Haskell 2021 - Evaluating Linear Functions to Symmetric Monoidal Categories

> None of these features require arr :: (x -> y) -> a x y (a “prearrow”), and it would be a huge advantage not to require the ability to lift arbitrary Haskell functions into every arrow. I think the paper Evaluating Linear Functions to Symmetric Monoidal Categories basically does that. It promises a better model of "boxes connected by wires". There's also a presentation on YouTube from the Haskell 2021 symposium. It is implemented in the `linear-smc` package on Hackage.

I think Arrows or more generally Symmetric Monoidal Categories or Cartesian Closed Categories are better abstractions if you want to explore languages that do not fit in the monadic model.

You may be interested in Conal Elliott's Compiling to Categories work and its later extension by KittyHawk. There's also some recent related work on converting between linear functions and symmetric monoidal categories.

I don't think arrows are really a good abstraction, see the beginning of this talk: link to this video They present an alternative using linear functions that you can use in Haskell today, but I think directly having support for compiling to (cartesian/monoidal closed) categories would be even nicer.