NumHask usage examples

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

>>> 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)