Needed parts for one-liner

[tomjaguarpaw]

Thanks!

Can you explain the meaning of end? If it's supposed to be the identity of +++! shouldn't it be end :: p Void a?

[tomjaguarpaw]

To be more precise. p Void a is equivalant to p Void Void but p a a is not, so I suspect we don't actually want p a a.

[sjoerdvisscher]

I actually need p a a to deal with constants that don't need to be touched. It's just a coincidence that zero can be implemented. I really just need it as "identity" but Identity and id are already used so often, and end isn't and still technically a correct term.

Oh, I now realise that the implementation can just be zero = end and probably is not worth including. In my code I had zero :: p (V1 a) (V1 b).

[tomjaguarpaw]

Hmm, so perhaps you actually want Strong?

[tomjaguarpaw]

https://hackage.haskell.org/package/profunctors-5.2/docs/Data-Profunctor-Strong.html

[tomjaguarpaw]

I'm very suspicious of p a a and I suspect that it's a coincidence that it works and you actually want something else.

[tomjaguarpaw]

Actually I'm not suspicious of it. It's a perfectly good class but it is strictly less general (in combination with ProductProfunctor) than Strong.

Is Strong sufficient for your needs?

[sjoerdvisscher]

This is the only place where I use it: https://github.com/sjoerdvisscher/one-liner/blob/master/src/Generics/OneLiner/Internal.hs#L110

So what I need is p (K1 i c a) (K1 i c b). K1 is from GHC.Generics and defined as

newtype K1 (i :: *) c (p :: *) = K1 { unK1 :: c }

so after dimap unK1 K1 I just need a p c c. I don't see how Strong would help me here.

[tomjaguarpaw]

At the very least you can get p c c from p () () and first' :: p a b -> p (a, c) (b, c).

I wonder if ProductProfunctor p, Strong p is actually equivalent to ProductProfunctor p, ProfunctorEnd p.

[sjoerdvisscher]

Ah, indeed! It looks like they are.

first' p = p ***! end
second' p = end **! p

And as you said you can get end from empty and first'. Scratch that class then.

[sjoerdvisscher]

The only ProfunctorEnd instance that isn't Strong is Joker. With the above the instance would become

instance Alternative f => Strong (Joker f) where
  first' (Joker fb) = Joker $ liftA2 (,) fb Alternative.empty

But I could work around this missing instance. Using Alternative just for its empty was ugly anyway.

[tomjaguarpaw]

The Product/SumProfunctor instances are uncontroversial so I merged them anyway.

Having thought about it some more I believe that ProfunctorEnd is a meaningful class so let me know if you want me to add that too.

[sjoerdvisscher]

With ProductProfunctor being Profunctor+Applicative and ProfunctorEnd being Strong+Applicative there only has to be a nice replacement for SumProfunctor and I would not need this whole package...

[sjoerdvisscher]

SumProfunctor p is the same as Decidable (Flip p) a.

But there's actually good reason to use this package after all! There can be different instances of Applicative (p a), depending on if you're seeing p as a Profunctor or as a Bifunctor. For example the instance for Clown f a would need Divisible f or Alternative f respectively.