Unify/throw away lmap and rmap

I will start quoting what many bloggers states about Profunctors:

A Profunctor is just a bifunctor that is contravariant in the first argument and covariant in the second.

So, if I have a type that is both a Contravariant and a Functor (covariant) at the same time, that type is a Profunctor where rmap is map and lmap is contramap.

If so, do we need that duplication?

In principle looks like we can safely throw away the LMap and RMap invokables, then we can define lmap and rmap as aliases of contramap and map respectively.

Or we can go even further and throw away lmap and rmap.

Also we can shorten contramapto cmap as they did in Purescript.

Finally (this might be a separate issue but let’s include it here) we can argue the same for Bifunctor’s second and map.

Any thoughts?

[gusty]

It’s been a long time thinking about unifying second and map.

At the moment, my thoughts converge in the direction that there will not be a function third. Actually first implies firstOf2 and second secondOf2.

When dealing with more that 2, we use different names, similarly to the naming in tuples, functions available are only fst and snd but for more than that we use itemX, same here. We already have ItemX and MapItemX Invokers.

So we can go ahead and unify them, making map and second aliases.

[gusty]

Cool, I have the feeling that these abstractions are more unfamiliar to F-Sharpers so they need probably more docs and examples.