\begin{code}
-{-# OPTIONS -fno-implicit-prelude #-}
+{-# OPTIONS_GHC -fno-implicit-prelude #-}
-----------------------------------------------------------------------------
-- |
-- Module : GHC.Num
import {-# SOURCE #-} GHC.Err
import GHC.Base
-import GHC.List
import GHC.Enum
import GHC.Show
%*********************************************************
\begin{code}
+-- | Basic numeric class.
+--
+-- Minimal complete definition: all except 'negate' or @(-)@
class (Eq a, Show a) => Num a where
(+), (-), (*) :: a -> a -> a
+ -- | Unary negation.
negate :: a -> a
- abs, signum :: a -> a
+ -- | Absolute value.
+ abs :: a -> a
+ -- | Sign of a number.
+ -- The functions 'abs' and 'signum' should satisfy the law:
+ --
+ -- > abs x * signum x == x
+ --
+ -- For real numbers, the 'signum' is either @-1@ (negative), @0@ (zero)
+ -- or @1@ (positive).
+ signum :: a -> a
+ -- | Conversion from an 'Integer'.
+ -- An integer literal represents the application of the function
+ -- 'fromInteger' to the appropriate value of type 'Integer',
+ -- so such literals have type @('Num' a) => a@.
fromInteger :: Integer -> a
x - y = x + negate y
negate x = 0 - x
+-- | the same as @'flip' ('-')@.
+--
+-- Because @-@ is treated specially in the Haskell grammar,
+-- @(-@ /e/@)@ is not a section, but an application of prefix negation.
+-- However, @('subtract'@ /exp/@)@ is equivalent to the disallowed section.
{-# INLINE subtract #-}
subtract :: (Num a) => a -> a -> a
subtract x y = y - x
| otherwise = 1
fromInteger = integer2Int
-\end{code}
-
-
-\begin{code}
--- These can't go in GHC.Base with the defn of Int, because
--- we don't have pairs defined at that time!
quotRemInt :: Int -> Int -> (Int, Int)
-a@(I# _) `quotRemInt` b@(I# _) = (a `quotInt` b, a `remInt` b)
+quotRemInt a@(I# _) b@(I# _) = (a `quotInt` b, a `remInt` b)
-- OK, so I made it a little stricter. Shoot me. (WDP 94/10)
divModInt :: Int -> Int -> (Int, Int)
-- Stricter. Sorry if you don't like it. (WDP 94/10)
\end{code}
-
%*********************************************************
%* *
\subsection{The @Integer@ type}