Multi-dimensional arrays for numhask.

import NumHask.Array

imports the fixed version of Array and Shape

In many situations, where shape is being tracked or otherwise only known at runtime, a clear module arrangement is:

import NumHask.Array.Shape
import qualified NumHask.Array.Fixed as F
import qualified NumHask.Array.Dynamic as D

Arrays are higher-kinded numbers that can be indexed into with an [Int]. Higher-kinded numbers are things with a non-primitive type that we wish to use the usual numerical operators on: +,-,*,/,abs,tan and so on.

The design of numhask-array:

• allows shape to be specified at both the type and value level.
• provides operators at value and type level to help manipulate shapes.
• provides fixed and dynamic arrays with the same API.

API of an array language

See http://hiperfit.dk/pdf/array14_final.pdf for context and a sketch of an intermediate typed array language effort.

The operators that result from using the Representable type - separation of size tracking at compile level, from computational at runtime - ends up looking like APL.

Matrix multiplication in APL is +.x and in numhask-array is dot sum (*). There is a slight increase in abstraction by explicitly exposing the fold in the algorithm, but the expressions are both very neat and abstracted away from the specialisation of multiplying matrices.

References:

https://blog.plover.com/prog/apl-matrix-product.html

https://en.wikipedia.org/wiki/Tensor_contraction

https://en.wikipedia.org/wiki/Tensor_(intrinsic_definition)#Definition:_Tensor_Product_of_Vector_Spaces