GHC/Base.lhs

\section[GHC.Base]{Module @GHC.Base@} The overall structure of the GHC Prelude is a bit tricky. a) We want to avoid "orphan modules", i.e. ones with instance decls that don't belong either to a tycon or a class defined in the same module b) We want to avoid giant modules So the rough structure is as follows, in (linearised) dependency order GHC.Prim Has no implementation. It defines built-in things, and by importing it you bring them into scope. The source file is GHC.Prim.hi-boot, which is just copied to make GHC.Prim.hi GHC.Base Classes: Eq, Ord, Functor, Monad Types: list, (), Int, Bool, Ordering, Char, String Data.Tuple Types: tuples, plus instances for GHC.Base classes GHC.Show Class: Show, plus instances for GHC.Base/GHC.Tup types GHC.Enum Class: Enum, plus instances for GHC.Base/GHC.Tup types Data.Maybe Type: Maybe, plus instances for GHC.Base classes GHC.List List functions GHC.Num Class: Num, plus instances for Int Type: Integer, plus instances for all classes so far (Eq, Ord, Num, Show) Integer is needed here because it is mentioned in the signature of 'fromInteger' in class Num GHC.Real Classes: Real, Integral, Fractional, RealFrac plus instances for Int, Integer Types: Ratio, Rational plus intances for classes so far Rational is needed here because it is mentioned in the signature of 'toRational' in class Real GHC.ST The ST monad, instances and a few helper functions Ix Classes: Ix, plus instances for Int, Bool, Char, Integer, Ordering, tuples GHC.Arr Types: Array, MutableArray, MutableVar Arrays are used by a function in GHC.Float GHC.Float Classes: Floating, RealFloat Types: Float, Double, plus instances of all classes so far This module contains everything to do with floating point. It is a big module (900 lines) With a bit of luck, many modules can be compiled without ever reading GHC.Float.hi Other Prelude modules are much easier with fewer complex dependencies. \begin{code}

    {-# LANGUAGE Unsafe #-}
    {-# LANGUAGE CPP
               , NoImplicitPrelude
               , BangPatterns
               , ExplicitForAll
               , MagicHash
               , UnboxedTuples
               , ExistentialQuantification
               , RankNTypes
      #-}
    -- -fno-warn-orphans is needed for things like:
    -- Orphan rule: "x# -# x#" ALWAYS forall x# :: Int# -# x# x# = 0
    {-# OPTIONS_GHC -fno-warn-orphans #-}
    {-# OPTIONS_HADDOCK hide #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  GHC.Base
    -- Copyright   :  (c) The University of Glasgow, 1992-2002
    -- License     :  see libraries/base/LICENSE
    --
    -- Maintainer  :  cvs-ghc@haskell.org
    -- Stability   :  internal
    -- Portability :  non-portable (GHC extensions)
    --
    -- Basic data types and classes.
    --
    -----------------------------------------------------------------------------

    #include "MachDeps.h"

    module GHC.Base
            (
            module GHC.Base,
            module GHC.Classes,
            module GHC.CString,
            module GHC.Magic,
            module GHC.Types,
            module GHC.Prim,        -- Re-export GHC.Prim and [boot] GHC.Err,
                                    -- to avoid lots of people having to
            module GHC.Err          -- import it explicitly
      )
            where

    import GHC.Types
    import GHC.Classes
    import GHC.CString
    import GHC.Magic
    import GHC.Prim
    import GHC.Err
    import {-# SOURCE #-} GHC.IO (failIO)

    -- This is not strictly speaking required by this module, but is an
    -- implicit dependency whenever () or tuples are mentioned, so adding it
    -- as an import here helps to get the dependencies right in the new
    -- build system.
    import GHC.Tuple ()
    -- Likewise we need Integer when deriving things like Eq instances, and
    -- this is a convenient place to force it to be built
    import GHC.Integer ()

    infixr 9  .
    infixr 5  ++
    infixl 4  <$
    infixl 1  >>, >>=
    infixr 0  $

    default ()              -- Double isn't available yet

\end{code} %********************************************************* %* * \subsection{DEBUGGING STUFF} %* (for use when compiling GHC.Base itself doesn't work) %* * %********************************************************* \begin{code}

    {-
    data  Bool  =  False | True
    data Ordering = LT | EQ | GT
    data Char = C# Char#
    type  String = [Char]
    data Int = I# Int#
    data  ()  =  ()
    data [] a = MkNil

    not True = False
    (&&) True True = True
    otherwise = True

    build = error "urk"
    foldr = error "urk"
    -}

\end{code} %********************************************************* %* * \subsection{Monadic classes @Functor@, @Monad@ } %* * %********************************************************* \begin{code}

    {- | The 'Functor' class is used for types that can be mapped over.
    Instances of 'Functor' should satisfy the following laws:

    > fmap id  ==  id
    > fmap (f . g)  ==  fmap f . fmap g

    The instances of 'Functor' for lists, 'Data.Maybe.Maybe' and 'System.IO.IO'
    satisfy these laws.
    -}

    class  Functor f  where
        fmap        :: (a -> b) -> f a -> f b

        -- | Replace all locations in the input with the same value.
        -- The default definition is @'fmap' . 'const'@, but this may be
        -- overridden with a more efficient version.
        (<$)        :: a -> f b -> f a
        (<$)        =  fmap . const

    {- | The 'Monad' class defines the basic operations over a /monad/,
    a concept from a branch of mathematics known as /category theory/.
    From the perspective of a Haskell programmer, however, it is best to
    think of a monad as an /abstract datatype/ of actions.
    Haskell's @do@ expressions provide a convenient syntax for writing
    monadic expressions.

    Minimal complete definition: '>>=' and 'return'.

    Instances of 'Monad' should satisfy the following laws:

    > return a >>= k  ==  k a
    > m >>= return  ==  m
    > m >>= (\x -> k x >>= h)  ==  (m >>= k) >>= h

    Instances of both 'Monad' and 'Functor' should additionally satisfy the law:

    > fmap f xs  ==  xs >>= return . f

    The instances of 'Monad' for lists, 'Data.Maybe.Maybe' and 'System.IO.IO'
    defined in the "Prelude" satisfy these laws.
    -}

    class  Monad m  where
        -- | Sequentially compose two actions, passing any value produced
        -- by the first as an argument to the second.
        (>>=)       :: forall a b. m a -> (a -> m b) -> m b
        -- | Sequentially compose two actions, discarding any value produced
        -- by the first, like sequencing operators (such as the semicolon)
        -- in imperative languages.
        (>>)        :: forall a b. m a -> m b -> m b
            -- Explicit for-alls so that we know what order to
            -- give type arguments when desugaring

        -- | Inject a value into the monadic type.
        return      :: a -> m a
        -- | Fail with a message.  This operation is not part of the
        -- mathematical definition of a monad, but is invoked on pattern-match
        -- failure in a @do@ expression.
        fail        :: String -> m a

        {-# INLINE (>>) #-}
        m >> k      = m >>= \_ -> k
        fail s      = error s

    instance Functor ((->) r) where
        fmap = (.)

    instance Monad ((->) r) where
        return = const
        f >>= k = \ r -> k (f r) r

    instance Functor ((,) a) where
        fmap f (x,y) = (x, f y)

\end{code} %********************************************************* %* * \subsection{The list type} %* * %********************************************************* \begin{code}

    instance Functor [] where
        fmap = map

    instance  Monad []  where
        m >>= k             = foldr ((++) . k) [] m
        m >> k              = foldr ((++) . (\ _ -> k)) [] m
        return x            = [x]
        fail _              = []

\end{code} A few list functions that appear here because they are used here. The rest of the prelude list functions are in GHC.List. ---------------------------------------------- -- foldr/build/augment ---------------------------------------------- \begin{code}

    -- | 'foldr', applied to a binary operator, a starting value (typically
    -- the right-identity of the operator), and a list, reduces the list
    -- using the binary operator, from right to left:
    --
    -- > foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

    foldr            :: (a -> b -> b) -> b -> [a] -> b
    -- foldr _ z []     =  z
    -- foldr f z (x:xs) =  f x (foldr f z xs)
    {-# INLINE [0] foldr #-}
    -- Inline only in the final stage, after the foldr/cons rule has had a chance
    -- Also note that we inline it when it has *two* parameters, which are the
    -- ones we are keen about specialising!
    foldr k z = go
              where
                go []     = z
                go (y:ys) = y `k` go ys

    -- | A list producer that can be fused with 'foldr'.
    -- This function is merely
    --
    -- >    build g = g (:) []
    --
    -- but GHC's simplifier will transform an expression of the form
    -- @'foldr' k z ('build' g)@, which may arise after inlining, to @g k z@,
    -- which avoids producing an intermediate list.

    build   :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
    {-# INLINE [1] build #-}
            -- The INLINE is important, even though build is tiny,
            -- because it prevents [] getting inlined in the version that
            -- appears in the interface file.  If [] *is* inlined, it
            -- won't match with [] appearing in rules in an importing module.
            --
            -- The "1" says to inline in phase 1

    build g = g (:) []

    -- | A list producer that can be fused with 'foldr'.
    -- This function is merely
    --
    -- >    augment g xs = g (:) xs
    --
    -- but GHC's simplifier will transform an expression of the form
    -- @'foldr' k z ('augment' g xs)@, which may arise after inlining, to
    -- @g k ('foldr' k z xs)@, which avoids producing an intermediate list.

    augment :: forall a. (forall b. (a->b->b) -> b -> b) -> [a] -> [a]
    {-# INLINE [1] augment #-}
    augment g xs = g (:) xs

    {-# RULES
    "fold/build"    forall k z (g::forall b. (a->b->b) -> b -> b) .
                    foldr k z (build g) = g k z

    "foldr/augment" forall k z xs (g::forall b. (a->b->b) -> b -> b) .
                    foldr k z (augment g xs) = g k (foldr k z xs)

    "foldr/id"                        foldr (:) [] = \x  -> x
    "foldr/app"     [1] forall ys. foldr (:) ys = \xs -> xs ++ ys
            -- Only activate this from phase 1, because that's
            -- when we disable the rule that expands (++) into foldr

    -- The foldr/cons rule looks nice, but it can give disastrously
    -- bloated code when commpiling
    --      array (a,b) [(1,2), (2,2), (3,2), ...very long list... ]
    -- i.e. when there are very very long literal lists
    -- So I've disabled it for now. We could have special cases
    -- for short lists, I suppose.
    -- "foldr/cons" forall k z x xs. foldr k z (x:xs) = k x (foldr k z xs)

    "foldr/single"  forall k z x. foldr k z [x] = k x z
    "foldr/nil"     forall k z.   foldr k z []  = z

    "augment/build" forall (g::forall b. (a->b->b) -> b -> b)
                           (h::forall b. (a->b->b) -> b -> b) .
                           augment g (build h) = build (\c n -> g c (h c n))
    "augment/nil"   forall (g::forall b. (a->b->b) -> b -> b) .
                            augment g [] = build g
     #-}

    -- This rule is true, but not (I think) useful:
    --      augment g (augment h t) = augment (\cn -> g c (h c n)) t

\end{code} ---------------------------------------------- -- map ---------------------------------------------- \begin{code}

    -- | 'map' @f xs@ is the list obtained by applying @f@ to each element
    -- of @xs@, i.e.,
    --
    -- > map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
    -- > map f [x1, x2, ...] == [f x1, f x2, ...]

    map :: (a -> b) -> [a] -> [b]
    {-# NOINLINE [1] map #-}    -- We want the RULE to fire first.
                                -- It's recursive, so won't inline anyway,
                                -- but saying so is more explicit
    map _ []     = []
    map f (x:xs) = f x : map f xs

    -- Note eta expanded
    mapFB ::  (elt -> lst -> lst) -> (a -> elt) -> a -> lst -> lst
    {-# INLINE [0] mapFB #-}
    mapFB c f = \x ys -> c (f x) ys

    -- The rules for map work like this.
    --
    -- Up to (but not including) phase 1, we use the "map" rule to
    -- rewrite all saturated applications of map with its build/fold
    -- form, hoping for fusion to happen.
    -- In phase 1 and 0, we switch off that rule, inline build, and
    -- switch on the "mapList" rule, which rewrites the foldr/mapFB
    -- thing back into plain map.
    --
    -- It's important that these two rules aren't both active at once
    -- (along with build's unfolding) else we'd get an infinite loop
    -- in the rules.  Hence the activation control below.
    --
    -- The "mapFB" rule optimises compositions of map.
    --
    -- This same pattern is followed by many other functions:
    -- e.g. append, filter, iterate, repeat, etc.

    {-# RULES
    "map"       [~1] forall f xs.   map f xs                = build (\c n -> foldr (mapFB c f) n xs)
    "mapList"   [1]  forall f.      foldr (mapFB (:) f) []  = map f
    "mapFB"     forall c f g.       mapFB (mapFB c f) g     = mapFB c (f.g)
      #-}

\end{code} ---------------------------------------------- -- append ---------------------------------------------- \begin{code}

    -- | Append two lists, i.e.,
    --
    -- > [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
    -- > [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
    --
    -- If the first list is not finite, the result is the first list.

    (++) :: [a] -> [a] -> [a]
    {-# NOINLINE [1] (++) #-}    -- We want the RULE to fire first.
                                 -- It's recursive, so won't inline anyway,
                                 -- but saying so is more explicit
    (++) []     ys = ys
    (++) (x:xs) ys = x : xs ++ ys

    {-# RULES
    "++"    [~1] forall xs ys. xs ++ ys = augment (\c n -> foldr c n xs) ys
      #-}

\end{code} %********************************************************* %* * \subsection{Type @Bool@} %* * %********************************************************* \begin{code}

    -- |'otherwise' is defined as the value 'True'.  It helps to make
    -- guards more readable.  eg.
    --
    -- >  f x | x < 0     = ...
    -- >      | otherwise = ...
    otherwise               :: Bool
    otherwise               =  True

\end{code} %********************************************************* %* * \subsection{Type @Char@ and @String@} %* * %********************************************************* \begin{code}

    -- | A 'String' is a list of characters.  String constants in Haskell are values
    -- of type 'String'.
    --
    type String = [Char]

    unsafeChr :: Int -> Char
    unsafeChr (I# i#) = C# (chr# i#)

    -- | The 'Prelude.fromEnum' method restricted to the type 'Data.Char.Char'.
    ord :: Char -> Int
    ord (C# c#) = I# (ord# c#)

\end{code} String equality is used when desugaring pattern-matches against strings. \begin{code}

    eqString :: String -> String -> Bool
    eqString []       []       = True
    eqString (c1:cs1) (c2:cs2) = c1 == c2 && cs1 `eqString` cs2
    eqString _        _        = False

    {-# RULES "eqString" (==) = eqString #-}
    -- eqString also has a BuiltInRule in PrelRules.lhs:
    --      eqString (unpackCString# (Lit s1)) (unpackCString# (Lit s2) = s1==s2

\end{code} %********************************************************* %* * \subsection{Type @Int@} %* * %********************************************************* \begin{code}

    maxInt, minInt :: Int

    {- Seems clumsy. Should perhaps put minInt and MaxInt directly into MachDeps.h -}
    #if WORD_SIZE_IN_BITS == 31
    minInt  = I# (-0x40000000#)
    maxInt  = I# 0x3FFFFFFF#
    #elif WORD_SIZE_IN_BITS == 32
    minInt  = I# (-0x80000000#)
    maxInt  = I# 0x7FFFFFFF#
    #else
    minInt  = I# (-0x8000000000000000#)
    maxInt  = I# 0x7FFFFFFFFFFFFFFF#
    #endif

\end{code} %********************************************************* %* * \subsection{The function type} %* * %********************************************************* \begin{code}

    -- | Identity function.
    id                      :: a -> a
    id x                    =  x

    -- Assertion function.  This simply ignores its boolean argument.
    -- The compiler may rewrite it to @('assertError' line)@.

    -- | If the first argument evaluates to 'True', then the result is the
    -- second argument.  Otherwise an 'AssertionFailed' exception is raised,
    -- containing a 'String' with the source file and line number of the
    -- call to 'assert'.
    --
    -- Assertions can normally be turned on or off with a compiler flag
    -- (for GHC, assertions are normally on unless optimisation is turned on
    -- with @-O@ or the @-fignore-asserts@
    -- option is given).  When assertions are turned off, the first
    -- argument to 'assert' is ignored, and the second argument is
    -- returned as the result.

    --      SLPJ: in 5.04 etc 'assert' is in GHC.Prim,
    --      but from Template Haskell onwards it's simply
    --      defined here in Base.lhs
    assert :: Bool -> a -> a
    assert _pred r = r

    breakpoint :: a -> a
    breakpoint r = r

    breakpointCond :: Bool -> a -> a
    breakpointCond _ r = r

    data Opaque = forall a. O a

    -- | Constant function.
    const                   :: a -> b -> a
    const x _               =  x

    -- | Function composition.
    {-# INLINE (.) #-}
    -- Make sure it has TWO args only on the left, so that it inlines
    -- when applied to two functions, even if there is no final argument
    (.)    :: (b -> c) -> (a -> b) -> a -> c
    (.) f g = \x -> f (g x)

    -- | @'flip' f@ takes its (first) two arguments in the reverse order of @f@.
    flip                    :: (a -> b -> c) -> b -> a -> c
    flip f x y              =  f y x

    -- | Application operator.  This operator is redundant, since ordinary
    -- application @(f x)@ means the same as @(f '$' x)@. However, '$' has
    -- low, right-associative binding precedence, so it sometimes allows
    -- parentheses to be omitted; for example:
    --
    -- >     f $ g $ h x  =  f (g (h x))
    --
    -- It is also useful in higher-order situations, such as @'map' ('$' 0) xs@,
    -- or @'Data.List.zipWith' ('$') fs xs@.
    {-# INLINE ($) #-}
    ($)                     :: (a -> b) -> a -> b
    f $ x                   =  f x

    -- | @'until' p f@ yields the result of applying @f@ until @p@ holds.
    until                   :: (a -> Bool) -> (a -> a) -> a -> a
    until p f = go
      where
        go x | p x          = x
             | otherwise    = go (f x)

    -- | 'asTypeOf' is a type-restricted version of 'const'.  It is usually
    -- used as an infix operator, and its typing forces its first argument
    -- (which is usually overloaded) to have the same type as the second.
    asTypeOf                :: a -> a -> a
    asTypeOf                =  const

\end{code} %********************************************************* %* * \subsection{@Functor@ and @Monad@ instances for @IO@} %* * %********************************************************* \begin{code}

    instance  Functor IO where
       fmap f x = x >>= (return . f)

    instance  Monad IO  where
        {-# INLINE return #-}
        {-# INLINE (>>)   #-}
        {-# INLINE (>>=)  #-}
        m >> k    = m >>= \ _ -> k
        return    = returnIO
        (>>=)     = bindIO
        fail s    = failIO s

    returnIO :: a -> IO a
    returnIO x = IO $ \ s -> (# s, x #)

    bindIO :: IO a -> (a -> IO b) -> IO b
    bindIO (IO m) k = IO $ \ s -> case m s of (# new_s, a #) -> unIO (k a) new_s

    thenIO :: IO a -> IO b -> IO b
    thenIO (IO m) k = IO $ \ s -> case m s of (# new_s, _ #) -> unIO k new_s

    unIO :: IO a -> (State# RealWorld -> (# State# RealWorld, a #))
    unIO (IO a) = a

\end{code} %********************************************************* %* * \subsection{@getTag@} %* * %********************************************************* Returns the 'tag' of a constructor application; this function is used by the deriving code for Eq, Ord and Enum. The primitive dataToTag# requires an evaluated constructor application as its argument, so we provide getTag as a wrapper that performs the evaluation before calling dataToTag#. We could have dataToTag# evaluate its argument, but we prefer to do it this way because (a) dataToTag# can be an inline primop if it doesn't need to do any evaluation, and (b) we want to expose the evaluation to the simplifier, because it might be possible to eliminate the evaluation in the case when the argument is already known to be evaluated. \begin{code}

    {-# INLINE getTag #-}
    getTag :: a -> Int#
    getTag x = x `seq` dataToTag# x

\end{code} %********************************************************* %* * \subsection{Numeric primops} %* * %********************************************************* Definitions of the boxed PrimOps; these will be used in the case of partial applications, etc. \begin{code}

    {-# INLINE quotInt #-}
    {-# INLINE remInt #-}

    quotInt, remInt, divInt, modInt :: Int -> Int -> Int
    (I# x) `quotInt`  (I# y) = I# (x `quotInt#` y)
    (I# x) `remInt`   (I# y) = I# (x `remInt#`  y)
    (I# x) `divInt`   (I# y) = I# (x `divInt#`  y)
    (I# x) `modInt`   (I# y) = I# (x `modInt#`  y)

    quotRemInt :: Int -> Int -> (Int, Int)
    (I# x) `quotRemInt` (I# y) = case x `quotRemInt#` y of
                                 (# q, r #) ->
                                     (I# q, I# r)

    divModInt :: Int -> Int -> (Int, Int)
    (I# x) `divModInt` (I# y) = case x `divModInt#` y of
                                (# q, r #) -> (I# q, I# r)

    divModInt# :: Int# -> Int# -> (# Int#, Int# #)
    x# `divModInt#` y#
     | isTrue# (x# ># 0#) && isTrue# (y# <# 0#) =
                                        case (x# -# 1#) `quotRemInt#` y# of
                                          (# q, r #) -> (# q -# 1#, r +# y# +# 1# #)
     | isTrue# (x# <# 0#) && isTrue# (y# ># 0#) =
                                        case (x# +# 1#) `quotRemInt#` y# of
                                          (# q, r #) -> (# q -# 1#, r +# y# -# 1# #)
     | otherwise                                =
                                        x# `quotRemInt#` y#

    -- Wrappers for the shift operations.  The uncheckedShift# family are
    -- undefined when the amount being shifted by is greater than the size
    -- in bits of Int#, so these wrappers perform a check and return
    -- either zero or -1 appropriately.
    --
    -- Note that these wrappers still produce undefined results when the
    -- second argument (the shift amount) is negative.

    -- | Shift the argument left by the specified number of bits
    -- (which must be non-negative).
    shiftL# :: Word# -> Int# -> Word#
    a `shiftL#` b   | isTrue# (b >=# WORD_SIZE_IN_BITS#) = 0##
                    | otherwise                          = a `uncheckedShiftL#` b

    -- | Shift the argument right by the specified number of bits
    -- (which must be non-negative).
    shiftRL# :: Word# -> Int# -> Word#
    a `shiftRL#` b  | isTrue# (b >=# WORD_SIZE_IN_BITS#) = 0##
                    | otherwise                          = a `uncheckedShiftRL#` b

    -- | Shift the argument left by the specified number of bits
    -- (which must be non-negative).
    iShiftL# :: Int# -> Int# -> Int#
    a `iShiftL#` b  | isTrue# (b >=# WORD_SIZE_IN_BITS#) = 0#
                    | otherwise                          = a `uncheckedIShiftL#` b

    -- | Shift the argument right (signed) by the specified number of bits
    -- (which must be non-negative).
    iShiftRA# :: Int# -> Int# -> Int#
    a `iShiftRA#` b | isTrue# (b >=# WORD_SIZE_IN_BITS#) = if isTrue# (a <# 0#)
                                                              then (-1#)
                                                              else 0#
                    | otherwise                          = a `uncheckedIShiftRA#` b

    -- | Shift the argument right (unsigned) by the specified number of bits
    -- (which must be non-negative).
    iShiftRL# :: Int# -> Int# -> Int#
    a `iShiftRL#` b | isTrue# (b >=# WORD_SIZE_IN_BITS#) = 0#
                    | otherwise                          = a `uncheckedIShiftRL#` b

    -- Rules for C strings (the functions themselves are now in GHC.CString)
    {-# RULES
    "unpack"       [~1] forall a   . unpackCString# a             = build (unpackFoldrCString# a)
    "unpack-list"  [1]  forall a   . unpackFoldrCString# a (:) [] = unpackCString# a
    "unpack-append"     forall a n . unpackFoldrCString# a (:) n  = unpackAppendCString# a n

    -- There's a built-in rule (in PrelRules.lhs) for
    --      unpackFoldr "foo" c (unpackFoldr "baz" c n)  =  unpackFoldr "foobaz" c n

      #-}

\end{code} #ifdef __HADDOCK__ \begin{code}

    -- | A special argument for the 'Control.Monad.ST.ST' type constructor,
    -- indexing a state embedded in the 'Prelude.IO' monad by
    -- 'Control.Monad.ST.stToIO'.
    data RealWorld

\end{code} #endif