numhask-array
===
[](https://travis-ci.org/tonyday567/numhask)
[](https://hackage.haskell.org/package/numhask-array)
Arrays are higher-kinded numbers that can be indexed into with an Int list. Higher-kinded numbers are things with a non-primitive type that we wish to use the usual numerical operators on (+,-,*,/,abs).
This is an experimental library that:
- 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.
Performance experiments are located in [numhask-bench](https://github.com/tonyday567/numhask-bench)
Usefulness of the array language that results from this treatment is yet to be explored.
API of an array language
---
https://en.wikipedia.org/wiki/APL_(programming_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