prelude/TysPrim.hs

    {-
    (c) The AQUA Project, Glasgow University, 1994-1998

    \section[TysPrim]{Wired-in knowledge about primitive types}
    -}

    {-# LANGUAGE CPP #-}

    -- | This module defines TyCons that can't be expressed in Haskell.
    --   They are all, therefore, wired-in TyCons.  C.f module TysWiredIn
    module TysPrim(
            mkPrimTyConName, -- For implicit parameters in TysWiredIn only

            mkTemplateTyVars,
            alphaTyVars, alphaTyVar, betaTyVar, gammaTyVar, deltaTyVar,
            alphaTys, alphaTy, betaTy, gammaTy, deltaTy,
            runtimeRep1TyVar, runtimeRep2TyVar, runtimeRep1Ty, runtimeRep2Ty,
            openAlphaTy, openBetaTy, openAlphaTyVar, openBetaTyVar,
            kKiVar,

            -- Kind constructors...
            tYPETyConName, unliftedTypeKindTyConName,

            -- Kinds
            tYPE,

            funTyCon, funTyConName,
            primTyCons,

            charPrimTyCon,          charPrimTy,
            intPrimTyCon,           intPrimTy,
            wordPrimTyCon,          wordPrimTy,
            addrPrimTyCon,          addrPrimTy,
            floatPrimTyCon,         floatPrimTy,
            doublePrimTyCon,        doublePrimTy,

            voidPrimTyCon,          voidPrimTy,
            statePrimTyCon,         mkStatePrimTy,
            realWorldTyCon,         realWorldTy, realWorldStatePrimTy,

            proxyPrimTyCon,         mkProxyPrimTy,

            arrayPrimTyCon, mkArrayPrimTy,
            byteArrayPrimTyCon,     byteArrayPrimTy,
            arrayArrayPrimTyCon, mkArrayArrayPrimTy,
            smallArrayPrimTyCon, mkSmallArrayPrimTy,
            mutableArrayPrimTyCon, mkMutableArrayPrimTy,
            mutableByteArrayPrimTyCon, mkMutableByteArrayPrimTy,
            mutableArrayArrayPrimTyCon, mkMutableArrayArrayPrimTy,
            smallMutableArrayPrimTyCon, mkSmallMutableArrayPrimTy,
            mutVarPrimTyCon, mkMutVarPrimTy,

            mVarPrimTyCon,                  mkMVarPrimTy,
            tVarPrimTyCon,                  mkTVarPrimTy,
            stablePtrPrimTyCon,             mkStablePtrPrimTy,
            stableNamePrimTyCon,            mkStableNamePrimTy,
            bcoPrimTyCon,                   bcoPrimTy,
            weakPrimTyCon,                  mkWeakPrimTy,
            threadIdPrimTyCon,              threadIdPrimTy,

            int32PrimTyCon,         int32PrimTy,
            word32PrimTyCon,        word32PrimTy,

            int64PrimTyCon,         int64PrimTy,
            word64PrimTyCon,        word64PrimTy,

            eqPrimTyCon,            -- ty1 ~# ty2
            eqReprPrimTyCon,        -- ty1 ~R# ty2  (at role Representational)
            eqPhantPrimTyCon,       -- ty1 ~P# ty2  (at role Phantom)

            -- * Any
            anyTy, anyTyCon, anyTypeOfKind,

            -- * SIMD
    #include "primop-vector-tys-exports.hs-incl"
      ) where

    #include "HsVersions.h"

    import {-# SOURCE #-} TysWiredIn
      ( runtimeRepTy, liftedTypeKind
      , vecRepDataConTyCon, ptrRepUnliftedDataConTyCon
      , voidRepDataConTy, intRepDataConTy
      , wordRepDataConTy, int64RepDataConTy, word64RepDataConTy, addrRepDataConTy
      , floatRepDataConTy, doubleRepDataConTy
      , vec2DataConTy, vec4DataConTy, vec8DataConTy, vec16DataConTy, vec32DataConTy
      , vec64DataConTy
      , int8ElemRepDataConTy, int16ElemRepDataConTy, int32ElemRepDataConTy
      , int64ElemRepDataConTy, word8ElemRepDataConTy, word16ElemRepDataConTy
      , word32ElemRepDataConTy, word64ElemRepDataConTy, floatElemRepDataConTy
      , doubleElemRepDataConTy )

    import Var              ( TyVar, KindVar, mkTyVar )
    import Name
    import TyCon
    import SrcLoc
    import Unique
    import PrelNames
    import FastString
    import Outputable
    import TyCoRep   -- doesn't need special access, but this is easier to avoid
                     -- import loops

    import Data.Char

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Primitive type constructors}
    *                                                                      *
    ************************************************************************
    -}

    primTyCons :: [TyCon]
    primTyCons
      = [ addrPrimTyCon
        , arrayPrimTyCon
        , byteArrayPrimTyCon
        , arrayArrayPrimTyCon
        , smallArrayPrimTyCon
        , charPrimTyCon
        , doublePrimTyCon
        , floatPrimTyCon
        , intPrimTyCon
        , int32PrimTyCon
        , int64PrimTyCon
        , bcoPrimTyCon
        , weakPrimTyCon
        , mutableArrayPrimTyCon
        , mutableByteArrayPrimTyCon
        , mutableArrayArrayPrimTyCon
        , smallMutableArrayPrimTyCon
        , mVarPrimTyCon
        , tVarPrimTyCon
        , mutVarPrimTyCon
        , realWorldTyCon
        , stablePtrPrimTyCon
        , stableNamePrimTyCon
        , statePrimTyCon
        , voidPrimTyCon
        , proxyPrimTyCon
        , threadIdPrimTyCon
        , wordPrimTyCon
        , word32PrimTyCon
        , word64PrimTyCon
        , anyTyCon
        , eqPrimTyCon
        , eqReprPrimTyCon
        , eqPhantPrimTyCon

        , unliftedTypeKindTyCon
        , tYPETyCon

    #include "primop-vector-tycons.hs-incl"
        ]

    mkPrimTc :: FastString -> Unique -> TyCon -> Name
    mkPrimTc fs unique tycon
      = mkWiredInName gHC_PRIM (mkTcOccFS fs)
                      unique
                      (ATyCon tycon)        -- Relevant TyCon
                      UserSyntax

    mkBuiltInPrimTc :: FastString -> Unique -> TyCon -> Name
    mkBuiltInPrimTc fs unique tycon
      = mkWiredInName gHC_PRIM (mkTcOccFS fs)
                      unique
                      (ATyCon tycon)        -- Relevant TyCon
                      BuiltInSyntax

    charPrimTyConName, intPrimTyConName, int32PrimTyConName, int64PrimTyConName, wordPrimTyConName, word32PrimTyConName, word64PrimTyConName, addrPrimTyConName, floatPrimTyConName, doublePrimTyConName, statePrimTyConName, proxyPrimTyConName, realWorldTyConName, arrayPrimTyConName, arrayArrayPrimTyConName, smallArrayPrimTyConName, byteArrayPrimTyConName, mutableArrayPrimTyConName, mutableByteArrayPrimTyConName, mutableArrayArrayPrimTyConName, smallMutableArrayPrimTyConName, mutVarPrimTyConName, mVarPrimTyConName, tVarPrimTyConName, stablePtrPrimTyConName, stableNamePrimTyConName, bcoPrimTyConName, weakPrimTyConName, threadIdPrimTyConName, eqPrimTyConName, eqReprPrimTyConName, eqPhantPrimTyConName, voidPrimTyConName :: Name
    charPrimTyConName             = mkPrimTc (fsLit "Char#") charPrimTyConKey charPrimTyCon
    intPrimTyConName              = mkPrimTc (fsLit "Int#") intPrimTyConKey  intPrimTyCon
    int32PrimTyConName            = mkPrimTc (fsLit "Int32#") int32PrimTyConKey int32PrimTyCon
    int64PrimTyConName            = mkPrimTc (fsLit "Int64#") int64PrimTyConKey int64PrimTyCon
    wordPrimTyConName             = mkPrimTc (fsLit "Word#") wordPrimTyConKey wordPrimTyCon
    word32PrimTyConName           = mkPrimTc (fsLit "Word32#") word32PrimTyConKey word32PrimTyCon
    word64PrimTyConName           = mkPrimTc (fsLit "Word64#") word64PrimTyConKey word64PrimTyCon
    addrPrimTyConName             = mkPrimTc (fsLit "Addr#") addrPrimTyConKey addrPrimTyCon
    floatPrimTyConName            = mkPrimTc (fsLit "Float#") floatPrimTyConKey floatPrimTyCon
    doublePrimTyConName           = mkPrimTc (fsLit "Double#") doublePrimTyConKey doublePrimTyCon
    statePrimTyConName            = mkPrimTc (fsLit "State#") statePrimTyConKey statePrimTyCon
    voidPrimTyConName             = mkPrimTc (fsLit "Void#") voidPrimTyConKey voidPrimTyCon
    proxyPrimTyConName            = mkPrimTc (fsLit "Proxy#") proxyPrimTyConKey proxyPrimTyCon
    eqPrimTyConName               = mkPrimTc (fsLit "~#") eqPrimTyConKey eqPrimTyCon
    eqReprPrimTyConName           = mkBuiltInPrimTc (fsLit "~R#") eqReprPrimTyConKey eqReprPrimTyCon
    eqPhantPrimTyConName          = mkBuiltInPrimTc (fsLit "~P#") eqPhantPrimTyConKey eqPhantPrimTyCon
    realWorldTyConName            = mkPrimTc (fsLit "RealWorld") realWorldTyConKey realWorldTyCon
    arrayPrimTyConName            = mkPrimTc (fsLit "Array#") arrayPrimTyConKey arrayPrimTyCon
    byteArrayPrimTyConName        = mkPrimTc (fsLit "ByteArray#") byteArrayPrimTyConKey byteArrayPrimTyCon
    arrayArrayPrimTyConName           = mkPrimTc (fsLit "ArrayArray#") arrayArrayPrimTyConKey arrayArrayPrimTyCon
    smallArrayPrimTyConName       = mkPrimTc (fsLit "SmallArray#") smallArrayPrimTyConKey smallArrayPrimTyCon
    mutableArrayPrimTyConName     = mkPrimTc (fsLit "MutableArray#") mutableArrayPrimTyConKey mutableArrayPrimTyCon
    mutableByteArrayPrimTyConName = mkPrimTc (fsLit "MutableByteArray#") mutableByteArrayPrimTyConKey mutableByteArrayPrimTyCon
    mutableArrayArrayPrimTyConName= mkPrimTc (fsLit "MutableArrayArray#") mutableArrayArrayPrimTyConKey mutableArrayArrayPrimTyCon
    smallMutableArrayPrimTyConName= mkPrimTc (fsLit "SmallMutableArray#") smallMutableArrayPrimTyConKey smallMutableArrayPrimTyCon
    mutVarPrimTyConName           = mkPrimTc (fsLit "MutVar#") mutVarPrimTyConKey mutVarPrimTyCon
    mVarPrimTyConName             = mkPrimTc (fsLit "MVar#") mVarPrimTyConKey mVarPrimTyCon
    tVarPrimTyConName             = mkPrimTc (fsLit "TVar#") tVarPrimTyConKey tVarPrimTyCon
    stablePtrPrimTyConName        = mkPrimTc (fsLit "StablePtr#") stablePtrPrimTyConKey stablePtrPrimTyCon
    stableNamePrimTyConName       = mkPrimTc (fsLit "StableName#") stableNamePrimTyConKey stableNamePrimTyCon
    bcoPrimTyConName              = mkPrimTc (fsLit "BCO#") bcoPrimTyConKey bcoPrimTyCon
    weakPrimTyConName             = mkPrimTc (fsLit "Weak#") weakPrimTyConKey weakPrimTyCon
    threadIdPrimTyConName         = mkPrimTc (fsLit "ThreadId#") threadIdPrimTyConKey threadIdPrimTyCon

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Support code}
    *                                                                      *
    ************************************************************************

    alphaTyVars is a list of type variables for use in templates:
            ["a", "b", ..., "z", "t1", "t2", ... ]
    -}

    mkTemplateTyVars :: [Kind] -> [TyVar]
    mkTemplateTyVars kinds =
      [ mkTyVar (mkInternalName (mkAlphaTyVarUnique u)
                                (mkTyVarOccFS (mkFastString name))
                                noSrcSpan) k
      | (k,u) <- zip kinds [2..],
        let name | c <= 'z'  = [c]
                 | otherwise = 't':show u
              where c = chr (u-2 + ord 'a')
      ]

    alphaTyVars :: [TyVar]
    alphaTyVars = mkTemplateTyVars $ repeat liftedTypeKind

    alphaTyVar, betaTyVar, gammaTyVar, deltaTyVar :: TyVar
    (alphaTyVar:betaTyVar:gammaTyVar:deltaTyVar:_) = alphaTyVars

    alphaTys :: [Type]
    alphaTys = mkTyVarTys alphaTyVars
    alphaTy, betaTy, gammaTy, deltaTy :: Type
    (alphaTy:betaTy:gammaTy:deltaTy:_) = alphaTys

    runtimeRep1TyVar, runtimeRep2TyVar :: TyVar
    (runtimeRep1TyVar : runtimeRep2TyVar : _)
      = drop 16 (mkTemplateTyVars (repeat runtimeRepTy))  -- selects 'q','r'

    runtimeRep1Ty, runtimeRep2Ty :: Type
    runtimeRep1Ty = mkTyVarTy runtimeRep1TyVar
    runtimeRep2Ty = mkTyVarTy runtimeRep2TyVar

    openAlphaTyVar, openBetaTyVar :: TyVar
    [openAlphaTyVar,openBetaTyVar]
      = mkTemplateTyVars [tYPE runtimeRep1Ty, tYPE runtimeRep2Ty]

    openAlphaTy, openBetaTy :: Type
    openAlphaTy = mkTyVarTy openAlphaTyVar
    openBetaTy  = mkTyVarTy openBetaTyVar

    kKiVar :: KindVar
    kKiVar = (mkTemplateTyVars $ repeat liftedTypeKind) !! 10
      -- the 10 selects the 11th letter in the alphabet: 'k'

    {-
    ************************************************************************
    *                                                                      *
                    FunTyCon
    *                                                                      *
    ************************************************************************
    -}

    funTyConName :: Name
    funTyConName = mkPrimTyConName (fsLit "(->)") funTyConKey funTyCon

    funTyCon :: TyCon
    funTyCon = mkFunTyCon funTyConName (map Anon [liftedTypeKind, liftedTypeKind])
                                       tc_rep_nm
      where
            -- You might think that (->) should have type (?? -> ? -> *), and you'd be right
            -- But if we do that we get kind errors when saying
            --      instance Control.Arrow (->)
            -- because the expected kind is (*->*->*).  The trouble is that the
            -- expected/actual stuff in the unifier does not go contra-variant, whereas
            -- the kind sub-typing does.  Sigh.  It really only matters if you use (->) in
            -- a prefix way, thus:  (->) Int# Int#.  And this is unusual.
            -- because they are never in scope in the source

        tc_rep_nm = mkPrelTyConRepName funTyConName

    {-
    ************************************************************************
    *                                                                      *
                    Kinds
    *                                                                      *
    ************************************************************************

    Note [TYPE]
    ~~~~~~~~~~~
    There are a few places where we wish to be able to deal interchangeably
    with kind * and kind #. unsafeCoerce#, error, and (->) are some of these
    places. The way we do this is to use runtime-representation polymorphism.

    We have

        data RuntimeRep = PtrRepLifted | PtrRepUnlifted | ...

    and a magical constant (tYPETyCon)

        TYPE :: RuntimeRep -> TYPE PtrRepLifted

    We then have synonyms (liftedTypeKindTyCon, unliftedTypeKindTyCon)

        type * = TYPE PtrRepLifted
        type # = TYPE PtrRepUnlifted

    The (...) in the definition for RuntimeRep includes possibilities for
    the unboxed, unlifted representations, isomorphic to the PrimRep type
    in TyCon. RuntimeRep is itself declared in GHC.Types.

    An alternative design would be to have

      data RuntimeRep = PtrRep Levity | ...
      data Levity = Lifted | Unlifted

    but this slowed down GHC because every time we looked at *, we had to
    follow a bunch of pointers. When we have unpackable sums, we should
    go back to the stratified representation. This would allow, for example:

        unsafeCoerce# :: forall (r1 :: RuntimeRep) (v2 :: Levity)
                                (a :: TYPE v1) (b :: TYPE v2). a -> b

    TYPE replaces the old sub-kinding machinery. We call variables `a` and `b`
    above "runtime-representation polymorphic".

    -}

    tYPETyCon, unliftedTypeKindTyCon :: TyCon
    tYPETyConName, unliftedTypeKindTyConName :: Name

    tYPETyCon = mkKindTyCon tYPETyConName
                            [Anon runtimeRepTy]
                            liftedTypeKind
                            [Nominal]
                            (mkPrelTyConRepName tYPETyConName)

       -- See Note [TYPE]
       -- NB: unlifted is wired in because there is no way to parse it in
       -- Haskell. That's the only reason for wiring it in.
    unliftedTypeKindTyCon = mkSynonymTyCon unliftedTypeKindTyConName
                              [] liftedTypeKind
                              [] []
                              (tYPE (TyConApp ptrRepUnliftedDataConTyCon []))

    --------------------------
    -- ... and now their names

    -- If you edit these, you may need to update the GHC formalism
    -- See Note [GHC Formalism] in coreSyn/CoreLint.hs
    tYPETyConName             = mkPrimTyConName (fsLit "TYPE") tYPETyConKey tYPETyCon
    unliftedTypeKindTyConName = mkPrimTyConName (fsLit "#") unliftedTypeKindTyConKey unliftedTypeKindTyCon

    mkPrimTyConName :: FastString -> Unique -> TyCon -> Name
    mkPrimTyConName = mkPrimTcName BuiltInSyntax
      -- All of the super kinds and kinds are defined in Prim,
      -- and use BuiltInSyntax, because they are never in scope in the source

    mkPrimTcName :: BuiltInSyntax -> FastString -> Unique -> TyCon -> Name
    mkPrimTcName built_in_syntax occ key tycon
      = mkWiredInName gHC_PRIM (mkTcOccFS occ) key (ATyCon tycon) built_in_syntax

    -----------------------------
    -- | Given a RuntimeRep, applies TYPE to it. See Note [TYPE].
    tYPE :: Type -> Type
    tYPE rr = TyConApp tYPETyCon [rr]

    {-
    ************************************************************************
    *                                                                      *
    \subsection[TysPrim-basic]{Basic primitive types (@Char#@, @Int#@, etc.)}
    *                                                                      *
    ************************************************************************
    -}

    -- only used herein
    pcPrimTyCon :: Name -> [Role] -> PrimRep -> TyCon
    pcPrimTyCon name roles rep
      = mkPrimTyCon name binders result_kind roles
      where
        binders     = map (const (Anon liftedTypeKind)) roles
        result_kind = tYPE rr

        rr = case rep of
          VoidRep       -> voidRepDataConTy
          PtrRep        -> TyConApp ptrRepUnliftedDataConTyCon []
          IntRep        -> intRepDataConTy
          WordRep       -> wordRepDataConTy
          Int64Rep      -> int64RepDataConTy
          Word64Rep     -> word64RepDataConTy
          AddrRep       -> addrRepDataConTy
          FloatRep      -> floatRepDataConTy
          DoubleRep     -> doubleRepDataConTy
          VecRep n elem -> TyConApp vecRepDataConTyCon [n', elem']
            where
              n' = case n of
                2  -> vec2DataConTy
                4  -> vec4DataConTy
                8  -> vec8DataConTy
                16 -> vec16DataConTy
                32 -> vec32DataConTy
                64 -> vec64DataConTy
                _  -> pprPanic "Disallowed VecCount" (ppr n)

              elem' = case elem of
                Int8ElemRep   -> int8ElemRepDataConTy
                Int16ElemRep  -> int16ElemRepDataConTy
                Int32ElemRep  -> int32ElemRepDataConTy
                Int64ElemRep  -> int64ElemRepDataConTy
                Word8ElemRep  -> word8ElemRepDataConTy
                Word16ElemRep -> word16ElemRepDataConTy
                Word32ElemRep -> word32ElemRepDataConTy
                Word64ElemRep -> word64ElemRepDataConTy
                FloatElemRep  -> floatElemRepDataConTy
                DoubleElemRep -> doubleElemRepDataConTy

    pcPrimTyCon0 :: Name -> PrimRep -> TyCon
    pcPrimTyCon0 name rep
      = pcPrimTyCon name [] rep

    charPrimTy :: Type
    charPrimTy      = mkTyConTy charPrimTyCon
    charPrimTyCon :: TyCon
    charPrimTyCon   = pcPrimTyCon0 charPrimTyConName WordRep

    intPrimTy :: Type
    intPrimTy       = mkTyConTy intPrimTyCon
    intPrimTyCon :: TyCon
    intPrimTyCon    = pcPrimTyCon0 intPrimTyConName IntRep

    int32PrimTy :: Type
    int32PrimTy     = mkTyConTy int32PrimTyCon
    int32PrimTyCon :: TyCon
    int32PrimTyCon  = pcPrimTyCon0 int32PrimTyConName IntRep

    int64PrimTy :: Type
    int64PrimTy     = mkTyConTy int64PrimTyCon
    int64PrimTyCon :: TyCon
    int64PrimTyCon  = pcPrimTyCon0 int64PrimTyConName Int64Rep

    wordPrimTy :: Type
    wordPrimTy      = mkTyConTy wordPrimTyCon
    wordPrimTyCon :: TyCon
    wordPrimTyCon   = pcPrimTyCon0 wordPrimTyConName WordRep

    word32PrimTy :: Type
    word32PrimTy    = mkTyConTy word32PrimTyCon
    word32PrimTyCon :: TyCon
    word32PrimTyCon = pcPrimTyCon0 word32PrimTyConName WordRep

    word64PrimTy :: Type
    word64PrimTy    = mkTyConTy word64PrimTyCon
    word64PrimTyCon :: TyCon
    word64PrimTyCon = pcPrimTyCon0 word64PrimTyConName Word64Rep

    addrPrimTy :: Type
    addrPrimTy      = mkTyConTy addrPrimTyCon
    addrPrimTyCon :: TyCon
    addrPrimTyCon   = pcPrimTyCon0 addrPrimTyConName AddrRep

    floatPrimTy     :: Type
    floatPrimTy     = mkTyConTy floatPrimTyCon
    floatPrimTyCon :: TyCon
    floatPrimTyCon  = pcPrimTyCon0 floatPrimTyConName FloatRep

    doublePrimTy :: Type
    doublePrimTy    = mkTyConTy doublePrimTyCon
    doublePrimTyCon :: TyCon
    doublePrimTyCon = pcPrimTyCon0 doublePrimTyConName DoubleRep

    {-
    ************************************************************************
    *                                                                      *
    \subsection[TysPrim-state]{The @State#@ type (and @_RealWorld@ types)}
    *                                                                      *
    ************************************************************************

    Note [The equality types story]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    GHC sports a veritable menagerie of equality types:

                  Hetero?   Levity      Result       Role      Defining module
                  ------------------------------------------------------------
      ~#          hetero    unlifted    #            nominal   GHC.Prim
      ~~          hetero    lifted      Constraint   nominal   GHC.Types
      ~           homo      lifted      Constraint   nominal   Data.Type.Equality
      :~:         homo      lifted      *            nominal   Data.Type.Equality

      ~R#         hetero    unlifted    #            repr      GHC.Prim
      Coercible   homo      lifted      Constraint   repr      GHC.Types
      Coercion    homo      lifted      *            repr      Data.Type.Coercion

      ~P#         hetero    unlifted                 phantom   GHC.Prim

    Recall that "hetero" means the equality can related types of different
    kinds. Knowing that (t1 ~# t2) or (t1 ~R# t2) or even that (t1 ~P# t2)
    also means that (k1 ~# k2), where (t1 :: k1) and (t2 :: k2).

    To produce less confusion for end users, when not dumping and without
    -fprint-equality-relations, each of these groups is printed as the bottommost
    listed equality. That is, (~#) and (~~) are both rendered as (~) in
    error messages, and (~R#) is rendered as Coercible.

    Let's take these one at a time:

        --------------------------
        (~#) :: forall k1 k2. k1 -> k2 -> #
        --------------------------
    This is The Type Of Equality in GHC. It classifies nominal coercions.
    This type is used in the solver for recording equality constraints.
    It responds "yes" to Type.isEqPred and classifies as an EqPred in
    Type.classifyPredType.

    All wanted constraints of this type are built with coercion holes.
    (See Note [Coercion holes] in TyCoRep.) But see also
    Note [Deferred errors for coercion holes] in TcErrors to see how
    equality constraints are deferred.

    Within GHC, ~# is called eqPrimTyCon, and it is defined in TysPrim.

        --------------------------
        (~~) :: forall k1 k2. k1 -> k2 -> Constraint
        --------------------------
    This is (almost) an ordinary class, defined as if by
      class a ~# b => a ~~ b
      instance a ~# b => a ~~ b
    Here's what's unusual about it:
     * We can't actually declare it that way because we don't have syntax for ~#.
       And ~# isn't a constraint, so even if we could write it, it wouldn't kind
       check.

     * Users cannot write instances of it.

     * It is "naturally coherent". This means that the solver won't hesitate to
       solve a goal of type (a ~~ b) even if there is, say (Int ~~ c) in the
       context. (Normally, it waits to learn more, just in case the given
       influences what happens next.) This is quite like having
       IncoherentInstances enabled.

     * It always terminates. That is, in the UndecidableInstances checks, we
       don't worry if a (~~) constraint is too big, as we know that solving
       equality terminates.

    On the other hand, this behaves just like any class w.r.t. eager superclass
    unpacking in the solver. So a lifted equality given quickly becomes an unlifted
    equality given. This is good, because the solver knows all about unlifted
    equalities. There is some special-casing in TcInteract.matchClassInst to
    pretend that there is an instance of this class, as we can't write the instance
    in Haskell.

    Within GHC, ~~ is called heqTyCon, and it is defined in TysWiredIn.

        --------------------------
        (~) :: forall k. k -> k -> Constraint
        --------------------------
    This is defined in Data.Type.Equality:
      class a ~~ b => (a :: k) ~ (b :: k)
      instance a ~~ b => a ~ b
    This is even more so an ordinary class than (~~), with the following exceptions:
     * Users cannot write instances of it.

     * It is "naturally coherent". (See (~~).)

     * (~) is magical syntax, as ~ is a reserved symbol. It cannot be exported
       or imported.

     * It always terminates.

    Within GHC, ~ is called eqTyCon, and it is defined in PrelNames. Note that
    it is *not* wired in.

        --------------------------
        (:~:) :: forall k. k -> k -> *
        --------------------------
    This is a perfectly ordinary GADT, wrapping (~). It is not defined within
    GHC at all.

        --------------------------
        (~R#) :: forall k1 k2. k1 -> k2 -> #
        --------------------------
    The is the representational analogue of ~#. This is the type of representational
    equalities that the solver works on. All wanted constraints of this type are
    built with coercion holes.

    Within GHC, ~R# is called eqReprPrimTyCon, and it is defined in TysPrim.

        --------------------------
        Coercible :: forall k. k -> k -> Constraint
        --------------------------
    This is quite like (~~) in the way it's defined and treated within GHC, but
    it's homogeneous. Homogeneity helps with type inference (as GHC can solve one
    kind from the other) and, in my (Richard's) estimation, will be more intuitive
    for users.

    An alternative design included HCoercible (like (~~)) and Coercible (like (~)).
    One annoyance was that we want `coerce :: Coercible a b => a -> b`, and
    we need the type of coerce to be fully wired-in. So the HCoercible/Coercible
    split required that both types be fully wired-in. Instead of doing this,
    I just got rid of HCoercible, as I'm not sure who would use it, anyway.

    Within GHC, Coercible is called coercibleTyCon, and it is defined in
    TysWiredIn.

        --------------------------
        Coercion :: forall k. k -> k -> *
        --------------------------
    This is a perfectly ordinary GADT, wrapping Coercible. It is not defined
    within GHC at all.

        --------------------------
        (~P#) :: forall k1 k2. k1 -> k2 -> #
        --------------------------
    This is the phantom analogue of ~# and it is barely used at all.
    (The solver has no idea about this one.) Here is the motivation:

        data Phant a = MkPhant
        type role Phant phantom

        Phant <Int, Bool>_P :: Phant Int ~P# Phant Bool

    We just need to have something to put on that last line. You probably
    don't need to worry about it.

    Note [The State# TyCon]
    ~~~~~~~~~~~~~~~~~~~~~~~
    State# is the primitive, unlifted type of states.  It has one type parameter,
    thus
            State# RealWorld
    or
            State# s

    where s is a type variable. The only purpose of the type parameter is to
    keep different state threads separate.  It is represented by nothing at all.

    The type parameter to State# is intended to keep separate threads separate.
    Even though this parameter is not used in the definition of State#, it is
    given role Nominal to enforce its intended use.
    -}

    mkStatePrimTy :: Type -> Type
    mkStatePrimTy ty = TyConApp statePrimTyCon [ty]

    statePrimTyCon :: TyCon   -- See Note [The State# TyCon]
    statePrimTyCon   = pcPrimTyCon statePrimTyConName [Nominal] VoidRep

    {-
    RealWorld is deeply magical.  It is *primitive*, but it is not
    *unlifted* (hence ptrArg).  We never manipulate values of type
    RealWorld; it's only used in the type system, to parameterise State#.
    -}

    realWorldTyCon :: TyCon
    realWorldTyCon = mkLiftedPrimTyCon realWorldTyConName [] liftedTypeKind []
    realWorldTy :: Type
    realWorldTy          = mkTyConTy realWorldTyCon
    realWorldStatePrimTy :: Type
    realWorldStatePrimTy = mkStatePrimTy realWorldTy        -- State# RealWorld

    -- Note: the ``state-pairing'' types are not truly primitive,
    -- so they are defined in \tr{TysWiredIn.hs}, not here.

    voidPrimTy :: Type
    voidPrimTy = TyConApp voidPrimTyCon []

    voidPrimTyCon :: TyCon
    voidPrimTyCon    = pcPrimTyCon voidPrimTyConName [] VoidRep

    mkProxyPrimTy :: Type -> Type -> Type
    mkProxyPrimTy k ty = TyConApp proxyPrimTyCon [k, ty]

    proxyPrimTyCon :: TyCon
    proxyPrimTyCon = mkPrimTyCon proxyPrimTyConName binders res_kind [Nominal,Nominal]
      where binders  = [ Named kv Specified
                       , Anon k ]
            res_kind = tYPE voidRepDataConTy
            kv       = kKiVar
            k        = mkTyVarTy kv

    {- *********************************************************************
    *                                                                      *
                    Primitive equality constraints
        See Note [The equality types story]
    *                                                                      *
    ********************************************************************* -}

    eqPrimTyCon :: TyCon  -- The representation type for equality predicates
                          -- See Note [The equality types story]
    eqPrimTyCon  = mkPrimTyCon eqPrimTyConName binders res_kind roles
      where binders = [ Named kv1 Specified
                      , Named kv2 Specified
                      , Anon k1
                      , Anon k2 ]
            res_kind = tYPE voidRepDataConTy
            [kv1, kv2] = mkTemplateTyVars [liftedTypeKind, liftedTypeKind]
            k1 = mkTyVarTy kv1
            k2 = mkTyVarTy kv2
            roles = [Nominal, Nominal, Nominal, Nominal]

    -- like eqPrimTyCon, but the type for *Representational* coercions
    -- this should only ever appear as the type of a covar. Its role is
    -- interpreted in coercionRole
    eqReprPrimTyCon :: TyCon   -- See Note [The equality types story]
    eqReprPrimTyCon = mkPrimTyCon eqReprPrimTyConName binders res_kind roles
      where binders = [ Named kv1 Specified
                      , Named kv2 Specified
                      , Anon k1
                      , Anon k2 ]
            res_kind = tYPE voidRepDataConTy
            [kv1, kv2]    = mkTemplateTyVars [liftedTypeKind, liftedTypeKind]
            k1            = mkTyVarTy kv1
            k2            = mkTyVarTy kv2
            roles         = [Nominal, Nominal, Representational, Representational]

    -- like eqPrimTyCon, but the type for *Phantom* coercions.
    -- This is only used to make higher-order equalities. Nothing
    -- should ever actually have this type!
    eqPhantPrimTyCon :: TyCon
    eqPhantPrimTyCon = mkPrimTyCon eqPhantPrimTyConName binders res_kind
                                   [Nominal, Nominal, Phantom, Phantom]
      where binders = [ Named kv1 Specified
                      , Named kv2 Specified
                      , Anon k1
                      , Anon k2 ]
            res_kind = tYPE voidRepDataConTy
            [kv1, kv2]    = mkTemplateTyVars [liftedTypeKind, liftedTypeKind]
            k1            = mkTyVarTy kv1
            k2            = mkTyVarTy kv2

    {- *********************************************************************
    *                                                                      *
                 The primitive array types
    *                                                                      *
    ********************************************************************* -}

    arrayPrimTyCon, mutableArrayPrimTyCon, mutableByteArrayPrimTyCon,
        byteArrayPrimTyCon, arrayArrayPrimTyCon, mutableArrayArrayPrimTyCon,
        smallArrayPrimTyCon, smallMutableArrayPrimTyCon :: TyCon
    arrayPrimTyCon             = pcPrimTyCon arrayPrimTyConName             [Representational] PtrRep
    mutableArrayPrimTyCon      = pcPrimTyCon  mutableArrayPrimTyConName     [Nominal, Representational] PtrRep
    mutableByteArrayPrimTyCon  = pcPrimTyCon mutableByteArrayPrimTyConName  [Nominal] PtrRep
    byteArrayPrimTyCon         = pcPrimTyCon0 byteArrayPrimTyConName        PtrRep
    arrayArrayPrimTyCon        = pcPrimTyCon0 arrayArrayPrimTyConName       PtrRep
    mutableArrayArrayPrimTyCon = pcPrimTyCon mutableArrayArrayPrimTyConName [Nominal] PtrRep
    smallArrayPrimTyCon        = pcPrimTyCon smallArrayPrimTyConName        [Representational] PtrRep
    smallMutableArrayPrimTyCon = pcPrimTyCon smallMutableArrayPrimTyConName [Nominal, Representational] PtrRep

    mkArrayPrimTy :: Type -> Type
    mkArrayPrimTy elt           = TyConApp arrayPrimTyCon [elt]
    byteArrayPrimTy :: Type
    byteArrayPrimTy             = mkTyConTy byteArrayPrimTyCon
    mkArrayArrayPrimTy :: Type
    mkArrayArrayPrimTy = mkTyConTy arrayArrayPrimTyCon
    mkSmallArrayPrimTy :: Type -> Type
    mkSmallArrayPrimTy elt = TyConApp smallArrayPrimTyCon [elt]
    mkMutableArrayPrimTy :: Type -> Type -> Type
    mkMutableArrayPrimTy s elt  = TyConApp mutableArrayPrimTyCon [s, elt]
    mkMutableByteArrayPrimTy :: Type -> Type
    mkMutableByteArrayPrimTy s  = TyConApp mutableByteArrayPrimTyCon [s]
    mkMutableArrayArrayPrimTy :: Type -> Type
    mkMutableArrayArrayPrimTy s = TyConApp mutableArrayArrayPrimTyCon [s]
    mkSmallMutableArrayPrimTy :: Type -> Type -> Type
    mkSmallMutableArrayPrimTy s elt = TyConApp smallMutableArrayPrimTyCon [s, elt]

    {- *********************************************************************
    *                                                                      *
                    The mutable variable type
    *                                                                      *
    ********************************************************************* -}

    mutVarPrimTyCon :: TyCon
    mutVarPrimTyCon = pcPrimTyCon mutVarPrimTyConName [Nominal, Representational] PtrRep

    mkMutVarPrimTy :: Type -> Type -> Type
    mkMutVarPrimTy s elt        = TyConApp mutVarPrimTyCon [s, elt]

    {-
    ************************************************************************
    *                                                                      *
    \subsection[TysPrim-synch-var]{The synchronizing variable type}
    *                                                                      *
    ************************************************************************
    -}

    mVarPrimTyCon :: TyCon
    mVarPrimTyCon = pcPrimTyCon mVarPrimTyConName [Nominal, Representational] PtrRep

    mkMVarPrimTy :: Type -> Type -> Type
    mkMVarPrimTy s elt          = TyConApp mVarPrimTyCon [s, elt]

    {-
    ************************************************************************
    *                                                                      *
    \subsection[TysPrim-stm-var]{The transactional variable type}
    *                                                                      *
    ************************************************************************
    -}

    tVarPrimTyCon :: TyCon
    tVarPrimTyCon = pcPrimTyCon tVarPrimTyConName [Nominal, Representational] PtrRep

    mkTVarPrimTy :: Type -> Type -> Type
    mkTVarPrimTy s elt = TyConApp tVarPrimTyCon [s, elt]

    {-
    ************************************************************************
    *                                                                      *
    \subsection[TysPrim-stable-ptrs]{The stable-pointer type}
    *                                                                      *
    ************************************************************************
    -}

    stablePtrPrimTyCon :: TyCon
    stablePtrPrimTyCon = pcPrimTyCon stablePtrPrimTyConName [Representational] AddrRep

    mkStablePtrPrimTy :: Type -> Type
    mkStablePtrPrimTy ty = TyConApp stablePtrPrimTyCon [ty]

    {-
    ************************************************************************
    *                                                                      *
    \subsection[TysPrim-stable-names]{The stable-name type}
    *                                                                      *
    ************************************************************************
    -}

    stableNamePrimTyCon :: TyCon
    stableNamePrimTyCon = pcPrimTyCon stableNamePrimTyConName [Representational] PtrRep

    mkStableNamePrimTy :: Type -> Type
    mkStableNamePrimTy ty = TyConApp stableNamePrimTyCon [ty]

    {-
    ************************************************************************
    *                                                                      *
    \subsection[TysPrim-BCOs]{The ``bytecode object'' type}
    *                                                                      *
    ************************************************************************
    -}

    bcoPrimTy    :: Type
    bcoPrimTy    = mkTyConTy bcoPrimTyCon
    bcoPrimTyCon :: TyCon
    bcoPrimTyCon = pcPrimTyCon0 bcoPrimTyConName PtrRep

    {-
    ************************************************************************
    *                                                                      *
    \subsection[TysPrim-Weak]{The ``weak pointer'' type}
    *                                                                      *
    ************************************************************************
    -}

    weakPrimTyCon :: TyCon
    weakPrimTyCon = pcPrimTyCon weakPrimTyConName [Representational] PtrRep

    mkWeakPrimTy :: Type -> Type
    mkWeakPrimTy v = TyConApp weakPrimTyCon [v]

    {-
    ************************************************************************
    *                                                                      *
    \subsection[TysPrim-thread-ids]{The ``thread id'' type}
    *                                                                      *
    ************************************************************************

    A thread id is represented by a pointer to the TSO itself, to ensure
    that they are always unique and we can always find the TSO for a given
    thread id.  However, this has the unfortunate consequence that a
    ThreadId# for a given thread is treated as a root by the garbage
    collector and can keep TSOs around for too long.

    Hence the programmer API for thread manipulation uses a weak pointer
    to the thread id internally.
    -}

    threadIdPrimTy :: Type
    threadIdPrimTy    = mkTyConTy threadIdPrimTyCon
    threadIdPrimTyCon :: TyCon
    threadIdPrimTyCon = pcPrimTyCon0 threadIdPrimTyConName PtrRep

    {-
    ************************************************************************
    *                                                                      *
                    Any
    *                                                                      *
    ************************************************************************

    Note [Any types]
    ~~~~~~~~~~~~~~~~
    The type constructor Any of kind forall k. k has these properties:

      * It is defined in module GHC.Prim, and exported so that it is
        available to users.  For this reason it's treated like any other
        primitive type:
          - has a fixed unique, anyTyConKey,
          - lives in the global name cache

      * It is a *closed* type family, with no instances.  This means that
        if   ty :: '(k1, k2)  we add a given coercion
                 g :: ty ~ (Fst ty, Snd ty)
        If Any was a *data* type, then we'd get inconsistency because 'ty'
        could be (Any '(k1,k2)) and then we'd have an equality with Any on
        one side and '(,) on the other. See also #9097.

      * It is lifted, and hence represented by a pointer

      * It is inhabited by at least one value, namely bottom

      * You can unsafely coerce any lifted type to Any, and back.

      * It does not claim to be a *data* type, and that's important for
        the code generator, because the code gen may *enter* a data value
        but never enters a function value.

      * It is used to instantiate otherwise un-constrained type variables
        For example         length Any []
        See Note [Strangely-kinded void TyCons]

    Note [Strangely-kinded void TyCons]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    See Trac #959 for more examples

    When the type checker finds a type variable with no binding, which
    means it can be instantiated with an arbitrary type, it usually
    instantiates it to Void.  Eg.

            length []
    ===>
            length Any (Nil Any)

    But in really obscure programs, the type variable might have a kind
    other than *, so we need to invent a suitably-kinded type.

    This commit uses
            Any for kind *
            Any(*->*) for kind *->*
            etc
    -}

    anyTyConName :: Name
    anyTyConName = mkPrimTc (fsLit "Any") anyTyConKey anyTyCon

    anyTy :: Type
    anyTy = mkTyConTy anyTyCon

    anyTyCon :: TyCon
    anyTyCon = mkFamilyTyCon anyTyConName binders res_kind [kKiVar] Nothing
                             (ClosedSynFamilyTyCon Nothing)
                             Nothing
                             NotInjective
      where
        binders  = [Named kKiVar Specified]
        res_kind = mkTyVarTy kKiVar

    anyTypeOfKind :: Kind -> Type
    anyTypeOfKind kind = TyConApp anyTyCon [kind]

    {-
    ************************************************************************
    *                                                                      *
    \subsection{SIMD vector types}
    *                                                                      *
    ************************************************************************
    -}

    #include "primop-vector-tys.hs-incl"