Laws for polymorphic optics

[kenbot]

It's a scandal that the laws only apply to the degenerate monomorphic optics -- they're living in sin!

It seems important that the full range of optic behaviour offered by Monocle is well-regulated by laws. A starting point could be unpicking the Haskell Lens functionality so that the laws there can be transcribed. For instance, for Isos:

f . from f ≡ id
from f . f ≡ id

The secret sauce appears to be the Van Laarhoven representation with profunctor constraints, that can unify the various representations with regular functions. We could put all this machinery privately in the laws package, although it might be hard for users to understand the code. The current monomorphic laws are wonderfully crisp and easy to read. Still, the alternative is lawless anarchy!

[julien-truffaut]

Hum I am wondering how is it possible to do f . from f
if f: PIso[S, T, A, B] then from f: PIso[B, A, T, S] so you shouldn't be able to compose them. I think it is the same point that #428

[kenbot]

Yep that's where I got stuck - I couldn't get the types to line up.
https://github.com/kenbot/Monocle/blob/piso-laws/core/shared/src/main/scala/monocle/law/PIsoLaws.scala

With regard to the Haskell implementation -- their profunctorial Exchange type is basically the same as Monocle's PIso. They use a type AnIso s t a b, which is basically PIso[...] => PIso[...], and a supertype of the main Iso s t a b. I didn't bother reproducing all the machinery, but I got stuck where I needed an S,T to compose, but had a T,S instead.

It would be great if we could make it work with simple Monocle concepts, all that code is pretty horrid.

[kenbot]

I found some relevant links:
http://stackoverflow.com/questions/26082221/relationship-between-forward-and-backward-map-in-isomorphism-lens-package
http://comonad.com/reader/2012/mirrored-lenses/

It seems that the S => A and B => T functions must both be bijective, but not necessarily related to each other. The Iso doesn't know about the reverse side of either bijection.

[julien-truffaut]

Polymorphic optics are likely to get dropped. So I will close that one.