typecheck/TcUnify.hs

    {-
    (c) The University of Glasgow 2006
    (c) The GRASP/AQUA Project, Glasgow University, 1992-1998

    Type subsumption and unification
    -}

    {-# LANGUAGE CPP, MultiWayIf, TupleSections, ScopedTypeVariables #-}

    module TcUnify (
      -- Full-blown subsumption
      tcWrapResult, tcWrapResultO, tcSkolemise, tcSkolemiseET,
      tcSubTypeHR, tcSubTypeO, tcSubType_NC, tcSubTypeDS,
      tcSubTypeDS_NC_O, tcSubTypeET,
      checkConstraints, buildImplicationFor,

      -- Various unifications
      unifyType, unifyTheta, unifyKind, noThing,
      uType, promoteTcType,
      swapOverTyVars, canSolveByUnification,

      --------------------------------
      -- Holes
      tcInferInst, tcInferNoInst,
      matchExpectedListTy,
      matchExpectedPArrTy,
      matchExpectedTyConApp,
      matchExpectedAppTy,
      matchExpectedFunTys,
      matchActualFunTys, matchActualFunTysPart,
      matchExpectedFunKind,

      wrapFunResCoercion,

      occCheckExpand, metaTyVarUpdateOK,
      occCheckForErrors, OccCheckResult(..)

      ) where

    #include "HsVersions.h"

    import HsSyn
    import TyCoRep
    import TcMType
    import TcRnMonad
    import TcType
    import Type
    import Coercion
    import TcEvidence
    import Name ( isSystemName )
    import Inst
    import TyCon
    import TysWiredIn
    import TysPrim( tYPE )
    import Var
    import VarSet
    import VarEnv
    import ErrUtils
    import DynFlags
    import BasicTypes
    import Name   ( Name )
    import Bag
    import Util
    import Pair( pFst )
    import qualified GHC.LanguageExtensions as LangExt
    import Outputable
    import FastString

    import Control.Monad
    import Control.Arrow ( second )

    {-
    ************************************************************************
    *                                                                      *
                 matchExpected functions
    *                                                                      *
    ************************************************************************

    Note [Herald for matchExpectedFunTys]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The 'herald' always looks like:
       "The equation(s) for 'f' have"
       "The abstraction (\x.e) takes"
       "The section (+ x) expects"
       "The function 'f' is applied to"

    This is used to construct a message of form

       The abstraction `\Just 1 -> ...' takes two arguments
       but its type `Maybe a -> a' has only one

       The equation(s) for `f' have two arguments
       but its type `Maybe a -> a' has only one

       The section `(f 3)' requires 'f' to take two arguments
       but its type `Int -> Int' has only one

       The function 'f' is applied to two arguments
       but its type `Int -> Int' has only one

    Note [matchExpectedFunTys]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    matchExpectedFunTys checks that a sigma has the form
    of an n-ary function.  It passes the decomposed type to the
    thing_inside, and returns a wrapper to coerce between the two types

    It's used wherever a language construct must have a functional type,
    namely:
            A lambda expression
            A function definition
         An operator section

    This function must be written CPS'd because it needs to fill in the
    ExpTypes produced for arguments before it can fill in the ExpType
    passed in.

    -}

    -- Use this one when you have an "expected" type.
    matchExpectedFunTys :: forall a.
                           SDoc   -- See Note [Herald for matchExpectedFunTys]
                        -> Arity
                        -> ExpRhoType  -- deeply skolemised
                        -> ([ExpSigmaType] -> ExpRhoType -> TcM a)
                              -- must fill in these ExpTypes here
                        -> TcM (a, HsWrapper)
    -- If    matchExpectedFunTys n ty = (_, wrap)
    -- then  wrap : (t1 -> ... -> tn -> ty_r) ~> ty,
    --   where [t1, ..., tn], ty_r are passed to the thing_inside
    matchExpectedFunTys herald arity orig_ty thing_inside
      = case orig_ty of
          Check ty -> go [] arity ty
          _        -> defer [] arity orig_ty
      where
        go acc_arg_tys 0 ty
          = do { result <- thing_inside (reverse acc_arg_tys) (mkCheckExpType ty)
               ; return (result, idHsWrapper) }

        go acc_arg_tys n ty
          | Just ty' <- tcView ty = go acc_arg_tys n ty'

        go acc_arg_tys n (FunTy arg_ty res_ty)
          = ASSERT( not (isPredTy arg_ty) )
            do { (result, wrap_res) <- go (mkCheckExpType arg_ty : acc_arg_tys)
                                          (n-1) res_ty
               ; return ( result
                        , mkWpFun idHsWrapper wrap_res arg_ty res_ty doc ) }
          where
            doc = text "When inferring the argument type of a function with type" <+>
                  quotes (ppr orig_ty)

        go acc_arg_tys n ty@(TyVarTy tv)
          | isMetaTyVar tv
          = do { cts <- readMetaTyVar tv
               ; case cts of
                   Indirect ty' -> go acc_arg_tys n ty'
                   Flexi        -> defer acc_arg_tys n (mkCheckExpType ty) }

           -- In all other cases we bale out into ordinary unification
           -- However unlike the meta-tyvar case, we are sure that the
           -- number of arguments doesn't match arity of the original
           -- type, so we can add a bit more context to the error message
           -- (cf Trac #7869).
           --
           -- It is not always an error, because specialized type may have
           -- different arity, for example:
           --
           -- > f1 = f2 'a'
           -- > f2 :: Monad m => m Bool
           -- > f2 = undefined
           --
           -- But in that case we add specialized type into error context
           -- anyway, because it may be useful. See also Trac #9605.
        go acc_arg_tys n ty = addErrCtxtM mk_ctxt $
                              defer acc_arg_tys n (mkCheckExpType ty)

        ------------
        defer :: [ExpSigmaType] -> Arity -> ExpRhoType -> TcM (a, HsWrapper)
        defer acc_arg_tys n fun_ty
          = do { more_arg_tys <- replicateM n newInferExpTypeNoInst
               ; res_ty       <- newInferExpTypeInst
               ; result       <- thing_inside (reverse acc_arg_tys ++ more_arg_tys) res_ty
               ; more_arg_tys <- mapM readExpType more_arg_tys
               ; res_ty       <- readExpType res_ty
               ; let unif_fun_ty = mkFunTys more_arg_tys res_ty
               ; wrap <- tcSubTypeDS AppOrigin GenSigCtxt unif_fun_ty fun_ty
                             -- Not a good origin at all :-(
               ; return (result, wrap) }

        ------------
        mk_ctxt :: TidyEnv -> TcM (TidyEnv, MsgDoc)
        mk_ctxt env = do { (env', ty) <- zonkTidyTcType env orig_tc_ty
                         ; let (args, _) = tcSplitFunTys ty
                               n_actual = length args
                               (env'', orig_ty') = tidyOpenType env' orig_tc_ty
                         ; return ( env''
                                  , mk_fun_tys_msg orig_ty' ty n_actual arity herald) }
          where
            orig_tc_ty = checkingExpType "matchExpectedFunTys" orig_ty
                -- this is safe b/c we're called from "go"

    -- Like 'matchExpectedFunTys', but used when you have an "actual" type,
    -- for example in function application
    matchActualFunTys :: Outputable a
                      => SDoc   -- See Note [Herald for matchExpectedFunTys]
                      -> CtOrigin
                      -> Maybe a   -- the thing with type TcSigmaType
                      -> Arity
                      -> TcSigmaType
                      -> TcM (HsWrapper, [TcSigmaType], TcSigmaType)
    -- If    matchActualFunTys n ty = (wrap, [t1,..,tn], ty_r)
    -- then  wrap : ty ~> (t1 -> ... -> tn -> ty_r)
    matchActualFunTys herald ct_orig mb_thing arity ty
      = matchActualFunTysPart herald ct_orig mb_thing arity ty [] arity

    -- | Variant of 'matchActualFunTys' that works when supplied only part
    -- (that is, to the right of some arrows) of the full function type
    matchActualFunTysPart :: Outputable a
                          => SDoc -- See Note [Herald for matchExpectedFunTys]
                          -> CtOrigin
                          -> Maybe a  -- the thing with type TcSigmaType
                          -> Arity
                          -> TcSigmaType
                          -> [TcSigmaType] -- reversed args. See (*) below.
                          -> Arity   -- overall arity of the function, for errs
                          -> TcM (HsWrapper, [TcSigmaType], TcSigmaType)
    matchActualFunTysPart herald ct_orig mb_thing arity orig_ty
                          orig_old_args full_arity
      = go arity orig_old_args orig_ty
    -- Does not allocate unnecessary meta variables: if the input already is
    -- a function, we just take it apart.  Not only is this efficient,
    -- it's important for higher rank: the argument might be of form
    --              (forall a. ty) -> other
    -- If allocated (fresh-meta-var1 -> fresh-meta-var2) and unified, we'd
    -- hide the forall inside a meta-variable

    -- (*) Sometimes it's necessary to call matchActualFunTys with only part
    -- (that is, to the right of some arrows) of the type of the function in
    -- question. (See TcExpr.tcArgs.) This argument is the reversed list of
    -- arguments already seen (that is, not part of the TcSigmaType passed
    -- in elsewhere).

      where
        -- This function has a bizarre mechanic: it accumulates arguments on
        -- the way down and also builds an argument list on the way up. Why:
        -- 1. The returns args list and the accumulated args list might be different.
        --    The accumulated args include all the arg types for the function,
        --    including those from before this function was called. The returned
        --    list should include only those arguments produced by this call of
        --    matchActualFunTys
        --
        -- 2. The HsWrapper can be built only on the way up. It seems (more)
        --    bizarre to build the HsWrapper but not the arg_tys.
        --
        -- Refactoring is welcome.
        go :: Arity
           -> [TcSigmaType] -- accumulator of arguments (reversed)
           -> TcSigmaType   -- the remainder of the type as we're processing
           -> TcM (HsWrapper, [TcSigmaType], TcSigmaType)
        go 0 _ ty = return (idHsWrapper, [], ty)

        go n acc_args ty
          | not (null tvs && null theta)
          = do { (wrap1, rho) <- topInstantiate ct_orig ty
               ; (wrap2, arg_tys, res_ty) <- go n acc_args rho
               ; return (wrap2 <.> wrap1, arg_tys, res_ty) }
          where
            (tvs, theta, _) = tcSplitSigmaTy ty

        go n acc_args ty
          | Just ty' <- tcView ty = go n acc_args ty'

        go n acc_args (FunTy arg_ty res_ty)
          = ASSERT( not (isPredTy arg_ty) )
            do { (wrap_res, tys, ty_r) <- go (n-1) (arg_ty : acc_args) res_ty
               ; return ( mkWpFun idHsWrapper wrap_res arg_ty ty_r doc
                        , arg_ty : tys, ty_r ) }
          where
            doc = text "When inferring the argument type of a function with type" <+>
                  quotes (ppr orig_ty)

        go n acc_args ty@(TyVarTy tv)
          | isMetaTyVar tv
          = do { cts <- readMetaTyVar tv
               ; case cts of
                   Indirect ty' -> go n acc_args ty'
                   Flexi        -> defer n ty }

           -- In all other cases we bale out into ordinary unification
           -- However unlike the meta-tyvar case, we are sure that the
           -- number of arguments doesn't match arity of the original
           -- type, so we can add a bit more context to the error message
           -- (cf Trac #7869).
           --
           -- It is not always an error, because specialized type may have
           -- different arity, for example:
           --
           -- > f1 = f2 'a'
           -- > f2 :: Monad m => m Bool
           -- > f2 = undefined
           --
           -- But in that case we add specialized type into error context
           -- anyway, because it may be useful. See also Trac #9605.
        go n acc_args ty = addErrCtxtM (mk_ctxt (reverse acc_args) ty) $
                           defer n ty

        ------------
        defer n fun_ty
          = do { arg_tys <- replicateM n newOpenFlexiTyVarTy
               ; res_ty  <- newOpenFlexiTyVarTy
               ; let unif_fun_ty = mkFunTys arg_tys res_ty
               ; co <- unifyType mb_thing fun_ty unif_fun_ty
               ; return (mkWpCastN co, arg_tys, res_ty) }

        ------------
        mk_ctxt :: [TcSigmaType] -> TcSigmaType -> TidyEnv -> TcM (TidyEnv, MsgDoc)
        mk_ctxt arg_tys res_ty env
          = do { let ty = mkFunTys arg_tys res_ty
               ; (env1, zonked) <- zonkTidyTcType env ty
                       -- zonking might change # of args
               ; let (zonked_args, _) = tcSplitFunTys zonked
                     n_actual         = length zonked_args
                     (env2, unzonked) = tidyOpenType env1 ty
               ; return ( env2
                        , mk_fun_tys_msg unzonked zonked n_actual full_arity herald) }

    mk_fun_tys_msg :: TcType  -- the full type passed in (unzonked)
                   -> TcType  -- the full type passed in (zonked)
                   -> Arity   -- the # of args found
                   -> Arity   -- the # of args wanted
                   -> SDoc    -- overall herald
                   -> SDoc
    mk_fun_tys_msg full_ty ty n_args full_arity herald
      = herald <+> speakNOf full_arity (text "argument") <> comma $$
        if n_args == full_arity
          then text "its type is" <+> quotes (pprType full_ty) <>
               comma $$
               text "it is specialized to" <+> quotes (pprType ty)
          else sep [text "but its type" <+> quotes (pprType ty),
                    if n_args == 0 then text "has none"
                    else text "has only" <+> speakN n_args]

    ----------------------
    matchExpectedListTy :: TcRhoType -> TcM (TcCoercionN, TcRhoType)
    -- Special case for lists
    matchExpectedListTy exp_ty
     = do { (co, [elt_ty]) <- matchExpectedTyConApp listTyCon exp_ty
          ; return (co, elt_ty) }

    ----------------------
    matchExpectedPArrTy :: TcRhoType -> TcM (TcCoercionN, TcRhoType)
    -- Special case for parrs
    matchExpectedPArrTy exp_ty
      = do { (co, [elt_ty]) <- matchExpectedTyConApp parrTyCon exp_ty
           ; return (co, elt_ty) }

    ---------------------
    matchExpectedTyConApp :: TyCon                -- T :: forall kv1 ... kvm. k1 -> ... -> kn -> *
                          -> TcRhoType            -- orig_ty
                          -> TcM (TcCoercionN,    -- T k1 k2 k3 a b c ~N orig_ty
                                  [TcSigmaType])  -- Element types, k1 k2 k3 a b c

    -- It's used for wired-in tycons, so we call checkWiredInTyCon
    -- Precondition: never called with FunTyCon
    -- Precondition: input type :: *
    -- Postcondition: (T k1 k2 k3 a b c) is well-kinded

    matchExpectedTyConApp tc orig_ty
      = ASSERT(tc /= funTyCon) go orig_ty
      where
        go ty
           | Just ty' <- tcView ty
           = go ty'

        go ty@(TyConApp tycon args)
           | tc == tycon  -- Common case
           = return (mkTcNomReflCo ty, args)

        go (TyVarTy tv)
           | isMetaTyVar tv
           = do { cts <- readMetaTyVar tv
                ; case cts of
                    Indirect ty -> go ty
                    Flexi       -> defer }

        go _ = defer

        -- If the common case does not occur, instantiate a template
        -- T k1 .. kn t1 .. tm, and unify with the original type
        -- Doing it this way ensures that the types we return are
        -- kind-compatible with T.  For example, suppose we have
        --       matchExpectedTyConApp T (f Maybe)
        -- where data T a = MkT a
        -- Then we don't want to instantate T's data constructors with
        --    (a::*) ~ Maybe
        -- because that'll make types that are utterly ill-kinded.
        -- This happened in Trac #7368
        defer
          = do { (_, arg_tvs) <- newMetaTyVars (tyConTyVars tc)
               ; traceTc "matchExpectedTyConApp" (ppr tc $$ ppr (tyConTyVars tc) $$ ppr arg_tvs)
               ; let args = mkTyVarTys arg_tvs
                     tc_template = mkTyConApp tc args
               ; co <- unifyType noThing tc_template orig_ty
               ; return (co, args) }

    ----------------------
    matchExpectedAppTy :: TcRhoType                         -- orig_ty
                       -> TcM (TcCoercion,                   -- m a ~N orig_ty
                               (TcSigmaType, TcSigmaType))  -- Returns m, a
    -- If the incoming type is a mutable type variable of kind k, then
    -- matchExpectedAppTy returns a new type variable (m: * -> k); note the *.

    matchExpectedAppTy orig_ty
      = go orig_ty
      where
        go ty
          | Just ty' <- tcView ty = go ty'

          | Just (fun_ty, arg_ty) <- tcSplitAppTy_maybe ty
          = return (mkTcNomReflCo orig_ty, (fun_ty, arg_ty))

        go (TyVarTy tv)
          | isMetaTyVar tv
          = do { cts <- readMetaTyVar tv
               ; case cts of
                   Indirect ty -> go ty
                   Flexi       -> defer }

        go _ = defer

        -- Defer splitting by generating an equality constraint
        defer
          = do { ty1 <- newFlexiTyVarTy kind1
               ; ty2 <- newFlexiTyVarTy kind2
               ; co <- unifyType noThing (mkAppTy ty1 ty2) orig_ty
               ; return (co, (ty1, ty2)) }

        orig_kind = typeKind orig_ty
        kind1 = mkFunTy liftedTypeKind orig_kind
        kind2 = liftedTypeKind    -- m :: * -> k
                                  -- arg type :: *

    {-
    ************************************************************************
    *                                                                      *
                    Subsumption checking
    *                                                                      *
    ************************************************************************

    Note [Subsumption checking: tcSubType]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    All the tcSubType calls have the form
                    tcSubType actual_ty expected_ty
    which checks
                    actual_ty <= expected_ty

    That is, that a value of type actual_ty is acceptable in
    a place expecting a value of type expected_ty.  I.e. that

        actual ty   is more polymorphic than   expected_ty

    It returns a coercion function
            co_fn :: actual_ty ~ expected_ty
    which takes an HsExpr of type actual_ty into one of type
    expected_ty.

    These functions do not actually check for subsumption. They check if
    expected_ty is an appropriate annotation to use for something of type
    actual_ty. This difference matters when thinking about visible type
    application. For example,

       forall a. a -> forall b. b -> b
          DOES NOT SUBSUME
       forall a b. a -> b -> b

    because the type arguments appear in a different order. (Neither does
    it work the other way around.) BUT, these types are appropriate annotations
    for one another. Because the user directs annotations, it's OK if some
    arguments shuffle around -- after all, it's what the user wants.
    Bottom line: none of this changes with visible type application.

    There are a number of wrinkles (below).

    Notice that Wrinkle 1 and 2 both require eta-expansion, which technically
    may increase termination.  We just put up with this, in exchange for getting
    more predictable type inference.

    Wrinkle 1: Note [Deep skolemisation]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We want   (forall a. Int -> a -> a)  <=  (Int -> forall a. a->a)
    (see section 4.6 of "Practical type inference for higher rank types")
    So we must deeply-skolemise the RHS before we instantiate the LHS.

    That is why tc_sub_type starts with a call to tcSkolemise (which does the
    deep skolemisation), and then calls the DS variant (which assumes
    that expected_ty is deeply skolemised)

    Wrinkle 2: Note [Co/contra-variance of subsumption checking]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider  g :: (Int -> Int) -> Int
      f1 :: (forall a. a -> a) -> Int
      f1 = g

      f2 :: (forall a. a -> a) -> Int
      f2 x = g x
    f2 will typecheck, and it would be odd/fragile if f1 did not.
    But f1 will only typecheck if we have that
        (Int->Int) -> Int  <=  (forall a. a->a) -> Int
    And that is only true if we do the full co/contravariant thing
    in the subsumption check.  That happens in the FunTy case of
    tcSubTypeDS_NC_O, and is the sole reason for the WpFun form of
    HsWrapper.

    Another powerful reason for doing this co/contra stuff is visible
    in Trac #9569, involving instantiation of constraint variables,
    and again involving eta-expansion.

    Wrinkle 3: Note [Higher rank types]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider tc150:
      f y = \ (x::forall a. a->a). blah
    The following happens:
    * We will infer the type of the RHS, ie with a res_ty = alpha.
    * Then the lambda will split  alpha := beta -> gamma.
    * And then we'll check tcSubType IsSwapped beta (forall a. a->a)

    So it's important that we unify beta := forall a. a->a, rather than
    skolemising the type.
    -}

    -- | Call this variant when you are in a higher-rank situation and
    -- you know the right-hand type is deeply skolemised.
    tcSubTypeHR :: Outputable a
                => CtOrigin    -- ^ of the actual type
                -> Maybe a     -- ^ If present, it has type ty_actual
                -> TcSigmaType -> ExpRhoType -> TcM HsWrapper
    tcSubTypeHR orig = tcSubTypeDS_NC_O orig GenSigCtxt

    ------------------------
    tcSubTypeET :: CtOrigin -> UserTypeCtxt
                -> ExpSigmaType -> TcSigmaType -> TcM HsWrapper
    -- If wrap = tc_sub_type_et t1 t2
    --    => wrap :: t1 ~> t2
    tcSubTypeET orig ctxt (Check ty_actual) ty_expected
      = tc_sub_tc_type eq_orig orig ctxt ty_actual ty_expected
      where
        eq_orig = TypeEqOrigin { uo_actual   = ty_expected
                               , uo_expected = ty_actual
                               , uo_thing    = Nothing }

    tcSubTypeET _ _ (Infer inf_res) ty_expected
      = ASSERT2( not (ir_inst inf_res), ppr inf_res $$ ppr ty_expected )
        do { co <- fillInferResult ty_expected inf_res
           ; return (mkWpCastN (mkTcSymCo co)) }

    ------------------------
    tcSubTypeO :: CtOrigin      -- ^ of the actual type
               -> UserTypeCtxt  -- ^ of the expected type
               -> TcSigmaType
               -> ExpRhoType
               -> TcM HsWrapper
    tcSubTypeO orig ctxt ty_actual ty_expected
      = addSubTypeCtxt ty_actual ty_expected $
        do { traceTc "tcSubTypeDS_O" (vcat [ pprCtOrigin orig
                                           , pprUserTypeCtxt ctxt
                                           , ppr ty_actual
                                           , ppr ty_expected ])
           ; tcSubTypeDS_NC_O orig ctxt noThing ty_actual ty_expected }

    addSubTypeCtxt :: TcType -> ExpType -> TcM a -> TcM a
    addSubTypeCtxt ty_actual ty_expected thing_inside
     | isRhoTy ty_actual        -- If there is no polymorphism involved, the
     , isRhoExpTy ty_expected   -- TypeEqOrigin stuff (added by the _NC functions)
     = thing_inside             -- gives enough context by itself
     | otherwise
     = addErrCtxtM mk_msg thing_inside
      where
        mk_msg tidy_env
          = do { (tidy_env, ty_actual)   <- zonkTidyTcType tidy_env ty_actual
                       -- might not be filled if we're debugging. ugh.
               ; mb_ty_expected          <- readExpType_maybe ty_expected
               ; (tidy_env, ty_expected) <- case mb_ty_expected of
                                              Just ty -> second mkCheckExpType <$>
                                                         zonkTidyTcType tidy_env ty
                                              Nothing -> return (tidy_env, ty_expected)
               ; ty_expected             <- readExpType ty_expected
               ; (tidy_env, ty_expected) <- zonkTidyTcType tidy_env ty_expected
               ; let msg = vcat [ hang (text "When checking that:")
                                     4 (ppr ty_actual)
                                , nest 2 (hang (text "is more polymorphic than:")
                                             2 (ppr ty_expected)) ]
               ; return (tidy_env, msg) }

    ---------------
    -- The "_NC" variants do not add a typechecker-error context;
    -- the caller is assumed to do that

    tcSubType_NC :: UserTypeCtxt -> TcSigmaType -> TcSigmaType -> TcM HsWrapper
    -- Checks that actual <= expected
    -- Returns HsWrapper :: actual ~ expected
    tcSubType_NC ctxt ty_actual ty_expected
      = do { traceTc "tcSubType_NC" (vcat [pprUserTypeCtxt ctxt, ppr ty_actual, ppr ty_expected])
           ; tc_sub_tc_type origin origin ctxt ty_actual ty_expected }
      where
        origin = TypeEqOrigin { uo_actual   = ty_actual
                              , uo_expected = ty_expected
                              , uo_thing    = Nothing }

    tcSubTypeDS :: CtOrigin -> UserTypeCtxt -> TcSigmaType -> ExpRhoType -> TcM HsWrapper
    -- Just like tcSubType, but with the additional precondition that
    -- ty_expected is deeply skolemised (hence "DS")
    tcSubTypeDS orig ctxt ty_actual ty_expected
      = addSubTypeCtxt ty_actual ty_expected $
        do { traceTc "tcSubTypeDS_NC" (vcat [pprUserTypeCtxt ctxt, ppr ty_actual, ppr ty_expected])
           ; tcSubTypeDS_NC_O orig ctxt noThing ty_actual ty_expected }

    tcSubTypeDS_NC_O :: Outputable a
                     => CtOrigin   -- origin used for instantiation only
                     -> UserTypeCtxt
                     -> Maybe a
                     -> TcSigmaType -> ExpRhoType -> TcM HsWrapper
    -- Just like tcSubType, but with the additional precondition that
    -- ty_expected is deeply skolemised
    tcSubTypeDS_NC_O inst_orig ctxt m_thing ty_actual ty_expected
      = case ty_expected of
          Infer inf_res -> fillInferResult_Inst inst_orig ty_actual inf_res
          Check ty      -> tc_sub_type_ds eq_orig inst_orig ctxt ty_actual ty
             where
               eq_orig = TypeEqOrigin { uo_actual = ty_actual, uo_expected = ty
                                      , uo_thing = mkErrorThing <$> m_thing }

    ---------------
    tc_sub_tc_type :: CtOrigin   -- used when calling uType
                   -> CtOrigin   -- used when instantiating
                   -> UserTypeCtxt -> TcSigmaType -> TcSigmaType -> TcM HsWrapper
    -- If wrap = tc_sub_type t1 t2
    --    => wrap :: t1 ~> t2
    tc_sub_tc_type eq_orig inst_orig ctxt ty_actual ty_expected
      | is_poly ty_expected      -- See Note [Don't skolemise unnecessarily]
      , not (is_poly ty_actual)
      = do { traceTc "tc_sub_tc_type (drop to equality)" $
             vcat [ text "ty_actual   =" <+> ppr ty_actual
                  , text "ty_expected =" <+> ppr ty_expected ]
           ; mkWpCastN <$>
             uType eq_orig TypeLevel ty_actual ty_expected }

      | otherwise   -- This is the general case
      = do { traceTc "tc_sub_tc_type (general case)" $
             vcat [ text "ty_actual   =" <+> ppr ty_actual
                  , text "ty_expected =" <+> ppr ty_expected ]
           ; (sk_wrap, inner_wrap) <- tcSkolemise ctxt ty_expected $
                                                       \ _ sk_rho ->
                                      tc_sub_type_ds eq_orig inst_orig ctxt
                                                     ty_actual sk_rho
           ; return (sk_wrap <.> inner_wrap) }
      where
        is_poly ty
          | isForAllTy ty                        = True
          | Just (_, res) <- splitFunTy_maybe ty = is_poly res
          | otherwise                            = False
          -- NB *not* tcSplitFunTy, because here we want
          -- to decompose type-class arguments too

    {- Note [Don't skolemise unnecessarily]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we are trying to solve
        (Char->Char) <= (forall a. a->a)
    We could skolemise the 'forall a', and then complain
    that (Char ~ a) is insoluble; but that's a pretty obscure
    error.  It's better to say that
        (Char->Char) ~ (forall a. a->a)
    fails.

    In general,
     * if the RHS type an outermost forall (i.e. skolemisation
       is the next thing we'd do)
     * and the LHS has no top-level polymorphism (but looking deeply)
    then we can revert to simple equality.
    -}

    ---------------
    tc_sub_type_ds :: CtOrigin    -- used when calling uType
                   -> CtOrigin    -- used when instantiating
                   -> UserTypeCtxt -> TcSigmaType -> TcRhoType -> TcM HsWrapper
    -- If wrap = tc_sub_type_ds t1 t2
    --    => wrap :: t1 ~> t2
    -- Here is where the work actually happens!
    -- Precondition: ty_expected is deeply skolemised
    tc_sub_type_ds eq_orig inst_orig ctxt ty_actual ty_expected
      = do { traceTc "tc_sub_type_ds" $
             vcat [ text "ty_actual   =" <+> ppr ty_actual
                  , text "ty_expected =" <+> ppr ty_expected ]
           ; go ty_actual ty_expected }
      where
        go ty_a ty_e | Just ty_a' <- tcView ty_a = go ty_a' ty_e
                     | Just ty_e' <- tcView ty_e = go ty_a  ty_e'

        go (TyVarTy tv_a) ty_e
          = do { lookup_res <- lookupTcTyVar tv_a
               ; case lookup_res of
                   Filled ty_a' ->
                     do { traceTc "tcSubTypeDS_NC_O following filled act meta-tyvar:"
                            (ppr tv_a <+> text "-->" <+> ppr ty_a')
                        ; tc_sub_type_ds eq_orig inst_orig ctxt ty_a' ty_e }
                   Unfilled _   -> unify }

        -- Historical note (Sept 16): there was a case here for
        --    go ty_a (TyVarTy alpha)
        -- which, in the impredicative case unified  alpha := ty_a
        -- where th_a is a polytype.  Not only is this probably bogus (we
        -- simply do not have decent story for imprdicative types), but it
        -- caused Trac #12616 because (also bizarrely) 'deriving' code had
        -- -XImpredicativeTypes on.  I deleted the entire case.

        go (FunTy act_arg act_res) (FunTy exp_arg exp_res)
          | not (isPredTy act_arg)
          , not (isPredTy exp_arg)
          = -- See Note [Co/contra-variance of subsumption checking]
            do { res_wrap <- tc_sub_type_ds eq_orig inst_orig  ctxt act_res exp_res
               ; arg_wrap <- tc_sub_tc_type eq_orig given_orig ctxt exp_arg act_arg
               ; return (mkWpFun arg_wrap res_wrap exp_arg exp_res doc) }
                   -- arg_wrap :: exp_arg ~> act_arg
                   -- res_wrap :: act-res ~> exp_res
          where
            given_orig = GivenOrigin (SigSkol GenSigCtxt exp_arg [])
            doc = text "When checking that" <+> quotes (ppr ty_actual) <+>
                  text "is more polymorphic than" <+> quotes (ppr ty_expected)

        go ty_a ty_e
          | let (tvs, theta, _) = tcSplitSigmaTy ty_a
          , not (null tvs && null theta)
          = do { (in_wrap, in_rho) <- topInstantiate inst_orig ty_a
               ; body_wrap <- tc_sub_type_ds
                                (eq_orig { uo_actual = in_rho
                                         , uo_expected = ty_expected })
                                inst_orig ctxt in_rho ty_e
               ; return (body_wrap <.> in_wrap) }

          | otherwise   -- Revert to unification
          = inst_and_unify
             -- It's still possible that ty_actual has nested foralls. Instantiate
             -- these, as there's no way unification will succeed with them in.
             -- See typecheck/should_compile/T11305 for an example of when this
             -- is important. The problem is that we're checking something like
             --  a -> forall b. b -> b     <=   alpha beta gamma
             -- where we end up with alpha := (->)

        inst_and_unify = do { (wrap, rho_a) <- deeplyInstantiate inst_orig ty_actual

                               -- if we haven't recurred through an arrow, then
                               -- the eq_orig will list ty_actual. In this case,
                               -- we want to update the origin to reflect the
                               -- instantiation. If we *have* recurred through
                               -- an arrow, it's better not to update.
                            ; let eq_orig' = case eq_orig of
                                    TypeEqOrigin { uo_actual   = orig_ty_actual }
                                      |  orig_ty_actual `tcEqType` ty_actual
                                      ,  not (isIdHsWrapper wrap)
                                      -> eq_orig { uo_actual = rho_a }
                                    _ -> eq_orig

                            ; cow <- uType eq_orig' TypeLevel rho_a ty_expected
                            ; return (mkWpCastN cow <.> wrap) }

         -- use versions without synonyms expanded
        unify = mkWpCastN <$> uType eq_orig TypeLevel ty_actual ty_expected

    -----------------
    -- needs both un-type-checked (for origins) and type-checked (for wrapping)
    -- expressions
    tcWrapResult :: HsExpr Name -> HsExpr TcId -> TcSigmaType -> ExpRhoType
                 -> TcM (HsExpr TcId)
    tcWrapResult rn_expr = tcWrapResultO (exprCtOrigin rn_expr)

    -- | Sometimes we don't have a @HsExpr Name@ to hand, and this is more
    -- convenient.
    tcWrapResultO :: CtOrigin -> HsExpr TcId -> TcSigmaType -> ExpRhoType
                   -> TcM (HsExpr TcId)
    tcWrapResultO orig expr actual_ty res_ty
      = do { traceTc "tcWrapResult" (vcat [ text "Actual:  " <+> ppr actual_ty
                                          , text "Expected:" <+> ppr res_ty ])
           ; cow <- tcSubTypeDS_NC_O orig GenSigCtxt
                                     (Just expr) actual_ty res_ty
           ; return (mkHsWrap cow expr) }

    -----------------------------------
    wrapFunResCoercion
            :: [TcType]        -- Type of args
            -> HsWrapper       -- HsExpr a -> HsExpr b
            -> TcM HsWrapper   -- HsExpr (arg_tys -> a) -> HsExpr (arg_tys -> b)
    wrapFunResCoercion arg_tys co_fn_res
      | isIdHsWrapper co_fn_res
      = return idHsWrapper
      | null arg_tys
      = return co_fn_res
      | otherwise
      = do  { arg_ids <- newSysLocalIds (fsLit "sub") arg_tys
            ; return (mkWpLams arg_ids <.> co_fn_res <.> mkWpEvVarApps arg_ids) }

    {- **********************************************************************
    %*                                                                      *
                ExpType functions: tcInfer, fillInferResult
    %*                                                                      *
    %********************************************************************* -}

    -- | Infer a type using a fresh ExpType
    -- See also Note [ExpType] in TcMType
    -- Does not attempt to instantiate the inferred type
    tcInferNoInst :: (ExpSigmaType -> TcM a) -> TcM (a, TcSigmaType)
    tcInferNoInst = tcInfer False

    tcInferInst :: (ExpRhoType -> TcM a) -> TcM (a, TcRhoType)
    tcInferInst = tcInfer True

    tcInfer :: Bool -> (ExpSigmaType -> TcM a) -> TcM (a, TcSigmaType)
    tcInfer instantiate tc_check
      = do { res_ty <- newInferExpType instantiate
           ; result <- tc_check res_ty
           ; res_ty <- readExpType res_ty
           ; return (result, res_ty) }

    fillInferResult_Inst :: CtOrigin -> TcType -> InferResult -> TcM HsWrapper
    -- If wrap = fillInferResult_Inst t1 t2
    --    => wrap :: t1 ~> t2
    -- See Note [Deep instantiation of InferResult]
    fillInferResult_Inst orig ty inf_res@(IR { ir_inst = instantiate_me })
      | instantiate_me
      = do { (wrap, rho) <- deeplyInstantiate orig ty
           ; co <- fillInferResult rho inf_res
           ; return (mkWpCastN co <.> wrap) }

      | otherwise
      = do { co <- fillInferResult ty inf_res
           ; return (mkWpCastN co) }

    fillInferResult :: TcType -> InferResult -> TcM TcCoercionN
    -- If wrap = fillInferResult t1 t2
    --    => wrap :: t1 ~> t2
    fillInferResult orig_ty (IR { ir_uniq = u, ir_lvl = res_lvl
                                , ir_ref = ref })
      = do { (ty_co, ty_to_fill_with) <- promoteTcType res_lvl orig_ty

           ; traceTc "Filling ExpType" $
             ppr u <+> text ":=" <+> ppr ty_to_fill_with

           ; when debugIsOn (check_hole ty_to_fill_with)

           ; writeTcRef ref (Just ty_to_fill_with)

           ; return ty_co }
      where
        check_hole ty   -- Debug check only
          = do { let ty_lvl = tcTypeLevel ty
               ; MASSERT2( not (ty_lvl `strictlyDeeperThan` res_lvl),
                           ppr u $$ ppr res_lvl $$ ppr ty_lvl $$
                           ppr ty <+> ppr (typeKind ty) $$ ppr orig_ty )
               ; cts <- readTcRef ref
               ; case cts of
                   Just already_there -> pprPanic "writeExpType"
                                           (vcat [ ppr u
                                                 , ppr ty
                                                 , ppr already_there ])
                   Nothing -> return () }

    {- Note [Deep instantiation of InferResult]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In some cases we want to deeply instantiate before filling in
    an InferResult, and in some cases not.  That's why InferReult
    has the ir_inst flag.

    * ir_inst = True: deeply instantantiate

      Consider
        f x = (*)
      We want to instantiate the type of (*) before returning, else we
      will infer the type
        f :: forall {a}. a -> forall b. Num b => b -> b -> b
      This is surely confusing for users.

      And worse, the the monomorphism restriction won't properly. The MR is
      dealt with in simplifyInfer, and simplifyInfer has no way of
      instantiating. This could perhaps be worked around, but it may be
      hard to know even when instantiation should happen.

      Another reason.  Consider
           f :: (?x :: Int) => a -> a
           g y = let ?x = 3::Int in f
      Here want to instantiate f's type so that the ?x::Int constraint
      gets discharged by the enclosing implicit-parameter binding.

    * ir_inst = False: do not instantantiate

      Consider this (which uses visible type application):

        (let { f :: forall a. a -> a; f x = x } in f) @Int

      We'll call TcExpr.tcInferFun to infer the type of the (let .. in f)
      And we don't want to instantite the type of 'f' when we reach it,
      else the outer visible type application won't work
    -}

    {- *********************************************************************
    *                                                                      *
                  Promoting types
    *                                                                      *
    ********************************************************************* -}

    promoteTcType :: TcLevel -> TcType -> TcM (TcCoercion, TcType)
    -- See Note [Promoting a type]
    -- promoteTcType level ty = (co, ty')
    --   * Returns ty'  whose max level is just 'level'
    --             and  whose kind is ~# to the kind of 'ty'
    --             and  whose kind has form TYPE rr
    --   * and co :: ty ~ ty'
    --   * and emits constraints to justify the coercion
    promoteTcType dest_lvl ty
      = do { cur_lvl <- getTcLevel
           ; if (cur_lvl `sameDepthAs` dest_lvl)
             then dont_promote_it
             else promote_it }
      where
        promote_it :: TcM (TcCoercion, TcType)
        promote_it  -- Emit a constraint  (alpha :: TYPE rr) ~ ty
                    -- where alpha and rr are fresh and from level dest_lvl
          = do { rr      <- newMetaTyVarTyAtLevel dest_lvl runtimeRepTy
               ; prom_ty <- newMetaTyVarTyAtLevel dest_lvl (tYPE rr)
               ; let eq_orig = TypeEqOrigin { uo_actual   = ty
                                            , uo_expected = prom_ty
                                            , uo_thing    = Nothing }

               ; co <- emitWantedEq eq_orig TypeLevel Nominal ty prom_ty
               ; return (co, prom_ty) }

        dont_promote_it :: TcM (TcCoercion, TcType)
        dont_promote_it  -- Check that ty :: TYPE rr, for some (fresh) rr
          = do { res_kind <- newOpenTypeKind
               ; let ty_kind = typeKind ty
                     kind_orig = TypeEqOrigin { uo_actual   = ty_kind
                                              , uo_expected = res_kind
                                              , uo_thing    = Nothing }
               ; ki_co <- uType kind_orig KindLevel (typeKind ty) res_kind
               ; let co = mkTcNomReflCo ty `mkTcCoherenceRightCo` ki_co
               ; return (co, ty `mkCastTy` ki_co) }

    {- Note [Promoting a type]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider (Trac #12427)

      data T where
        MkT :: (Int -> Int) -> a -> T

      h y = case y of MkT v w -> v

    We'll infer the RHS type with an expected type ExpType of
      (IR { ir_lvl = l, ir_ref = ref, ... )
    where 'l' is the TcLevel of the RHS of 'h'.  Then the MkT pattern
    match will increase the level, so we'll end up in tcSubType, trying to
    unify the type of v,
      v :: Int -> Int
    with the expected type.  But this attempt takes place at level (l+1),
    rightly so, since v's type could have mentioned existential variables,
    (like w's does) and we want to catch that.

    So we
      - create a new meta-var alpha[l+1]
      - fill in the InferRes ref cell 'ref' with alpha
      - emit an equality constraint, thus
            [W] alpha[l+1] ~ (Int -> Int)

    That constraint will float outwards, as it should, unless v's
    type mentions a skolem-captured variable.

    This approach fails if v has a higher rank type; see
    Note [Promotion and higher rank types]

    Note [Promotion and higher rank types]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    If v had a higher-rank type, say v :: (forall a. a->a) -> Int,
    then we'd emit an equality
            [W] alpha[l+1] ~ ((forall a. a->a) -> Int)
    which will sadly fail because we can't unify a unification variable
    with a polytype.  But there is nothing really wrong with the program
    here.

    We could just about solve this by "promote the type" of v, to expose
    its polymorphic "shape" while still leaving constraints that will
    prevent existential escape.  But we must be careful!  Exposing
    the "shape" of the type is precisely what we must NOT do under
    a GADT pattern match!  So in this case we might promote the type
    to
            (forall a. a->a) -> alpha[l+1]
    and emit the constraint
            [W] alpha[l+1] ~ Int
    Now the poromoted type can fill the ref cell, while the emitted
    equality can float or not, according to the usual rules.

    But that's not quite right!  We are exposing the arrow! We could
    deal with that too:
            (forall a. mu[l+1] a a) -> alpha[l+1]
    with constraints
            [W] alpha[l+1] ~ Int
            [W] mu[l+1] ~ (->)
    Here we abstract over the '->' inside the forall, in case that
    is subject to an equality constraint from a GADT match.

    Note that we kept the outer (->) because that's part of
    the polymorphic "shape".  And becauuse of impredicativity,
    GADT matches can't give equalities that affect polymorphic
    shape.

    This reasoning just seems too complicated, so I decided not
    to do it.  These higher-rank notes are just here to record
    the thinking.
    -}

    {- *********************************************************************
    *                                                                      *
                        Generalisation
    *                                                                      *
    ********************************************************************* -}

    -- | Take an "expected type" and strip off quantifiers to expose the
    -- type underneath, binding the new skolems for the @thing_inside@.
    -- The returned 'HsWrapper' has type @specific_ty -> expected_ty@.
    tcSkolemise :: UserTypeCtxt -> TcSigmaType
                -> ([TcTyVar] -> TcType -> TcM result)
             -- ^ These are only ever used for scoped type variables.
                -> TcM (HsWrapper, result)
            -- ^ The expression has type: spec_ty -> expected_ty

    tcSkolemise ctxt expected_ty thing_inside
       -- We expect expected_ty to be a forall-type
       -- If not, the call is a no-op
      = do  { traceTc "tcSkolemise" Outputable.empty
            ; (wrap, tv_prs, given, rho') <- deeplySkolemise expected_ty

            ; lvl <- getTcLevel
            ; when debugIsOn $
                  traceTc "tcSkolemise" $ vcat [
                    ppr lvl,
                    text "expected_ty" <+> ppr expected_ty,
                    text "inst tyvars" <+> ppr tv_prs,
                    text "given"       <+> ppr given,
                    text "inst type"   <+> ppr rho' ]

            -- Generally we must check that the "forall_tvs" havn't been constrained
            -- The interesting bit here is that we must include the free variables
            -- of the expected_ty.  Here's an example:
            --       runST (newVar True)
            -- Here, if we don't make a check, we'll get a type (ST s (MutVar s Bool))
            -- for (newVar True), with s fresh.  Then we unify with the runST's arg type
            -- forall s'. ST s' a. That unifies s' with s, and a with MutVar s Bool.
            -- So now s' isn't unconstrained because it's linked to a.
            --
            -- However [Oct 10] now that the untouchables are a range of
            -- TcTyVars, all this is handled automatically with no need for
            -- extra faffing around

            ; let tvs' = map snd tv_prs
                  skol_info = SigSkol ctxt expected_ty tv_prs

            ; (ev_binds, result) <- checkConstraints skol_info tvs' given $
                                    thing_inside tvs' rho'

            ; return (wrap <.> mkWpLet ev_binds, result) }
              -- The ev_binds returned by checkConstraints is very
              -- often empty, in which case mkWpLet is a no-op

    -- | Variant of 'tcSkolemise' that takes an ExpType
    tcSkolemiseET :: UserTypeCtxt -> ExpSigmaType
                  -> (ExpRhoType -> TcM result)
                  -> TcM (HsWrapper, result)
    tcSkolemiseET _ et@(Infer {}) thing_inside
      = (idHsWrapper, ) <$> thing_inside et
    tcSkolemiseET ctxt (Check ty) thing_inside
      = tcSkolemise ctxt ty $ \_ -> thing_inside . mkCheckExpType

    checkConstraints :: SkolemInfo
                     -> [TcTyVar]           -- Skolems
                     -> [EvVar]             -- Given
                     -> TcM result
                     -> TcM (TcEvBinds, result)

    checkConstraints skol_info skol_tvs given thing_inside
      = do { (implics, ev_binds, result)
                <- buildImplication skol_info skol_tvs given thing_inside
           ; emitImplications implics
           ; return (ev_binds, result) }

    buildImplication :: SkolemInfo
                     -> [TcTyVar]           -- Skolems
                     -> [EvVar]             -- Given
                     -> TcM result
                     -> TcM (Bag Implication, TcEvBinds, result)
    buildImplication skol_info skol_tvs given thing_inside
      = do { tc_lvl <- getTcLevel
           ; deferred_type_errors <- goptM Opt_DeferTypeErrors <||>
                                     goptM Opt_DeferTypedHoles
           ; if null skol_tvs && null given && (not deferred_type_errors ||
                                                not (isTopTcLevel tc_lvl))
             then do { res <- thing_inside
                     ; return (emptyBag, emptyTcEvBinds, res) }
          -- Fast path.  We check every function argument with
          -- tcPolyExpr, which uses tcSkolemise and hence checkConstraints.
          -- But with the solver producing unlifted equalities, we need
          -- to have an EvBindsVar for them when they might be deferred to
          -- runtime. Otherwise, they end up as top-level unlifted bindings,
          -- which are verboten. See also Note [Deferred errors for coercion holes]
          -- in TcErrors.
             else
        do { (tclvl, wanted, result) <- pushLevelAndCaptureConstraints thing_inside
           ; (implics, ev_binds) <- buildImplicationFor tclvl skol_info skol_tvs given wanted
           ; return (implics, ev_binds, result) }}

    buildImplicationFor :: TcLevel -> SkolemInfo -> [TcTyVar]
                       -> [EvVar] -> WantedConstraints
                       -> TcM (Bag Implication, TcEvBinds)
    buildImplicationFor tclvl skol_info skol_tvs given wanted
      | isEmptyWC wanted && null given
                 -- Optimisation : if there are no wanteds, and no givens
                 -- don't generate an implication at all.
                 -- Reason for the (null given): we don't want to lose
                 -- the "inaccessible alternative" error check
      = return (emptyBag, emptyTcEvBinds)

      | otherwise
      = ASSERT2( all isSkolemTyVar skol_tvs, ppr skol_tvs )
        do { ev_binds_var <- newTcEvBinds
           ; env <- getLclEnv
           ; let implic = Implic { ic_tclvl = tclvl
                                 , ic_skols = skol_tvs
                                 , ic_no_eqs = False
                                 , ic_given = given
                                 , ic_wanted = wanted
                                 , ic_status  = IC_Unsolved
                                 , ic_binds = ev_binds_var
                                 , ic_env = env
                                 , ic_needed = emptyVarSet
                                 , ic_info = skol_info }

           ; return (unitBag implic, TcEvBinds ev_binds_var) }

    {-
    ************************************************************************
    *                                                                      *
                    Boxy unification
    *                                                                      *
    ************************************************************************

    The exported functions are all defined as versions of some
    non-exported generic functions.
    -}

    unifyType :: Outputable a => Maybe a   -- ^ If present, has type 'ty1'
              -> TcTauType -> TcTauType -> TcM TcCoercionN
    -- Actual and expected types
    -- Returns a coercion : ty1 ~ ty2
    unifyType thing ty1 ty2 = uType origin TypeLevel ty1 ty2
      where
        origin = TypeEqOrigin { uo_actual = ty1, uo_expected = ty2
                              , uo_thing  = mkErrorThing <$> thing }

    -- | Use this instead of 'Nothing' when calling 'unifyType' without
    -- a good "thing" (where the "thing" has the "actual" type passed in)
    -- This has an 'Outputable' instance, avoiding amgiguity problems.
    noThing :: Maybe (HsExpr Name)
    noThing = Nothing

    unifyKind :: Outputable a => Maybe a -> TcKind -> TcKind -> TcM CoercionN
    unifyKind thing ty1 ty2 = uType origin KindLevel ty1 ty2
      where origin = TypeEqOrigin { uo_actual = ty1, uo_expected = ty2
                                  , uo_thing  = mkErrorThing <$> thing }

    ---------------
    unifyPred :: PredType -> PredType -> TcM TcCoercionN
    -- Actual and expected types
    unifyPred = unifyType noThing

    ---------------
    unifyTheta :: TcThetaType -> TcThetaType -> TcM [TcCoercionN]
    -- Actual and expected types
    unifyTheta theta1 theta2
      = do  { checkTc (equalLength theta1 theta2)
                      (vcat [text "Contexts differ in length",
                             nest 2 $ parens $ text "Use RelaxedPolyRec to allow this"])
            ; zipWithM unifyPred theta1 theta2 }

    {-
    %************************************************************************
    %*                                                                      *
                     uType and friends
    %*                                                                      *
    %************************************************************************

    uType is the heart of the unifier.
    -}

    uType, uType_defer
      :: CtOrigin
      -> TypeOrKind
      -> TcType    -- ty1 is the *actual* type
      -> TcType    -- ty2 is the *expected* type
      -> TcM Coercion

    --------------
    -- It is always safe to defer unification to the main constraint solver
    -- See Note [Deferred unification]
    uType_defer origin t_or_k ty1 ty2
      = do { co <- emitWantedEq origin t_or_k Nominal ty1 ty2

           -- Error trace only
           -- NB. do *not* call mkErrInfo unless tracing is on,
           --     because it is hugely expensive (#5631)
           ; whenDOptM Opt_D_dump_tc_trace $ do
                { ctxt <- getErrCtxt
                ; doc <- mkErrInfo emptyTidyEnv ctxt
                ; traceTc "utype_defer" (vcat [ppr co, ppr ty1,
                                               ppr ty2, pprCtOrigin origin, doc])
                }
           ; return co }

    --------------
    uType origin t_or_k orig_ty1 orig_ty2
      = do { tclvl <- getTcLevel
           ; traceTc "u_tys" $ vcat
                  [ text "tclvl" <+> ppr tclvl
                  , sep [ ppr orig_ty1, text "~", ppr orig_ty2]
                  , pprCtOrigin origin]
           ; co <- go orig_ty1 orig_ty2
           ; if isReflCo co
                then traceTc "u_tys yields no coercion" Outputable.empty
                else traceTc "u_tys yields coercion:" (ppr co)
           ; return co }
      where
        go :: TcType -> TcType -> TcM Coercion
            -- The arguments to 'go' are always semantically identical
            -- to orig_ty{1,2} except for looking through type synonyms

            -- Variables; go for uVar
            -- Note that we pass in *original* (before synonym expansion),
            -- so that type variables tend to get filled in with
            -- the most informative version of the type
        go (TyVarTy tv1) ty2
          = do { lookup_res <- lookupTcTyVar tv1
               ; case lookup_res of
                   Filled ty1   -> do { traceTc "found filled tyvar" (ppr tv1 <+> text ":->" <+> ppr ty1)
                                      ; go ty1 ty2 }
                   Unfilled _ -> uUnfilledVar origin t_or_k NotSwapped tv1 ty2 }
        go ty1 (TyVarTy tv2)
          = do { lookup_res <- lookupTcTyVar tv2
               ; case lookup_res of
                   Filled ty2   -> do { traceTc "found filled tyvar" (ppr tv2 <+> text ":->" <+> ppr ty2)
                                      ; go ty1 ty2 }
                   Unfilled _ -> uUnfilledVar origin t_or_k IsSwapped tv2 ty1 }

          -- See Note [Expanding synonyms during unification]
        go ty1@(TyConApp tc1 []) (TyConApp tc2 [])
          | tc1 == tc2
          = return $ mkReflCo Nominal ty1

            -- See Note [Expanding synonyms during unification]
            --
            -- Also NB that we recurse to 'go' so that we don't push a
            -- new item on the origin stack. As a result if we have
            --   type Foo = Int
            -- and we try to unify  Foo ~ Bool
            -- we'll end up saying "can't match Foo with Bool"
            -- rather than "can't match "Int with Bool".  See Trac #4535.
        go ty1 ty2
          | Just ty1' <- tcView ty1 = go ty1' ty2
          | Just ty2' <- tcView ty2 = go ty1  ty2'

        go (CastTy t1 co1) t2
          = do { co_tys <- go t1 t2
               ; return (mkCoherenceLeftCo co_tys co1) }

        go t1 (CastTy t2 co2)
          = do { co_tys <- go t1 t2
               ; return (mkCoherenceRightCo co_tys co2) }

            -- Functions (or predicate functions) just check the two parts
        go (FunTy fun1 arg1) (FunTy fun2 arg2)
          = do { co_l <- uType origin t_or_k fun1 fun2
               ; co_r <- uType origin t_or_k arg1 arg2
               ; return $ mkFunCo Nominal co_l co_r }

            -- Always defer if a type synonym family (type function)
            -- is involved.  (Data families behave rigidly.)
        go ty1@(TyConApp tc1 _) ty2
          | isTypeFamilyTyCon tc1 = defer ty1 ty2
        go ty1 ty2@(TyConApp tc2 _)
          | isTypeFamilyTyCon tc2 = defer ty1 ty2

        go (TyConApp tc1 tys1) (TyConApp tc2 tys2)
          -- See Note [Mismatched type lists and application decomposition]
          | tc1 == tc2, length tys1 == length tys2
          = ASSERT2( isGenerativeTyCon tc1 Nominal, ppr tc1 )
            do { cos <- zipWithM (uType origin t_or_k) tys1 tys2
               ; return $ mkTyConAppCo Nominal tc1 cos }

        go (LitTy m) ty@(LitTy n)
          | m == n
          = return $ mkNomReflCo ty

            -- See Note [Care with type applications]
            -- Do not decompose FunTy against App;
            -- it's often a type error, so leave it for the constraint solver
        go (AppTy s1 t1) (AppTy s2 t2)
          = go_app s1 t1 s2 t2

        go (AppTy s1 t1) (TyConApp tc2 ts2)
          | Just (ts2', t2') <- snocView ts2
          = ASSERT( mightBeUnsaturatedTyCon tc2 )
            go_app s1 t1 (TyConApp tc2 ts2') t2'

        go (TyConApp tc1 ts1) (AppTy s2 t2)
          | Just (ts1', t1') <- snocView ts1
          = ASSERT( mightBeUnsaturatedTyCon tc1 )
            go_app (TyConApp tc1 ts1') t1' s2 t2

        go (CoercionTy co1) (CoercionTy co2)
          = do { let ty1 = coercionType co1
                     ty2 = coercionType co2
               ; kco <- uType (KindEqOrigin orig_ty1 (Just orig_ty2) origin
                                            (Just t_or_k))
                              KindLevel
                              ty1 ty2
               ; return $ mkProofIrrelCo Nominal kco co1 co2 }

            -- Anything else fails
            -- E.g. unifying for-all types, which is relative unusual
        go ty1 ty2 = defer ty1 ty2

        ------------------
        defer ty1 ty2   -- See Note [Check for equality before deferring]
          | ty1 `tcEqType` ty2 = return (mkNomReflCo ty1)
          | otherwise          = uType_defer origin t_or_k ty1 ty2

        ------------------
        go_app s1 t1 s2 t2
          = do { co_s <- uType origin t_or_k s1 s2
               ; co_t <- uType origin t_or_k t1 t2
               ; return $ mkAppCo co_s co_t }

    {- Note [Check for equality before deferring]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Particularly in ambiguity checks we can get equalities like (ty ~ ty).
    If ty involves a type function we may defer, which isn't very sensible.
    An egregious example of this was in test T9872a, which has a type signature
           Proxy :: Proxy (Solutions Cubes)
    Doing the ambiguity check on this signature generates the equality
       Solutions Cubes ~ Solutions Cubes
    and currently the constraint solver normalises both sides at vast cost.
    This little short-cut in 'defer' helps quite a bit.

    Note [Care with type applications]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Note: type applications need a bit of care!
    They can match FunTy and TyConApp, so use splitAppTy_maybe
    NB: we've already dealt with type variables and Notes,
    so if one type is an App the other one jolly well better be too

    Note [Mismatched type lists and application decomposition]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When we find two TyConApps, you might think that the argument lists
    are guaranteed equal length.  But they aren't. Consider matching
            w (T x) ~ Foo (T x y)
    We do match (w ~ Foo) first, but in some circumstances we simply create
    a deferred constraint; and then go ahead and match (T x ~ T x y).
    This came up in Trac #3950.

    So either
       (a) either we must check for identical argument kinds
           when decomposing applications,

       (b) or we must be prepared for ill-kinded unification sub-problems

    Currently we adopt (b) since it seems more robust -- no need to maintain
    a global invariant.

    Note [Expanding synonyms during unification]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We expand synonyms during unification, but:
     * We expand *after* the variable case so that we tend to unify
       variables with un-expanded type synonym. This just makes it
       more likely that the inferred types will mention type synonyms
       understandable to the user

     * We expand *before* the TyConApp case.  For example, if we have
          type Phantom a = Int
       and are unifying
          Phantom Int ~ Phantom Char
       it is *wrong* to unify Int and Char.

     * The problem case immediately above can happen only with arguments
       to the tycon. So we check for nullary tycons *before* expanding.
       This is particularly helpful when checking (* ~ *), because * is
       now a type synonym.

    Note [Deferred Unification]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We may encounter a unification ty1 ~ ty2 that cannot be performed syntactically,
    and yet its consistency is undetermined. Previously, there was no way to still
    make it consistent. So a mismatch error was issued.

    Now these unifications are deferred until constraint simplification, where type
    family instances and given equations may (or may not) establish the consistency.
    Deferred unifications are of the form
                    F ... ~ ...
    or              x ~ ...
    where F is a type function and x is a type variable.
    E.g.
            id :: x ~ y => x -> y
            id e = e

    involves the unification x = y. It is deferred until we bring into account the
    context x ~ y to establish that it holds.

    If available, we defer original types (rather than those where closed type
    synonyms have already been expanded via tcCoreView).  This is, as usual, to
    improve error messages.

    ************************************************************************
    *                                                                      *
                     uVar and friends
    *                                                                      *
    ************************************************************************

    @uVar@ is called when at least one of the types being unified is a
    variable.  It does {\em not} assume that the variable is a fixed point
    of the substitution; rather, notice that @uVar@ (defined below) nips
    back into @uTys@ if it turns out that the variable is already bound.
    -}

    ----------
    uUnfilledVar :: CtOrigin
                 -> TypeOrKind
                 -> SwapFlag
                 -> TcTyVar        -- Tyvar 1
                 -> TcTauType      -- Type 2
                 -> TcM Coercion
    -- "Unfilled" means that the variable is definitely not a filled-in meta tyvar
    --            It might be a skolem, or untouchable, or meta

    uUnfilledVar origin t_or_k swapped tv1 ty2
      = do { ty2 <- zonkTcType ty2
                 -- Zonk to expose things to the
                 -- occurs check, and so that if ty2
                 -- looks like a type variable then it
                 -- /is/ a type variable
           ; uUnfilledVar1 origin t_or_k swapped tv1 ty2 }

    ----------
    uUnfilledVar1 :: CtOrigin
                  -> TypeOrKind
                  -> SwapFlag
                  -> TcTyVar        -- Tyvar 1
                  -> TcTauType      -- Type 2, zonked
                  -> TcM Coercion
    uUnfilledVar1 origin t_or_k swapped tv1 ty2
      | Just tv2 <- tcGetTyVar_maybe ty2
      = go tv2

      | otherwise
      = uUnfilledVar2 origin t_or_k swapped tv1 ty2

      where
        -- 'go' handles the case where both are
        -- tyvars so we might want to swap
        go tv2 | tv1 == tv2  -- Same type variable => no-op
               = return (mkNomReflCo (mkTyVarTy tv1))

               | swapOverTyVars tv1 tv2   -- Distinct type variables
               = uUnfilledVar2 origin t_or_k (flipSwap swapped)
                               tv2 (mkTyVarTy tv1)

               | otherwise
               = uUnfilledVar2 origin t_or_k swapped tv1 ty2

    ----------
    uUnfilledVar2 :: CtOrigin
                  -> TypeOrKind
                  -> SwapFlag
                  -> TcTyVar        -- Tyvar 1
                  -> TcTauType      -- Type 2, zonked
                  -> TcM Coercion
    uUnfilledVar2 origin t_or_k swapped tv1 ty2
      = do { dflags  <- getDynFlags
           ; cur_lvl <- getTcLevel
           ; go dflags cur_lvl }
      where
        go dflags cur_lvl
          | canSolveByUnification cur_lvl tv1 ty2
          , Just ty2' <- metaTyVarUpdateOK dflags tv1 ty2
          = do { co_k <- uType kind_origin KindLevel (typeKind ty2') (tyVarKind tv1)
               ; co   <- updateMeta tv1 ty2' co_k
               ; return (maybe_sym swapped co) }

          | otherwise
          = unSwap swapped (uType_defer origin t_or_k) ty1 ty2
                   -- Occurs check or an untouchable: just defer
                   -- NB: occurs check isn't necessarily fatal:
                   --     eg tv1 occured in type family parameter

        ty1 = mkTyVarTy tv1
        kind_origin = KindEqOrigin ty1 (Just ty2) origin (Just t_or_k)

    -- | apply sym iff swapped
    maybe_sym :: SwapFlag -> Coercion -> Coercion
    maybe_sym IsSwapped  = mkSymCo
    maybe_sym NotSwapped = id

    swapOverTyVars :: TcTyVar -> TcTyVar -> Bool
    swapOverTyVars tv1 tv2
      | isFmvTyVar tv1 = False  -- See Note [Fmv Orientation Invariant]
      | isFmvTyVar tv2 = True

      | Just lvl1 <- metaTyVarTcLevel_maybe tv1
          -- 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]
      = 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 (including FlatMetaTv)

      -- If only one is a flatten skolem, put it on the left
      -- See Note [Eliminate flat-skols]
      | not (isFlattenTyVar tv1), isFlattenTyVar tv2 = True

      | otherwise = False

      where
        nicer_to_update tv2
          =  (isSigTyVar tv1                 && not (isSigTyVar tv2))
          || (isSystemName (Var.varName tv2) && not (isSystemName (Var.varName tv1)))

    -- @trySpontaneousSolve wi@ solves equalities where one side is a
    -- touchable unification variable.
    -- Returns True <=> spontaneous solve happened
    canSolveByUnification :: TcLevel -> TcTyVar -> TcType -> Bool
    canSolveByUnification tclvl tv xi
      | isTouchableMetaTyVar tclvl tv
      = case metaTyVarInfo tv of
          SigTv -> is_tyvar xi
          _     -> True

      | otherwise    -- Untouchable
      = False
      where
        is_tyvar xi
          = case tcGetTyVar_maybe xi of
              Nothing -> False
              Just tv -> case tcTyVarDetails tv of
                           MetaTv { mtv_info = info }
                                       -> case info of
                                            SigTv -> True
                                            _     -> False
                           SkolemTv {} -> True
                           FlatSkol {} -> False
                           RuntimeUnk  -> True

    {- Note [Fmv Orientation Invariant]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
       * We always orient a constraint
            fmv ~ alpha
         with fmv on the left, even if alpha is
         a touchable unification variable

    Reason: doing it the other way round would unify alpha:=fmv, but that
    really doesn't add any info to alpha.  But a later constraint alpha ~
    Int might unlock everything.  Comment:9 of #12526 gives a detailed
    example.

    WARNING: I've gone to and fro on this one several times.
    I'm now pretty sure that unifying alpha:=fmv is a bad idea!
    So orienting with fmvs on the left is a good thing.

    This example comes from IndTypesPerfMerge. (Others include
    T10226, T10009.)
        From the ambiguity check for
          f :: (F a ~ a) => a
        we get:
              [G] F a ~ a
              [WD] F alpha ~ alpha, alpha ~ a

        From Givens we get
              [G] F a ~ fsk, fsk ~ a

        Now if we flatten we get
              [WD] alpha ~ fmv, F alpha ~ fmv, alpha ~ a

        Now, if we unified alpha := fmv, we'd get
              [WD] F fmv ~ fmv, [WD] fmv ~ a
        And now we are stuck.

    So instead the Fmv Orientation Invariant puts te fmv on the
    left, giving
          [WD] fmv ~ alpha, [WD] F alpha ~ fmv, [WD] alpha ~ a

        Now we get alpha:=a, and everything works out

    Note [Prevent unification with type families]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We prevent unification with type families because of an uneasy compromise.
    It's perfectly sound to unify with type families, and it even improves the
    error messages in the testsuite. It also modestly improves performance, at
    least in some cases. But it's disastrous for test case perf/compiler/T3064.
    Here is the problem: Suppose we have (F ty) where we also have [G] F ty ~ a.
    What do we do? Do we reduce F? Or do we use the given? Hard to know what's
    best. GHC reduces. This is a disaster for T3064, where the type's size
    spirals out of control during reduction. (We're not helped by the fact that
    the flattener re-flattens all the arguments every time around.) If we prevent
    unification with type families, then the solver happens to use the equality
    before expanding the type family.

    It would be lovely in the future to revisit this problem and remove this
    extra, unnecessary check. But we retain it for now as it seems to work
    better in practice.

    Note [Refactoring hazard: checkTauTvUpdate]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    I (Richard E.) have a sad story about refactoring this code, retained here
    to prevent others (or a future me!) from falling into the same traps.

    It all started with #11407, which was caused by the fact that the TyVarTy
    case of defer_me didn't look in the kind. But it seemed reasonable to
    simply remove the defer_me check instead.

    It referred to two Notes (since removed) that were out of date, and the
    fast_check code in occurCheckExpand seemed to do just about the same thing as
    defer_me. The one piece that defer_me did that wasn't repeated by
    occurCheckExpand was the type-family check. (See Note [Prevent unification
    with type families].) So I checked the result of occurCheckExpand for any
    type family occurrences and deferred if there were any. This was done
    in commit e9bf7bb5cc9fb3f87dd05111aa23da76b86a8967 .

    This approach turned out not to be performant, because the expanded
    type was bigger than the original type, and tyConsOfType (needed to
    see if there are any type family occurrences) looks through type
    synonyms. So it then struck me that we could dispense with the
    defer_me check entirely. This simplified the code nicely, and it cut
    the allocations in T5030 by half. But, as documented in Note [Prevent
    unification with type families], this destroyed performance in
    T3064. Regardless, I missed this regression and the change was
    committed as 3f5d1a13f112f34d992f6b74656d64d95a3f506d .

    Bottom lines:
     * defer_me is back, but now fixed w.r.t. #11407.
     * Tread carefully before you start to refactor here. There can be
       lots of hard-to-predict consequences.

    Note [Type synonyms and the occur check]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Generally speaking we try to update a variable with type synonyms not
    expanded, which improves later error messages, unless looking
    inside a type synonym may help resolve a spurious occurs check
    error. Consider:
              type A a = ()

              f :: (A a -> a -> ()) -> ()
              f = \ _ -> ()

              x :: ()
              x = f (\ x p -> p x)

    We will eventually get a constraint of the form t ~ A t. The ok function above will
    properly expand the type (A t) to just (), which is ok to be unified with t. If we had
    unified with the original type A t, we would lead the type checker into an infinite loop.

    Hence, if the occurs check fails for a type synonym application, then (and *only* then),
    the ok function expands the synonym to detect opportunities for occurs check success using
    the underlying definition of the type synonym.

    The same applies later on in the constraint interaction code; see TcInteract,
    function @occ_check_ok@.

    Note [Non-TcTyVars in TcUnify]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Because the same code is now shared between unifying types and unifying
    kinds, we sometimes will see proper TyVars floating around the unifier.
    Example (from test case polykinds/PolyKinds12):

        type family Apply (f :: k1 -> k2) (x :: k1) :: k2
        type instance Apply g y = g y

    When checking the instance declaration, we first *kind-check* the LHS
    and RHS, discovering that the instance really should be

        type instance Apply k3 k4 (g :: k3 -> k4) (y :: k3) = g y

    During this kind-checking, all the tyvars will be TcTyVars. Then, however,
    as a second pass, we desugar the RHS (which is done in functions prefixed
    with "tc" in TcTyClsDecls"). By this time, all the kind-vars are proper
    TyVars, not TcTyVars, get some kind unification must happen.

    Thus, we always check if a TyVar is a TcTyVar before asking if it's a
    meta-tyvar.

    This used to not be necessary for type-checking (that is, before * :: *)
    because expressions get desugared via an algorithm separate from
    type-checking (with wrappers, etc.). Types get desugared very differently,
    causing this wibble in behavior seen here.
    -}

    data LookupTyVarResult  -- The result of a lookupTcTyVar call
      = Unfilled TcTyVarDetails     -- SkolemTv or virgin MetaTv
      | Filled   TcType

    lookupTcTyVar :: TcTyVar -> TcM LookupTyVarResult
    lookupTcTyVar tyvar
      | MetaTv { mtv_ref = ref } <- details
      = do { meta_details <- readMutVar ref
           ; case meta_details of
               Indirect ty -> return (Filled ty)
               Flexi -> do { is_touchable <- isTouchableTcM tyvar
                                 -- Note [Unifying untouchables]
                           ; if is_touchable then
                                return (Unfilled details)
                             else
                                return (Unfilled vanillaSkolemTv) } }
      | otherwise
      = return (Unfilled details)
      where
        details = tcTyVarDetails tyvar

    -- | Fill in a meta-tyvar
    updateMeta :: TcTyVar            -- ^ tv to fill in, tv :: k1
               -> TcType             -- ^ ty2 :: k2
               -> Coercion           -- ^ kind_co :: k2 ~N k1
               -> TcM Coercion       -- ^ :: tv ~N ty2 (= ty2 |> kind_co ~N ty2)
    updateMeta tv1 ty2 kind_co
      = do { let ty2'     = ty2 `mkCastTy` kind_co
                 ty2_refl = mkNomReflCo ty2
                 co       = mkCoherenceLeftCo ty2_refl kind_co
           ; writeMetaTyVar tv1 ty2'
           ; return co }

    {-
    Note [Unifying untouchables]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We treat an untouchable type variable as if it was a skolem.  That
    ensures it won't unify with anything.  It's a slight had, because
    we return a made-up TcTyVarDetails, but I think it works smoothly.
    -}

    -- | Breaks apart a function kind into its pieces.
    matchExpectedFunKind :: Arity           -- ^ # of args remaining, only for errors
                         -> TcType          -- ^ type, only for errors
                         -> TcKind          -- ^ function kind
                         -> TcM (Coercion, TcKind, TcKind)
                                      -- ^ co :: old_kind ~ arg -> res
    matchExpectedFunKind num_args_remaining ty = go
      where
        go k | Just k' <- tcView k = go k'

        go k@(TyVarTy kvar)
          | isTcTyVar kvar, isMetaTyVar kvar
          = do { maybe_kind <- readMetaTyVar kvar
               ; case maybe_kind of
                    Indirect fun_kind -> go fun_kind
                    Flexi ->             defer k }

        go k@(FunTy arg res) = return (mkNomReflCo k, arg, res)
        go other             = defer other

        defer k
          = do { arg_kind <- newMetaKindVar
               ; res_kind <- newMetaKindVar
               ; let new_fun = mkFunTy arg_kind res_kind
                     thing   = mkTypeErrorThingArgs ty num_args_remaining
                     origin  = TypeEqOrigin { uo_actual   = k
                                            , uo_expected = new_fun
                                            , uo_thing    = Just thing
                                            }
               ; co <- uType origin KindLevel k new_fun
               ; return (co, arg_kind, res_kind) }

    {- *********************************************************************
    *                                                                      *
                     Occurrence checking
    *                                                                      *
    ********************************************************************* -}

    {- Note [Occurs check expansion]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    (occurCheckExpand tv xi) expands synonyms in xi just enough to get rid
    of occurrences of tv outside type function arguments, if that is
    possible; otherwise, it returns Nothing.

    For example, suppose we have
      type F a b = [a]
    Then
      occCheckExpand b (F Int b) = Just [Int]
    but
      occCheckExpand a (F a Int) = Nothing

    We don't promise to do the absolute minimum amount of expanding
    necessary, but we try not to do expansions we don't need to.  We
    prefer doing inner expansions first.  For example,
      type F a b = (a, Int, a, [a])
      type G b   = Char
    We have
      occCheckExpand b (F (G b)) = Just (F Char)
    even though we could also expand F to get rid of b.

    The two variants of the function are to support TcUnify.checkTauTvUpdate,
    which wants to prevent unification with type families. For more on this
    point, see Note [Prevent unification with type families] in TcUnify.

    Note [Occurrence checking: look inside kinds]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we are considering unifying
       (alpha :: *)  ~  Int -> (beta :: alpha -> alpha)
    This may be an error (what is that alpha doing inside beta's kind?),
    but we must not make the mistake of actuallyy unifying or we'll
    build an infinite data structure.  So when looking for occurrences
    of alpha in the rhs, we must look in the kinds of type variables
    that occur there.

    NB: we may be able to remove the problem via expansion; see
        Note [Occurs check expansion].  So we have to try that.

    Note [Checking for foralls]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Unless we have -XImpredicativeTypes (which is a totally unsupported
    feature), we do not want to unify
        alpha ~ (forall a. a->a) -> Int
    So we look for foralls hidden inside the type, and it's convenient
    to do that at the same time as the occurs check (which looks for
    occurrences of alpha).

    However, it's not just a question of looking for foralls /anywhere/!
    Consider
       (alpha :: forall k. k->*)  ~  (beta :: forall k. k->*)
    This is legal; e.g. dependent/should_compile/T11635.

    We don't want to reject it because of the forall in beta's kind,
    but (see Note [Occurrence checking: look inside kinds]) we do
    need to look in beta's kind.  So we carry a flag saying if a 'forall'
    is OK, and sitch the flag on when stepping inside a kind.

    Why is it OK?  Why does it not count as impredicative polymorphism?
    The reason foralls are bad is because we reply on "seeing" foralls
    when doing implicit instantiation.  But the forall inside the kind is
    fine.  We'll generate a kind equality constraint
      (forall k. k->*) ~ (forall k. k->*)
    to check that the kinds of lhs and rhs are compatible.  If alpha's
    kind had instead been
      (alpha :: kappa)
    then this kind equality would rightly complain about unifying kappa
    with (forall k. k->*)

    -}

    data OccCheckResult a
      = OC_OK a
      | OC_Bad     -- Forall or type family
      | OC_Occurs

    instance Functor OccCheckResult where
          fmap = liftM

    instance Applicative OccCheckResult where
          pure = OC_OK
          (<*>) = ap

    instance Monad OccCheckResult where
      OC_OK x    >>= k = k x
      OC_Bad     >>= _ = OC_Bad
      OC_Occurs  >>= _ = OC_Occurs

    occCheckForErrors :: DynFlags -> TcTyVar -> Type -> OccCheckResult ()
    -- Just for error-message generation; so we return OccCheckResult
    -- so the caller can report the right kind of error
    -- Check whether
    --   a) the given variable occurs in the given type.
    --   b) there is a forall in the type (unless we have -XImpredicativeTypes)
    occCheckForErrors dflags tv ty
      = case preCheck dflags True tv ty of
          OC_OK _   -> OC_OK ()
          OC_Bad    -> OC_Bad
          OC_Occurs -> case occCheckExpand tv ty of
                         Nothing -> OC_Occurs
                         Just _  -> OC_OK ()

    ----------------
    metaTyVarUpdateOK :: DynFlags
                      -> TcTyVar             -- tv :: k1
                      -> TcType              -- ty :: k2
                      -> Maybe TcType        -- possibly-expanded ty
    -- (metaTyFVarUpdateOK tv ty)
    -- We are about to update the meta-tyvar tv with ty
    -- Check (a) that tv doesn't occur in ty (occurs check)
    --       (b) that ty does not have any foralls
    --           (in the impredicative case), or type functions
    --
    -- We have two possible outcomes:
    -- (1) Return the type to update the type variable with,
    --        [we know the update is ok]
    -- (2) Return Nothing,
    --        [the update might be dodgy]
    --
    -- Note that "Nothing" does not mean "definite error".  For example
    --   type family F a
    --   type instance F Int = Int
    -- consider
    --   a ~ F a
    -- This is perfectly reasonable, if we later get a ~ Int.  For now, though,
    -- we return Nothing, leaving it to the later constraint simplifier to
    -- sort matters out.
    --
    -- See Note [Refactoring hazard: checkTauTvUpdate]

    metaTyVarUpdateOK dflags tv ty
      = case preCheck dflags False tv ty of
             -- False <=> type families not ok
             -- See Note [Prevent unification with type families]
          OC_OK _   -> Just ty
          OC_Bad    -> Nothing  -- forall or type function
          OC_Occurs -> occCheckExpand tv ty

    preCheck :: DynFlags -> Bool -> TcTyVar -> TcType -> OccCheckResult ()
    -- A quick check for
    --   (a) a forall type (unless -XImpredivativeTypes)
    --   (b) a type family
    --   (c) an occurrence of the type variable (occurs check)
    --
    -- For (a) and (b) we check only the top level of the type, NOT
    -- inside the kinds of variables it mentions.  But for (c) we do
    -- look in the kinds of course.

    preCheck dflags ty_fam_ok tv ty
      = fast_check ty
      where
        details          = tcTyVarDetails tv
        impredicative_ok = canUnifyWithPolyType dflags details

        ok :: OccCheckResult ()
        ok = OC_OK ()

        fast_check :: TcType -> OccCheckResult ()
        fast_check (TyVarTy tv')
          | tv == tv' = OC_Occurs
          | otherwise = fast_check_occ (tyVarKind tv')
               -- See Note [Occurrence checking: look inside kinds]

        fast_check (TyConApp tc tys)
          | bad_tc tc              = OC_Bad
          | otherwise              = mapM fast_check tys >> ok
        fast_check (LitTy {})      = ok
        fast_check (FunTy a r)     = fast_check a   >> fast_check r
        fast_check (AppTy fun arg) = fast_check fun >> fast_check arg
        fast_check (CastTy ty co)  = fast_check ty  >> fast_check_co co
        fast_check (CoercionTy co) = fast_check_co co
        fast_check (ForAllTy (TvBndr tv' _) ty)
           | not impredicative_ok = OC_Bad
           | tv == tv'            = ok
           | otherwise = do { fast_check_occ (tyVarKind tv')
                            ; fast_check_occ ty }
           -- Under a forall we look only for occurrences of
           -- the type variable

         -- For kinds, we only do an occurs check; we do not worry
         -- about type families or foralls
         -- See Note [Checking for foralls]
        fast_check_occ k | tv `elemVarSet` tyCoVarsOfType k = OC_Occurs
                         | otherwise                        = ok

         -- For coercions, we are only doing an occurs check here;
         -- no bother about impredicativity in coercions, as they're
         -- inferred
        fast_check_co co | tv `elemVarSet` tyCoVarsOfCo co = OC_Occurs
                         | otherwise                       = ok

        bad_tc :: TyCon -> Bool
        bad_tc tc
          | not (impredicative_ok || isTauTyCon tc)     = True
          | not (ty_fam_ok        || isFamFreeTyCon tc) = True
          | otherwise                                   = False

    occCheckExpand :: TcTyVar -> TcType -> Maybe TcType
    -- See Note [Occurs check expansion]
    -- We may have needed to do some type synonym unfolding in order to
    -- get rid of the variable (or forall), so we also return the unfolded
    -- version of the type, which is guaranteed to be syntactically free
    -- of the given type variable.  If the type is already syntactically
    -- free of the variable, then the same type is returned.
    occCheckExpand tv ty
      = go emptyVarEnv ty
      where
        go :: VarEnv TyVar -> Type -> Maybe Type
              -- The VarEnv carries mappings necessary
              -- because of kind expansion
        go env (TyVarTy tv')
          | tv == tv'                         = Nothing
          | Just tv'' <- lookupVarEnv env tv' = return (mkTyVarTy tv'')
          | otherwise                         = do { k' <- go env (tyVarKind tv')
                                                   ; return (mkTyVarTy $
                                                             setTyVarKind tv' k') }
               -- See Note [Occurrence checking: look inside kinds]

        go _   ty@(LitTy {}) = return ty
        go env (AppTy ty1 ty2) = do { ty1' <- go env ty1
                                    ; ty2' <- go env ty2
                                    ; return (mkAppTy ty1' ty2') }
        go env (FunTy ty1 ty2) = do { ty1' <- go env ty1
                                    ; ty2' <- go env ty2
                                    ; return (mkFunTy ty1' ty2') }
        go env ty@(ForAllTy (TvBndr tv' vis) body_ty)
           | tv == tv'         = return ty
           | otherwise         = do { ki' <- go env (tyVarKind tv')
                                    ; let tv'' = setTyVarKind tv' ki'
                                          env' = extendVarEnv env tv' tv''
                                    ; body' <- go env' body_ty
                                    ; return (ForAllTy (TvBndr tv'' vis) body') }

        -- For a type constructor application, first try expanding away the
        -- offending variable from the arguments.  If that doesn't work, next
        -- see if the type constructor is a type synonym, and if so, expand
        -- it and try again.
        go env ty@(TyConApp tc tys)
          = case mapM (go env) tys of
              Just tys' -> return (mkTyConApp tc tys')
              Nothing | Just ty' <- tcView ty -> go env ty'
                      | otherwise             -> Nothing
                          -- Failing that, try to expand a synonym

        go env (CastTy ty co) =  do { ty' <- go env ty
                                    ; co' <- go_co env co
                                    ; return (mkCastTy ty' co') }
        go env (CoercionTy co) = do { co' <- go_co env co
                                    ; return (mkCoercionTy co') }

        ------------------
        go_co env (Refl r ty)               = do { ty' <- go env ty
                                                 ; return (mkReflCo r ty') }
          -- Note: Coercions do not contain type synonyms
        go_co env (TyConAppCo r tc args)    = do { args' <- mapM (go_co env) args
                                                 ; return (mkTyConAppCo r tc args') }
        go_co env (AppCo co arg)            = do { co' <- go_co env co
                                                 ; arg' <- go_co env arg
                                                 ; return (mkAppCo co' arg') }
        go_co env co@(ForAllCo tv' kind_co body_co)
          | tv == tv'         = return co
          | otherwise         = do { kind_co' <- go_co env kind_co
                                   ; let tv'' = setTyVarKind tv' $
                                                pFst (coercionKind kind_co')
                                         env' = extendVarEnv env tv' tv''
                                   ; body' <- go_co env' body_co
                                   ; return (ForAllCo tv'' kind_co' body') }
        go_co env (FunCo r co1 co2)         = do { co1' <- go_co env co1
                                                 ; co2' <- go_co env co2
                                                 ; return (mkFunCo r co1' co2') }
        go_co env (CoVarCo c)               = do { k' <- go env (varType c)
                                                 ; return (mkCoVarCo (setVarType c k')) }
        go_co env (AxiomInstCo ax ind args) = do { args' <- mapM (go_co env) args
                                                 ; return (mkAxiomInstCo ax ind args') }
        go_co env (UnivCo p r ty1 ty2)      = do { p' <- go_prov env p
                                                 ; ty1' <- go env ty1
                                                 ; ty2' <- go env ty2
                                                 ; return (mkUnivCo p' r ty1' ty2') }
        go_co env (SymCo co)                = do { co' <- go_co env co
                                                 ; return (mkSymCo co') }
        go_co env (TransCo co1 co2)         = do { co1' <- go_co env co1
                                                 ; co2' <- go_co env co2
                                                 ; return (mkTransCo co1' co2') }
        go_co env (NthCo n co)              = do { co' <- go_co env co
                                                 ; return (mkNthCo n co') }
        go_co env (LRCo lr co)              = do { co' <- go_co env co
                                                 ; return (mkLRCo lr co') }
        go_co env (InstCo co arg)           = do { co' <- go_co env co
                                                 ; arg' <- go_co env arg
                                                 ; return (mkInstCo co' arg') }
        go_co env (CoherenceCo co1 co2)     = do { co1' <- go_co env co1
                                                 ; co2' <- go_co env co2
                                                 ; return (mkCoherenceCo co1' co2') }
        go_co env (KindCo co)               = do { co' <- go_co env co
                                                 ; return (mkKindCo co') }
        go_co env (SubCo co)                = do { co' <- go_co env co
                                                 ; return (mkSubCo co') }
        go_co env (AxiomRuleCo ax cs)       = do { cs' <- mapM (go_co env) cs
                                                 ; return (mkAxiomRuleCo ax cs') }

        ------------------
        go_prov _   UnsafeCoerceProv    = return UnsafeCoerceProv
        go_prov env (PhantomProv co)    = PhantomProv <$> go_co env co
        go_prov env (ProofIrrelProv co) = ProofIrrelProv <$> go_co env co
        go_prov _   p@(PluginProv _)    = return p
        go_prov _   p@(HoleProv _)      = return p

    canUnifyWithPolyType :: DynFlags -> TcTyVarDetails -> Bool
    canUnifyWithPolyType dflags details
      = case details of
          MetaTv { mtv_info = SigTv }    -> False
          MetaTv { mtv_info = TauTv }    -> xopt LangExt.ImpredicativeTypes dflags
          _other                         -> True
              -- We can have non-meta tyvars in given constraints