numhask-prelude-0.5.0: A numeric prelude

Safe HaskellNone
LanguageHaskell2010

NumHask.Examples

Contents

Description

NumHask usage examples

Synopsis

    Imports and Pragmas

    NumHask.Prelude is a replacement for the standard prelude with the NoImplicitPrelude extension explicitly required.

    >>> :set -XNoImplicitPrelude
    >>> :set -XFlexibleContexts
    >>> :set -XRebindableSyntax
    >>> import NumHask.Prelude
    

    Int, Integer, Double and Float are from base. NumHask takes these classes and redefines the basic arithmetic operators.

    >>> 1 + 1
    2
    >>> 1 - 1
    0
    >>> 1 * 1
    1
    
    >>> 1.0 / 1.0
    1.0
    

    Note that the literal numbers in the divide above defaulted to Float rather than Int.

    >>> 1 / (1::Int)
    ...
    ... No instance for (Divisive Int) ...
    ...
    
    >>> 1.0 / fromInteger 1
    1.0
    

    RebindableSyntax removes the Haskell98 link between literal numbers and prelude. Literal numbers are pre-pended by ghc with fromInteger for integers and fromRational for decimals.

    >>> :set -XNoRebindableSyntax
    >>> :t 1
    1 :: Num p => p
    
    >>> :t 1.0
    1.0 :: Fractional p => p
    
    >>> :set -XRebindableSyntax
    >>> :t 1
    1 :: FromInteger a => a
    
    >>> :t 1.0
    1.0 :: FromRational a => a
    

    Float and Double are Field instances.

    >>> zero == 0.0
    True
    >>> one == 1.0
    True
    >>> 1.0 + 1.0
    2.0
    >>> 1.0 - 1.0
    0.0
    >>> 1.0 * 1.0
    1.0
    >>> 1.0 / 1.0
    1.0
    

    QuotientField

    >>> 1 `div` 2
    0
    >>> 3 `mod` 2
    1
    

    BoundedField

    >>> 1.0/0.0
    Infinity
    >>> -1.0/0.0
    -Infinity
    >>> 0.0/0.0 + 1.0
    NaN
    
    >>> one/zero
    Infinity
    
    >>> -one/zero
    -Infinity
    
    >>> zero/zero+one
    NaN
    

    ExpField

    >>> logBase 2 4
    2.0
    >>> 2 ** 2
    4.0
    >>> sqrt 4
    2.0
    >>> exp 2
    7.38905609893065
    >>> log 2
    0.6931471805599453
    

    Complex numbers

    >>> let a = 1 :+ 2
    >>> a
    1 :+ 2
    >>> zero - a
    (-1) :+ (-2)
    >>> (1 :+ (-2)) * ((-2) :+ 4)
    6 :+ 8
    
    >>> (1.0 :+ (-1.0)) / (2.0 :+ 2.0)
    0.0 :+ (-0.5)
    

    Vectors

    Matrices