types/TyCon.hs

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

    The @TyCon@ datatype
    -}

    {-# LANGUAGE CPP, FlexibleInstances #-}

    module TyCon(
            -- * Main TyCon data types
            TyCon,
            AlgTyConRhs(..), visibleDataCons,
            AlgTyConFlav(..), isNoParent,
            FamTyConFlav(..), Role(..), Injectivity(..),
            RuntimeRepInfo(..), TyConFlavour(..),

            -- * TyConBinder
            TyConBinder, TyConBndrVis(..), TyConTyCoBinder,
            mkNamedTyConBinder, mkNamedTyConBinders,
            mkRequiredTyConBinder,
            mkAnonTyConBinder, mkAnonTyConBinders,
            tyConBinderArgFlag, tyConBndrVisArgFlag, isNamedTyConBinder,
            isVisibleTyConBinder, isInvisibleTyConBinder,

            -- ** Field labels
            tyConFieldLabels, lookupTyConFieldLabel,

            -- ** Constructing TyCons
            mkAlgTyCon,
            mkClassTyCon,
            mkFunTyCon,
            mkPrimTyCon,
            mkKindTyCon,
            mkLiftedPrimTyCon,
            mkTupleTyCon,
            mkSumTyCon,
            mkDataTyConRhs,
            mkSynonymTyCon,
            mkFamilyTyCon,
            mkPromotedDataCon,
            mkTcTyCon,
            noTcTyConScopedTyVars,

            -- ** Predicates on TyCons
            isAlgTyCon, isVanillaAlgTyCon,
            isClassTyCon, isFamInstTyCon,
            isFunTyCon,
            isPrimTyCon,
            isTupleTyCon, isUnboxedTupleTyCon, isBoxedTupleTyCon,
            isUnboxedSumTyCon, isPromotedTupleTyCon,
            isTypeSynonymTyCon,
            mustBeSaturated,
            isPromotedDataCon, isPromotedDataCon_maybe,
            isKindTyCon, isLiftedTypeKindTyConName,
            isTauTyCon, isFamFreeTyCon,

            isDataTyCon, isProductTyCon, isDataProductTyCon_maybe,
            isDataSumTyCon_maybe,
            isEnumerationTyCon,
            isNewTyCon, isAbstractTyCon,
            isFamilyTyCon, isOpenFamilyTyCon,
            isTypeFamilyTyCon, isDataFamilyTyCon,
            isOpenTypeFamilyTyCon, isClosedSynFamilyTyConWithAxiom_maybe,
            tyConInjectivityInfo,
            isBuiltInSynFamTyCon_maybe,
            isUnliftedTyCon,
            isGadtSyntaxTyCon, isInjectiveTyCon, isGenerativeTyCon, isGenInjAlgRhs,
            isTyConAssoc, tyConAssoc_maybe, tyConFlavourAssoc_maybe,
            isImplicitTyCon,
            isTyConWithSrcDataCons,
            isTcTyCon, setTcTyConKind,
            isTcLevPoly,

            -- ** Extracting information out of TyCons
            tyConName,
            tyConSkolem,
            tyConKind,
            tyConUnique,
            tyConTyVars, tyConVisibleTyVars,
            tyConCType, tyConCType_maybe,
            tyConDataCons, tyConDataCons_maybe,
            tyConSingleDataCon_maybe, tyConSingleDataCon,
            tyConSingleAlgDataCon_maybe,
            tyConFamilySize,
            tyConStupidTheta,
            tyConArity,
            tyConRoles,
            tyConFlavour,
            tyConTuple_maybe, tyConClass_maybe, tyConATs,
            tyConFamInst_maybe, tyConFamInstSig_maybe, tyConFamilyCoercion_maybe,
            tyConFamilyResVar_maybe,
            synTyConDefn_maybe, synTyConRhs_maybe,
            famTyConFlav_maybe, famTcResVar,
            algTyConRhs,
            newTyConRhs, newTyConEtadArity, newTyConEtadRhs,
            unwrapNewTyCon_maybe, unwrapNewTyConEtad_maybe,
            newTyConDataCon_maybe,
            algTcFields,
            tyConRuntimeRepInfo,
            tyConBinders, tyConResKind, tyConTyVarBinders,
            tcTyConScopedTyVars, tcTyConIsPoly,
            mkTyConTagMap,

            -- ** Manipulating TyCons
            expandSynTyCon_maybe,
            newTyConCo, newTyConCo_maybe,
            pprPromotionQuote, mkTyConKind,

            -- ** Predicated on TyConFlavours
            tcFlavourIsOpen,

            -- * Runtime type representation
            TyConRepName, tyConRepName_maybe,
            mkPrelTyConRepName,
            tyConRepModOcc,

            -- * Primitive representations of Types
            PrimRep(..), PrimElemRep(..),
            isVoidRep, isGcPtrRep,
            primRepSizeB,
            primElemRepSizeB,
            primRepIsFloat,
            primRepsCompatible,
            primRepCompatible,

            -- * Recursion breaking
            RecTcChecker, initRecTc, defaultRecTcMaxBound,
            setRecTcMaxBound, checkRecTc

    ) where

    #include "HsVersions.h"

    import GhcPrelude

    import {-# SOURCE #-} TyCoRep    ( Kind, Type, PredType, mkForAllTy, mkFunTy )
    import {-# SOURCE #-} TyCoPpr    ( pprType )
    import {-# SOURCE #-} TysWiredIn ( runtimeRepTyCon, constraintKind
                                     , vecCountTyCon, vecElemTyCon, liftedTypeKind )
    import {-# SOURCE #-} DataCon    ( DataCon, dataConExTyCoVars, dataConFieldLabels
                                     , dataConTyCon, dataConFullSig
                                     , isUnboxedSumCon )

    import Binary
    import Var
    import VarSet
    import Class
    import BasicTypes
    import DynFlags
    import ForeignCall
    import Name
    import NameEnv
    import CoAxiom
    import PrelNames
    import Maybes
    import Outputable
    import FastStringEnv
    import FieldLabel
    import Constants
    import Util
    import Unique( tyConRepNameUnique, dataConTyRepNameUnique )
    import UniqSet
    import Module

    import qualified Data.Data as Data

    {-
    -----------------------------------------------
            Notes about type families
    -----------------------------------------------

    Note [Type synonym families]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    * Type synonym families, also known as "type functions", map directly
      onto the type functions in FC:

            type family F a :: *
            type instance F Int = Bool
            ..etc...

    * Reply "yes" to isTypeFamilyTyCon, and isFamilyTyCon

    * From the user's point of view (F Int) and Bool are simply
      equivalent types.

    * A Haskell 98 type synonym is a degenerate form of a type synonym
      family.

    * Type functions can't appear in the LHS of a type function:
            type instance F (F Int) = ...   -- BAD!

    * Translation of type family decl:
            type family F a :: *
      translates to
        a FamilyTyCon 'F', whose FamTyConFlav is OpenSynFamilyTyCon

            type family G a :: * where
              G Int = Bool
              G Bool = Char
              G a = ()
      translates to
        a FamilyTyCon 'G', whose FamTyConFlav is ClosedSynFamilyTyCon, with the
        appropriate CoAxiom representing the equations

    We also support injective type families -- see Note [Injective type families]

    Note [Data type families]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    See also Note [Wrappers for data instance tycons] in MkId.hs

    * Data type families are declared thus
            data family T a :: *
            data instance T Int = T1 | T2 Bool

      Here T is the "family TyCon".

    * Reply "yes" to isDataFamilyTyCon, and isFamilyTyCon

    * The user does not see any "equivalent types" as he did with type
      synonym families.  He just sees constructors with types
            T1 :: T Int
            T2 :: Bool -> T Int

    * Here's the FC version of the above declarations:

            data T a
            data R:TInt = T1 | T2 Bool
            axiom ax_ti : T Int ~R R:TInt

      Note that this is a *representational* coercion
      The R:TInt is the "representation TyCons".
      It has an AlgTyConFlav of
            DataFamInstTyCon T [Int] ax_ti

    * The axiom ax_ti may be eta-reduced; see
      Note [Eta reduction for data families] in FamInstEnv

    * Data family instances may have a different arity than the data family.
      See Note [Arity of data families] in FamInstEnv

    * The data constructor T2 has a wrapper (which is what the
      source-level "T2" invokes):

            $WT2 :: Bool -> T Int
            $WT2 b = T2 b `cast` sym ax_ti

    * A data instance can declare a fully-fledged GADT:

            data instance T (a,b) where
              X1 :: T (Int,Bool)
              X2 :: a -> b -> T (a,b)

      Here's the FC version of the above declaration:

            data R:TPair a b where
              X1 :: R:TPair Int Bool
              X2 :: a -> b -> R:TPair a b
            axiom ax_pr :: T (a,b)  ~R  R:TPair a b

            $WX1 :: forall a b. a -> b -> T (a,b)
            $WX1 a b (x::a) (y::b) = X2 a b x y `cast` sym (ax_pr a b)

      The R:TPair are the "representation TyCons".
      We have a bit of work to do, to unpick the result types of the
      data instance declaration for T (a,b), to get the result type in the
      representation; e.g.  T (a,b) --> R:TPair a b

      The representation TyCon R:TList, has an AlgTyConFlav of

            DataFamInstTyCon T [(a,b)] ax_pr

    * Notice that T is NOT translated to a FC type function; it just
      becomes a "data type" with no constructors, which can be coerced
      into R:TInt, R:TPair by the axioms.  These axioms
      axioms come into play when (and *only* when) you
            - use a data constructor
            - do pattern matching
      Rather like newtype, in fact

      As a result

      - T behaves just like a data type so far as decomposition is concerned

      - (T Int) is not implicitly converted to R:TInt during type inference.
        Indeed the latter type is unknown to the programmer.

      - There *is* an instance for (T Int) in the type-family instance
        environment, but it is only used for overlap checking

      - It's fine to have T in the LHS of a type function:
        type instance F (T a) = [a]

      It was this last point that confused me!  The big thing is that you
      should not think of a data family T as a *type function* at all, not
      even an injective one!  We can't allow even injective type functions
      on the LHS of a type function:
            type family injective G a :: *
            type instance F (G Int) = Bool
      is no good, even if G is injective, because consider
            type instance G Int = Bool
            type instance F Bool = Char

      So a data type family is not an injective type function. It's just a
      data type with some axioms that connect it to other data types.

    * The tyConTyVars of the representation tycon are the tyvars that the
      user wrote in the patterns. This is important in TcDeriv, where we
      bring these tyvars into scope before type-checking the deriving
      clause. This fact is arranged for in TcInstDecls.tcDataFamInstDecl.

    Note [Associated families and their parent class]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    *Associated* families are just like *non-associated* families, except
    that they have a famTcParent field of (Just cls_tc), which identifies the
    parent class.

    However there is an important sharing relationship between
      * the tyConTyVars of the parent Class
      * the tyConTyVars of the associated TyCon

       class C a b where
         data T p a
         type F a q b

    Here the 'a' and 'b' are shared with the 'Class'; that is, they have
    the same Unique.

    This is important. In an instance declaration we expect
      * all the shared variables to be instantiated the same way
      * the non-shared variables of the associated type should not
        be instantiated at all

      instance C [x] (Tree y) where
         data T p [x] = T1 x | T2 p
         type F [x] q (Tree y) = (x,y,q)

    Note [TyCon Role signatures]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Every tycon has a role signature, assigning a role to each of the tyConTyVars
    (or of equal length to the tyConArity, if there are no tyConTyVars). An
    example demonstrates these best: say we have a tycon T, with parameters a at
    nominal, b at representational, and c at phantom. Then, to prove
    representational equality between T a1 b1 c1 and T a2 b2 c2, we need to have
    nominal equality between a1 and a2, representational equality between b1 and
    b2, and nothing in particular (i.e., phantom equality) between c1 and c2. This
    might happen, say, with the following declaration:

      data T a b c where
        MkT :: b -> T Int b c

    Data and class tycons have their roles inferred (see inferRoles in TcTyDecls),
    as do vanilla synonym tycons. Family tycons have all parameters at role N,
    though it is conceivable that we could relax this restriction. (->)'s and
    tuples' parameters are at role R. Each primitive tycon declares its roles;
    it's worth noting that (~#)'s parameters are at role N. Promoted data
    constructors' type arguments are at role R. All kind arguments are at role
    N.

    Note [Unboxed tuple RuntimeRep vars]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The contents of an unboxed tuple may have any representation. Accordingly,
    the kind of the unboxed tuple constructor is runtime-representation
    polymorphic.

    Type constructor (2 kind arguments)
       (#,#) :: forall (q :: RuntimeRep) (r :: RuntimeRep).
                       TYPE q -> TYPE r -> TYPE (TupleRep [q, r])
    Data constructor (4 type arguments)
       (#,#) :: forall (q :: RuntimeRep) (r :: RuntimeRep)
                       (a :: TYPE q) (b :: TYPE r). a -> b -> (# a, b #)

    These extra tyvars (q and r) cause some delicate processing around tuples,
    where we need to manually insert RuntimeRep arguments.
    The same situation happens with unboxed sums: each alternative
    has its own RuntimeRep.
    For boxed tuples, there is no levity polymorphism, and therefore
    we add RuntimeReps only for the unboxed version.

    Type constructor (no kind arguments)
       (,) :: Type -> Type -> Type
    Data constructor (2 type arguments)
       (,) :: forall a b. a -> b -> (a, b)

    Note [Injective type families]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We allow injectivity annotations for type families (both open and closed):

      type family F (a :: k) (b :: k) = r | r -> a
      type family G a b = res | res -> a b where ...

    Injectivity information is stored in the `famTcInj` field of `FamilyTyCon`.
    `famTcInj` maybe stores a list of Bools, where each entry corresponds to a
    single element of `tyConTyVars` (both lists should have identical length). If no
    injectivity annotation was provided `famTcInj` is Nothing. From this follows an
    invariant that if `famTcInj` is a Just then at least one element in the list
    must be True.

    See also:
     * [Injectivity annotation] in GHC.Hs.Decls
     * [Renaming injectivity annotation] in RnSource
     * [Verifying injectivity annotation] in FamInstEnv
     * [Type inference for type families with injectivity] in TcInteract

    ************************************************************************
    *                                                                      *
                        TyConBinder, TyConTyCoBinder
    *                                                                      *
    ************************************************************************
    -}

    type TyConBinder = VarBndr TyVar TyConBndrVis

    -- In the whole definition of @data TyCon@, only @PromotedDataCon@ will really
    -- contain CoVar.
    type TyConTyCoBinder = VarBndr TyCoVar TyConBndrVis

    data TyConBndrVis
      = NamedTCB ArgFlag
      | AnonTCB  AnonArgFlag

    instance Outputable TyConBndrVis where
      ppr (NamedTCB flag) = text "NamedTCB" <> ppr flag
      ppr (AnonTCB af)    = text "AnonTCB"  <> ppr af

    mkAnonTyConBinder :: AnonArgFlag -> TyVar -> TyConBinder
    mkAnonTyConBinder af tv = ASSERT( isTyVar tv)
                              Bndr tv (AnonTCB af)

    mkAnonTyConBinders :: AnonArgFlag -> [TyVar] -> [TyConBinder]
    mkAnonTyConBinders af tvs = map (mkAnonTyConBinder af) tvs

    mkNamedTyConBinder :: ArgFlag -> TyVar -> TyConBinder
    -- The odd argument order supports currying
    mkNamedTyConBinder vis tv = ASSERT( isTyVar tv )
                                Bndr tv (NamedTCB vis)

    mkNamedTyConBinders :: ArgFlag -> [TyVar] -> [TyConBinder]
    -- The odd argument order supports currying
    mkNamedTyConBinders vis tvs = map (mkNamedTyConBinder vis) tvs

    -- | Make a Required TyConBinder. It chooses between NamedTCB and
    -- AnonTCB based on whether the tv is mentioned in the dependent set
    mkRequiredTyConBinder :: TyCoVarSet  -- these are used dependently
                          -> TyVar
                          -> TyConBinder
    mkRequiredTyConBinder dep_set tv
      | tv `elemVarSet` dep_set = mkNamedTyConBinder Required tv
      | otherwise               = mkAnonTyConBinder  VisArg   tv

    tyConBinderArgFlag :: TyConBinder -> ArgFlag
    tyConBinderArgFlag (Bndr _ vis) = tyConBndrVisArgFlag vis

    tyConBndrVisArgFlag :: TyConBndrVis -> ArgFlag
    tyConBndrVisArgFlag (NamedTCB vis)     = vis
    tyConBndrVisArgFlag (AnonTCB VisArg)   = Required
    tyConBndrVisArgFlag (AnonTCB InvisArg) = Inferred    -- See Note [AnonTCB InvisArg]

    isNamedTyConBinder :: TyConBinder -> Bool
    -- Identifies kind variables
    -- E.g. data T k (a:k) = blah
    -- Here 'k' is a NamedTCB, a variable used in the kind of other binders
    isNamedTyConBinder (Bndr _ (NamedTCB {})) = True
    isNamedTyConBinder _                      = False

    isVisibleTyConBinder :: VarBndr tv TyConBndrVis -> Bool
    -- Works for IfaceTyConBinder too
    isVisibleTyConBinder (Bndr _ tcb_vis) = isVisibleTcbVis tcb_vis

    isVisibleTcbVis :: TyConBndrVis -> Bool
    isVisibleTcbVis (NamedTCB vis)     = isVisibleArgFlag vis
    isVisibleTcbVis (AnonTCB VisArg)   = True
    isVisibleTcbVis (AnonTCB InvisArg) = False

    isInvisibleTyConBinder :: VarBndr tv TyConBndrVis -> Bool
    -- Works for IfaceTyConBinder too
    isInvisibleTyConBinder tcb = not (isVisibleTyConBinder tcb)

    -- Build the 'tyConKind' from the binders and the result kind.
    -- Keep in sync with 'mkTyConKind' in iface/IfaceType.
    mkTyConKind :: [TyConBinder] -> Kind -> Kind
    mkTyConKind bndrs res_kind = foldr mk res_kind bndrs
      where
        mk :: TyConBinder -> Kind -> Kind
        mk (Bndr tv (AnonTCB af))   k = mkFunTy af (varType tv) k
        mk (Bndr tv (NamedTCB vis)) k = mkForAllTy tv vis k

    tyConTyVarBinders :: [TyConBinder]   -- From the TyCon
                      -> [TyVarBinder]   -- Suitable for the foralls of a term function
    -- See Note [Building TyVarBinders from TyConBinders]
    tyConTyVarBinders tc_bndrs
     = map mk_binder tc_bndrs
     where
       mk_binder (Bndr tv tc_vis) = mkTyVarBinder vis tv
          where
            vis = case tc_vis of
                    AnonTCB VisArg    -> Specified
                    AnonTCB InvisArg  -> Inferred   -- See Note [AnonTCB InvisArg]
                    NamedTCB Required -> Specified
                    NamedTCB vis      -> vis

    -- Returns only tyvars, as covars are always inferred
    tyConVisibleTyVars :: TyCon -> [TyVar]
    tyConVisibleTyVars tc
      = [ tv | Bndr tv vis <- tyConBinders tc
             , isVisibleTcbVis vis ]

    {- Note [AnonTCB InvisArg]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    It's pretty rare to have an (AnonTCB InvisArg) binder.  The
    only way it can occur is through equality constraints in kinds. These
    can arise in one of two ways:

    * In a PromotedDataCon whose kind has an equality constraint:

        'MkT :: forall a b. (a~b) => blah

      See Note [Constraints in kinds] in TyCoRep, and
      Note [Promoted data constructors] in this module.
    * In a data type whose kind has an equality constraint, as in the
      following example from #12102:

        data T :: forall a. (IsTypeLit a ~ 'True) => a -> Type

    When mapping an (AnonTCB InvisArg) to an ArgFlag, in
    tyConBndrVisArgFlag, we use "Inferred" to mean "the user cannot
    specify this arguments, even with visible type/kind application;
    instead the type checker must fill it in.

    We map (AnonTCB VisArg) to Required, of course: the user must
    provide it. It would be utterly wrong to do this for constraint
    arguments, which is why AnonTCB must have the AnonArgFlag in
    the first place.

    Note [Building TyVarBinders from TyConBinders]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We sometimes need to build the quantified type of a value from
    the TyConBinders of a type or class.  For that we need not
    TyConBinders but TyVarBinders (used in forall-type)  E.g:

     *  From   data T a = MkT (Maybe a)
        we are going to make a data constructor with type
               MkT :: forall a. Maybe a -> T a
        See the TyCoVarBinders passed to buildDataCon

     * From    class C a where { op :: a -> Maybe a }
       we are going to make a default method
               $dmop :: forall a. C a => a -> Maybe a
       See the TyCoVarBinders passed to mkSigmaTy in mkDefaultMethodType

    Both of these are user-callable.  (NB: default methods are not callable
    directly by the user but rather via the code generated by 'deriving',
    which uses visible type application; see mkDefMethBind.)

    Since they are user-callable we must get their type-argument visibility
    information right; and that info is in the TyConBinders.
    Here is an example:

      data App a b = MkApp (a b) -- App :: forall {k}. (k->*) -> k -> *

    The TyCon has

      tyConTyBinders = [ Named (Bndr (k :: *) Inferred), Anon (k->*), Anon k ]

    The TyConBinders for App line up with App's kind, given above.

    But the DataCon MkApp has the type
      MkApp :: forall {k} (a:k->*) (b:k). a b -> App k a b

    That is, its TyCoVarBinders should be

      dataConUnivTyVarBinders = [ Bndr (k:*)    Inferred
                                , Bndr (a:k->*) Specified
                                , Bndr (b:k)    Specified ]

    So tyConTyVarBinders converts TyCon's TyConBinders into TyVarBinders:
      - variable names from the TyConBinders
      - but changing Anon/Required to Specified

    The last part about Required->Specified comes from this:
      data T k (a:k) b = MkT (a b)
    Here k is Required in T's kind, but we don't have Required binders in
    the TyCoBinders for a term (see Note [No Required TyCoBinder in terms]
    in TyCoRep), so we change it to Specified when making MkT's TyCoBinders
    -}

    {- Note [The binders/kind/arity fields of a TyCon]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    All TyCons have this group of fields
      tyConBinders   :: [TyConBinder/TyConTyCoBinder]
      tyConResKind   :: Kind
      tyConTyVars    :: [TyVar]   -- Cached = binderVars tyConBinders
                                  --   NB: Currently (Aug 2018), TyCons that own this
                                  --   field really only contain TyVars. So it is
                                  --   [TyVar] instead of [TyCoVar].
      tyConKind      :: Kind      -- Cached = mkTyConKind tyConBinders tyConResKind
      tyConArity     :: Arity     -- Cached = length tyConBinders

    They fit together like so:

    * tyConBinders gives the telescope of type/coercion variables on the LHS of the
      type declaration.  For example:

        type App a (b :: k) = a b

      tyConBinders = [ Bndr (k::*)   (NamedTCB Inferred)
                     , Bndr (a:k->*) AnonTCB
                     , Bndr (b:k)    AnonTCB ]

      Note that that are three binders here, including the
      kind variable k.

    * See Note [VarBndrs, TyCoVarBinders, TyConBinders, and visibility] in TyCoRep
      for what the visibility flag means.

    * Each TyConBinder tyConBinders has a TyVar (sometimes it is TyCoVar), and
      that TyVar may scope over some other part of the TyCon's definition. Eg
          type T a = a -> a
      we have
          tyConBinders = [ Bndr (a:*) AnonTCB ]
          synTcRhs     = a -> a
      So the 'a' scopes over the synTcRhs

    * From the tyConBinders and tyConResKind we can get the tyConKind
      E.g for our App example:
          App :: forall k. (k->*) -> k -> *

      We get a 'forall' in the kind for each NamedTCB, and an arrow
      for each AnonTCB

      tyConKind is the full kind of the TyCon, not just the result kind

    * For type families, tyConArity is the arguments this TyCon must be
      applied to, to be considered saturated.  Here we mean "applied to in
      the actual Type", not surface syntax; i.e. including implicit kind
      variables.  So it's just (length tyConBinders)

    * For an algebraic data type, or data instance, the tyConResKind is
      always (TYPE r); that is, the tyConBinders are enough to saturate
      the type constructor.  I'm not quite sure why we have this invariant,
      but it's enforced by etaExpandAlgTyCon
    -}

    instance Outputable tv => Outputable (VarBndr tv TyConBndrVis) where
      ppr (Bndr v bi) = ppr_bi bi <+> parens (ppr v)
        where
          ppr_bi (AnonTCB VisArg)     = text "anon-vis"
          ppr_bi (AnonTCB InvisArg)   = text "anon-invis"
          ppr_bi (NamedTCB Required)  = text "req"
          ppr_bi (NamedTCB Specified) = text "spec"
          ppr_bi (NamedTCB Inferred)  = text "inf"

    instance Binary TyConBndrVis where
      put_ bh (AnonTCB af)   = do { putByte bh 0; put_ bh af }
      put_ bh (NamedTCB vis) = do { putByte bh 1; put_ bh vis }

      get bh = do { h <- getByte bh
                  ; case h of
                      0 -> do { af  <- get bh; return (AnonTCB af) }
                      _ -> do { vis <- get bh; return (NamedTCB vis) } }

    {- *********************************************************************
    *                                                                      *
                   The TyCon type
    *                                                                      *
    ************************************************************************
    -}

    -- | TyCons represent type constructors. Type constructors are introduced by
    -- things such as:
    --
    -- 1) Data declarations: @data Foo = ...@ creates the @Foo@ type constructor of
    --    kind @*@
    --
    -- 2) Type synonyms: @type Foo = ...@ creates the @Foo@ type constructor
    --
    -- 3) Newtypes: @newtype Foo a = MkFoo ...@ creates the @Foo@ type constructor
    --    of kind @* -> *@
    --
    -- 4) Class declarations: @class Foo where@ creates the @Foo@ type constructor
    --    of kind @*@
    --
    -- This data type also encodes a number of primitive, built in type constructors
    -- such as those for function and tuple types.

    -- If you edit this type, you may need to update the GHC formalism
    -- See Note [GHC Formalism] in coreSyn/CoreLint.hs
    data TyCon
      = -- | The function type constructor, @(->)@
        FunTyCon {
            tyConUnique :: Unique,   -- ^ A Unique of this TyCon. Invariant:
                                     -- identical to Unique of Name stored in
                                     -- tyConName field.

            tyConName   :: Name,     -- ^ Name of the constructor

            -- See Note [The binders/kind/arity fields of a TyCon]
            tyConBinders :: [TyConBinder], -- ^ Full binders
            tyConResKind :: Kind,             -- ^ Result kind
            tyConKind    :: Kind,             -- ^ Kind of this TyCon
            tyConArity   :: Arity,            -- ^ Arity

            tcRepName :: TyConRepName
        }

      -- | Algebraic data types, from
      --     - @data@ declarations
      --     - @newtype@ declarations
      --     - data instance declarations
      --     - type instance declarations
      --     - the TyCon generated by a class declaration
      --     - boxed tuples
      --     - unboxed tuples
      --     - constraint tuples
      -- All these constructors are lifted and boxed except unboxed tuples
      -- which should have an 'UnboxedAlgTyCon' parent.
      -- Data/newtype/type /families/ are handled by 'FamilyTyCon'.
      -- See 'AlgTyConRhs' for more information.
      | AlgTyCon {
            tyConUnique  :: Unique,  -- ^ A Unique of this TyCon. Invariant:
                                     -- identical to Unique of Name stored in
                                     -- tyConName field.

            tyConName    :: Name,    -- ^ Name of the constructor

            -- See Note [The binders/kind/arity fields of a TyCon]
            tyConBinders :: [TyConBinder], -- ^ Full binders
            tyConTyVars  :: [TyVar],          -- ^ TyVar binders
            tyConResKind :: Kind,             -- ^ Result kind
            tyConKind    :: Kind,             -- ^ Kind of this TyCon
            tyConArity   :: Arity,            -- ^ Arity

                  -- The tyConTyVars scope over:
                  --
                  -- 1. The 'algTcStupidTheta'
                  -- 2. The cached types in algTyConRhs.NewTyCon
                  -- 3. The family instance types if present
                  --
                  -- Note that it does /not/ scope over the data
                  -- constructors.

            tcRoles      :: [Role],  -- ^ The role for each type variable
                                     -- This list has length = tyConArity
                                     -- See also Note [TyCon Role signatures]

            tyConCType   :: Maybe CType,-- ^ The C type that should be used
                                        -- for this type when using the FFI
                                        -- and CAPI

            algTcGadtSyntax  :: Bool,   -- ^ Was the data type declared with GADT
                                        -- syntax?  If so, that doesn't mean it's a
                                        -- true GADT; only that the "where" form
                                        -- was used.  This field is used only to
                                        -- guide pretty-printing

            algTcStupidTheta :: [PredType], -- ^ The \"stupid theta\" for the data
                                            -- type (always empty for GADTs).  A
                                            -- \"stupid theta\" is the context to
                                            -- the left of an algebraic type
                                            -- declaration, e.g. @Eq a@ in the
                                            -- declaration @data Eq a => T a ...@.

            algTcRhs    :: AlgTyConRhs, -- ^ Contains information about the
                                        -- data constructors of the algebraic type

            algTcFields :: FieldLabelEnv, -- ^ Maps a label to information
                                          -- about the field

            algTcParent :: AlgTyConFlav -- ^ Gives the class or family declaration
                                           -- 'TyCon' for derived 'TyCon's representing
                                           -- class or family instances, respectively.

        }

      -- | Represents type synonyms
      | SynonymTyCon {
            tyConUnique  :: Unique,  -- ^ A Unique of this TyCon. Invariant:
                                     -- identical to Unique of Name stored in
                                     -- tyConName field.

            tyConName    :: Name,    -- ^ Name of the constructor

            -- See Note [The binders/kind/arity fields of a TyCon]
            tyConBinders :: [TyConBinder], -- ^ Full binders
            tyConTyVars  :: [TyVar],          -- ^ TyVar binders
            tyConResKind :: Kind,             -- ^ Result kind
            tyConKind    :: Kind,             -- ^ Kind of this TyCon
            tyConArity   :: Arity,            -- ^ Arity
                 -- tyConTyVars scope over: synTcRhs

            tcRoles      :: [Role],  -- ^ The role for each type variable
                                     -- This list has length = tyConArity
                                     -- See also Note [TyCon Role signatures]

            synTcRhs     :: Type,    -- ^ Contains information about the expansion
                                     -- of the synonym

            synIsTau     :: Bool,   -- True <=> the RHS of this synonym does not
                                     --          have any foralls, after expanding any
                                     --          nested synonyms
            synIsFamFree  :: Bool    -- True <=> the RHS of this synonym does not mention
                                     --          any type synonym families (data families
                                     --          are fine), again after expanding any
                                     --          nested synonyms
        }

      -- | Represents families (both type and data)
      -- Argument roles are all Nominal
      | FamilyTyCon {
            tyConUnique  :: Unique,  -- ^ A Unique of this TyCon. Invariant:
                                     -- identical to Unique of Name stored in
                                     -- tyConName field.

            tyConName    :: Name,    -- ^ Name of the constructor

            -- See Note [The binders/kind/arity fields of a TyCon]
            tyConBinders :: [TyConBinder], -- ^ Full binders
            tyConTyVars  :: [TyVar],          -- ^ TyVar binders
            tyConResKind :: Kind,             -- ^ Result kind
            tyConKind    :: Kind,             -- ^ Kind of this TyCon
            tyConArity   :: Arity,            -- ^ Arity
                -- tyConTyVars connect an associated family TyCon
                -- with its parent class; see TcValidity.checkConsistentFamInst

            famTcResVar  :: Maybe Name,   -- ^ Name of result type variable, used
                                          -- for pretty-printing with --show-iface
                                          -- and for reifying TyCon in Template
                                          -- Haskell

            famTcFlav    :: FamTyConFlav, -- ^ Type family flavour: open, closed,
                                          -- abstract, built-in. See comments for
                                          -- FamTyConFlav

            famTcParent  :: Maybe TyCon,  -- ^ For *associated* type/data families
                                          -- The class tycon in which the family is declared
                                          -- See Note [Associated families and their parent class]

            famTcInj     :: Injectivity   -- ^ is this a type family injective in
                                          -- its type variables? Nothing if no
                                          -- injectivity annotation was given
        }

      -- | Primitive types; cannot be defined in Haskell. This includes
      -- the usual suspects (such as @Int#@) as well as foreign-imported
      -- types and kinds (@*@, @#@, and @?@)
      | PrimTyCon {
            tyConUnique   :: Unique, -- ^ A Unique of this TyCon. Invariant:
                                     -- identical to Unique of Name stored in
                                     -- tyConName field.

            tyConName     :: Name,   -- ^ Name of the constructor

            -- See Note [The binders/kind/arity fields of a TyCon]
            tyConBinders :: [TyConBinder], -- ^ Full binders
            tyConResKind :: Kind,             -- ^ Result kind
            tyConKind    :: Kind,             -- ^ Kind of this TyCon
            tyConArity   :: Arity,            -- ^ Arity

            tcRoles       :: [Role], -- ^ The role for each type variable
                                     -- This list has length = tyConArity
                                     -- See also Note [TyCon Role signatures]

            isUnlifted   :: Bool,    -- ^ Most primitive tycons are unlifted (may
                                     -- not contain bottom) but other are lifted,
                                     -- e.g. @RealWorld@
                                     -- Only relevant if tyConKind = *

            primRepName :: Maybe TyConRepName   -- Only relevant for kind TyCons
                                                -- i.e, *, #, ?
        }

      -- | Represents promoted data constructor.
      | PromotedDataCon {          -- See Note [Promoted data constructors]
            tyConUnique  :: Unique,     -- ^ Same Unique as the data constructor
            tyConName    :: Name,       -- ^ Same Name as the data constructor

            -- See Note [The binders/kind/arity fields of a TyCon]
            tyConBinders :: [TyConTyCoBinder], -- ^ Full binders
            tyConResKind :: Kind,             -- ^ Result kind
            tyConKind    :: Kind,             -- ^ Kind of this TyCon
            tyConArity   :: Arity,            -- ^ Arity

            tcRoles       :: [Role],    -- ^ Roles: N for kind vars, R for type vars
            dataCon       :: DataCon,   -- ^ Corresponding data constructor
            tcRepName     :: TyConRepName,
            promDcRepInfo :: RuntimeRepInfo  -- ^ See comments with 'RuntimeRepInfo'
        }

      -- | These exist only during type-checking. See Note [How TcTyCons work]
      -- in TcTyClsDecls
      | TcTyCon {
            tyConUnique :: Unique,
            tyConName   :: Name,

            -- See Note [The binders/kind/arity fields of a TyCon]
            tyConBinders :: [TyConBinder], -- ^ Full binders
            tyConTyVars  :: [TyVar],       -- ^ TyVar binders
            tyConResKind :: Kind,          -- ^ Result kind
            tyConKind    :: Kind,          -- ^ Kind of this TyCon
            tyConArity   :: Arity,         -- ^ Arity

              -- NB: the TyConArity of a TcTyCon must match
              -- the number of Required (positional, user-specified)
              -- arguments to the type constructor; see the use
              -- of tyConArity in generaliseTcTyCon

            tcTyConScopedTyVars :: [(Name,TyVar)],
              -- ^ Scoped tyvars over the tycon's body
              -- See Note [Scoped tyvars in a TcTyCon]

            tcTyConIsPoly     :: Bool, -- ^ Is this TcTyCon already generalized?

            tcTyConFlavour :: TyConFlavour
                               -- ^ What sort of 'TyCon' this represents.
          }
    {- Note [Scoped tyvars in a TcTyCon]

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The tcTyConScopedTyVars field records the lexicial-binding connection
    between the original, user-specified Name (i.e. thing in scope) and
    the TcTyVar that the Name is bound to.

    Order *does* matter; the tcTyConScopedTyvars list consists of
         specified_tvs ++ required_tvs

    where
       * specified ones first
       * required_tvs the same as tyConTyVars
       * tyConArity = length required_tvs

    See also Note [How TcTyCons work] in TcTyClsDecls
    -}

    -- | Represents right-hand-sides of 'TyCon's for algebraic types
    data AlgTyConRhs

        -- | Says that we know nothing about this data type, except that
        -- it's represented by a pointer.  Used when we export a data type
        -- abstractly into an .hi file.
      = AbstractTyCon

        -- | Information about those 'TyCon's derived from a @data@
        -- declaration. This includes data types with no constructors at
        -- all.
      | DataTyCon {
            data_cons :: [DataCon],
                              -- ^ The data type constructors; can be empty if the
                              --   user declares the type to have no constructors
                              --
                              -- INVARIANT: Kept in order of increasing 'DataCon'
                              -- tag (see the tag assignment in mkTyConTagMap)
            data_cons_size :: Int,
                              -- ^ Cached value: length data_cons
            is_enum :: Bool   -- ^ Cached value: is this an enumeration type?
                              --   See Note [Enumeration types]
        }

      | TupleTyCon {                   -- A boxed, unboxed, or constraint tuple
            data_con :: DataCon,       -- NB: it can be an *unboxed* tuple
            tup_sort :: TupleSort      -- ^ Is this a boxed, unboxed or constraint
                                       -- tuple?
        }

      -- | An unboxed sum type.
      | SumTyCon {
            data_cons :: [DataCon],
            data_cons_size :: Int  -- ^ Cached value: length data_cons
        }

      -- | Information about those 'TyCon's derived from a @newtype@ declaration
      | NewTyCon {
            data_con :: DataCon,    -- ^ The unique constructor for the @newtype@.
                                    --   It has no existentials

            nt_rhs :: Type,         -- ^ Cached value: the argument type of the
                                    -- constructor, which is just the representation
                                    -- type of the 'TyCon' (remember that @newtype@s
                                    -- do not exist at runtime so need a different
                                    -- representation type).
                                    --
                                    -- The free 'TyVar's of this type are the
                                    -- 'tyConTyVars' from the corresponding 'TyCon'

            nt_etad_rhs :: ([TyVar], Type),
                            -- ^ Same as the 'nt_rhs', but this time eta-reduced.
                            -- Hence the list of 'TyVar's in this field may be
                            -- shorter than the declared arity of the 'TyCon'.

                            -- See Note [Newtype eta]
            nt_co :: CoAxiom Unbranched,
                                 -- The axiom coercion that creates the @newtype@
                                 -- from the representation 'Type'.

                                 -- See Note [Newtype coercions]
                                 -- Invariant: arity = #tvs in nt_etad_rhs;
                                 -- See Note [Newtype eta]
                                 -- Watch out!  If any newtypes become transparent
                                 -- again check #1072.
            nt_lev_poly :: Bool
                            -- 'True' if the newtype can be levity polymorphic when
                            -- fully applied to its arguments, 'False' otherwise.
                            -- This can only ever be 'True' with UnliftedNewtypes.
                            --
                            -- Invariant: nt_lev_poly nt = isTypeLevPoly (nt_rhs nt)
                            --
                            -- This is cached to make it cheaper to check if a
                            -- variable binding is levity polymorphic, as used by
                            -- isTcLevPoly.
        }

    mkSumTyConRhs :: [DataCon] -> AlgTyConRhs
    mkSumTyConRhs data_cons = SumTyCon data_cons (length data_cons)

    mkDataTyConRhs :: [DataCon] -> AlgTyConRhs
    mkDataTyConRhs cons
      = DataTyCon {
            data_cons = cons,
            data_cons_size = length cons,
            is_enum = not (null cons) && all is_enum_con cons
                      -- See Note [Enumeration types] in TyCon
        }
      where
        is_enum_con con
           | (_univ_tvs, ex_tvs, eq_spec, theta, arg_tys, _res)
               <- dataConFullSig con
           = null ex_tvs && null eq_spec && null theta && null arg_tys

    -- | Some promoted datacons signify extra info relevant to GHC. For example,
    -- the @IntRep@ constructor of @RuntimeRep@ corresponds to the 'IntRep'
    -- constructor of 'PrimRep'. This data structure allows us to store this
    -- information right in the 'TyCon'. The other approach would be to look
    -- up things like @RuntimeRep@'s @PrimRep@ by known-key every time.
    -- See also Note [Getting from RuntimeRep to PrimRep] in RepType
    data RuntimeRepInfo
      = NoRRI       -- ^ an ordinary promoted data con
      | RuntimeRep ([Type] -> [PrimRep])
          -- ^ A constructor of @RuntimeRep@. The argument to the function should
          -- be the list of arguments to the promoted datacon.
      | VecCount Int         -- ^ A constructor of @VecCount@
      | VecElem PrimElemRep  -- ^ A constructor of @VecElem@

    -- | Extract those 'DataCon's that we are able to learn about.  Note
    -- that visibility in this sense does not correspond to visibility in
    -- the context of any particular user program!
    visibleDataCons :: AlgTyConRhs -> [DataCon]
    visibleDataCons (AbstractTyCon {})            = []
    visibleDataCons (DataTyCon{ data_cons = cs }) = cs
    visibleDataCons (NewTyCon{ data_con = c })    = [c]
    visibleDataCons (TupleTyCon{ data_con = c })  = [c]
    visibleDataCons (SumTyCon{ data_cons = cs })  = cs

    -- ^ Both type classes as well as family instances imply implicit
    -- type constructors.  These implicit type constructors refer to their parent
    -- structure (ie, the class or family from which they derive) using a type of
    -- the following form.
    data AlgTyConFlav
      = -- | An ordinary type constructor has no parent.
        VanillaAlgTyCon
           TyConRepName

        -- | An unboxed type constructor. The TyConRepName is a Maybe since we
        -- currently don't allow unboxed sums to be Typeable since there are too
        -- many of them. See #13276.
      | UnboxedAlgTyCon
           (Maybe TyConRepName)

      -- | Type constructors representing a class dictionary.
      -- See Note [ATyCon for classes] in TyCoRep
      | ClassTyCon
            Class           -- INVARIANT: the classTyCon of this Class is the
                            -- current tycon
            TyConRepName

      -- | Type constructors representing an *instance* of a *data* family.
      -- Parameters:
      --
      --  1) The type family in question
      --
      --  2) Instance types; free variables are the 'tyConTyVars'
      --  of the current 'TyCon' (not the family one). INVARIANT:
      --  the number of types matches the arity of the family 'TyCon'
      --
      --  3) A 'CoTyCon' identifying the representation
      --  type with the type instance family
      | DataFamInstTyCon          -- See Note [Data type families]
            (CoAxiom Unbranched)  -- The coercion axiom.
                   -- A *Representational* coercion,
                   -- of kind   T ty1 ty2   ~R   R:T a b c
                   -- where T is the family TyCon,
                   -- and R:T is the representation TyCon (ie this one)
                   -- and a,b,c are the tyConTyVars of this TyCon
                   --
                   -- BUT may be eta-reduced; see FamInstEnv
                   --     Note [Eta reduction for data families]

              -- Cached fields of the CoAxiom, but adjusted to
              -- use the tyConTyVars of this TyCon
            TyCon   -- The family TyCon
            [Type]  -- Argument types (mentions the tyConTyVars of this TyCon)
                    -- No shorter in length than the tyConTyVars of the family TyCon
                    -- How could it be longer? See [Arity of data families] in FamInstEnv

            -- E.g.  data instance T [a] = ...
            -- gives a representation tycon:
            --      data R:TList a = ...
            --      axiom co a :: T [a] ~ R:TList a
            -- with R:TList's algTcParent = DataFamInstTyCon T [a] co

    instance Outputable AlgTyConFlav where
        ppr (VanillaAlgTyCon {})        = text "Vanilla ADT"
        ppr (UnboxedAlgTyCon {})        = text "Unboxed ADT"
        ppr (ClassTyCon cls _)          = text "Class parent" <+> ppr cls
        ppr (DataFamInstTyCon _ tc tys) = text "Family parent (family instance)"
                                          <+> ppr tc <+> sep (map pprType tys)

    -- | Checks the invariants of a 'AlgTyConFlav' given the appropriate type class
    -- name, if any
    okParent :: Name -> AlgTyConFlav -> Bool
    okParent _       (VanillaAlgTyCon {})            = True
    okParent _       (UnboxedAlgTyCon {})            = True
    okParent tc_name (ClassTyCon cls _)              = tc_name == tyConName (classTyCon cls)
    okParent _       (DataFamInstTyCon _ fam_tc tys) = tys `lengthAtLeast` tyConArity fam_tc

    isNoParent :: AlgTyConFlav -> Bool
    isNoParent (VanillaAlgTyCon {}) = True
    isNoParent _                   = False

    --------------------

    data Injectivity
      = NotInjective
      | Injective [Bool]   -- 1-1 with tyConTyVars (incl kind vars)
      deriving( Eq )

    -- | Information pertaining to the expansion of a type synonym (@type@)
    data FamTyConFlav
      = -- | Represents an open type family without a fixed right hand
        -- side.  Additional instances can appear at any time.
        --
        -- These are introduced by either a top level declaration:
        --
        -- > data family T a :: *
        --
        -- Or an associated data type declaration, within a class declaration:
        --
        -- > class C a b where
        -- >   data T b :: *
         DataFamilyTyCon
           TyConRepName

         -- | An open type synonym family  e.g. @type family F x y :: * -> *@
       | OpenSynFamilyTyCon

       -- | A closed type synonym family  e.g.
       -- @type family F x where { F Int = Bool }@
       | ClosedSynFamilyTyCon (Maybe (CoAxiom Branched))
         -- See Note [Closed type families]

       -- | A closed type synonym family declared in an hs-boot file with
       -- type family F a where ..
       | AbstractClosedSynFamilyTyCon

       -- | Built-in type family used by the TypeNats solver
       | BuiltInSynFamTyCon BuiltInSynFamily

    instance Outputable FamTyConFlav where
        ppr (DataFamilyTyCon n) = text "data family" <+> ppr n
        ppr OpenSynFamilyTyCon = text "open type family"
        ppr (ClosedSynFamilyTyCon Nothing) = text "closed type family"
        ppr (ClosedSynFamilyTyCon (Just coax)) = text "closed type family" <+> ppr coax
        ppr AbstractClosedSynFamilyTyCon = text "abstract closed type family"
        ppr (BuiltInSynFamTyCon _) = text "built-in type family"

    {- Note [Closed type families]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    * In an open type family you can add new instances later.  This is the
      usual case.

    * In a closed type family you can only put equations where the family
      is defined.

    A non-empty closed type family has a single axiom with multiple
    branches, stored in the 'ClosedSynFamilyTyCon' constructor.  A closed
    type family with no equations does not have an axiom, because there is
    nothing for the axiom to prove!

    Note [Promoted data constructors]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    All data constructors can be promoted to become a type constructor,
    via the PromotedDataCon alternative in TyCon.

    * The TyCon promoted from a DataCon has the *same* Name and Unique as
      the DataCon.  Eg. If the data constructor Data.Maybe.Just(unique 78,
      say) is promoted to a TyCon whose name is Data.Maybe.Just(unique 78)

    * We promote the *user* type of the DataCon.  Eg
         data T = MkT {-# UNPACK #-} !(Bool, Bool)
      The promoted kind is
         'MkT :: (Bool,Bool) -> T
      *not*
         'MkT :: Bool -> Bool -> T

    * Similarly for GADTs:
         data G a where
           MkG :: forall b. b -> G [b]
      The promoted data constructor has kind
           'MkG :: forall b. b -> G [b]
      *not*
           'MkG :: forall a b. (a ~# [b]) => b -> G a

    Note [Enumeration types]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    We define datatypes with no constructors to *not* be
    enumerations; this fixes trac #2578,  Otherwise we
    end up generating an empty table for
      <mod>_<type>_closure_tbl
    which is used by tagToEnum# to map Int# to constructors
    in an enumeration. The empty table apparently upset
    the linker.

    Moreover, all the data constructor must be enumerations, meaning
    they have type  (forall abc. T a b c).  GADTs are not enumerations.
    For example consider
        data T a where
          T1 :: T Int
          T2 :: T Bool
          T3 :: T a
    What would [T1 ..] be?  [T1,T3] :: T Int? Easiest thing is to exclude them.
    See #4528.

    Note [Newtype coercions]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    The NewTyCon field nt_co is a CoAxiom which is used for coercing from
    the representation type of the newtype, to the newtype itself. For
    example,

       newtype T a = MkT (a -> a)

    the NewTyCon for T will contain nt_co = CoT where CoT t : T t ~ t -> t.

    In the case that the right hand side is a type application
    ending with the same type variables as the left hand side, we
    "eta-contract" the coercion.  So if we had

       newtype S a = MkT [a]

    then we would generate the arity 0 axiom CoS : S ~ [].  The
    primary reason we do this is to make newtype deriving cleaner.

    In the paper we'd write
            axiom CoT : (forall t. T t) ~ (forall t. [t])
    and then when we used CoT at a particular type, s, we'd say
            CoT @ s
    which encodes as (TyConApp instCoercionTyCon [TyConApp CoT [], s])

    Note [Newtype eta]
    ~~~~~~~~~~~~~~~~~~
    Consider
            newtype Parser a = MkParser (IO a) deriving Monad
    Are these two types equal (to Core)?
            Monad Parser
            Monad IO
    which we need to make the derived instance for Monad Parser.

    Well, yes.  But to see that easily we eta-reduce the RHS type of
    Parser, in this case to ([], Froogle), so that even unsaturated applications
    of Parser will work right.  This eta reduction is done when the type
    constructor is built, and cached in NewTyCon.

    Here's an example that I think showed up in practice
    Source code:
            newtype T a = MkT [a]
            newtype Foo m = MkFoo (forall a. m a -> Int)

            w1 :: Foo []
            w1 = ...

            w2 :: Foo T
            w2 = MkFoo (\(MkT x) -> case w1 of MkFoo f -> f x)

    After desugaring, and discarding the data constructors for the newtypes,
    we get:
            w2 = w1 `cast` Foo CoT
    so the coercion tycon CoT must have
            kind:    T ~ []
     and    arity:   0

    This eta-reduction is implemented in BuildTyCl.mkNewTyConRhs.

    ************************************************************************
    *                                                                      *
                     TyConRepName
    *                                                                      *
    ********************************************************************* -}

    type TyConRepName = Name -- The Name of the top-level declaration
                             --    $tcMaybe :: Data.Typeable.Internal.TyCon
                             --    $tcMaybe = TyCon { tyConName = "Maybe", ... }

    tyConRepName_maybe :: TyCon -> Maybe TyConRepName
    tyConRepName_maybe (FunTyCon   { tcRepName = rep_nm })
      = Just rep_nm
    tyConRepName_maybe (PrimTyCon  { primRepName = mb_rep_nm })
      = mb_rep_nm
    tyConRepName_maybe (AlgTyCon { algTcParent = parent })
      | VanillaAlgTyCon rep_nm <- parent = Just rep_nm
      | ClassTyCon _ rep_nm    <- parent = Just rep_nm
      | UnboxedAlgTyCon rep_nm <- parent = rep_nm
    tyConRepName_maybe (FamilyTyCon { famTcFlav = DataFamilyTyCon rep_nm })
      = Just rep_nm
    tyConRepName_maybe (PromotedDataCon { dataCon = dc, tcRepName = rep_nm })
      | isUnboxedSumCon dc   -- see #13276
      = Nothing
      | otherwise
      = Just rep_nm
    tyConRepName_maybe _ = Nothing

    -- | Make a 'Name' for the 'Typeable' representation of the given wired-in type
    mkPrelTyConRepName :: Name -> TyConRepName
    -- See Note [Grand plan for Typeable] in 'TcTypeable' in TcTypeable.
    mkPrelTyConRepName tc_name  -- Prelude tc_name is always External,
                                -- so nameModule will work
      = mkExternalName rep_uniq rep_mod rep_occ (nameSrcSpan tc_name)
      where
        name_occ  = nameOccName tc_name
        name_mod  = nameModule  tc_name
        name_uniq = nameUnique  tc_name
        rep_uniq | isTcOcc name_occ = tyConRepNameUnique   name_uniq
                 | otherwise        = dataConTyRepNameUnique name_uniq
        (rep_mod, rep_occ) = tyConRepModOcc name_mod name_occ

    -- | The name (and defining module) for the Typeable representation (TyCon) of a
    -- type constructor.
    --
    -- See Note [Grand plan for Typeable] in 'TcTypeable' in TcTypeable.
    tyConRepModOcc :: Module -> OccName -> (Module, OccName)
    tyConRepModOcc tc_module tc_occ = (rep_module, mkTyConRepOcc tc_occ)
      where
        rep_module
          | tc_module == gHC_PRIM = gHC_TYPES
          | otherwise             = tc_module

    {- *********************************************************************
    *                                                                      *
                     PrimRep
    *                                                                      *
    ************************************************************************

    Note [rep swamp]

    GHC has a rich selection of types that represent "primitive types" of
    one kind or another.  Each of them makes a different set of
    distinctions, and mostly the differences are for good reasons,
    although it's probably true that we could merge some of these.

    Roughly in order of "includes more information":

     - A Width (cmm/CmmType) is simply a binary value with the specified
       number of bits.  It may represent a signed or unsigned integer, a
       floating-point value, or an address.

        data Width = W8 | W16 | W32 | W64  | W128

     - Size, which is used in the native code generator, is Width +
       floating point information.

       data Size = II8 | II16 | II32 | II64 | FF32 | FF64

       it is necessary because e.g. the instruction to move a 64-bit float
       on x86 (movsd) is different from the instruction to move a 64-bit
       integer (movq), so the mov instruction is parameterised by Size.

     - CmmType wraps Width with more information: GC ptr, float, or
       other value.

        data CmmType = CmmType CmmCat Width

        data CmmCat     -- "Category" (not exported)
           = GcPtrCat   -- GC pointer
           | BitsCat    -- Non-pointer
           | FloatCat   -- Float

       It is important to have GcPtr information in Cmm, since we generate
       info tables containing pointerhood for the GC from this.  As for
       why we have float (and not signed/unsigned) here, see Note [Signed
       vs unsigned].

     - ArgRep makes only the distinctions necessary for the call and
       return conventions of the STG machine.  It is essentially CmmType
       + void.

     - PrimRep makes a few more distinctions than ArgRep: it divides
       non-GC-pointers into signed/unsigned and addresses, information
       that is necessary for passing these values to foreign functions.

    There's another tension here: whether the type encodes its size in
    bytes, or whether its size depends on the machine word size.  Width
    and CmmType have the size built-in, whereas ArgRep and PrimRep do not.

    This means to turn an ArgRep/PrimRep into a CmmType requires DynFlags.

    On the other hand, CmmType includes some "nonsense" values, such as
    CmmType GcPtrCat W32 on a 64-bit machine.

    The PrimRep type is closely related to the user-visible RuntimeRep type.
    See Note [RuntimeRep and PrimRep] in RepType.

    -}

    -- | A 'PrimRep' is an abstraction of a type.  It contains information that
    -- the code generator needs in order to pass arguments, return results,
    -- and store values of this type. See also Note [RuntimeRep and PrimRep] in RepType
    -- and Note [VoidRep] in RepType.
    data PrimRep
      = VoidRep
      | LiftedRep
      | UnliftedRep   -- ^ Unlifted pointer
      | Int8Rep       -- ^ Signed, 8-bit value
      | Int16Rep      -- ^ Signed, 16-bit value
      | Int32Rep      -- ^ Signed, 32-bit value
      | Int64Rep      -- ^ Signed, 64 bit value (with 32-bit words only)
      | IntRep        -- ^ Signed, word-sized value
      | Word8Rep      -- ^ Unsigned, 8 bit value
      | Word16Rep     -- ^ Unsigned, 16 bit value
      | Word32Rep     -- ^ Unsigned, 32 bit value
      | Word64Rep     -- ^ Unsigned, 64 bit value (with 32-bit words only)
      | WordRep       -- ^ Unsigned, word-sized value
      | AddrRep       -- ^ A pointer, but /not/ to a Haskell value (use '(Un)liftedRep')
      | FloatRep
      | DoubleRep
      | VecRep Int PrimElemRep  -- ^ A vector
      deriving( Show )

    data PrimElemRep
      = Int8ElemRep
      | Int16ElemRep
      | Int32ElemRep
      | Int64ElemRep
      | Word8ElemRep
      | Word16ElemRep
      | Word32ElemRep
      | Word64ElemRep
      | FloatElemRep
      | DoubleElemRep
       deriving( Eq, Show )

    instance Outputable PrimRep where
      ppr r = text (show r)

    instance Outputable PrimElemRep where
      ppr r = text (show r)

    isVoidRep :: PrimRep -> Bool
    isVoidRep VoidRep = True
    isVoidRep _other  = False

    isGcPtrRep :: PrimRep -> Bool
    isGcPtrRep LiftedRep   = True
    isGcPtrRep UnliftedRep = True
    isGcPtrRep _           = False

    -- A PrimRep is compatible with another iff one can be coerced to the other.
    -- See Note [bad unsafe coercion] in CoreLint for when are two types coercible.
    primRepCompatible :: DynFlags -> PrimRep -> PrimRep -> Bool
    primRepCompatible dflags rep1 rep2 =
        (isUnboxed rep1 == isUnboxed rep2) &&
        (primRepSizeB dflags rep1 == primRepSizeB dflags rep2) &&
        (primRepIsFloat rep1 == primRepIsFloat rep2)
      where
        isUnboxed = not . isGcPtrRep

    -- More general version of `primRepCompatible` for types represented by zero or
    -- more than one PrimReps.
    primRepsCompatible :: DynFlags -> [PrimRep] -> [PrimRep] -> Bool
    primRepsCompatible dflags reps1 reps2 =
        length reps1 == length reps2 &&
        and (zipWith (primRepCompatible dflags) reps1 reps2)

    -- | The size of a 'PrimRep' in bytes.
    --
    -- This applies also when used in a constructor, where we allow packing the
    -- fields. For instance, in @data Foo = Foo Float# Float#@ the two fields will
    -- take only 8 bytes, which for 64-bit arch will be equal to 1 word.
    -- See also mkVirtHeapOffsetsWithPadding for details of how data fields are
    -- layed out.
    primRepSizeB :: DynFlags -> PrimRep -> Int
    primRepSizeB dflags IntRep           = wORD_SIZE dflags
    primRepSizeB dflags WordRep          = wORD_SIZE dflags
    primRepSizeB _      Int8Rep          = 1
    primRepSizeB _      Int16Rep         = 2
    primRepSizeB _      Int32Rep         = 4
    primRepSizeB _      Int64Rep         = wORD64_SIZE
    primRepSizeB _      Word8Rep         = 1
    primRepSizeB _      Word16Rep        = 2
    primRepSizeB _      Word32Rep        = 4
    primRepSizeB _      Word64Rep        = wORD64_SIZE
    primRepSizeB _      FloatRep         = fLOAT_SIZE
    primRepSizeB dflags DoubleRep        = dOUBLE_SIZE dflags
    primRepSizeB dflags AddrRep          = wORD_SIZE dflags
    primRepSizeB dflags LiftedRep        = wORD_SIZE dflags
    primRepSizeB dflags UnliftedRep      = wORD_SIZE dflags
    primRepSizeB _      VoidRep          = 0
    primRepSizeB _      (VecRep len rep) = len * primElemRepSizeB rep

    primElemRepSizeB :: PrimElemRep -> Int
    primElemRepSizeB Int8ElemRep   = 1
    primElemRepSizeB Int16ElemRep  = 2
    primElemRepSizeB Int32ElemRep  = 4
    primElemRepSizeB Int64ElemRep  = 8
    primElemRepSizeB Word8ElemRep  = 1
    primElemRepSizeB Word16ElemRep = 2
    primElemRepSizeB Word32ElemRep = 4
    primElemRepSizeB Word64ElemRep = 8
    primElemRepSizeB FloatElemRep  = 4
    primElemRepSizeB DoubleElemRep = 8

    -- | Return if Rep stands for floating type,
    -- returns Nothing for vector types.
    primRepIsFloat :: PrimRep -> Maybe Bool
    primRepIsFloat  FloatRep     = Just True
    primRepIsFloat  DoubleRep    = Just True
    primRepIsFloat  (VecRep _ _) = Nothing
    primRepIsFloat  _            = Just False

    {-
    ************************************************************************
    *                                                                      *
                                 Field labels
    *                                                                      *
    ************************************************************************
    -}

    -- | The labels for the fields of this particular 'TyCon'
    tyConFieldLabels :: TyCon -> [FieldLabel]
    tyConFieldLabels tc = dFsEnvElts $ tyConFieldLabelEnv tc

    -- | The labels for the fields of this particular 'TyCon'
    tyConFieldLabelEnv :: TyCon -> FieldLabelEnv
    tyConFieldLabelEnv tc
      | isAlgTyCon tc = algTcFields tc
      | otherwise     = emptyDFsEnv

    -- | Look up a field label belonging to this 'TyCon'
    lookupTyConFieldLabel :: FieldLabelString -> TyCon -> Maybe FieldLabel
    lookupTyConFieldLabel lbl tc = lookupDFsEnv (tyConFieldLabelEnv tc) lbl

    -- | Make a map from strings to FieldLabels from all the data
    -- constructors of this algebraic tycon
    fieldsOfAlgTcRhs :: AlgTyConRhs -> FieldLabelEnv
    fieldsOfAlgTcRhs rhs = mkDFsEnv [ (flLabel fl, fl)
                                    | fl <- dataConsFields (visibleDataCons rhs) ]
      where
        -- Duplicates in this list will be removed by 'mkFsEnv'
        dataConsFields dcs = concatMap dataConFieldLabels dcs

    {-
    ************************************************************************
    *                                                                      *
    \subsection{TyCon Construction}
    *                                                                      *
    ************************************************************************

    Note: the TyCon constructors all take a Kind as one argument, even though
    they could, in principle, work out their Kind from their other arguments.
    But to do so they need functions from Types, and that makes a nasty
    module mutual-recursion.  And they aren't called from many places.
    So we compromise, and move their Kind calculation to the call site.
    -}

    -- | Given the name of the function type constructor and it's kind, create the
    -- corresponding 'TyCon'. It is recommended to use 'TyCoRep.funTyCon' if you want
    -- this functionality
    mkFunTyCon :: Name -> [TyConBinder] -> Name -> TyCon
    mkFunTyCon name binders rep_nm
      = FunTyCon {
            tyConUnique  = nameUnique name,
            tyConName    = name,
            tyConBinders = binders,
            tyConResKind = liftedTypeKind,
            tyConKind    = mkTyConKind binders liftedTypeKind,
            tyConArity   = length binders,
            tcRepName    = rep_nm
        }

    -- | This is the making of an algebraic 'TyCon'. Notably, you have to
    -- pass in the generic (in the -XGenerics sense) information about the
    -- type constructor - you can get hold of it easily (see Generics
    -- module)
    mkAlgTyCon :: Name
               -> [TyConBinder]  -- ^ Binders of the 'TyCon'
               -> Kind              -- ^ Result kind
               -> [Role]            -- ^ The roles for each TyVar
               -> Maybe CType       -- ^ The C type this type corresponds to
                                    --   when using the CAPI FFI
               -> [PredType]        -- ^ Stupid theta: see 'algTcStupidTheta'
               -> AlgTyConRhs       -- ^ Information about data constructors
               -> AlgTyConFlav      -- ^ What flavour is it?
                                    -- (e.g. vanilla, type family)
               -> Bool              -- ^ Was the 'TyCon' declared with GADT syntax?
               -> TyCon
    mkAlgTyCon name binders res_kind roles cType stupid rhs parent gadt_syn
      = AlgTyCon {
            tyConName        = name,
            tyConUnique      = nameUnique name,
            tyConBinders     = binders,
            tyConResKind     = res_kind,
            tyConKind        = mkTyConKind binders res_kind,
            tyConArity       = length binders,
            tyConTyVars      = binderVars binders,
            tcRoles          = roles,
            tyConCType       = cType,
            algTcStupidTheta = stupid,
            algTcRhs         = rhs,
            algTcFields      = fieldsOfAlgTcRhs rhs,
            algTcParent      = ASSERT2( okParent name parent, ppr name $$ ppr parent ) parent,
            algTcGadtSyntax  = gadt_syn
        }

    -- | Simpler specialization of 'mkAlgTyCon' for classes
    mkClassTyCon :: Name -> [TyConBinder]
                 -> [Role] -> AlgTyConRhs -> Class
                 -> Name -> TyCon
    mkClassTyCon name binders roles rhs clas tc_rep_name
      = mkAlgTyCon name binders constraintKind roles Nothing [] rhs
                   (ClassTyCon clas tc_rep_name)
                   False

    mkTupleTyCon :: Name
                 -> [TyConBinder]
                 -> Kind    -- ^ Result kind of the 'TyCon'
                 -> Arity   -- ^ Arity of the tuple 'TyCon'
                 -> DataCon
                 -> TupleSort    -- ^ Whether the tuple is boxed or unboxed
                 -> AlgTyConFlav
                 -> TyCon
    mkTupleTyCon name binders res_kind arity con sort parent
      = AlgTyCon {
            tyConUnique      = nameUnique name,
            tyConName        = name,
            tyConBinders     = binders,
            tyConTyVars      = binderVars binders,
            tyConResKind     = res_kind,
            tyConKind        = mkTyConKind binders res_kind,
            tyConArity       = arity,
            tcRoles          = replicate arity Representational,
            tyConCType       = Nothing,
            algTcGadtSyntax  = False,
            algTcStupidTheta = [],
            algTcRhs         = TupleTyCon { data_con = con,
                                            tup_sort = sort },
            algTcFields      = emptyDFsEnv,
            algTcParent      = parent
        }

    mkSumTyCon :: Name
                 -> [TyConBinder]
                 -> Kind    -- ^ Kind of the resulting 'TyCon'
                 -> Arity   -- ^ Arity of the sum
                 -> [TyVar] -- ^ 'TyVar's scoped over: see 'tyConTyVars'
                 -> [DataCon]
                 -> AlgTyConFlav
                 -> TyCon
    mkSumTyCon name binders res_kind arity tyvars cons parent
      = AlgTyCon {
            tyConUnique      = nameUnique name,
            tyConName        = name,
            tyConBinders     = binders,
            tyConTyVars      = tyvars,
            tyConResKind     = res_kind,
            tyConKind        = mkTyConKind binders res_kind,
            tyConArity       = arity,
            tcRoles          = replicate arity Representational,
            tyConCType       = Nothing,
            algTcGadtSyntax  = False,
            algTcStupidTheta = [],
            algTcRhs         = mkSumTyConRhs cons,
            algTcFields      = emptyDFsEnv,
            algTcParent      = parent
        }

    -- | Makes a tycon suitable for use during type-checking. It stores
    -- a variety of details about the definition of the TyCon, but no
    -- right-hand side. It lives only during the type-checking of a
    -- mutually-recursive group of tycons; it is then zonked to a proper
    -- TyCon in zonkTcTyCon.
    -- See also Note [Kind checking recursive type and class declarations]
    -- in TcTyClsDecls.
    mkTcTyCon :: Name
              -> [TyConBinder]
              -> Kind                -- ^ /result/ kind only
              -> [(Name,TcTyVar)]    -- ^ Scoped type variables;
                                     -- see Note [How TcTyCons work] in TcTyClsDecls
              -> Bool                -- ^ Is this TcTyCon generalised already?
              -> TyConFlavour        -- ^ What sort of 'TyCon' this represents
              -> TyCon
    mkTcTyCon name binders res_kind scoped_tvs poly flav
      = TcTyCon { tyConUnique  = getUnique name
                , tyConName    = name
                , tyConTyVars  = binderVars binders
                , tyConBinders = binders
                , tyConResKind = res_kind
                , tyConKind    = mkTyConKind binders res_kind
                , tyConArity   = length binders
                , tcTyConScopedTyVars = scoped_tvs
                , tcTyConIsPoly       = poly
                , tcTyConFlavour      = flav }

    -- | No scoped type variables (to be used with mkTcTyCon).
    noTcTyConScopedTyVars :: [(Name, TcTyVar)]
    noTcTyConScopedTyVars = []

    -- | Create an unlifted primitive 'TyCon', such as @Int#@.
    mkPrimTyCon :: Name -> [TyConBinder]
                -> Kind   -- ^ /result/ kind, never levity-polymorphic
                -> [Role] -> TyCon
    mkPrimTyCon name binders res_kind roles
      = mkPrimTyCon' name binders res_kind roles True (Just $ mkPrelTyConRepName name)

    -- | Kind constructors
    mkKindTyCon :: Name -> [TyConBinder]
                -> Kind  -- ^ /result/ kind
                -> [Role] -> Name -> TyCon
    mkKindTyCon name binders res_kind roles rep_nm
      = tc
      where
        tc = mkPrimTyCon' name binders res_kind roles False (Just rep_nm)

    -- | Create a lifted primitive 'TyCon' such as @RealWorld@
    mkLiftedPrimTyCon :: Name -> [TyConBinder]
                      -> Kind   -- ^ /result/ kind
                      -> [Role] -> TyCon
    mkLiftedPrimTyCon name binders res_kind roles
      = mkPrimTyCon' name binders res_kind roles False (Just rep_nm)
      where rep_nm = mkPrelTyConRepName name

    mkPrimTyCon' :: Name -> [TyConBinder]
                 -> Kind    -- ^ /result/ kind, never levity-polymorphic
                            -- (If you need a levity-polymorphic PrimTyCon, change
                            --  isTcLevPoly.)
                 -> [Role]
                 -> Bool -> Maybe TyConRepName -> TyCon
    mkPrimTyCon' name binders res_kind roles is_unlifted rep_nm
      = PrimTyCon {
            tyConName    = name,
            tyConUnique  = nameUnique name,
            tyConBinders = binders,
            tyConResKind = res_kind,
            tyConKind    = mkTyConKind binders res_kind,
            tyConArity   = length roles,
            tcRoles      = roles,
            isUnlifted   = is_unlifted,
            primRepName  = rep_nm
        }

    -- | Create a type synonym 'TyCon'
    mkSynonymTyCon :: Name -> [TyConBinder] -> Kind   -- ^ /result/ kind
                   -> [Role] -> Type -> Bool -> Bool -> TyCon
    mkSynonymTyCon name binders res_kind roles rhs is_tau is_fam_free
      = SynonymTyCon {
            tyConName    = name,
            tyConUnique  = nameUnique name,
            tyConBinders = binders,
            tyConResKind = res_kind,
            tyConKind    = mkTyConKind binders res_kind,
            tyConArity   = length binders,
            tyConTyVars  = binderVars binders,
            tcRoles      = roles,
            synTcRhs     = rhs,
            synIsTau     = is_tau,
            synIsFamFree = is_fam_free
        }

    -- | Create a type family 'TyCon'
    mkFamilyTyCon :: Name -> [TyConBinder] -> Kind  -- ^ /result/ kind
                  -> Maybe Name -> FamTyConFlav
                  -> Maybe Class -> Injectivity -> TyCon
    mkFamilyTyCon name binders res_kind resVar flav parent inj
      = FamilyTyCon
          { tyConUnique  = nameUnique name
          , tyConName    = name
          , tyConBinders = binders
          , tyConResKind = res_kind
          , tyConKind    = mkTyConKind binders res_kind
          , tyConArity   = length binders
          , tyConTyVars  = binderVars binders
          , famTcResVar  = resVar
          , famTcFlav    = flav
          , famTcParent  = classTyCon <$> parent
          , famTcInj     = inj
          }

    -- | Create a promoted data constructor 'TyCon'
    -- Somewhat dodgily, we give it the same Name
    -- as the data constructor itself; when we pretty-print
    -- the TyCon we add a quote; see the Outputable TyCon instance
    mkPromotedDataCon :: DataCon -> Name -> TyConRepName
                      -> [TyConTyCoBinder] -> Kind -> [Role]
                      -> RuntimeRepInfo -> TyCon
    mkPromotedDataCon con name rep_name binders res_kind roles rep_info
      = PromotedDataCon {
            tyConUnique   = nameUnique name,
            tyConName     = name,
            tyConArity    = length roles,
            tcRoles       = roles,
            tyConBinders  = binders,
            tyConResKind  = res_kind,
            tyConKind     = mkTyConKind binders res_kind,
            dataCon       = con,
            tcRepName     = rep_name,
            promDcRepInfo = rep_info
      }

    isFunTyCon :: TyCon -> Bool
    isFunTyCon (FunTyCon {}) = True
    isFunTyCon _             = False

    -- | Test if the 'TyCon' is algebraic but abstract (invisible data constructors)
    isAbstractTyCon :: TyCon -> Bool
    isAbstractTyCon (AlgTyCon { algTcRhs = AbstractTyCon }) = True
    isAbstractTyCon _ = False

    -- | Does this 'TyCon' represent something that cannot be defined in Haskell?
    isPrimTyCon :: TyCon -> Bool
    isPrimTyCon (PrimTyCon {}) = True
    isPrimTyCon _              = False

    -- | Is this 'TyCon' unlifted (i.e. cannot contain bottom)? Note that this can
    -- only be true for primitive and unboxed-tuple 'TyCon's
    isUnliftedTyCon :: TyCon -> Bool
    isUnliftedTyCon (PrimTyCon  {isUnlifted = is_unlifted})
      = is_unlifted
    isUnliftedTyCon (AlgTyCon { algTcRhs = rhs } )
      | TupleTyCon { tup_sort = sort } <- rhs
      = not (isBoxed (tupleSortBoxity sort))
    isUnliftedTyCon (AlgTyCon { algTcRhs = rhs } )
      | SumTyCon {} <- rhs
      = True
    isUnliftedTyCon _ = False

    -- | Returns @True@ if the supplied 'TyCon' resulted from either a
    -- @data@ or @newtype@ declaration
    isAlgTyCon :: TyCon -> Bool
    isAlgTyCon (AlgTyCon {})   = True
    isAlgTyCon _               = False

    -- | Returns @True@ for vanilla AlgTyCons -- that is, those created
    -- with a @data@ or @newtype@ declaration.
    isVanillaAlgTyCon :: TyCon -> Bool
    isVanillaAlgTyCon (AlgTyCon { algTcParent = VanillaAlgTyCon _ }) = True
    isVanillaAlgTyCon _                                              = False

    isDataTyCon :: TyCon -> Bool
    -- ^ Returns @True@ for data types that are /definitely/ represented by
    -- heap-allocated constructors.  These are scrutinised by Core-level
    -- @case@ expressions, and they get info tables allocated for them.
    --
    -- Generally, the function will be true for all @data@ types and false
    -- for @newtype@s, unboxed tuples, unboxed sums and type family
    -- 'TyCon's. But it is not guaranteed to return @True@ in all cases
    -- that it could.
    --
    -- NB: for a data type family, only the /instance/ 'TyCon's
    --     get an info table.  The family declaration 'TyCon' does not
    isDataTyCon (AlgTyCon {algTcRhs = rhs})
      = case rhs of
            TupleTyCon { tup_sort = sort }
                               -> isBoxed (tupleSortBoxity sort)
            SumTyCon {}        -> False
            DataTyCon {}       -> True
            NewTyCon {}        -> False
            AbstractTyCon {}   -> False      -- We don't know, so return False
    isDataTyCon _ = False

    -- | 'isInjectiveTyCon' is true of 'TyCon's for which this property holds
    -- (where X is the role passed in):
    --   If (T a1 b1 c1) ~X (T a2 b2 c2), then (a1 ~X1 a2), (b1 ~X2 b2), and (c1 ~X3 c2)
    -- (where X1, X2, and X3, are the roles given by tyConRolesX tc X)
    -- See also Note [Decomposing equality] in TcCanonical
    isInjectiveTyCon :: TyCon -> Role -> Bool
    isInjectiveTyCon _                             Phantom          = False
    isInjectiveTyCon (FunTyCon {})                 _                = True
    isInjectiveTyCon (AlgTyCon {})                 Nominal          = True
    isInjectiveTyCon (AlgTyCon {algTcRhs = rhs})   Representational
      = isGenInjAlgRhs rhs
    isInjectiveTyCon (SynonymTyCon {})             _                = False
    isInjectiveTyCon (FamilyTyCon { famTcFlav = DataFamilyTyCon _ })
                                                   Nominal          = True
    isInjectiveTyCon (FamilyTyCon { famTcInj = Injective inj }) Nominal = and inj
    isInjectiveTyCon (FamilyTyCon {})              _                = False
    isInjectiveTyCon (PrimTyCon {})                _                = True
    isInjectiveTyCon (PromotedDataCon {})          _                = True
    isInjectiveTyCon (TcTyCon {})                  _                = True
      -- Reply True for TcTyCon to minimise knock on type errors
      -- See Note [How TcTyCons work] item (1) in TcTyClsDecls

    -- | 'isGenerativeTyCon' is true of 'TyCon's for which this property holds
    -- (where X is the role passed in):
    --   If (T tys ~X t), then (t's head ~X T).
    -- See also Note [Decomposing equality] in TcCanonical
    isGenerativeTyCon :: TyCon -> Role -> Bool
    isGenerativeTyCon (FamilyTyCon { famTcFlav = DataFamilyTyCon _ }) Nominal = True
    isGenerativeTyCon (FamilyTyCon {}) _ = False
      -- in all other cases, injectivity implies generativity
    isGenerativeTyCon tc               r = isInjectiveTyCon tc r

    -- | Is this an 'AlgTyConRhs' of a 'TyCon' that is generative and injective
    -- with respect to representational equality?
    isGenInjAlgRhs :: AlgTyConRhs -> Bool
    isGenInjAlgRhs (TupleTyCon {})          = True
    isGenInjAlgRhs (SumTyCon {})            = True
    isGenInjAlgRhs (DataTyCon {})           = True
    isGenInjAlgRhs (AbstractTyCon {})       = False
    isGenInjAlgRhs (NewTyCon {})            = False

    -- | Is this 'TyCon' that for a @newtype@
    isNewTyCon :: TyCon -> Bool
    isNewTyCon (AlgTyCon {algTcRhs = NewTyCon {}}) = True
    isNewTyCon _                                   = False

    -- | Take a 'TyCon' apart into the 'TyVar's it scopes over, the 'Type' it
    -- expands into, and (possibly) a coercion from the representation type to the
    -- @newtype@.
    -- Returns @Nothing@ if this is not possible.
    unwrapNewTyCon_maybe :: TyCon -> Maybe ([TyVar], Type, CoAxiom Unbranched)
    unwrapNewTyCon_maybe (AlgTyCon { tyConTyVars = tvs,
                                     algTcRhs = NewTyCon { nt_co = co,
                                                           nt_rhs = rhs }})
                               = Just (tvs, rhs, co)
    unwrapNewTyCon_maybe _     = Nothing

    unwrapNewTyConEtad_maybe :: TyCon -> Maybe ([TyVar], Type, CoAxiom Unbranched)
    unwrapNewTyConEtad_maybe (AlgTyCon { algTcRhs = NewTyCon { nt_co = co,
                                                               nt_etad_rhs = (tvs,rhs) }})
                               = Just (tvs, rhs, co)
    unwrapNewTyConEtad_maybe _ = Nothing

    isProductTyCon :: TyCon -> Bool
    -- True of datatypes or newtypes that have
    --   one, non-existential, data constructor
    -- See Note [Product types]
    isProductTyCon tc@(AlgTyCon {})
      = case algTcRhs tc of
          TupleTyCon {} -> True
          DataTyCon{ data_cons = [data_con] }
                        -> null (dataConExTyCoVars data_con)
          NewTyCon {}   -> True
          _             -> False
    isProductTyCon _ = False

    isDataProductTyCon_maybe :: TyCon -> Maybe DataCon
    -- True of datatypes (not newtypes) with
    --   one, vanilla, data constructor
    -- See Note [Product types]
    isDataProductTyCon_maybe (AlgTyCon { algTcRhs = rhs })
      = case rhs of
           DataTyCon { data_cons = [con] }
             | null (dataConExTyCoVars con)  -- non-existential
             -> Just con
           TupleTyCon { data_con = con }
             -> Just con
           _ -> Nothing
    isDataProductTyCon_maybe _ = Nothing

    isDataSumTyCon_maybe :: TyCon -> Maybe [DataCon]
    isDataSumTyCon_maybe (AlgTyCon { algTcRhs = rhs })
      = case rhs of
          DataTyCon { data_cons = cons }
            | cons `lengthExceeds` 1
            , all (null . dataConExTyCoVars) cons -- FIXME(osa): Why do we need this?
            -> Just cons
          SumTyCon { data_cons = cons }
            | all (null . dataConExTyCoVars) cons -- FIXME(osa): Why do we need this?
            -> Just cons
          _ -> Nothing
    isDataSumTyCon_maybe _ = Nothing

    {- Note [Product types]
    ~~~~~~~~~~~~~~~~~~~~~~~
    A product type is
     * A data type (not a newtype)
     * With one, boxed data constructor
     * That binds no existential type variables

    The main point is that product types are amenable to unboxing for
      * Strict function calls; we can transform
            f (D a b) = e
        to
            fw a b = e
        via the worker/wrapper transformation.  (Question: couldn't this
        work for existentials too?)

      * CPR for function results; we can transform
            f x y = let ... in D a b
        to
            fw x y = let ... in (# a, b #)

    Note that the data constructor /can/ have evidence arguments: equality
    constraints, type classes etc.  So it can be GADT.  These evidence
    arguments are simply value arguments, and should not get in the way.
    -}

    -- | Is this a 'TyCon' representing a regular H98 type synonym (@type@)?
    isTypeSynonymTyCon :: TyCon -> Bool
    isTypeSynonymTyCon (SynonymTyCon {}) = True
    isTypeSynonymTyCon _                 = False

    isTauTyCon :: TyCon -> Bool
    isTauTyCon (SynonymTyCon { synIsTau = is_tau }) = is_tau
    isTauTyCon _                                    = True

    isFamFreeTyCon :: TyCon -> Bool
    isFamFreeTyCon (SynonymTyCon { synIsFamFree = fam_free }) = fam_free
    isFamFreeTyCon (FamilyTyCon { famTcFlav = flav })         = isDataFamFlav flav
    isFamFreeTyCon _                                          = True

    -- As for newtypes, it is in some contexts important to distinguish between
    -- closed synonyms and synonym families, as synonym families have no unique
    -- right hand side to which a synonym family application can expand.
    --

    -- | True iff we can decompose (T a b c) into ((T a b) c)
    --   I.e. is it injective and generative w.r.t nominal equality?
    --   That is, if (T a b) ~N d e f, is it always the case that
    --            (T ~N d), (a ~N e) and (b ~N f)?
    -- Specifically NOT true of synonyms (open and otherwise)
    --
    -- It'd be unusual to call mustBeSaturated on a regular H98
    -- type synonym, because you should probably have expanded it first
    -- But regardless, it's not decomposable
    mustBeSaturated :: TyCon -> Bool
    mustBeSaturated = tcFlavourMustBeSaturated . tyConFlavour

    -- | Is this an algebraic 'TyCon' declared with the GADT syntax?
    isGadtSyntaxTyCon :: TyCon -> Bool
    isGadtSyntaxTyCon (AlgTyCon { algTcGadtSyntax = res }) = res
    isGadtSyntaxTyCon _                                    = False

    -- | Is this an algebraic 'TyCon' which is just an enumeration of values?
    isEnumerationTyCon :: TyCon -> Bool
    -- See Note [Enumeration types] in TyCon
    isEnumerationTyCon (AlgTyCon { tyConArity = arity, algTcRhs = rhs })
      = case rhs of
           DataTyCon { is_enum = res } -> res
           TupleTyCon {}               -> arity == 0
           _                           -> False
    isEnumerationTyCon _ = False

    -- | Is this a 'TyCon', synonym or otherwise, that defines a family?
    isFamilyTyCon :: TyCon -> Bool
    isFamilyTyCon (FamilyTyCon {}) = True
    isFamilyTyCon _                = False

    -- | Is this a 'TyCon', synonym or otherwise, that defines a family with
    -- instances?
    isOpenFamilyTyCon :: TyCon -> Bool
    isOpenFamilyTyCon (FamilyTyCon {famTcFlav = flav })
      | OpenSynFamilyTyCon <- flav = True
      | DataFamilyTyCon {} <- flav = True
    isOpenFamilyTyCon _            = False

    -- | Is this a synonym 'TyCon' that can have may have further instances appear?
    isTypeFamilyTyCon :: TyCon -> Bool
    isTypeFamilyTyCon (FamilyTyCon { famTcFlav = flav }) = not (isDataFamFlav flav)
    isTypeFamilyTyCon _                                  = False

    -- | Is this a synonym 'TyCon' that can have may have further instances appear?
    isDataFamilyTyCon :: TyCon -> Bool
    isDataFamilyTyCon (FamilyTyCon { famTcFlav = flav }) = isDataFamFlav flav
    isDataFamilyTyCon _                                  = False

    -- | Is this an open type family TyCon?
    isOpenTypeFamilyTyCon :: TyCon -> Bool
    isOpenTypeFamilyTyCon (FamilyTyCon {famTcFlav = OpenSynFamilyTyCon }) = True
    isOpenTypeFamilyTyCon _                                               = False

    -- | Is this a non-empty closed type family? Returns 'Nothing' for
    -- abstract or empty closed families.
    isClosedSynFamilyTyConWithAxiom_maybe :: TyCon -> Maybe (CoAxiom Branched)
    isClosedSynFamilyTyConWithAxiom_maybe
      (FamilyTyCon {famTcFlav = ClosedSynFamilyTyCon mb}) = mb
    isClosedSynFamilyTyConWithAxiom_maybe _               = Nothing

    -- | @'tyConInjectivityInfo' tc@ returns @'Injective' is@ is @tc@ is an
    -- injective tycon (where @is@ states for which 'tyConBinders' @tc@ is
    -- injective), or 'NotInjective' otherwise.
    tyConInjectivityInfo :: TyCon -> Injectivity
    tyConInjectivityInfo tc
      | FamilyTyCon { famTcInj = inj } <- tc
      = inj
      | isInjectiveTyCon tc Nominal
      = Injective (replicate (tyConArity tc) True)
      | otherwise
      = NotInjective

    isBuiltInSynFamTyCon_maybe :: TyCon -> Maybe BuiltInSynFamily
    isBuiltInSynFamTyCon_maybe
      (FamilyTyCon {famTcFlav = BuiltInSynFamTyCon ops }) = Just ops
    isBuiltInSynFamTyCon_maybe _                          = Nothing

    isDataFamFlav :: FamTyConFlav -> Bool
    isDataFamFlav (DataFamilyTyCon {}) = True   -- Data family
    isDataFamFlav _                    = False  -- Type synonym family

    -- | Is this TyCon for an associated type?
    isTyConAssoc :: TyCon -> Bool
    isTyConAssoc = isJust . tyConAssoc_maybe

    -- | Get the enclosing class TyCon (if there is one) for the given TyCon.
    tyConAssoc_maybe :: TyCon -> Maybe TyCon
    tyConAssoc_maybe = tyConFlavourAssoc_maybe . tyConFlavour

    -- | Get the enclosing class TyCon (if there is one) for the given TyConFlavour
    tyConFlavourAssoc_maybe :: TyConFlavour -> Maybe TyCon
    tyConFlavourAssoc_maybe (DataFamilyFlavour mb_parent)     = mb_parent
    tyConFlavourAssoc_maybe (OpenTypeFamilyFlavour mb_parent) = mb_parent
    tyConFlavourAssoc_maybe _                                 = Nothing

    -- The unit tycon didn't used to be classed as a tuple tycon
    -- but I thought that was silly so I've undone it
    -- If it can't be for some reason, it should be a AlgTyCon
    isTupleTyCon :: TyCon -> Bool
    -- ^ Does this 'TyCon' represent a tuple?
    --
    -- NB: when compiling @Data.Tuple@, the tycons won't reply @True@ to
    -- 'isTupleTyCon', because they are built as 'AlgTyCons'.  However they
    -- get spat into the interface file as tuple tycons, so I don't think
    -- it matters.
    isTupleTyCon (AlgTyCon { algTcRhs = TupleTyCon {} }) = True
    isTupleTyCon _ = False

    tyConTuple_maybe :: TyCon -> Maybe TupleSort
    tyConTuple_maybe (AlgTyCon { algTcRhs = rhs })
      | TupleTyCon { tup_sort = sort} <- rhs = Just sort
    tyConTuple_maybe _                       = Nothing

    -- | Is this the 'TyCon' for an unboxed tuple?
    isUnboxedTupleTyCon :: TyCon -> Bool
    isUnboxedTupleTyCon (AlgTyCon { algTcRhs = rhs })
      | TupleTyCon { tup_sort = sort } <- rhs
      = not (isBoxed (tupleSortBoxity sort))
    isUnboxedTupleTyCon _ = False

    -- | Is this the 'TyCon' for a boxed tuple?
    isBoxedTupleTyCon :: TyCon -> Bool
    isBoxedTupleTyCon (AlgTyCon { algTcRhs = rhs })
      | TupleTyCon { tup_sort = sort } <- rhs
      = isBoxed (tupleSortBoxity sort)
    isBoxedTupleTyCon _ = False

    -- | Is this the 'TyCon' for an unboxed sum?
    isUnboxedSumTyCon :: TyCon -> Bool
    isUnboxedSumTyCon (AlgTyCon { algTcRhs = rhs })
      | SumTyCon {} <- rhs
      = True
    isUnboxedSumTyCon _ = False

    -- | Is this the 'TyCon' for a /promoted/ tuple?
    isPromotedTupleTyCon :: TyCon -> Bool
    isPromotedTupleTyCon tyCon
      | Just dataCon <- isPromotedDataCon_maybe tyCon
      , isTupleTyCon (dataConTyCon dataCon) = True
      | otherwise                           = False

    -- | Is this a PromotedDataCon?
    isPromotedDataCon :: TyCon -> Bool
    isPromotedDataCon (PromotedDataCon {}) = True
    isPromotedDataCon _                    = False

    -- | Retrieves the promoted DataCon if this is a PromotedDataCon;
    isPromotedDataCon_maybe :: TyCon -> Maybe DataCon
    isPromotedDataCon_maybe (PromotedDataCon { dataCon = dc }) = Just dc
    isPromotedDataCon_maybe _ = Nothing

    -- | Is this tycon really meant for use at the kind level? That is,
    -- should it be permitted without -XDataKinds?
    isKindTyCon :: TyCon -> Bool
    isKindTyCon tc = getUnique tc `elementOfUniqSet` kindTyConKeys

    -- | These TyCons should be allowed at the kind level, even without
    -- -XDataKinds.
    kindTyConKeys :: UniqSet Unique
    kindTyConKeys = unionManyUniqSets
      ( mkUniqSet [ liftedTypeKindTyConKey, constraintKindTyConKey, tYPETyConKey ]
      : map (mkUniqSet . tycon_with_datacons) [ runtimeRepTyCon
                                              , vecCountTyCon, vecElemTyCon ] )
      where
        tycon_with_datacons tc = getUnique tc : map getUnique (tyConDataCons tc)

    isLiftedTypeKindTyConName :: Name -> Bool
    isLiftedTypeKindTyConName = (`hasKey` liftedTypeKindTyConKey)

    -- | Identifies implicit tycons that, in particular, do not go into interface
    -- files (because they are implicitly reconstructed when the interface is
    -- read).
    --
    -- Note that:
    --
    -- * Associated families are implicit, as they are re-constructed from
    --   the class declaration in which they reside, and
    --
    -- * Family instances are /not/ implicit as they represent the instance body
    --   (similar to a @dfun@ does that for a class instance).
    --
    -- * Tuples are implicit iff they have a wired-in name
    --   (namely: boxed and unboxed tuples are wired-in and implicit,
    --            but constraint tuples are not)
    isImplicitTyCon :: TyCon -> Bool
    isImplicitTyCon (FunTyCon {})        = True
    isImplicitTyCon (PrimTyCon {})       = True
    isImplicitTyCon (PromotedDataCon {}) = True
    isImplicitTyCon (AlgTyCon { algTcRhs = rhs, tyConName = name })
      | TupleTyCon {} <- rhs             = isWiredInName name
      | SumTyCon {} <- rhs               = True
      | otherwise                        = False
    isImplicitTyCon (FamilyTyCon { famTcParent = parent }) = isJust parent
    isImplicitTyCon (SynonymTyCon {})    = False
    isImplicitTyCon (TcTyCon {})         = False

    tyConCType_maybe :: TyCon -> Maybe CType
    tyConCType_maybe tc@(AlgTyCon {}) = tyConCType tc
    tyConCType_maybe _ = Nothing

    -- | Is this a TcTyCon? (That is, one only used during type-checking?)
    isTcTyCon :: TyCon -> Bool
    isTcTyCon (TcTyCon {}) = True
    isTcTyCon _            = False

    setTcTyConKind :: TyCon -> Kind -> TyCon
    -- Update the Kind of a TcTyCon
    -- The new kind is always a zonked version of its previous
    -- kind, so we don't need to update any other fields.
    -- See Note [The Purely Kinded Invariant] in TcHsType
    setTcTyConKind tc@(TcTyCon {}) kind = tc { tyConKind = kind }
    setTcTyConKind tc              _    = pprPanic "setTcTyConKind" (ppr tc)

    -- | Could this TyCon ever be levity-polymorphic when fully applied?
    -- True is safe. False means we're sure. Does only a quick check
    -- based on the TyCon's category.
    -- Precondition: The fully-applied TyCon has kind (TYPE blah)
    isTcLevPoly :: TyCon -> Bool
    isTcLevPoly FunTyCon{}           = False
    isTcLevPoly (AlgTyCon { algTcParent = parent, algTcRhs = rhs })
      | UnboxedAlgTyCon _ <- parent
      = True
      | NewTyCon { nt_lev_poly = lev_poly } <- rhs
      = lev_poly -- Newtypes can be levity polymorphic with UnliftedNewtypes (#17360)
      | otherwise
      = False
    isTcLevPoly SynonymTyCon{}       = True
    isTcLevPoly FamilyTyCon{}        = True
    isTcLevPoly PrimTyCon{}          = False
    isTcLevPoly TcTyCon{}            = False
    isTcLevPoly tc@PromotedDataCon{} = pprPanic "isTcLevPoly datacon" (ppr tc)

    {-
    -----------------------------------------------
    --      Expand type-constructor applications
    -----------------------------------------------
    -}

    expandSynTyCon_maybe
            :: TyCon
            -> [tyco]                 -- ^ Arguments to 'TyCon'
            -> Maybe ([(TyVar,tyco)],
                      Type,
                      [tyco])         -- ^ Returns a 'TyVar' substitution, the body
                                      -- type of the synonym (not yet substituted)
                                      -- and any arguments remaining from the
                                      -- application

    -- ^ Expand a type synonym application, if any
    expandSynTyCon_maybe tc tys
      | SynonymTyCon { tyConTyVars = tvs, synTcRhs = rhs, tyConArity = arity } <- tc
      = case tys `listLengthCmp` arity of
            GT -> Just (tvs `zip` tys, rhs, drop arity tys)
            EQ -> Just (tvs `zip` tys, rhs, [])
            LT -> Nothing
       | otherwise
       = Nothing

    ----------------

    -- | Check if the tycon actually refers to a proper `data` or `newtype`
    --  with user defined constructors rather than one from a class or other
    --  construction.

    -- NB: This is only used in TcRnExports.checkPatSynParent to determine if an
    -- exported tycon can have a pattern synonym bundled with it, e.g.,
    -- module Foo (TyCon(.., PatSyn)) where
    isTyConWithSrcDataCons :: TyCon -> Bool
    isTyConWithSrcDataCons (AlgTyCon { algTcRhs = rhs, algTcParent = parent }) =
      case rhs of
        DataTyCon {}  -> isSrcParent
        NewTyCon {}   -> isSrcParent
        TupleTyCon {} -> isSrcParent
        _ -> False
      where
        isSrcParent = isNoParent parent
    isTyConWithSrcDataCons (FamilyTyCon { famTcFlav = DataFamilyTyCon {} })
                             = True -- #14058
    isTyConWithSrcDataCons _ = False

    -- | As 'tyConDataCons_maybe', but returns the empty list of constructors if no
    -- constructors could be found
    tyConDataCons :: TyCon -> [DataCon]
    -- It's convenient for tyConDataCons to return the
    -- empty list for type synonyms etc
    tyConDataCons tycon = tyConDataCons_maybe tycon `orElse` []

    -- | Determine the 'DataCon's originating from the given 'TyCon', if the 'TyCon'
    -- is the sort that can have any constructors (note: this does not include
    -- abstract algebraic types)
    tyConDataCons_maybe :: TyCon -> Maybe [DataCon]
    tyConDataCons_maybe (AlgTyCon {algTcRhs = rhs})
      = case rhs of
           DataTyCon { data_cons = cons } -> Just cons
           NewTyCon { data_con = con }    -> Just [con]
           TupleTyCon { data_con = con }  -> Just [con]
           SumTyCon { data_cons = cons }  -> Just cons
           _                              -> Nothing
    tyConDataCons_maybe _ = Nothing

    -- | If the given 'TyCon' has a /single/ data constructor, i.e. it is a @data@
    -- type with one alternative, a tuple type or a @newtype@ then that constructor
    -- is returned. If the 'TyCon' has more than one constructor, or represents a
    -- primitive or function type constructor then @Nothing@ is returned. In any
    -- other case, the function panics
    tyConSingleDataCon_maybe :: TyCon -> Maybe DataCon
    tyConSingleDataCon_maybe (AlgTyCon { algTcRhs = rhs })
      = case rhs of
          DataTyCon { data_cons = [c] } -> Just c
          TupleTyCon { data_con = c }   -> Just c
          NewTyCon { data_con = c }     -> Just c
          _                             -> Nothing
    tyConSingleDataCon_maybe _           = Nothing

    tyConSingleDataCon :: TyCon -> DataCon
    tyConSingleDataCon tc
      = case tyConSingleDataCon_maybe tc of
          Just c  -> c
          Nothing -> pprPanic "tyConDataCon" (ppr tc)

    tyConSingleAlgDataCon_maybe :: TyCon -> Maybe DataCon
    -- Returns (Just con) for single-constructor
    -- *algebraic* data types *not* newtypes
    tyConSingleAlgDataCon_maybe (AlgTyCon { algTcRhs = rhs })
      = case rhs of
          DataTyCon { data_cons = [c] } -> Just c
          TupleTyCon { data_con = c }   -> Just c
          _                             -> Nothing
    tyConSingleAlgDataCon_maybe _        = Nothing

    -- | Determine the number of value constructors a 'TyCon' has. Panics if the
    -- 'TyCon' is not algebraic or a tuple
    tyConFamilySize  :: TyCon -> Int
    tyConFamilySize tc@(AlgTyCon { algTcRhs = rhs })
      = case rhs of
          DataTyCon { data_cons_size = size } -> size
          NewTyCon {}                    -> 1
          TupleTyCon {}                  -> 1
          SumTyCon { data_cons_size = size }  -> size
          _                              -> pprPanic "tyConFamilySize 1" (ppr tc)
    tyConFamilySize tc = pprPanic "tyConFamilySize 2" (ppr tc)

    -- | Extract an 'AlgTyConRhs' with information about data constructors from an
    -- algebraic or tuple 'TyCon'. Panics for any other sort of 'TyCon'
    algTyConRhs :: TyCon -> AlgTyConRhs
    algTyConRhs (AlgTyCon {algTcRhs = rhs}) = rhs
    algTyConRhs other = pprPanic "algTyConRhs" (ppr other)

    -- | Extract type variable naming the result of injective type family
    tyConFamilyResVar_maybe :: TyCon -> Maybe Name
    tyConFamilyResVar_maybe (FamilyTyCon {famTcResVar = res}) = res
    tyConFamilyResVar_maybe _                                 = Nothing

    -- | Get the list of roles for the type parameters of a TyCon
    tyConRoles :: TyCon -> [Role]
    -- See also Note [TyCon Role signatures]
    tyConRoles tc
      = case tc of
        { FunTyCon {}                         -> [Nominal, Nominal, Representational, Representational]
        ; AlgTyCon { tcRoles = roles }        -> roles
        ; SynonymTyCon { tcRoles = roles }    -> roles
        ; FamilyTyCon {}                      -> const_role Nominal
        ; PrimTyCon { tcRoles = roles }       -> roles
        ; PromotedDataCon { tcRoles = roles } -> roles
        ; TcTyCon {}                          -> const_role Nominal
        }
      where
        const_role r = replicate (tyConArity tc) r

    -- | Extract the bound type variables and type expansion of a type synonym
    -- 'TyCon'. Panics if the 'TyCon' is not a synonym
    newTyConRhs :: TyCon -> ([TyVar], Type)
    newTyConRhs (AlgTyCon {tyConTyVars = tvs, algTcRhs = NewTyCon { nt_rhs = rhs }})
        = (tvs, rhs)
    newTyConRhs tycon = pprPanic "newTyConRhs" (ppr tycon)

    -- | The number of type parameters that need to be passed to a newtype to
    -- resolve it. May be less than in the definition if it can be eta-contracted.
    newTyConEtadArity :: TyCon -> Int
    newTyConEtadArity (AlgTyCon {algTcRhs = NewTyCon { nt_etad_rhs = tvs_rhs }})
            = length (fst tvs_rhs)
    newTyConEtadArity tycon = pprPanic "newTyConEtadArity" (ppr tycon)

    -- | Extract the bound type variables and type expansion of an eta-contracted
    -- type synonym 'TyCon'.  Panics if the 'TyCon' is not a synonym
    newTyConEtadRhs :: TyCon -> ([TyVar], Type)
    newTyConEtadRhs (AlgTyCon {algTcRhs = NewTyCon { nt_etad_rhs = tvs_rhs }}) = tvs_rhs
    newTyConEtadRhs tycon = pprPanic "newTyConEtadRhs" (ppr tycon)

    -- | Extracts the @newtype@ coercion from such a 'TyCon', which can be used to
    -- construct something with the @newtype@s type from its representation type
    -- (right hand side). If the supplied 'TyCon' is not a @newtype@, returns
    -- @Nothing@
    newTyConCo_maybe :: TyCon -> Maybe (CoAxiom Unbranched)
    newTyConCo_maybe (AlgTyCon {algTcRhs = NewTyCon { nt_co = co }}) = Just co
    newTyConCo_maybe _                                               = Nothing

    newTyConCo :: TyCon -> CoAxiom Unbranched
    newTyConCo tc = case newTyConCo_maybe tc of
                     Just co -> co
                     Nothing -> pprPanic "newTyConCo" (ppr tc)

    newTyConDataCon_maybe :: TyCon -> Maybe DataCon
    newTyConDataCon_maybe (AlgTyCon {algTcRhs = NewTyCon { data_con = con }}) = Just con
    newTyConDataCon_maybe _ = Nothing

    -- | Find the \"stupid theta\" of the 'TyCon'. A \"stupid theta\" is the context
    -- to the left of an algebraic type declaration, e.g. @Eq a@ in the declaration
    -- @data Eq a => T a ...@
    tyConStupidTheta :: TyCon -> [PredType]
    tyConStupidTheta (AlgTyCon {algTcStupidTheta = stupid}) = stupid
    tyConStupidTheta (FunTyCon {}) = []
    tyConStupidTheta tycon = pprPanic "tyConStupidTheta" (ppr tycon)

    -- | Extract the 'TyVar's bound by a vanilla type synonym
    -- and the corresponding (unsubstituted) right hand side.
    synTyConDefn_maybe :: TyCon -> Maybe ([TyVar], Type)
    synTyConDefn_maybe (SynonymTyCon {tyConTyVars = tyvars, synTcRhs = ty})
      = Just (tyvars, ty)
    synTyConDefn_maybe _ = Nothing

    -- | Extract the information pertaining to the right hand side of a type synonym
    -- (@type@) declaration.
    synTyConRhs_maybe :: TyCon -> Maybe Type
    synTyConRhs_maybe (SynonymTyCon {synTcRhs = rhs}) = Just rhs
    synTyConRhs_maybe _                               = Nothing

    -- | Extract the flavour of a type family (with all the extra information that
    -- it carries)
    famTyConFlav_maybe :: TyCon -> Maybe FamTyConFlav
    famTyConFlav_maybe (FamilyTyCon {famTcFlav = flav}) = Just flav
    famTyConFlav_maybe _                                = Nothing

    -- | Is this 'TyCon' that for a class instance?
    isClassTyCon :: TyCon -> Bool
    isClassTyCon (AlgTyCon {algTcParent = ClassTyCon {}}) = True
    isClassTyCon _                                        = False

    -- | If this 'TyCon' is that for a class instance, return the class it is for.
    -- Otherwise returns @Nothing@
    tyConClass_maybe :: TyCon -> Maybe Class
    tyConClass_maybe (AlgTyCon {algTcParent = ClassTyCon clas _}) = Just clas
    tyConClass_maybe _                                            = Nothing

    -- | Return the associated types of the 'TyCon', if any
    tyConATs :: TyCon -> [TyCon]
    tyConATs (AlgTyCon {algTcParent = ClassTyCon clas _}) = classATs clas
    tyConATs _                                            = []

    ----------------------------------------------------------------------------
    -- | Is this 'TyCon' that for a data family instance?
    isFamInstTyCon :: TyCon -> Bool
    isFamInstTyCon (AlgTyCon {algTcParent = DataFamInstTyCon {} })
      = True
    isFamInstTyCon _ = False

    tyConFamInstSig_maybe :: TyCon -> Maybe (TyCon, [Type], CoAxiom Unbranched)
    tyConFamInstSig_maybe (AlgTyCon {algTcParent = DataFamInstTyCon ax f ts })
      = Just (f, ts, ax)
    tyConFamInstSig_maybe _ = Nothing

    -- | If this 'TyCon' is that of a data family instance, return the family in question
    -- and the instance types. Otherwise, return @Nothing@
    tyConFamInst_maybe :: TyCon -> Maybe (TyCon, [Type])
    tyConFamInst_maybe (AlgTyCon {algTcParent = DataFamInstTyCon _ f ts })
      = Just (f, ts)
    tyConFamInst_maybe _ = Nothing

    -- | If this 'TyCon' is that of a data family instance, return a 'TyCon' which
    -- represents a coercion identifying the representation type with the type
    -- instance family.  Otherwise, return @Nothing@
    tyConFamilyCoercion_maybe :: TyCon -> Maybe (CoAxiom Unbranched)
    tyConFamilyCoercion_maybe (AlgTyCon {algTcParent = DataFamInstTyCon ax _ _ })
      = Just ax
    tyConFamilyCoercion_maybe _ = Nothing

    -- | Extract any 'RuntimeRepInfo' from this TyCon
    tyConRuntimeRepInfo :: TyCon -> RuntimeRepInfo
    tyConRuntimeRepInfo (PromotedDataCon { promDcRepInfo = rri }) = rri
    tyConRuntimeRepInfo _                                         = NoRRI
      -- could panic in that second case. But Douglas Adams told me not to.

    {-
    Note [Constructor tag allocation]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When typechecking we need to allocate constructor tags to constructors.
    They are allocated based on the position in the data_cons field of TyCon,
    with the first constructor getting fIRST_TAG.

    We used to pay linear cost per constructor, with each constructor looking up
    its relative index in the constructor list. That was quadratic and prohibitive
    for large data types with more than 10k constructors.

    The current strategy is to build a NameEnv with a mapping from costructor's
    Name to ConTag and pass it down to buildDataCon for efficient lookup.

    Relevant ticket: #14657
    -}

    mkTyConTagMap :: TyCon -> NameEnv ConTag
    mkTyConTagMap tycon =
      mkNameEnv $ map getName (tyConDataCons tycon) `zip` [fIRST_TAG..]
      -- See Note [Constructor tag allocation]

    {-
    ************************************************************************
    *                                                                      *
    \subsection[TyCon-instances]{Instance declarations for @TyCon@}
    *                                                                      *
    ************************************************************************

    @TyCon@s are compared by comparing their @Unique@s.
    -}

    instance Eq TyCon where
        a == b = getUnique a == getUnique b
        a /= b = getUnique a /= getUnique b

    instance Uniquable TyCon where
        getUnique tc = tyConUnique tc

    instance Outputable TyCon where
      -- At the moment a promoted TyCon has the same Name as its
      -- corresponding TyCon, so we add the quote to distinguish it here
      ppr tc = pprPromotionQuote tc <> ppr (tyConName tc) <> pp_tc
        where
          pp_tc = getPprStyle $ \sty -> if ((debugStyle sty || dumpStyle sty) && isTcTyCon tc)
                                        then text "[tc]"
                                        else empty

    -- | Paints a picture of what a 'TyCon' represents, in broad strokes.
    -- This is used towards more informative error messages.
    data TyConFlavour
      = ClassFlavour
      | TupleFlavour Boxity
      | SumFlavour
      | DataTypeFlavour
      | NewtypeFlavour
      | AbstractTypeFlavour
      | DataFamilyFlavour (Maybe TyCon)     -- Just tc <=> (tc == associated class)
      | OpenTypeFamilyFlavour (Maybe TyCon) -- Just tc <=> (tc == associated class)
      | ClosedTypeFamilyFlavour
      | TypeSynonymFlavour
      | BuiltInTypeFlavour -- ^ e.g., the @(->)@ 'TyCon'.
      | PromotedDataConFlavour
      deriving Eq

    instance Outputable TyConFlavour where
      ppr = text . go
        where
          go ClassFlavour = "class"
          go (TupleFlavour boxed) | isBoxed boxed = "tuple"
                                  | otherwise     = "unboxed tuple"
          go SumFlavour              = "unboxed sum"
          go DataTypeFlavour         = "data type"
          go NewtypeFlavour          = "newtype"
          go AbstractTypeFlavour     = "abstract type"
          go (DataFamilyFlavour (Just _))  = "associated data family"
          go (DataFamilyFlavour Nothing)   = "data family"
          go (OpenTypeFamilyFlavour (Just _)) = "associated type family"
          go (OpenTypeFamilyFlavour Nothing)  = "type family"
          go ClosedTypeFamilyFlavour = "type family"
          go TypeSynonymFlavour      = "type synonym"
          go BuiltInTypeFlavour      = "built-in type"
          go PromotedDataConFlavour  = "promoted data constructor"

    tyConFlavour :: TyCon -> TyConFlavour
    tyConFlavour (AlgTyCon { algTcParent = parent, algTcRhs = rhs })
      | ClassTyCon _ _ <- parent = ClassFlavour
      | otherwise = case rhs of
                      TupleTyCon { tup_sort = sort }
                                         -> TupleFlavour (tupleSortBoxity sort)
                      SumTyCon {}        -> SumFlavour
                      DataTyCon {}       -> DataTypeFlavour
                      NewTyCon {}        -> NewtypeFlavour
                      AbstractTyCon {}   -> AbstractTypeFlavour
    tyConFlavour (FamilyTyCon { famTcFlav = flav, famTcParent = parent })
      = case flav of
          DataFamilyTyCon{}            -> DataFamilyFlavour parent
          OpenSynFamilyTyCon           -> OpenTypeFamilyFlavour parent
          ClosedSynFamilyTyCon{}       -> ClosedTypeFamilyFlavour
          AbstractClosedSynFamilyTyCon -> ClosedTypeFamilyFlavour
          BuiltInSynFamTyCon{}         -> ClosedTypeFamilyFlavour
    tyConFlavour (SynonymTyCon {})    = TypeSynonymFlavour
    tyConFlavour (FunTyCon {})        = BuiltInTypeFlavour
    tyConFlavour (PrimTyCon {})       = BuiltInTypeFlavour
    tyConFlavour (PromotedDataCon {}) = PromotedDataConFlavour
    tyConFlavour (TcTyCon { tcTyConFlavour = flav }) = flav

    -- | Can this flavour of 'TyCon' appear unsaturated?
    tcFlavourMustBeSaturated :: TyConFlavour -> Bool
    tcFlavourMustBeSaturated ClassFlavour            = False
    tcFlavourMustBeSaturated DataTypeFlavour         = False
    tcFlavourMustBeSaturated NewtypeFlavour          = False
    tcFlavourMustBeSaturated DataFamilyFlavour{}     = False
    tcFlavourMustBeSaturated TupleFlavour{}          = False
    tcFlavourMustBeSaturated SumFlavour              = False
    tcFlavourMustBeSaturated AbstractTypeFlavour     = False
    tcFlavourMustBeSaturated BuiltInTypeFlavour      = False
    tcFlavourMustBeSaturated PromotedDataConFlavour  = False
    tcFlavourMustBeSaturated TypeSynonymFlavour      = True
    tcFlavourMustBeSaturated OpenTypeFamilyFlavour{} = True
    tcFlavourMustBeSaturated ClosedTypeFamilyFlavour = True

    -- | Is this flavour of 'TyCon' an open type family or a data family?
    tcFlavourIsOpen :: TyConFlavour -> Bool
    tcFlavourIsOpen DataFamilyFlavour{}     = True
    tcFlavourIsOpen OpenTypeFamilyFlavour{} = True
    tcFlavourIsOpen ClosedTypeFamilyFlavour = False
    tcFlavourIsOpen ClassFlavour            = False
    tcFlavourIsOpen DataTypeFlavour         = False
    tcFlavourIsOpen NewtypeFlavour          = False
    tcFlavourIsOpen TupleFlavour{}          = False
    tcFlavourIsOpen SumFlavour              = False
    tcFlavourIsOpen AbstractTypeFlavour     = False
    tcFlavourIsOpen BuiltInTypeFlavour      = False
    tcFlavourIsOpen PromotedDataConFlavour  = False
    tcFlavourIsOpen TypeSynonymFlavour      = False

    pprPromotionQuote :: TyCon -> SDoc
    -- Promoted data constructors already have a tick in their OccName
    pprPromotionQuote tc
      = case tc of
          PromotedDataCon {} -> char '\'' -- Always quote promoted DataCons in types
          _                  -> empty

    instance NamedThing TyCon where
        getName = tyConName

    instance Data.Data TyCon where
        -- don't traverse?
        toConstr _   = abstractConstr "TyCon"
        gunfold _ _  = error "gunfold"
        dataTypeOf _ = mkNoRepType "TyCon"

    instance Binary Injectivity where
        put_ bh NotInjective   = putByte bh 0
        put_ bh (Injective xs) = putByte bh 1 >> put_ bh xs

        get bh = do { h <- getByte bh
                    ; case h of
                        0 -> return NotInjective
                        _ -> do { xs <- get bh
                                ; return (Injective xs) } }

    {-
    ************************************************************************
    *                                                                      *
               Walking over recursive TyCons
    *                                                                      *
    ************************************************************************

    Note [Expanding newtypes and products]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When expanding a type to expose a data-type constructor, we need to be
    careful about newtypes, lest we fall into an infinite loop. Here are
    the key examples:

      newtype Id  x = MkId x
      newtype Fix f = MkFix (f (Fix f))
      newtype T     = MkT (T -> T)

      Type           Expansion
     --------------------------
      T              T -> T
      Fix Maybe      Maybe (Fix Maybe)
      Id (Id Int)    Int
      Fix Id         NO NO NO

    Notice that
     * We can expand T, even though it's recursive.
     * We can expand Id (Id Int), even though the Id shows up
       twice at the outer level, because Id is non-recursive

    So, when expanding, we keep track of when we've seen a recursive
    newtype at outermost level; and bail out if we see it again.

    We sometimes want to do the same for product types, so that the
    strictness analyser doesn't unbox infinitely deeply.

    More precisely, we keep a *count* of how many times we've seen it.
    This is to account for
       data instance T (a,b) = MkT (T a) (T b)
    Then (#10482) if we have a type like
            T (Int,(Int,(Int,(Int,Int))))
    we can still unbox deeply enough during strictness analysis.
    We have to treat T as potentially recursive, but it's still
    good to be able to unwrap multiple layers.

    The function that manages all this is checkRecTc.
    -}

    data RecTcChecker = RC !Int (NameEnv Int)
      -- The upper bound, and the number of times
      -- we have encountered each TyCon

    -- | Initialise a 'RecTcChecker' with 'defaultRecTcMaxBound'.
    initRecTc :: RecTcChecker
    initRecTc = RC defaultRecTcMaxBound emptyNameEnv

    -- | The default upper bound (100) for the number of times a 'RecTcChecker' is
    -- allowed to encounter each 'TyCon'.
    defaultRecTcMaxBound :: Int
    defaultRecTcMaxBound = 100
    -- Should we have a flag for this?

    -- | Change the upper bound for the number of times a 'RecTcChecker' is allowed
    -- to encounter each 'TyCon'.
    setRecTcMaxBound :: Int -> RecTcChecker -> RecTcChecker
    setRecTcMaxBound new_bound (RC _old_bound rec_nts) = RC new_bound rec_nts

    checkRecTc :: RecTcChecker -> TyCon -> Maybe RecTcChecker
    -- Nothing      => Recursion detected
    -- Just rec_tcs => Keep going
    checkRecTc (RC bound rec_nts) tc
      = case lookupNameEnv rec_nts tc_name of
          Just n | n >= bound -> Nothing
                 | otherwise  -> Just (RC bound (extendNameEnv rec_nts tc_name (n+1)))
          Nothing             -> Just (RC bound (extendNameEnv rec_nts tc_name 1))
      where
        tc_name = tyConName tc

    -- | Returns whether or not this 'TyCon' is definite, or a hole
    -- that may be filled in at some later point.  See Note [Skolem abstract data]
    tyConSkolem :: TyCon -> Bool
    tyConSkolem = isHoleName . tyConName

    -- Note [Skolem abstract data]
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    -- Skolem abstract data arises from data declarations in an hsig file.
    --
    -- The best analogy is to interpret the types declared in signature files as
    -- elaborating to universally quantified type variables; e.g.,
    --
    --    unit p where
    --        signature H where
    --            data T
    --            data S
    --        module M where
    --            import H
    --            f :: (T ~ S) => a -> b
    --            f x = x
    --
    -- elaborates as (with some fake structural types):
    --
    --    p :: forall t s. { f :: forall a b. t ~ s => a -> b }
    --    p = { f = \x -> x } -- ill-typed
    --
    -- It is clear that inside p, t ~ s is not provable (and
    -- if we tried to write a function to cast t to s, that
    -- would not work), but if we call p @Int @Int, clearly Int ~ Int
    -- is provable.  The skolem variables are all distinct from
    -- one another, but we can't make assumptions like "f is
    -- inaccessible", because the skolem variables will get
    -- instantiated eventually!
    --
    -- Skolem abstractness can apply to "non-abstract" data as well):
    --
    --    unit p where
    --        signature H1 where
    --            data T = MkT
    --        signature H2 where
    --            data T = MkT
    --        module M where
    --            import qualified H1
    --            import qualified H2
    --            f :: (H1.T ~ H2.T) => a -> b
    --            f x = x
    --
    -- This is why the test is on the original name of the TyCon,
    -- not whether it is abstract or not.