraints are
         Derived. Derived constraints have an identity (for now), but
         we don't do anything with their evidence. For instance they
         are never used to rewrite other constraints.
  
         See also [New Wanted Superclass Work] in TcInteract.
  
  
  For Deriveds:
         We do nothing.
  
  Here's an example that demonstrates why we chose to NOT add
  superclasses during simplification: [Comes from ticket #4497]
  
     class Num (RealOf t) => Normed t
     type family RealOf x
  
  Assume the generated wanted constraint is:
     RealOf e ~ e, Normed e
  If we were to be adding the superclasses during simplification we'd get:
     Num uf, Normed e, RealOf e ~ e, RealOf e ~ uf
  ==>
     e ~ uf, Num uf, Normed e, RealOf e ~ e
  ==> [Spontaneous solve]
     Num uf, Normed uf, RealOf uf ~ uf
  
  While looks exactly like our original constraint. If we add the superclass again we'd loop.
  By adding superclasses definitely only once, during canonicalisation, this situation can't
  happen.
  -}
  
  newSCWorkFromFlavored :: CtEvidence -> Class -> [Xi] -> TcS ()
  -- Returns superclasses, see Note [Adding superclasses]
  newSCWorkFromFlavored flavor cls xis
    | isDerived flavor
    = return ()  -- Deriveds don't yield more superclasses because we will
                 -- add them transitively in the case of wanteds.
  
    | isGiven flavor
    = do { let sc_theta = immSuperClasses cls xis
               xev_decomp x = zipWith (\_ i -> EvSuperClass x i) sc_theta [0..]
               xev = XEvTerm { ev_preds  =  sc_theta
                             , ev_comp   = panic "Can't compose for given!"
                             , ev_decomp = xev_decomp }
         ; xCtEvidence flavor xev }
  
    | isEmptyVarSet (tyVarsOfTypes xis)
    = return () -- Wanteds with no variables yield no deriveds.
                -- See Note [Improvement from Ground Wanteds]
  
    | otherwise -- Wanted case, just add those SC that can lead to improvement.
    = do { let sc_rec_theta = transSuperClasses cls xis
               impr_theta   = filter is_improvement_pty sc_rec_theta
               loc          = ctEvLoc flavor
         ; traceTcS "newSCWork/Derived" $ text "impr_theta =" <+> ppr impr_theta
         ; mapM_ (emitNewDerived loc) impr_theta }
  
  is_improvement_pty :: PredType -> Bool
  -- Either it's an equality, or has some functional dependency
  is_improvement_pty ty = go (classifyPredType ty)
    where
      go (EqPred NomEq t1 t2) = not (t1 `tcEqType` t2)
      go (EqPred ReprEq _ _)  = False
      go (ClassPred cls _tys) = not $ null fundeps
                              where (_,fundeps) = classTvsFds cls
      go (TuplePred ts)       = any is_improvement_pty ts
      go (IrredPred {})       = True -- Might have equalities after reduction?
  
  {-
  ************************************************************************
  *                                                                      *
  *                      Irreducibles canonicalization
  *                                                                      *
  ************************************************************************
  -}
  
  canIrred :: CtEvidence -> TcS (StopOrContinue Ct)
  -- Precondition: ty not a tuple and no other evidence form
  canIrred old_ev
    = do { let old_ty = ctEvPred old_ev
         ; traceTcS "can_pred" (text "IrredPred = " <+> ppr old_ty)
         ; (xi,co) <- flatten FM_FlattenAll old_ev old_ty -- co :: xi ~ old_ty
         ; rewriteEvidence old_ev xi co `andWhenContinue` \ new_ev ->
      do { -- Re-classify, in case flattening has improved its shape
         ; case classifyPredType (ctEvPred new_ev) of
             ClassPred cls tys     -> canClassNC new_ev cls tys
             TuplePred tys         -> canTuple   new_ev tys
             EqPred eq_rel ty1 ty2 -> canEqNC new_ev eq_rel ty1 ty2
             _                     -> continueWith $
                                      CIrredEvCan { cc_ev = new_ev } } }
  
  canHole :: CtEvidence -> OccName -> HoleSort -> TcS (StopOrContinue Ct)
  canHole ev occ hole_sort
    = do { let ty = ctEvPred ev
         ; (xi,co) <- flatten FM_SubstOnly ev ty -- co :: xi ~ ty
         ; rewriteEvidence ev xi co `andWhenContinue` \ new_ev ->
      do { emitInsoluble (CHoleCan { cc_ev = new_ev
                                   , cc_occ = occ
                                   , cc_hole = hole_sort })
         ; stopWith new_ev "Emit insoluble hole" } }
  
  {-
  ************************************************************************
  *                                                                      *
  *        Equalities
  *                                                                      *
  ************************************************************************
  -}
  
  canEqNC :: CtEvidence -> EqRel -> Type -> Type -> TcS (StopOrContinue Ct)
  canEqNC ev eq_rel ty1 ty2
    = can_eq_nc ev eq_rel ty1 ty1 ty2 ty2
  
  can_eq_nc
     :: CtEvidence
     -> EqRel
     -> Type -> Type    -- LHS, after and before type-synonym expansion, resp
     -> Type -> Type    -- RHS, after and before type-synonym expansion, resp
     -> TcS (StopOrContinue Ct)
  can_eq_nc ev eq_rel ty1 ps_ty1 ty2 ps_ty2
    = do { traceTcS "can_eq_nc" $
           vcat [ ppr ev, ppr eq_rel, ppr ty1, ppr ps_ty1, ppr ty2, ppr ps_ty2 ]
         ; rdr_env <- getGlobalRdrEnvTcS
         ; fam_insts <- getFamInstEnvs
         ; can_eq_nc' rdr_env fam_insts ev eq_rel ty1 ps_ty1 ty2 ps_ty2 }
  
  can_eq_nc'
     :: GlobalRdrEnv   -- needed to see which newtypes are in scope
     -> FamInstEnvs    -- needed to unwrap data instances
     -> CtEvidence
     -> EqRel
     -> Type -> Type    -- LHS, after and before type-synonym expansion, resp
     -> Type -> Type    -- RHS, after and before type-synonym expansion, resp
     -> TcS (StopOrContinue Ct)
  
  -- Expand synonyms first; see Note [Type synonyms and canonicalization]
  can_eq_nc' _rdr_env _envs ev eq_rel ty1 ps_ty1 ty2 ps_ty2
    | Just ty1' <- tcView ty1 = can_eq_nc ev eq_rel ty1' ps_ty1 ty2  ps_ty2
    | Just ty2' <- tcView ty2 = can_eq_nc ev eq_rel ty1  ps_ty1 ty2' ps_ty2
  
  -- Type family on LHS or RHS take priority over tyvars,
  -- so that  tv ~ F ty gets flattened
  -- Otherwise  F a ~ F a  might not get solved!
  can_eq_nc' _rdr_env _envs ev eq_rel (TyConApp fn1 tys1) _ ty2 ps_ty2
    | isTypeFamilyTyCon fn1
    = can_eq_fam_nc ev eq_rel NotSwapped fn1 tys1 ty2 ps_ty2
  can_eq_nc' _rdr_env _envs ev eq_rel ty1 ps_ty1 (TyConApp fn2 tys2) _
    | isTypeFamilyTyCon fn2
    = can_eq_fam_nc ev eq_rel IsSwapped fn2 tys2 ty1 ps_ty1
  
  -- When working with ReprEq, unwrap newtypes next.
  -- Otherwise, a ~ Id a wouldn't get solved
  can_eq_nc' rdr_env envs ev ReprEq ty1 _ ty2 ps_ty2
    | Just (co, ty1') <- tcTopNormaliseNewTypeTF_maybe envs rdr_env ty1
    = can_eq_newtype_nc rdr_env ev NotSwapped co ty1 ty1' ty2 ps_ty2
  can_eq_nc' rdr_env envs ev ReprEq ty1 ps_ty1 ty2 _
    | Just (co, ty2') <- tcTopNormaliseNewTypeTF_maybe envs rdr_env ty2
    = can_eq_newtype_nc rdr_env ev IsSwapped  co ty2 ty2' ty1 ps_ty1
  
  -- Type variable on LHS or RHS are next
  can_eq_nc' _rdr_env _envs ev eq_rel (TyVarTy tv1) _ ty2 ps_ty2
    = canEqTyVar ev eq_rel NotSwapped tv1 ty2 ps_ty2
  can_eq_nc' _rdr_env _envs ev eq_rel ty1 ps_ty1 (TyVarTy tv2) _
    = canEqTyVar ev eq_rel IsSwapped tv2 ty1 ps_ty1
  
  ----------------------
  -- Otherwise try to decompose
  ----------------------
  
  -- Literals
  can_eq_nc' _rdr_env _envs ev eq_rel ty1@(LitTy l1) _ (LitTy l2) _
   | l1 == l2
    = do { when (isWanted ev) $
           setEvBind (ctev_evar ev) (EvCoercion $
                                     mkTcReflCo (eqRelRole eq_rel) ty1)
         ; stopWith ev "Equal LitTy" }
  
  -- Decomposable type constructor applications
  -- Synonyms and type functions (which are not decomposable)
  -- have already been dealt with
  can_eq_nc' _rdr_env _envs ev eq_rel (TyConApp tc1 tys1) _ (TyConApp tc2 tys2) _
    | isDecomposableTyCon tc1
    , isDecomposableTyCon tc2
    = canDecomposableTyConApp ev eq_rel tc1 tys1 tc2 tys2
  
  can_eq_nc' _rdr_env _envs ev eq_rel (TyConApp tc1 _) ps_ty1 (FunTy {}) ps_ty2
    | isDecomposableTyCon tc1
        -- The guard is important
        -- e.g.  (x -> y) ~ (F x y) where F has arity 1
        --       should not fail, but get the app/app case
    = canEqHardFailure ev eq_rel ps_ty1 ps_ty2
  
  can_eq_nc' _rdr_env _envs ev eq_rel (FunTy s1 t1) _ (FunTy s2 t2) _
    = do { canDecomposableTyConAppOK ev eq_rel funTyCon [s1,t1] [s2,t2]
         ; stopWith ev "Decomposed FunTyCon" }
  
  can_eq_nc' _rdr_env _envs ev eq_rel (FunTy {}) ps_ty1 (TyConApp tc2 _) ps_ty2
    | isDecomposableTyCon tc2
    = canEqHardFailure ev eq_rel ps_ty1 ps_ty2
  
  can_eq_nc' _rdr_env _envs ev eq_rel s1@(ForAllTy {}) _ s2@(ForAllTy {}) _
   | CtWanted { ctev_loc = loc, ctev_evar = orig_ev } <- ev
   = do { let (tvs1,body1) = tcSplitForAllTys s1
              (tvs2,body2) = tcSplitForAllTys s2
        ; if not (equalLength tvs1 tvs2) then
            canEqHardFailure ev eq_rel s1 s2
          else
            do { traceTcS "Creating implication for polytype equality" $ ppr ev
               ; ev_term <- deferTcSForAllEq (eqRelRole eq_rel)
                                             loc (tvs1,body1) (tvs2,body2)
               ; setEvBind orig_ev ev_term
               ; stopWith ev "Deferred polytype equality" } }
   | otherwise
   = do { traceTcS "Ommitting decomposition of given polytype equality" $
          pprEq s1 s2    -- See Note [Do not decompose given polytype equalities]
        ; stopWith ev "Discard given polytype equality" }
  
  can_eq_nc' _rdr_env _envs ev eq_rel ty1@(AppTy {}) _ ty2 _
    | isGiven ev = try_decompose_app ev eq_rel ty1 ty2
    | otherwise  = can_eq_wanted_app ev eq_rel ty1 ty2
  can_eq_nc' _rdr_env _envs ev eq_rel ty1 _ ty2@(AppTy {}) _
    | isGiven ev = try_decompose_app ev eq_rel ty1 ty2
    | otherwise  = can_eq_wanted_app ev eq_rel ty1 ty2
  
  -- Everything else is a definite type error, eg LitTy ~ TyConApp
  can_eq_nc' _rdr_env _envs ev eq_rel _ ps_ty1 _ ps_ty2
    = canEqHardFailure ev eq_rel ps_ty1 ps_ty2
  
  ------------
  can_eq_fam_nc :: CtEvidence -> EqRel -> SwapFlag
                -> TyCon -> [TcType]
                -> TcType -> TcType
                -> TcS (StopOrContinue Ct)
  -- Canonicalise a non-canonical equality of form (F tys ~ ty)
  --   or the swapped version thereof
  -- Flatten both sides and go round again
  can_eq_fam_nc ev eq_rel swapped fn tys rhs ps_rhs
    = do { (xi_lhs, co_lhs) <- flattenFamApp FM_FlattenAll ev fn tys
         ; rewriteEqEvidence ev eq_rel swapped xi_lhs rhs co_lhs
                             (mkTcReflCo (eqRelRole eq_rel) rhs)
           `andWhenContinue` \ new_ev ->
           can_eq_nc new_ev eq_rel xi_lhs xi_lhs rhs ps_rhs }
  
  {-
  Note [Eager reflexivity check]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Suppose we have
  
    newtype X = MkX (Int -> X)
  
  and
  
    [W] X ~R X
  
  Naively, we would start unwrapping X and end up in a loop. Instead,
  we do this eager reflexivity check. This is necessary only for representational
  equality because the flattener technology deals with the similar case
  (recursive type families) for nominal equality.
  
  As an alternative, suppose we also have
  
    newtype Y = MkY (Int -> Y)
  
  and now wish to prove
  
    [W] X ~R Y
  
  This new Wanted will loop, expanding out the newtypes ever deeper looking
  for a solid match or a solid discrepancy. Indeed, there is something
  appropriate to this looping, because X and Y *do* have the same representation,
  in the limit -- they're both (Fix ((->) Int)). However, no finitely-sized
  coercion will ever witness it. This loop won't actually cause GHC to hang,
  though, because of the stack-blowing check in can_eq_newtype_nc, along
  with the fact that rewriteEqEvidence bumps the stack depth.
  
  Note [AppTy reflexivity check]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Consider trying to prove (f a) ~R (f a). The AppTys in there can't
  be decomposed, because representational equality isn't congruent with respect
  to AppTy. So, when canonicalising the equality above, we get stuck and
  would normally produce a CIrredEvCan. However, we really do want to
  be able to solve (f a) ~R (f a). So, in the representational case only,
  we do a reflexivity check.
  
  (This would be sound in the nominal case, but unnecessary, and I [Richard
  E.] am worried that it would slow down the common case.)
  -}
  
  ------------------------
  -- | We're able to unwrap a newtype. Update the bits accordingly.
  can_eq_newtype_nc :: GlobalRdrEnv
                    -> CtEvidence           -- ^ :: ty1 ~ ty2
                    -> SwapFlag
                    -> TcCoercion           -- ^ :: ty1 ~ ty1'
                    -> TcType               -- ^ ty1
                    -> TcType               -- ^ ty1'
                    -> TcType               -- ^ ty2
                    -> TcType               -- ^ ty2, with type synonyms
                    -> TcS (StopOrContinue Ct)
  can_eq_newtype_nc rdr_env ev swapped co ty1 ty1' ty2 ps_ty2
    = do { traceTcS "can_eq_newtype_nc" $
           vcat [ ppr ev, ppr swapped, ppr co, ppr ty1', ppr ty2 ]
  
           -- check for blowing our stack:
           -- See Note [Eager reflexivity check] for an example of
           -- when this is necessary
         ; dflags <- getDynFlags
         ; if isJust $ subGoalDepthExceeded (maxSubGoalDepth dflags)
                                            (ctLocDepth (ctEvLoc ev))
           then do { emitInsoluble (mkNonCanonical ev)
                   ; stopWith ev "unwrapping newtypes blew stack" }
           else do
         { if ty1 `eqType` ty2   -- See Note [Eager reflexivity check]
           then canEqReflexive ev ReprEq ty1
           else do
         { markDataConsAsUsed rdr_env (tyConAppTyCon ty1)
             -- we have actually used the newtype constructor here, so
             -- make sure we don't warn about importing it!
  
         ; rewriteEqEvidence ev ReprEq swapped ty1' ps_ty2
                             (mkTcSymCo co) (mkTcReflCo Representational ps_ty2)
           `andWhenContinue` \ new_ev ->
           can_eq_nc new_ev ReprEq ty1' ty1' ty2 ps_ty2 }}}
  
  -- | Mark all the datacons of the given 'TyCon' as used in this module,
  -- avoiding "redundant import" warnings.
  markDataConsAsUsed :: GlobalRdrEnv -> TyCon -> TcS ()
  markDataConsAsUsed rdr_env tc = addUsedRdrNamesTcS
    [ mkRdrQual (is_as (is_decl imp_spec)) occ
    | dc <- tyConDataCons tc
    , let dc_name = dataConName dc
          occ  = nameOccName dc_name
    , gre : _               <- return $ lookupGRE_Name rdr_env dc_name
    , Imported (imp_spec:_) <- return $ gre_prov gre ]
  
  -------------------------------------------------
  can_eq_wanted_app :: CtEvidence -> EqRel -> TcType -> TcType
                    -> TcS (StopOrContinue Ct)
  -- One or the other is an App; neither is a type variable
  -- See Note [Canonicalising type applications]
  can_eq_wanted_app ev eq_rel ty1 ty2
    = do { (xi1, co1) <- flatten FM_FlattenAll ev ty1
         ; (xi2, co2) <- flatten FM_FlattenAll ev ty2
          ; rewriteEqEvidence ev eq_rel NotSwapped xi1 xi2 co1 co2
            `andWhenContinue` \ new_ev ->
            try_decompose_app new_ev eq_rel xi1 xi2 }
  
  ---------
  try_decompose_app :: CtEvidence -> EqRel
                    -> TcType -> TcType -> TcS (StopOrContinue Ct)
  -- Preconditions: one or the other is an App;
  --                but neither is a type variable
  --                so can't turn it into an application if it
  --                   doesn't look like one already
  -- See Note [Canonicalising type applications]
  try_decompose_app ev eq_rel ty1 ty2
    = case eq_rel of
        NomEq  -> try_decompose_nom_app  ev ty1 ty2
        ReprEq -> try_decompose_repr_app ev ty1 ty2
  
  ---------
  try_decompose_repr_app :: CtEvidence
                         -> TcType -> TcType -> TcS (StopOrContinue Ct)
  -- Preconditions: like try_decompose_app, but also
  --                ev has a representational
  try_decompose_repr_app ev ty1 ty2
    | ty1 `eqType` ty2   -- See Note [AppTy reflexivity check]
    = canEqReflexive ev ReprEq ty1
  
    | AppTy {} <- ty1
    = canEqFailure ev ReprEq ty1 ty2
  
    | AppTy {} <- ty2
    = canEqFailure ev ReprEq ty1 ty2
  
    | otherwise  -- flattening in can_eq_wanted_app exposed some TyConApps!
    = ASSERT2( isJust (tcSplitTyConApp_maybe ty1) || isJust (tcSplitTyConApp_maybe ty2)
            , ppr ty1 $$ ppr ty2 )  -- If this assertion fails, we may fall
                                    -- into an infinite loop
      canEqNC ev ReprEq ty1 ty2
  
  ---------
  try_decompose_nom_app :: CtEvidence
                        -> TcType -> TcType -> TcS (StopOrContinue Ct)
  -- Preconditions: like try_decompose_app, but also
  --                ev has a nominal role
  try_decompose_nom_app ev ty1 ty2
     | AppTy s1 t1 <- ty1
     = case tcSplitAppTy_maybe ty2 of
         Nothing      -> canEqHardFailure ev NomEq ty1 ty2
         Just (s2,t2) -> do_decompose s1 t1 s2 t2
  
     | AppTy s2 t2 <- ty2
     = case tcSplitAppTy_maybe ty1 of
         Nothing      -> canEqHardFailure ev NomEq ty1 ty2
         Just (s1,t1) -> do_decompose s1 t1 s2 t2
  
     | otherwise  -- Neither is an AppTy; but one or other started that way
                  -- (precondition to can_eq_wanted_app)
                  -- So presumably one has become a TyConApp, which
                  -- is good: See Note [Canonicalising type applications]
     = ASSERT2( isJust (tcSplitTyConApp_maybe ty1) || isJust (tcSplitTyConApp_maybe ty2)
              , ppr ty1 $$ ppr ty2 )  -- If this assertion fails, we may fall
                                      -- into an infinite loop (Trac #9971)
       canEqNC ev NomEq ty1 ty2
     where
       -- do_decompose is like xCtEvidence, but recurses
       -- to try_decompose_nom_app to decompose a chain of AppTys
       do_decompose s1 t1 s2 t2
         | CtDerived { ctev_loc = loc } <- ev
         = do { emitNewDerived loc (mkTcEqPred t1 t2)
              ; canEqNC ev NomEq s1 s2 }
         | CtWanted { ctev_evar = evar, ctev_loc = loc } <- ev
         = do { ev_s <- newWantedEvVarNC loc (mkTcEqPred s1 s2)
              ; co_t <- unifyWanted loc Nominal t1 t2
              ; let co = mkTcAppCo (ctEvCoercion ev_s) co_t
              ; setEvBind evar (EvCoercion co)
              ; canEqNC ev_s NomEq s1 s2 }
         | CtGiven { ctev_evtm = ev_tm, ctev_loc = loc } <- ev
         = do { let co   = evTermCoercion ev_tm
                    co_s = mkTcLRCo CLeft  co
                    co_t = mkTcLRCo CRight co
              ; evar_s <- newGivenEvVar loc (mkTcEqPred s1 s2, EvCoercion co_s)
              ; evar_t <- newGivenEvVar loc (mkTcEqPred t1 t2, EvCoercion co_t)
              ; emitWorkNC [evar_t]
              ; canEqNC evar_s NomEq s1 s2 }
         | otherwise  -- Can't happen
         = error "try_decompose_app"
  
  ------------------------
  canDecomposableTyConApp :: CtEvidence -> EqRel
                          -> TyCon -> [TcType]
                          -> TyCon -> [TcType]
                          -> TcS (StopOrContinue Ct)
  -- See Note [Decomposing TyConApps]
  canDecomposableTyConApp ev eq_rel tc1 tys1 tc2 tys2
    | tc1 == tc2
    , length tys1 == length tys2
    = if eq_rel == NomEq || ctEvFlavour ev /= Given || isDistinctTyCon tc1
         -- See Note [Decomposing newtypes]
      then do { traceTcS "canDecomposableTyConApp"
                    (ppr ev $$ ppr eq_rel $$ ppr tc1 $$ ppr tys1 $$ ppr tys2)
              ; canDecomposableTyConAppOK ev eq_rel tc1 tys1 tys2
              ; stopWith ev "Decomposed TyConApp" }
      else canEqFailure ev eq_rel ty1 ty2
  
    -- Fail straight away for better error messages
    -- See Note [Use canEqFailure in canDecomposableTyConApp]
    | isDataFamilyTyCon tc1 || isDataFamilyTyCon tc2
    = canEqFailure ev eq_rel ty1 ty2
    | otherwise
    = canEqHardFailure ev eq_rel ty1 ty2
    where
      ty1 = mkTyConApp tc1 tys1
      ty2 = mkTyConApp tc2 tys2
  
  {-
  Note [Use canEqFailure in canDecomposableTyConApp]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  We must use canEqFailure, not canEqHardFailure here, because there is
  the possibility of success if working with a representational equality.
  Here is the case:
  
    type family TF a where TF Char = Bool
    data family DF a
    newtype instance DF Bool = MkDF Int
  
  Suppose we are canonicalising (Int ~R DF (T a)), where we don't yet
  know `a`. This is *not* a hard failure, because we might soon learn
  that `a` is, in fact, Char, and then the equality succeeds.
  
  Note [Decomposing newtypes]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~
  As explained in Note [NthCo and newtypes] in Coercion, we can't use
  NthCo on representational coercions over newtypes. So we avoid doing
  so.
  
  But is it sensible to decompose *Wanted* constraints over newtypes?
  Yes. By the time we reach canDecomposableTyConApp, we know that any
  newtypes that can be unwrapped have been. So, without importing more
  constructors, say, we know there is no way forward other than decomposition.
  So we take the one route we have available. This *does* mean that
  importing a newtype's constructor might make code that previously
  compiled fail to do so. (If that newtype is perversely recursive, say.)
  -}
  
  canDecomposableTyConAppOK :: CtEvidence -> EqRel
                            -> TyCon -> [TcType] -> [TcType]
                            -> TcS ()
  -- Precondition: tys1 and tys2 are the same length, hence "OK"
  canDecomposableTyConAppOK ev eq_rel tc tys1 tys2
    = case ev of
       CtDerived { ctev_loc = loc }
          -> unifyDeriveds loc tc_roles tys1 tys2
  
       CtWanted { ctev_evar = evar, ctev_loc = loc }
          -> do { cos <- zipWith3M (unifyWanted loc) tc_roles tys1 tys2
                ; setEvBind evar (EvCoercion (mkTcTyConAppCo role tc cos)) }
  
       CtGiven { ctev_evtm = ev_tm, ctev_loc = loc }
          -> do { let ev_co = evTermCoercion ev_tm
                ; given_evs <- newGivenEvVars loc $
                               [ ( mkTcEqPredRole r ty1 ty2
                                 , EvCoercion (mkTcNthCo i ev_co) )
                               | (r, ty1, ty2, i) <- zip4 tc_roles tys1 tys2 [0..]
                               , r /= Phantom ]
                ; emitWorkNC given_evs }
    where
      role     = eqRelRole eq_rel
      tc_roles = tyConRolesX role tc
  
  -- | Call when canonicalizing an equality fails, but if the equality is
  -- representational, there is some hope for the future.
  -- Examples in Note [Flatten irreducible representational equalities]
  canEqFailure :: CtEvidence -> EqRel
               -> TcType -> TcType -> TcS (StopOrContinue Ct)
  canEqFailure ev ReprEq ty1 ty2
    = do { -- See Note [Flatten irreducible representational equalities]
           (xi1, co1) <- flatten FM_FlattenAll ev ty1
         ; (xi2, co2) <- flatten FM_FlattenAll ev ty2
         ; traceTcS "canEqFailure with ReprEq" $
           vcat [ ppr ev, ppr ty1, ppr ty2, ppr xi1, ppr xi2 ]
         ; if xi1 `eqType` ty1 && xi2 `eqType` ty2
           then continueWith (CIrredEvCan { cc_ev = ev })  -- co1/2 must be refl
           else rewriteEqEvidence ev ReprEq NotSwapped xi1 xi2 co1 co2
                `andWhenContinue` \ new_ev ->
                can_eq_nc new_ev ReprEq xi1 xi1 xi2 xi2 }
  canEqFailure ev NomEq ty1 ty2 = canEqHardFailure ev NomEq ty1 ty2
  
  -- | Call when canonicalizing an equality fails with utterly no hope.
  canEqHardFailure :: CtEvidence -> EqRel
                   -> TcType -> TcType -> TcS (StopOrContinue Ct)
  -- See Note [Make sure that insolubles are fully rewritten]
  canEqHardFailure ev eq_rel ty1 ty2
    = do { (s1, co1) <- flatten FM_SubstOnly ev ty1
         ; (s2, co2) <- flatten FM_SubstOnly ev ty2
         ; rewriteEqEvidence ev eq_rel NotSwapped s1 s2 co1 co2
           `andWhenContinue` \ new_ev ->
      do { emitInsoluble (mkNonCanonical new_ev)
         ; stopWith new_ev "Definitely not equal" }}
  
  {-
  Note [Flatten irreducible representational equalities]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  When we can't make any progress with a representational equality, but
  we haven't given up all hope, we must flatten before producing the
  CIrredEvCan. There are two reasons to do this:
  
    * See case in Note [Use canEqFailure in canDecomposableTyConApp].
      Flattening here can expose that we know enough information to unwrap
      a newtype.
  
    * This case, which was encountered in the testsuite (T9117_3):
  
        work item: [W] c1: f a ~R g a
        inert set: [G] c2: g ~R f
  
      In can_eq_app, we try to flatten the LHS of c1. This causes no effect,
      because `f` cannot be rewritten. So, we go to can_eq_flat_app. Without
      flattening the RHS, the reflexivity check fails, and we give up. However,
      flattening the RHS rewrites `g` to `f`, the reflexivity check succeeds,
      and we go on to glory.
  
  Note [Decomposing TyConApps]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  If we see (T s1 t1 ~ T s2 t2), then we can just decompose to
    (s1 ~ s2, t1 ~ t2)
  and push those back into the work list.  But if
    s1 = K k1    s2 = K k2
  then we will jus decomopose s1~s2, and it might be better to
  do so on the spot.  An important special case is where s1=s2,
  and we get just Refl.
  
  So canDecomposableTyCon is a fast-path decomposition that uses
  unifyWanted etc to short-cut that work.
  
  Note [Canonicalising type applications]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Given (s1 t1) ~ ty2, how should we proceed?
  The simple things is to see if ty2 is of form (s2 t2), and
  decompose.  By this time s1 and s2 can't be saturated type
  function applications, because those have been dealt with
  by an earlier equation in can_eq_nc, so it is always sound to
  decompose.
  
  However, over-eager decomposition gives bad error messages
  for things like
     a b ~ Maybe c
     e f ~ p -> q
  Suppose (in the first example) we already know a~Array.  Then if we
  decompose the application eagerly, yielding
     a ~ Maybe
     b ~ c
  we get an error        "Can't match Array ~ Maybe",
  but we'd prefer to get "Can't match Array b ~ Maybe c".
  
  So instead can_eq_wanted_app flattens the LHS and RHS, in the hope of
  replacing (a b) by (Array b), before using try_decompose_app to
  decompose it.
  
  Note [Make sure that insolubles are fully rewritten]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  When an equality fails, we still want to rewrite the equality
  all the way down, so that it accurately reflects
   (a) the mutable reference substitution in force at start of solving
   (b) any ty-binds in force at this point in solving
  See Note [Kick out insolubles] in TcInteract.
  And if we don't do this there is a bad danger that
  TcSimplify.applyTyVarDefaulting will find a variable
  that has in fact been substituted.
  
  Note [Do not decompose Given polytype equalities]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Consider [G] (forall a. t1 ~ forall a. t2).  Can we decompose this?
  No -- what would the evidence look like?  So instead we simply discard
  this given evidence.
  
  
  Note [Combining insoluble constraints]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  As this point we have an insoluble constraint, like Int~Bool.
  
   * If it is Wanted, delete it from the cache, so that subsequent
     Int~Bool constraints give rise to separate error messages
  
   * But if it is Derived, DO NOT delete from cache.  A class constraint
     may get kicked out of the inert set, and then have its functional
     dependency Derived constraints generated a second time. In that
     case we don't want to get two (or more) error messages by
     generating two (or more) insoluble fundep constraints from the same
     class constraint.
  
  Note [No top-level newtypes on RHS of representational equalities]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Suppose we're in this situation:
  
   work item:  [W] c1 : a ~R b
       inert:  [G] c2 : b ~R Id a
  
  where
    newtype Id a = Id a
  
  Further, suppose flattening `a` doesn't do anything. Then, we'll flatten the
  RHS of c1 and have a new [W] c3 : a ~R Id a. If we just blindly proceed, we'll
  fail in canEqTyVar2 with an occurs-check. What we really need to do is to
  unwrap the `Id a` in the RHS. This is exactly analogous to the requirement for
  no top-level type families on the RHS of a nominal equality. The only
  annoyance is that the flattener doesn't do this work for us when flattening
  the RHS, so we have to catch this case here and then go back to the beginning
  of can_eq_nc. We know that this can't loop forever because we require that
  flattening the RHS actually made progress. (If it didn't, then we really
  *should* fail with an occurs-check!)
  
  Note [Occurs check error]
  ~~~~~~~~~~~~~~~~~~~~~~~~~
  If we have an occurs check error, are we necessarily hosed? Say our
  tyvar is tv1 and the type it appears in is xi2. Because xi2 is function
  free, then if we're computing w.r.t. nominal equality, then, yes, we're
  hosed. Nothing good can come from (a ~ [a]). If we're computing w.r.t.
  representational equality, this is a little subtler. Once again, (a ~R [a])
  is a bad thing, but (a ~R N a) for a newtype N might be just fine. This
  means also that (a ~ b a) might be fine, because `b` might become a newtype.
  
  So, we must check: does tv1 appear in xi2 under any type constructor that
  is generative w.r.t. representational equality? That's what isTyVarUnderDatatype
  does. (The other name I considered, isTyVarUnderTyConGenerativeWrtReprEq was
  a bit verbose. And the shorter name gets the point across.)
  
  See also #10715, which induced this addition.
  
  -}
  
  canCFunEqCan :: CtEvidence
               -> TyCon -> [TcType]   -- LHS
               -> TcTyVar             -- RHS
               -> TcS (StopOrContinue Ct)
  -- ^ Canonicalise a CFunEqCan.  We know that
  --     the arg types are already flat,
  -- and the RHS is a fsk, which we must *not* substitute.
  -- So just substitute in the LHS
  canCFunEqCan ev fn tys fsk
    = do { (tys', cos) <- flattenMany FM_FlattenAll ev (repeat Nominal) tys
                          -- cos :: tys' ~ tys
         ; let lhs_co  = mkTcTyConAppCo Nominal fn cos
                          -- :: F tys' ~ F tys
               new_lhs = mkTyConApp fn tys'
               fsk_ty  = mkTyVarTy fsk
         ; rewriteEqEvidence ev NomEq NotSwapped new_lhs fsk_ty
                             lhs_co (mkTcNomReflCo fsk_ty)
           `andWhenContinue` \ ev' ->
      do { extendFlatCache fn tys' (ctEvCoercion ev', fsk_ty, ctEvFlavour ev')
         ; continueWith (CFunEqCan { cc_ev = ev', cc_fun = fn
                                   , cc_tyargs = tys', cc_fsk = fsk }) } }
  
  ---------------------
  canEqTyVar :: CtEvidence -> EqRel -> SwapFlag
             -> TcTyVar
             -> TcType -> TcType
             -> TcS (StopOrContinue Ct)
  -- A TyVar on LHS, but so far un-zonked
  canEqTyVar ev eq_rel swapped tv1 ty2 ps_ty2              -- ev :: tv ~ s2
    = do { traceTcS "canEqTyVar" (ppr tv1 $$ ppr ty2 $$ ppr swapped)
         ; let fmode = mkFlattenEnv FM_FlattenAll ev  -- the FM_ param is ignored
         ; mb_yes <- flattenTyVarOuter fmode tv1
         ; case mb_yes of
           { Right (ty1, co1) -> -- co1 :: ty1 ~ tv1
               do { traceTcS "canEqTyVar2"
                             (vcat [ ppr tv1, ppr ty2, ppr swapped
                                   , ppr ty1 , ppUnless (isDerived ev) (ppr co1)])
                  ; rewriteEqEvidence ev eq_rel swapped ty1 ps_ty2
                                      co1 (mkTcReflCo (eqRelRole eq_rel) ps_ty2)
                    `andWhenContinue` \ new_ev ->
                    can_eq_nc new_ev eq_rel ty1 ty1 ty2 ps_ty2 }
  
           ; Left tv1' ->
      do { -- FM_Avoid commented out: see Note [Lazy flattening] in TcFlatten
           -- let fmode = FE { fe_ev = ev, fe_mode = FM_Avoid tv1' True }
           -- Flatten the RHS less vigorously, to avoid gratuitous flattening
           -- True <=> xi2 should not itself be a type-function application
         ; (xi2, co2) <- flatten FM_FlattenAll ev ps_ty2 -- co2 :: xi2 ~ ps_ty2
                        -- Use ps_ty2 to preserve type synonyms if poss
         ; traceTcS "canEqTyVar flat LHS"
             (vcat [ ppr tv1, ppr tv1', ppr ty2, ppr swapped, ppr xi2 ])
         ; dflags <- getDynFlags
         ; case eq_rel of
        -- See Note [No top-level newtypes on RHS of representational equalities]
             ReprEq
               | Just (tc2, _) <- tcSplitTyConApp_maybe xi2
               , isNewTyCon tc2
               , not (ps_ty2 `eqType` xi2)
               -> do { let xi1  = mkTyVarTy tv1'
                           role = eqRelRole eq_rel
                     ; traceTcS "canEqTyVar exposed newtype"
                         (vcat [ ppr tv1', ppr ps_ty2, ppr xi2, ppr tc2 ])
                     ; rewriteEqEvidence ev eq_rel swapped xi1 xi2
                                         (mkTcReflCo role xi1) co2
                       `andWhenContinue` \ new_ev ->
                       can_eq_nc new_ev eq_rel xi1 xi1 xi2 xi2 }
             _ -> canEqTyVar2 dflags ev eq_rel swapped tv1' xi2 co2 } } }
  
  canEqTyVar2 :: DynFlags
              -> CtEvidence   -- olhs ~ orhs (or, if swapped, orhs ~ olhs)
              -> EqRel
              -> SwapFlag
              -> TcTyVar      -- olhs
              -> TcType       -- nrhs
              -> TcCoercion   -- nrhs ~ orhs
              -> TcS (StopOrContinue Ct)
  -- LHS is an inert type variable,
  -- and RHS is fully rewritten, but with type synonyms
  -- preserved as much as possible
  
  canEqTyVar2 dflags ev eq_rel swapped tv1 xi2 co2
    | Just tv2 <- getTyVar_maybe xi2
    = canEqTyVarTyVar ev eq_rel swapped tv1 tv2 co2
  
    | OC_OK xi2' <- occurCheckExpand dflags tv1 xi2  -- No occurs check
    = do { let k1 = tyVarKind tv1
               k2 = typeKind xi2'
         ; rewriteEqEvidence ev eq_rel swapped xi1 xi2' co1 co2
                  -- Ensure that the new goal has enough type synonyms
                  -- expanded by the occurCheckExpand; hence using xi2' here
                  -- See Note [occurCheckExpand]
           `andWhenContinue` \ new_ev ->
           if k2 `isSubKind` k1
           then   -- Establish CTyEqCan kind invariant
                  -- Reorientation has done its best, but the kinds might
                  -- simply be incompatible
                 continueWith (CTyEqCan { cc_ev = new_ev
                                        , cc_tyvar  = tv1, cc_rhs = xi2'
                                        , cc_eq_rel = eq_rel })
           else incompatibleKind new_ev xi1 k1 xi2' k2 }
  
    | otherwise  -- Occurs check error
    = rewriteEqEvidence ev eq_rel swapped xi1 xi2 co1 co2
      `andWhenContinue` \ new_ev ->
      if eq_rel == NomEq || isTyVarUnderDatatype tv1 xi2
        -- See Note [Occurs check error]
  
      then do { emitInsoluble (mkNonCanonical new_ev)
                -- If we have a ~ [a], it is not canonical, and in particular
                -- we don't want to rewrite existing inerts with it, otherwise
                -- we'd risk divergence in the constraint solver
              ; stopWith new_ev "Occurs check" }
  
          -- A representational equality with an occurs-check problem isn't
          -- insoluble! For example:
          --   a ~R b a
          -- We might learn that b is the newtype Id.
          -- But, the occurs-check certainly prevents the equality from being
          -- canonical, and we might loop if we were to use it in rewriting.
      else do { traceTcS "Occurs-check in representational equality"
                                (ppr xi1 $$ ppr xi2)
              ; continueWith (CIrredEvCan { cc_ev = new_ev }) }
    where
      xi1 = mkTyVarTy tv1
      co1 = mkTcReflCo (eqRelRole eq_rel) xi1
  
  
  
  canEqTyVarTyVar :: CtEvidence           -- tv1 ~ orhs (or orhs ~ tv1, if swapped)
                  -> EqRel
                  -> SwapFlag
                  -> TcTyVar -> TcTyVar   -- tv2, tv2
                  -> TcCoercion           -- tv2 ~ orhs
                  -> TcS (StopOrContinue Ct)
  -- Both LHS and RHS rewrote to a type variable,
  -- If swapped = NotSwapped, then
  --     rw_orhs = tv1, rw_olhs = orhs
  --     rw_nlhs = tv2, rw_nrhs = xi1
  -- See Note [Canonical orientation for tyvar/tyvar equality constraints]
  canEqTyVarTyVar ev eq_rel swapped tv1 tv2 co2
    | tv1 == tv2
    = do { when (isWanted ev) $
           ASSERT( tcCoercionRole co2 == eqRelRole eq_rel )
           setEvBind (ctev_evar ev) (EvCoercion (maybeSym swapped co2))
         ; stopWith ev "Equal tyvars" }
  
    | incompat_kind   = incompat
    | isFmvTyVar tv1  = do_fmv swapped            tv1 xi1 xi2 co1 co2
    | isFmvTyVar tv2  = do_fmv (flipSwap swapped) tv2 xi2 xi1 co2 co1
    | same_kind       = if swap_over then do_swap else no_swap
    | k1_sub_k2       = do_swap   -- Note [Kind orientation for CTyEqCan]
    | otherwise       = no_swap   -- k2_sub_k1
    where
      xi1 = mkTyVarTy tv1
      xi2 = mkTyVarTy tv2
      k1  = tyVarKind tv1
      k2  = tyVarKind tv2
      co1 = mkTcReflCo (eqRelRole eq_rel) xi1
      k1_sub_k2     = k1 `isSubKind` k2
      k2_sub_k1     = k2 `isSubKind` k1
      same_kind     = k1_sub_k2 && k2_sub_k1
      incompat_kind = not (k1_sub_k2 || k2_sub_k1)
  
      no_swap = canon_eq swapped            tv1 xi1 xi2 co1 co2
      do_swap = canon_eq (flipSwap swapped) tv2 xi2 xi1 co2 co1
  
      canon_eq swapped tv1 xi1 xi2 co1 co2
          -- ev  : tv1 ~ orhs  (not swapped) or   orhs ~ tv1   (swapped)
          -- co1 : xi1 ~ tv1
          -- co2 : xi2 ~ tv2
        = do { mb <- rewriteEqEvidence ev eq_rel swapped xi1 xi2 co1 co2
             ; let mk_ct ev' = CTyEqCan { cc_ev = ev', cc_tyvar = tv1
                                        , cc_rhs = xi2 , cc_eq_rel = eq_rel }
             ; return (fmap mk_ct mb) }
  
      -- See Note [Orient equalities with flatten-meta-vars on the left] in TcFlatten
      do_fmv swapped tv1 xi1 xi2 co1 co2
        | same_kind
        = canon_eq swapped tv1 xi1 xi2 co1 co2
        | otherwise  -- Presumably tv1 `subKind` tv2, which is the wrong way round
        = ASSERT2( k1_sub_k2, ppr tv1 $$ ppr tv2 )
          ASSERT2( isWanted ev, ppr ev )  -- Only wanteds have flatten meta-vars
          do { tv_ty <- newFlexiTcSTy (tyVarKind tv1)
             ; new_ev <- newWantedEvVarNC (ctEvLoc ev)
                                          (mkTcEqPredRole (eqRelRole eq_rel)
                                                          tv_ty xi2)
             ; emitWorkNC [new_ev]
             ; canon_eq swapped tv1 xi1 tv_ty co1 (ctEvCoercion new_ev `mkTcTransCo` co2) }
  
      incompat
        = rewriteEqEvidence ev eq_rel swapped xi1 xi2 (mkTcNomReflCo xi1) co2
          `andWhenContinue` \ ev' ->
          incompatibleKind ev' xi1 k1 xi2 k2
  
      swap_over
        -- If tv1 is touchable, swap only if tv2 is also
        -- touchable and it's strictly better to update the latter
        -- But see Note [Avoid unnecessary swaps]
        | Just lvl1 <- metaTyVarTcLevel_maybe tv1
        = case metaTyVarTcLevel_maybe tv2 of
            Nothing   -> False
            Just lvl2 | lvl2 `strictlyDeeperThan` lvl1 -> True
                      | lvl1 `strictlyDeeperThan` lvl2 -> False
                      | otherwise                      -> nicer_to_update_tv2
  
        -- So tv1 is not a meta tyvar
        -- If only one is a meta tyvar, put it on the left
        -- This is not because it'll be solved; but because
        -- the floating step looks for meta tyvars on the left
        | isMetaTyVar tv2 = True
  
        -- So neither is a meta tyvar
  
        -- If only one is a flatten tyvar, put it on the left
        -- See Note [Eliminate flat-skols]
        | not (isFlattenTyVar tv1), isFlattenTyVar tv2 = True
  
        | otherwise = False
  
      nicer_to_update_tv2
        =  (isSigTyVar tv1                 && not (isSigTyVar tv2))
        || (isSystemName (Var.varName tv2) && not (isSystemName (Var.varName tv1)))
  
  -- | Solve a reflexive equality constraint
  canEqReflexive :: CtEvidence    -- ty ~ ty
                 -> EqRel
                 -> TcType        -- ty
                 -> TcS (StopOrContinue Ct)   -- always Stop
  canEqReflexive ev eq_rel ty
    = do { when (isWanted ev) $
           setEvBind (ctev_evar ev) (EvCoercion $
                                     mkTcReflCo (eqRelRole eq_rel) ty)
         ; stopWith ev "Solved by reflexivity" }
  
  incompatibleKind :: CtEvidence         -- t1~t2
                   -> TcType -> TcKind
                   -> TcType -> TcKind   -- s1~s2, flattened and zonked
                   -> TcS (StopOrContinue Ct)
  -- LHS and RHS have incompatible kinds, so emit an "irreducible" constraint
  --       CIrredEvCan (NOT CTyEqCan or CFunEqCan)
  -- for the type equality; and continue with the kind equality constraint.
  -- When the latter is solved, it'll kick out the irreducible equality for
  -- a second attempt at solving
  --
  -- See Note [Equalities with incompatible kinds]
  
  incompatibleKind new_ev s1 k1 s2 k2   -- See Note [Equalities with incompatible kinds]
    = ASSERT( isKind k1 && isKind k2 )
      do { traceTcS "canEqLeaf: incompatible kinds" (vcat [ppr k1, ppr k2])
  
           -- Create a derived kind-equality, and solve it
         ; emitNewDerived kind_co_loc (mkTcEqPred k1 k2)
  
           -- Put the not-currently-soluble thing into the inert set
         ; continueWith (CIrredEvCan { cc_ev = new_ev }) }
    where
      loc = ctEvLoc new_ev
      kind_co_loc = setCtLocOrigin loc (KindEqOrigin s1 s2 (ctLocOrigin loc))
  
  {-
  Note [Canonical orientation for tyvar/tyvar equality constraints]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  When we have a ~ b where both 'a' and 'b' are TcTyVars, which way
  round should be oriented in the CTyEqCan?  The rules, implemented by
  canEqTyVarTyVar, are these
  
   * If either is a flatten-meta-variables, it goes on the left.
  
   * If one is a strict sub-kind of the other e.g.
         (alpha::?) ~ (beta::*)
     orient them so RHS is a subkind of LHS.  That way we will replace
     'a' with 'b', correctly narrowing the kind.
     This establishes the subkind invariant of CTyEqCan.
  
   * Put a meta-tyvar on the left if possible
         alpha[3] ~ r
  
   * If both are meta-tyvars, put the more touchable one (deepest level
     number) on the left, so there is the best chance of unifying it
          alpha[3] ~ beta[2]
  
   * If both are meta-tyvars and both at the same level, put a SigTv
     on the right if possible
          alpha[2] ~ beta[2](sig-tv)
     That way, when we unify alpha := beta, we don't lose the SigTv flag.
  
   * Put a meta-tv with a System Name on the left if possible so it
     gets eliminated (improves error messages)
  
   * If one is a flatten-skolem, put it on the left so that it is
     substituted out  Note [Elminate flat-skols]
          fsk ~ a
  
  Note [Avoid unnecessary swaps]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  If we swap without actually improving matters, we can get an infnite loop.
  Consider
      work item:  a ~ b
     inert item:  b ~ c
  We canonicalise the work-time to (a ~ c).  If we then swap it before
  aeding to the inert set, we'll add (c ~ a), and therefore kick out the
  inert guy, so we get
     new work item:  b ~ c
     inert item:     c ~ a
  And now the cycle just repeats
  
  Note [Eliminate flat-skols]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Suppose we have  [G] Num (F [a])
  then we flatten to
       [G] Num fsk
       [G] F [a] ~ fsk
  where fsk is a flatten-skolem (FlatSkol). Suppose we have
        type instance F [a] = a
  then we'll reduce the second constraint to
       [G] a ~ fsk
  and then replace all uses of 'a' with fsk.  That's bad because
  in error messages intead of saying 'a' we'll say (F [a]).  In all
  places, including those where the programmer wrote 'a' in the first
  place.  Very confusing!  See Trac #7862.
  
  Solution: re-orient a~fsk to fsk~a, so that we preferentially eliminate
  the fsk.
  
  Note [Equalities with incompatible kinds]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  canEqLeaf is about to make a CTyEqCan or CFunEqCan; but both have the
  invariant that LHS and RHS satisfy the kind invariants for CTyEqCan,
  CFunEqCan.  What if we try to unify two things with incompatible
  kinds?
  
  eg    a ~ b  where a::*, b::*->*
  or    a ~ b  where a::*, b::k, k is a kind variable
  
  The CTyEqCan compatKind invariant is important.  If we make a CTyEqCan
  for a~b, then we might well *substitute* 'b' for 'a', and that might make
  a well-kinded type ill-kinded; and that is bad (eg typeKind can crash, see
  Trac #7696).
  
  So instead for these ill-kinded equalities we generate a CIrredCan,
  and put it in the inert set, which keeps it out of the way until a
  subsequent substitution (on kind variables, say) re-activates it.
  
  NB: it is important that the types s1,s2 are flattened and zonked
      so that their kinds k1, k2 are inert wrt the substitution.  That
      means that they can only become the same if we change the inert
      set, which in turn will kick out the irreducible equality
      E.g. it is WRONG to make an irred (a:k1)~(b:k2)
           if we already have a substitution k1:=k2
  
  NB: it's important that the new CIrredCan goes in the inert set rather
  than back into the work list. We used to do the latter, but that led
  to an infinite loop when we encountered it again, and put it back in
  the work list again.
  
  See also Note [Kind orientation for CTyEqCan] and
           Note [Kind orientation for CFunEqCan] in TcRnTypes
  
  Note [Type synonyms and canonicalization]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  We treat type synonym applications as xi types, that is, they do not
  count as type function applications.  However, we do need to be a bit
  careful with type synonyms: like type functions they may not be
  generative or injective.  However, unlike type functions, they are
  parametric, so there is no problem in expanding them whenever we see
  them, since we do not need to know anything about their arguments in
  order to expand them; this is what justifies not having to treat them
  as specially as type function applications.  The thing that causes
  some subtleties is that we prefer to leave type synonym applications
  *unexpanded* whenever possible, in order to generate better error
  messages.
  
  If we encounter an equality constraint with type synonym applications
  on both sides, or a type synonym application on one side and some sort
  of type application on the other, we simply must expand out the type
  synonyms in order to continue decomposing the equality constraint into
  primitive equality constraints.  For example, suppose we have
  
    type F a = [Int]
  
  and we encounter the equality
  
    F a ~ [b]
  
  In order to continue we must expand F a into [Int], giving us the
  equality
  
    [Int] ~ [b]
  
  which we can then decompose into the more primitive equality
  constraint
  
    Int ~ b.
  
  However, if we encounter an equality constraint with a type synonym
  application on one side and a variable on the other side, we should
  NOT (necessarily) expand the type synonym, since for the purpose of
  good error messages we want to leave type synonyms unexpanded as much
  as possible.  Hence the ps_ty1, ps_ty2 argument passed to canEqTyVar.
  
  
  Note [occurCheckExpand]
  ~~~~~~~~~~~~~~~~~~~~~~~
  There is a subtle point with type synonyms and the occurs check that
  takes place for equality constraints of the form tv ~ xi.  As an
  example, suppose we have
  
    type F a = Int
  
  and we come across the equality constraint
  
    a ~ F a
  
  This should not actually fail the occurs check, since expanding out
  the type synonym results in the legitimate equality constraint a ~
  Int.  We must actually do this expansion, because unifying a with F a
  will lead the type checker into infinite loops later.  Put another
  way, canonical equality constraints should never *syntactically*
  contain the LHS variable in the RHS type.  However, we don't always
  need to expand type synonyms when doing an occurs check; for example,
  the constraint
  
    a ~ F b
  
  is obviously fine no matter what F expands to. And in this case we
  would rather unify a with F b (rather than F b's expansion) in order
  to get better error messages later.
  
  So, when doing an occurs check with a type synonym application on the
  RHS, we use some heuristics to find an expansion of the RHS which does
  not contain the variable from the LHS.  In particular, given
  
    a ~ F t1 ... tn
  
  we first try expanding each of the ti to types which no longer contain
  a.  If this turns out to be impossible, we next try expanding F
  itself, and so on.  See Note [Occurs check expansion] in TcType
  -}
  
  {-
  ************************************************************************
  *                                                                      *
                    Evidence transformation
  *                                                                      *
  ************************************************************************
  -}
  
  {-
  Note [xCtEvidence]
  ~~~~~~~~~~~~~~~~~~
  A call might look like this:
  
      xCtEvidence ev evidence-transformer
  
    ev is Given   => use ev_decomp to create new Givens for ev_preds,
                     and return them
  
    ev is Wanted  => create new wanteds for ev_preds,
                     use ev_comp to bind ev,
                     return fresh wanteds (ie ones not cached in inert_cans or solved)
  
    ev is Derived => create new deriveds for ev_preds
                        (unless cached in inert_cans or solved)
  
  Note: The [CtEvidence] returned is a subset of the subgoal-preds passed in
        Ones that are already cached are not returned
  
  Example
      ev : Tree a b ~ Tree c d
      xCtEvidence ev [a~c, b~d] (XEvTerm { ev_comp = \[c1 c2]. <Tree> c1 c2
                                         , ev_decomp = \c. [nth 1 c, nth 2 c] })
                (\fresh-goals.  stuff)
  
  Note [Bind new Givens immediately]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  For Givens we make new EvVars and bind them immediately. We don't worry
  about caching, but we don't expect complicated calculations among Givens.
  It is important to bind each given:
        class (a~b) => C a b where ....
        f :: C a b => ....
  Then in f's Givens we have g:(C a b) and the superclass sc(g,0):a~b.
  But that superclass selector can't (yet) appear in a coercion
  (see evTermCoercion), so the easy thing is to bind it to an Id.
  
  See Note [Coercion evidence terms] in TcEvidence.
  -}
  
  xCtEvidence :: CtEvidence            -- Original evidence
              -> XEvTerm               -- Instructions about how to manipulate evidence
              -> TcS ()
  
  xCtEvidence (CtWanted { ctev_evar = evar, ctev_loc = loc })
              (XEvTerm { ev_preds = ptys, ev_comp = comp_fn })
    = do { new_evars <- mapM (newWantedEvVar loc) ptys
         ; setEvBind evar (comp_fn (map (ctEvTerm . fst) new_evars))
         ; emitWorkNC (freshGoals new_evars) }
           -- Note the "NC": these are fresh goals, not necessarily canonical
  
  xCtEvidence (CtGiven { ctev_evtm = tm, ctev_loc = loc })
              (XEvTerm { ev_preds = ptys, ev_decomp = decomp_fn })
    = ASSERT( equalLength ptys (decomp_fn tm) )
      do { given_evs <- newGivenEvVars loc (ptys `zip` decomp_fn tm)
         ; emitWorkNC given_evs }
  
  xCtEvidence (CtDerived { ctev_loc = loc })
              (XEvTerm { ev_preds = ptys })
    = mapM_ (emitNewDerived loc) ptys
  
  -----------------------------
  data StopOrContinue a
    = ContinueWith a    -- The constraint was not solved, although it may have
                        --   been rewritten
  
    | Stop CtEvidence   -- The (rewritten) constraint was solved
           SDoc         -- Tells how it was solved
                        -- Any new sub-goals have been put on the work list
  
  instance Functor StopOrContinue where
    fmap f (ContinueWith x) = ContinueWith (f x)
    fmap _ (Stop ev s)      = Stop ev s
  
  instance Outputable a => Outputable (StopOrContinue a) where
    ppr (Stop ev s)      = ptext (sLit "Stop") <> parens s <+> ppr ev
    ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w
  
  continueWith :: a -> TcS (StopOrContinue a)
  continueWith = return . ContinueWith
  
  stopWith :: CtEvidence -> String -> TcS (StopOrContinue a)
  stopWith ev s = return (Stop ev (text s))
  
  andWhenContinue :: TcS (StopOrContinue a)
                  -> (a -> TcS (StopOrContinue b))
                  -> TcS (StopOrContinue b)
  andWhenContinue tcs1 tcs2
    = do { r <- tcs1
         ; case r of
             Stop ev s       -> return (Stop ev s)
             ContinueWith ct -> tcs2 ct }
  infixr 0 `andWhenContinue`    -- allow chaining with ($)
  
  rewriteEvidence :: CtEvidence   -- old evidence
                  -> TcPredType   -- new predicate
                  -> TcCoercion   -- Of type :: new predicate ~ <type of old evidence>
                  -> TcS (StopOrContinue CtEvidence)
  -- Returns Just new_ev iff either (i)  'co' is reflexivity
  --                             or (ii) 'co' is not reflexivity, and 'new_pred' not cached
  -- In either case, there is nothing new to do with new_ev
  {-
       rewriteEvidence old_ev new_pred co
  Main purpose: create new evidence for new_pred;
                unless new_pred is cached already
  * Returns a new_ev : new_pred, with same wanted/given/derived flag as old_ev
  * If old_ev was wanted, create a binding for old_ev, in terms of new_ev
  * If old_ev was given, AND not cached, create a binding for new_ev, in terms of old_ev
  * Returns Nothing if new_ev is already cached
  
          Old evidence    New predicate is               Return new evidence
          flavour                                        of same flavor
          -------------------------------------------------------------------
          Wanted          Already solved or in inert     Nothing
          or Derived      Not                            Just new_evidence
  
          Given           Already in inert               Nothing
                          Not                            Just new_evidence
  
  Note [Rewriting with Refl]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~
  If the coercion is just reflexivity then you may re-use the same
  variable.  But be careful!  Although the coercion is Refl, new_pred
  may reflect the result of unification alpha := ty, so new_pred might
  not _look_ the same as old_pred, and it's vital to proceed from now on
  using new_pred.
  
  The flattener preserves type synonyms, so they should appear in new_pred
  as well as in old_pred; that is important for good error messages.
   -}
  
  
  rewriteEvidence old_ev@(CtDerived { ctev_loc = loc }) new_pred _co
    = -- If derived, don't even look at the coercion.
      -- This is very important, DO NOT re-order the equations for
      -- rewriteEvidence to put the isTcReflCo test first!
      -- Why?  Because for *Derived* constraints, c, the coercion, which
      -- was produced by flattening, may contain suspended calls to
      -- (ctEvTerm c), which fails for Derived constraints.
      -- (Getting this wrong caused Trac #7384.)
      do { mb_ev <- newDerived loc new_pred
         ; case mb_ev of
             Just new_ev -> continueWith new_ev
             Nothing     -> stopWith old_ev "Cached derived" }
  
  rewriteEvidence old_ev new_pred co
    | isTcReflCo co -- See Note [Rewriting with Refl]
    = return (ContinueWith (old_ev { ctev_pred = new_pred }))
  
  rewriteEvidence ev@(CtGiven { ctev_evtm = old_tm , ctev_loc = loc }) new_pred co
    = do { new_ev <- newGivenEvVar loc (new_pred, new_tm)  -- See Note [Bind new Givens immediately]
         ; return (ContinueWith new_ev) }
    where
      -- mkEvCast optimises ReflCo
      new_tm = mkEvCast old_tm (tcDowngradeRole Representational
                                                (ctEvRole ev)
                                                (mkTcSymCo co))
  
  rewriteEvidence ev@(CtWanted { ctev_evar = evar, ctev_loc = loc }) new_pred co
    = do { (new_ev, freshness) <- newWantedEvVar loc new_pred
         ; MASSERT( tcCoercionRole co == ctEvRole ev )
         ; setEvBind evar (mkEvCast (ctEvTerm new_ev)
                             (tcDowngradeRole Representational (ctEvRole ev) co))
         ; case freshness of
              Fresh  -> continueWith new_ev
              Cached -> stopWith ev "Cached wanted" }
  
  
  rewriteEqEvidence :: CtEvidence         -- Old evidence :: olhs ~ orhs (not swapped)
                                          --              or orhs ~ olhs (swapped)
                    -> EqRel
                    -> SwapFlag
                    -> TcType -> TcType   -- New predicate  nlhs ~ nrhs
                                          -- Should be zonked, because we use typeKind on nlhs/nrhs
                    -> TcCoercion         -- lhs_co, of type :: nlhs ~ olhs
                    -> TcCoercion         -- rhs_co, of type :: nrhs ~ orhs
                    -> TcS (StopOrContinue CtEvidence)  -- Of type nlhs ~ nrhs
  -- For (rewriteEqEvidence (Given g olhs orhs) False nlhs nrhs lhs_co rhs_co)
  -- we generate
  -- If not swapped
  --      g1 : nlhs ~ nrhs = lhs_co ; g ; sym rhs_co
  -- If 'swapped'
  --      g1 : nlhs ~ nrhs = lhs_co ; Sym g ; sym rhs_co
  --
  -- For (Wanted w) we do the dual thing.
  -- New  w1 : nlhs ~ nrhs
  -- If not swapped
  --      w : olhs ~ orhs = sym lhs_co ; w1 ; rhs_co
  -- If swapped
  --      w : orhs ~ olhs = sym rhs_co ; sym w1 ; lhs_co
  --
  -- It's all a form of rewwriteEvidence, specialised for equalities
  rewriteEqEvidence old_ev eq_rel swapped nlhs nrhs lhs_co rhs_co
    | CtDerived {} <- old_ev
    = do { mb <- newDerived loc' new_pred
         ; case mb of
             Just new_ev -> continueWith new_ev
             Nothing     -> stopWith old_ev "Cached derived" }
  
    | NotSwapped <- swapped
    , isTcReflCo lhs_co      -- See Note [Rewriting with Refl]
    , isTcReflCo rhs_co
    = return (ContinueWith (old_ev { ctev_pred = new_pred }))
  
    | CtGiven { ctev_evtm = old_tm } <- old_ev
    = do { let new_tm = EvCoercion (lhs_co
                                    `mkTcTransCo` maybeSym swapped (evTermCoercion old_tm)
                                    `mkTcTransCo` mkTcSymCo rhs_co)
         ; new_ev <- newGivenEvVar loc' (new_pred, new_tm)
                     -- See Note [Bind new Givens immediately]
         ; return (ContinueWith new_ev) }
  
    | CtWanted { ctev_evar = evar } <- old_ev
    = do { new_evar <- newWantedEvVarNC loc' new_pred
         ; let co = maybeSym swapped $
                    mkTcSymCo lhs_co
                    `mkTcTransCo` ctEvCoercion new_evar
                    `mkTcTransCo` rhs_co
         ; setEvBind evar (EvCoercion co)
         ; traceTcS "rewriteEqEvidence" (vcat [ppr old_ev, ppr nlhs, ppr nrhs, ppr co])
         ; return (ContinueWith new_evar) }
  
    | otherwise
    = panic "rewriteEvidence"
    where
      new_pred = mkTcEqPredRole (eqRelRole eq_rel) nlhs nrhs
  
        -- equality is like a type class. Bumping the depth is necessary because
        -- of recursive newtypes, where "reducing" a newtype can actually make
        -- it bigger. See Note [Eager reflexivity check] in TcCanonical before
        -- considering changing this behavior.
      loc'     = bumpCtLocDepth CountConstraints (ctEvLoc old_ev)
  
  {- Note [unifyWanted and unifyDerived]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  When decomposing equalities we often create new wanted constraints for
  (s ~ t).  But what if s=t?  Then it'd be faster to return Refl right away.
  Similar remarks apply for Derived.
  
  Rather than making an equality test (which traverses the structure of the
  type, perhaps fruitlessly, unifyWanted traverses the common structure, and
  bales out when it finds a difference by creating a new Wanted constraint.
  But where it succeeds in finding common structure, it just builds a coercion
  to reflect it.
  -}
  
  unifyWanted :: CtLoc -> Role -> TcType -> TcType -> TcS TcCoercion
  -- Return coercion witnessing the equality of the two types,
  -- emitting new work equalities where necessary to achieve that
  -- Very good short-cut when the two types are equal, or nearly so
  -- See Note [unifyWanted and unifyDerived]
  -- The returned coercion's role matches the input parameter
  unifyWanted _   Phantom ty1      ty2      = return (mkTcPhantomCo ty1 ty2)
  unifyWanted loc role    orig_ty1 orig_ty2
    = go orig_ty1 orig_ty2
    where
      go ty1 ty2 | Just ty1' <- tcView ty1 = go ty1' ty2
      go ty1 ty2 | Just ty2' <- tcView ty2 = go ty1 ty2'
  
      go (FunTy s1 t1) (FunTy s2 t2)
        = do { co_s <- unifyWanted loc role s1 s2
             ; co_t <- unifyWanted loc role t1 t2
             ; return (mkTcTyConAppCo role funTyCon [co_s,co_t]) }
      go (TyConApp tc1 tys1) (TyConApp tc2 tys2)
        | tc1 == tc2, isDecomposableTyCon tc1, tys1 `equalLength` tys2
        , (not (isNewTyCon tc1) && not (isDataFamilyTyCon tc1)) || role == Nominal
           -- don't look under newtypes!
        = do { cos <- zipWith3M (unifyWanted loc) (tyConRolesX role tc1) tys1 tys2
             ; return (mkTcTyConAppCo role tc1 cos) }
      go (TyVarTy tv) ty2
        = do { mb_ty <- isFilledMetaTyVar_maybe tv
             ; case mb_ty of
                  Just ty1' -> go ty1' ty2
                  Nothing   -> bale_out }
      go ty1 (TyVarTy tv)
        = do { mb_ty <- isFilledMetaTyVar_maybe tv
             ; case mb_ty of
                  Just ty2' -> go ty1 ty2'
                  Nothing   -> bale_out }
      go _ _ = bale_out
  
      bale_out = do { ev <- newWantedEvVarNC loc (mkTcEqPredRole role
                                                    orig_ty1 orig_ty2)
                    ; emitWorkNC [ev]
                    ; return (ctEvCoercion ev) }
  
  unifyDeriveds :: CtLoc -> [Role] -> [TcType] -> [TcType] -> TcS ()
  -- See Note [unifyWanted and unifyDerived]
  unifyDeriveds loc roles tys1 tys2 = zipWith3M_ (unify_derived loc) roles tys1 tys2
  
  unifyDerived :: CtLoc -> Role -> Pair TcType -> TcS ()
  -- See Note [unifyWanted and unifyDerived]
  unifyDerived loc role (Pair ty1 ty2) = unify_derived loc role ty1 ty2
  
  unify_derived :: CtLoc -> Role -> TcType -> TcType -> TcS ()
  -- Create new Derived and put it in the work list
  -- Should do nothing if the two types are equal
  -- See Note [unifyWanted and unifyDerived]
  unify_derived _   Phantom _        _        = return ()
  unify_derived loc role    orig_ty1 orig_ty2
    = go orig_ty1 orig_ty2
    where
      go ty1 ty2 | Just ty1' <- tcView ty1 = go ty1' ty2
      go ty1 ty2 | Just ty2' <- tcView ty2 = go ty1 ty2'
  
      go (FunTy s1 t1) (FunTy s2 t2)
        = do { unify_derived loc role s1 s2
             ; unify_derived loc role t1 t2 }
      go (TyConApp tc1 tys1) (TyConApp tc2 tys2)
        | tc1 == tc2, isDecomposableTyCon tc1, tys1 `equalLength` tys2
        , (not (isNewTyCon tc1) && not (isDataFamilyTyCon tc1)) || role == Nominal
        = unifyDeriveds loc (tyConRolesX role tc1) tys1 tys2
      go (TyVarTy tv) ty2
        = do { mb_ty <- isFilledMetaTyVar_maybe tv
             ; case mb_ty of
                  Just ty1' -> go ty1' ty2
                  Nothing   -> bale_out }
      go ty1 (TyVarTy tv)
        = do { mb_ty <- isFilledMetaTyVar_maybe tv
             ; case mb_ty of
                  Just ty2' -> go ty1 ty2'
                  Nothing   -> bale_out }
      go _ _ = bale_out
  
      bale_out = emitNewDerived loc (mkTcEqPredRole role orig_ty1 orig_ty2)
  
  maybeSym :: SwapFlag -> TcCoercion -> TcCoercion
  maybeSym IsSwapped  co = mkTcSymCo co
  maybeSym NotSwapped co = co
  