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Sun Jun 17 01:41:02 EDT 2018

## Arrows?

It would be just Kleisli.
But basically, after Conal indoctrination, I really like the
applicative version more. Functions, be it monadic functions, seem to
make more sense.
But maybe just try it?
https://www.reddit.com/r/haskell/comments/4fkkzo/when_does_one_consider_using_arrows/
While the exact mathematics doesn't seem to have been worked out
exactly yet, it is well known that Applicative+Category has "about
the same" expressiveness as Arrows.
Using Strong from profunctors, you can prove Strong + Category has
exactly the same expressiveness.
http://www.fceia.unr.edu.ar/~mauro/pubs/Notions_of_Computation_as_Monoids.pdf
gives most of the story and
http://www-kb.is.s.u-tokyo.ac.jp/~asada/papers/arrStrMnd.pdf gives
the rest, but you need to read between the lines and see that using
Category gives you a way to model monads in Prof.
class (Strong p, Category p) => Arrow p
instance (Strong p, Category p) => Arrow p
There. I fixed it.
So basically, forget arrows.

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