    {-# LANGUAGE Trustworthy #-}
    {-# LANGUAGE NoImplicitPrelude, MagicHash, StandaloneDeriving, BangPatterns #-}
    {-# OPTIONS_GHC -fno-warn-unused-imports #-}
    -- XXX -fno-warn-unused-imports needed for the GHC.Tuple import below. Sigh.
    {-# OPTIONS_HADDOCK hide #-}
    -----------------------------------------------------------------------------
    -- |
    -- Module      :  GHC.Classes
    -- 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 classes.
    --
    -----------------------------------------------------------------------------

    module GHC.Classes where

    -- GHC.Magic is used in some derived instances
    import GHC.Magic ()
    import GHC.Prim
    import GHC.Tuple
    import GHC.Types

    infix  4  ==, /=, <, <=, >=, >
    infixr 3  &&
    infixr 2  ||

    default ()              -- Double isn't available yet

    -- | The 'Eq' class defines equality ('==') and inequality ('/=').
    -- All the basic datatypes exported by the "Prelude" are instances of 'Eq',
    -- and 'Eq' may be derived for any datatype whose constituents are also
    -- instances of 'Eq'.
    --
    -- Minimal complete definition: either '==' or '/='.
    --
    class  Eq a  where
        (==), (/=)           :: a -> a -> Bool

        {-# INLINE (/=) #-}
        {-# INLINE (==) #-}
        x /= y               = not (x == y)
        x == y               = not (x /= y)
        {-# MINIMAL (==) | (/=) #-}

    deriving instance Eq ()
    deriving instance (Eq  a, Eq  b) => Eq  (a, b)
    deriving instance (Eq  a, Eq  b, Eq  c) => Eq  (a, b, c)
    deriving instance (Eq  a, Eq  b, Eq  c, Eq  d) => Eq  (a, b, c, d)
    deriving instance (Eq  a, Eq  b, Eq  c, Eq  d, Eq  e) => Eq  (a, b, c, d, e)
    deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f)
                   => Eq (a, b, c, d, e, f)
    deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g)
                   => Eq (a, b, c, d, e, f, g)
    deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g,
                       Eq h)
                   => Eq (a, b, c, d, e, f, g, h)
    deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g,
                       Eq h, Eq i)
                   => Eq (a, b, c, d, e, f, g, h, i)
    deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g,
                       Eq h, Eq i, Eq j)
                   => Eq (a, b, c, d, e, f, g, h, i, j)
    deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g,
                       Eq h, Eq i, Eq j, Eq k)
                   => Eq (a, b, c, d, e, f, g, h, i, j, k)
    deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g,
                       Eq h, Eq i, Eq j, Eq k, Eq l)
                   => Eq (a, b, c, d, e, f, g, h, i, j, k, l)
    deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g,
                       Eq h, Eq i, Eq j, Eq k, Eq l, Eq m)
                   => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m)
    deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g,
                       Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n)
                   => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n)
    deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g,
                       Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o)
                   => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

    instance (Eq a) => Eq [a] where
        {-# SPECIALISE instance Eq [[Char]] #-}
        {-# SPECIALISE instance Eq [Char] #-}
        {-# SPECIALISE instance Eq [Int] #-}
        []     == []     = True
        (x:xs) == (y:ys) = x == y && xs == ys
        _xs    == _ys    = False

    deriving instance Eq Bool
    deriving instance Eq Ordering
    deriving instance Eq Word

    instance Eq Char where
        (C# c1) == (C# c2) = isTrue# (c1 `eqChar#` c2)
        (C# c1) /= (C# c2) = isTrue# (c1 `neChar#` c2)

    instance Eq Float where
        (F# x) == (F# y) = isTrue# (x `eqFloat#` y)

    instance Eq Double where
        (D# x) == (D# y) = isTrue# (x ==## y)

    instance Eq Int where
        (==) = eqInt
        (/=) = neInt

    {-# INLINE eqInt #-}
    {-# INLINE neInt #-}
    eqInt, neInt :: Int -> Int -> Bool
    (I# x) `eqInt` (I# y) = isTrue# (x ==# y)
    (I# x) `neInt` (I# y) = isTrue# (x /=# y)

    -- | The 'Ord' class is used for totally ordered datatypes.
    --
    -- Instances of 'Ord' can be derived for any user-defined
    -- datatype whose constituent types are in 'Ord'.  The declared order
    -- of the constructors in the data declaration determines the ordering
    -- in derived 'Ord' instances.  The 'Ordering' datatype allows a single
    -- comparison to determine the precise ordering of two objects.
    --
    -- Minimal complete definition: either 'compare' or '<='.
    -- Using 'compare' can be more efficient for complex types.
    --
    class  (Eq a) => Ord a  where
        compare              :: a -> a -> Ordering
        (<), (<=), (>), (>=) :: a -> a -> Bool
        max, min             :: a -> a -> a

        compare x y = if x == y then EQ
                      -- NB: must be '<=' not '<' to validate the
                      -- above claim about the minimal things that
                      -- can be defined for an instance of Ord:
                      else if x <= y then LT
                      else GT

        x <  y = case compare x y of { LT -> True;  _ -> False }
        x <= y = case compare x y of { GT -> False; _ -> True }
        x >  y = case compare x y of { GT -> True;  _ -> False }
        x >= y = case compare x y of { LT -> False; _ -> True }

            -- These two default methods use '<=' rather than 'compare'
            -- because the latter is often more expensive
        max x y = if x <= y then y else x
        min x y = if x <= y then x else y
        {-# MINIMAL compare | (<=) #-}

    deriving instance Ord ()
    deriving instance (Ord a, Ord b) => Ord (a, b)
    deriving instance (Ord a, Ord b, Ord c) => Ord (a, b, c)
    deriving instance (Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d)
    deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e)
    deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f)
                   => Ord (a, b, c, d, e, f)
    deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g)
                   => Ord (a, b, c, d, e, f, g)
    deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g,
                       Ord h)
                   => Ord (a, b, c, d, e, f, g, h)
    deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g,
                       Ord h, Ord i)
                   => Ord (a, b, c, d, e, f, g, h, i)
    deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g,
                       Ord h, Ord i, Ord j)
                   => Ord (a, b, c, d, e, f, g, h, i, j)
    deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g,
                       Ord h, Ord i, Ord j, Ord k)
                   => Ord (a, b, c, d, e, f, g, h, i, j, k)
    deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g,
                       Ord h, Ord i, Ord j, Ord k, Ord l)
                   => Ord (a, b, c, d, e, f, g, h, i, j, k, l)
    deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g,
                       Ord h, Ord i, Ord j, Ord k, Ord l, Ord m)
                   => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m)
    deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g,
                       Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n)
                   => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n)
    deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g,
                       Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o)
                   => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

    instance (Ord a) => Ord [a] where
        {-# SPECIALISE instance Ord [[Char]] #-}
        {-# SPECIALISE instance Ord [Char] #-}
        {-# SPECIALISE instance Ord [Int] #-}
        compare []     []     = EQ
        compare []     (_:_)  = LT
        compare (_:_)  []     = GT
        compare (x:xs) (y:ys) = case compare x y of
                                    EQ    -> compare xs ys
                                    other -> other

    deriving instance Ord Bool
    deriving instance Ord Ordering
    deriving instance Ord Word

    -- We don't use deriving for Ord Char, because for Ord the derived
    -- instance defines only compare, which takes two primops.  Then
    -- '>' uses compare, and therefore takes two primops instead of one.
    instance Ord Char where
        (C# c1) >  (C# c2) = isTrue# (c1 `gtChar#` c2)
        (C# c1) >= (C# c2) = isTrue# (c1 `geChar#` c2)
        (C# c1) <= (C# c2) = isTrue# (c1 `leChar#` c2)
        (C# c1) <  (C# c2) = isTrue# (c1 `ltChar#` c2)

    instance Ord Float where
        (F# x) `compare` (F# y)
            = if      isTrue# (x `ltFloat#` y) then LT
              else if isTrue# (x `eqFloat#` y) then EQ
              else                                  GT

        (F# x) <  (F# y) = isTrue# (x `ltFloat#` y)
        (F# x) <= (F# y) = isTrue# (x `leFloat#` y)
        (F# x) >= (F# y) = isTrue# (x `geFloat#` y)
        (F# x) >  (F# y) = isTrue# (x `gtFloat#` y)

    instance Ord Double where
        (D# x) `compare` (D# y)
            = if      isTrue# (x <##  y) then LT
              else if isTrue# (x ==## y) then EQ
              else                            GT

        (D# x) <  (D# y) = isTrue# (x <##  y)
        (D# x) <= (D# y) = isTrue# (x <=## y)
        (D# x) >= (D# y) = isTrue# (x >=## y)
        (D# x) >  (D# y) = isTrue# (x >##  y)

    instance Ord Int where
        compare = compareInt
        (<)     = ltInt
        (<=)    = leInt
        (>=)    = geInt
        (>)     = gtInt

    {-# INLINE gtInt #-}
    {-# INLINE geInt #-}
    {-# INLINE ltInt #-}
    {-# INLINE leInt #-}
    gtInt, geInt, ltInt, leInt :: Int -> Int -> Bool
    (I# x) `gtInt` (I# y) = isTrue# (x >#  y)
    (I# x) `geInt` (I# y) = isTrue# (x >=# y)
    (I# x) `ltInt` (I# y) = isTrue# (x <#  y)
    (I# x) `leInt` (I# y) = isTrue# (x <=# y)

    compareInt :: Int -> Int -> Ordering
    (I# x#) `compareInt` (I# y#) = compareInt# x# y#

    compareInt# :: Int# -> Int# -> Ordering
    compareInt# x# y#
        | isTrue# (x# <#  y#) = LT
        | isTrue# (x# ==# y#) = EQ
        | True                = GT

    -- OK, so they're technically not part of a class...:

    -- Boolean functions

    -- | Boolean \"and\"
    (&&)                    :: Bool -> Bool -> Bool
    True  && x              =  x
    False && _              =  False

    -- | Boolean \"or\"
    (||)                    :: Bool -> Bool -> Bool
    True  || _              =  True
    False || x              =  x

    -- | Boolean \"not\"
    not                     :: Bool -> Bool
    not True                =  False
    not False               =  True

    ------------------------------------------------------------------------
    -- These don't really belong here, but we don't have a better place to
    -- put them

    divInt# :: Int# -> Int# -> Int#
    x# `divInt#` y#
            -- Be careful NOT to overflow if we do any additional arithmetic
            -- on the arguments...  the following  previous version of this
            -- code has problems with overflow:
    --    | (x# ># 0#) && (y# <# 0#) = ((x# -# y#) -# 1#) `quotInt#` y#
    --    | (x# <# 0#) && (y# ># 0#) = ((x# -# y#) +# 1#) `quotInt#` y#
        =      if isTrue# (x# ># 0#) && isTrue# (y# <# 0#) then ((x# -# 1#) `quotInt#` y#) -# 1#
          else if isTrue# (x# <# 0#) && isTrue# (y# ># 0#) then ((x# +# 1#) `quotInt#` y#) -# 1#
          else x# `quotInt#` y#

    modInt# :: Int# -> Int# -> Int#
    x# `modInt#` y#
        = if isTrue# (x# ># 0#) && isTrue# (y# <# 0#) ||
             isTrue# (x# <# 0#) && isTrue# (y# ># 0#)
          then if isTrue# (r# /=# 0#) then r# +# y# else 0#
          else r#
        where
        !r# = x# `remInt#` y#