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Is there any intermediate abstraction between applicative functors and monads? And if yes, what is it? In a new paper with @geo2A, @simonmar and @dimenix we explore "selective functors", which are essentially applicative functors with branching: https://www.staff.ncl.ac.uk/andrey.mokhov/selective-functors.pdf …pic.twitter.com/tOgdlb1sGG
We've implemented selective functors in Haskell: https://github.com/snowleopard/selective …, OCaml: https://github.com/snowleopard/selective-ocaml …, and even Coq: https://github.com/tuura/selective-theory-coq … (the Coq repository contains some proofs of correctness that our selective instances are lawful). And there is also a PureScript fork!
The Haskell library is now available on Hackage: http://hackage.haskell.org/package/selective ….
Selective Applicative Functors in 17 minutes:https://www.youtube.com/watch?v=h3XEHRX4isk …
Maybe a "knee-jerk" question, but do "selective functors" have a category theoretic counterpart? :-)
I think yes, but I haven't yet had time to explore selective functors from the categorical viewpoint. Selective functors are monoids too, with the following functor product: data (:|:) f g a where (:|:) :: f (Either x a) -> g (x -> a) -> (:|:) f g a Does this make sense?
and is there an instance Selective ZipList
instance Selective ZipList where (<*?) :: ZipList (a + a') -> ZipList (a -> a') -> ZipList a' ZipList sums <*? ZipList fs = ZipList [ either f id sum | sum <- sums | f <- fs ] maybe
This is so cool, it is always like "how comes we never thought about this before?", but eventually you did! Congratulations Andrey, I can't wait to refractor my code to use it.
Thanks, Aloïs! Actually, as it turned out similar ideas have been discussed previously, e.g. see here: https://github.com/snowleopard/selective/blob/master/paper/irc-log-branchy.md …, but for some reason they were never really pursued. I guess there are many cases where "selective functors" are simply hardcoded in one way or another.
so, basically, applicatives with imperative if?
I think so, yes. All branches are predetermined, no monadic generation of effects on the spot.
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