[Haskell-cafe] ANNOUNCE: mezzolens 0.0.0 & a puzzle

[roconnor at theorem.ca]

This is a pre-release of mezzolens, a library of first-order functional 
references based purely on profunctors.  I wrote it because 
https://www.reddit.com/user/Faucelme asked for one.  You can find it at 
https://hackage.haskell.org/package/mezzolens

The main purpose of this pre-release is to provide background for framing 
the following question:

In a pure profunctor lens libray, how do you write choosing and beside in 
such a way that it supports all the following types?

choosing :: Lens ta tb a b -> Lens sa sb a b -> Lens (Either ta sa) (Either sa sb) a b
choosing :: Traversal ta tb a b -> Travesal sa sb a b -> Traversal (Either ta sa) (Either sa sb) a b
choosing :: SEC ta tb a b -> SEC sa sb a b -> SEC (Either ta sa) (Either sa sb) a b

beside :: Traversal ta tb a b -> Travesal sa sb a b -> Traversal (Either ta sa) (Either sa sb) a b
beside :: SEC ta tb a b -> SEC sa sb a b -> SEC (Either ta sa) (Either sa sb) a b


One sufficent solution for choosing would be to write a single function 
that combines

lensVL :: (forall f. Functor f => (a -> f b) -> ta -> f tb) -> Lens ta tb a b
traversal :: (forall f. Applicative f => (a -> f b) -> ta -> f tb) -> Traversal ta tb a b

into one.

The obvious approach is to write an suitable adaptor that transforms any 
(strong) profunctor into a functor, and if the profunctor is wandering, it 
produces an applicative functor.  But I haven't been able to devise such a 
suitable adaptor.

-- 
Russell O'Connor                                      <http://r6.ca/>
``All talk about `theft,''' the general counsel of the American Graphophone
Company wrote, ``is the merest claptrap, for there exists no property in
ideas musical, literary or artistic, except as defined by statute.''