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
Usefulness of the array language that results from this treatment is yet to be explored.
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.