NumHask usage examples

NumHask.Prelude is a complete replacement for the standard prelude.

NoImplicitPrelude is explicitly required as a pragma, and ExtendedDefaultRules is needed to avoid having to explicitly type literal numbers.

>>> :set -XNoImplicitPrelude
>>> :set -XExtendedDefaultRules
>>> 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 / 1
1.0

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

>>> 1 / (1::Int)
...
... No instance for (MultiplicativeGroup Int)
... arising from a use of ‘/’
...

>>> 1 / fromIntegral (1::Int)
1.0

>>> 1 `div` 2
0

>>> 3 `mod` 2
1

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

BoundedField lets divide by zero work for Floats and Doubles.

>>> one/zero
Infinity

>>> -one/zero
-Infinity

>>> zero/zero+one
NaN

>>> logBase 2 4
2.0

>>> 2 ** 2
4.0

>>> sqrt 4
2.0

>>> exp 2
7.38905609893065

>>> log 2
0.6931471805599453

A Vector is a number by virtue of it being a Representable Functor where the representation is an Int.

>>> import NumHask.Vector
>>> :set -XDataKinds
>>> :set -XOverloadedLists
>>> [] :: Vector 3 Int
[0,0,0]

>>> let a = [1..] :: Vector 3 Int
>>> a
[1,2,3]

>>> let b = [3,2] :: Vector 3 Int
>>> b
[3,2,0]

>>> let c = [1.0,2.0] :: Vector 3 Float
>>> let d = [3.0,2.0] :: Vector 3 Float

>>> a+zero==a
True
>>> zero+a==a
True
>>> a+b
[4,4,3]

>>> a-a == zero
True

>>> a * b
[3,4,0]

>>> let a' = unsafeToVector . someVector $ a :: Vector 2 Int
>>> let b' = unsafeToVector . someVector $ b :: Vector 2 Int
>>> a' `divMod` b'
([0,1],[1,0])

>>> c / d
[0.33333334,1.0,NaN]

>>> size c :: Float
2.236068

>>> distance c d :: Float
2.0

>>> c <.> d :: Float
7.0

The type of an outer product of two vectors is a Vector m (Vector n), and is a perfectly formed Matrix representation.

>>> a >< b
[[3,2,0],[6,4,0],[9,6,0]]

>>> (a >< b) >< (b >< a)
[[[9,12,0],[6,8,0],[0,0,0]],[[18,24,0],[12,16,0],[0,0,0]],[[27,36,0],[18,24,0],[0,0,0]]]