JAjackpirate·Jan 20, 2019
I've done quite a lot of work trying to solve this problem in Haskell, and I'm of the opinion that current type system technology is not strong enough for real world machine learning.
At the most basic level, the sizes of tensors are often not known until runtime, so some sort of dependent typing is necessary. Idris is currently the most practical dependently typed language, and it's missing a number of features that would be needed for machine learning work. For example, it only supports 64bit floating point operations, whereas 32bit ops are standard and the industry is moving to 16 bit and fewer ops.
There's ways in Haskell to get most of the benefits of dependent typing, but they're pretty ugly. My subhask library [1] I think did a reasonable job for vector/matrix math, but once you get into higher order tensors everything becomes e
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ither far too verbose or impossible to specify. For example, permuting the axes of a tensor takes roughly a full page of code, and it's not even properly type safe. At the bottom of the link [1], there's a list of type system features that I think would be necessary to add to Haskell before it has a chance of a good linear algebra system... but in all honestly, I'm not even convinced yet that a usable linear algebra system can even be implemented in a language with proper dependent types.
[1] http://github.com/mikeizbicki/subhask