Add commonly known operators to algebra type classes

[ldeluigi]

Currently, Spire is the only place where commonly known mathematical operators are provided to algebra type classes users.

For the general use case, writing custom algebraic types almost always means to also provide at least the most common operators (+, -, *, /) and often the less common ones (**, @, %, ...) to work with those types.

These operators implementation and behavior should be derived from the implemented type classes for a type, as they are standardized in their behaviour through many programming languages and DSLs.

Finally, I think that the full adoption of the algebra library for developers is hindered by the lack of these overloads, and many DSLs would benefit from the possibility to have also laws checking their correctness.

Let me know what you think!

[armanbilge]

Pinging @johnynek who I think may be more familiar with the history. I have a vague recollection that the original design goals of Algebra were to keep it focused on typeclasses and otherwise unopinionated (e.g., no syntax), to serve as a shared abstraction between Spire and Algebird. Are these design goals still important/relevant? Algebird seems to be pinned to Algebra v2.0.0 (from 2019) anyway.

I think it could be reasonable to move some of the syntax currently introduced in Spire to an algebra.syntax package.

[johnynek]

Yeah, I think those original motivations are no longer so relevant. Also, I left Twitter long ago and don't really know if anyone is maintaining Algebird anymore, unfortunately. Given that cats has a lot of syntax, I think following some good mix of cats practices with the spire's notation would be a good idea.

I think the main thing is that it shouldn't break anyone, and it definitely shouldn't break spire + cats users.

[ldeluigi]

I'll try work on a PR

[ldeluigi]

I've explored the library repository and I found too much design freedom within my scope.
In particular, I see one syntax design within cats.syntax, which links to sources defined in scala-version-specifc projects: I don't think I'm supposed to add the corresponding scala-version-specific packages with algebra; in addition to that, the design involves a concept called "AllSyntaxBinCompat" which it's not quite clear to me and I don't know if I'm supposed to use it.

Another design is present in Spire syntax, which is a little simpler but still not quite clear how's meant to work and why it's like that.

Moreover, I'm quite rusty with Scala 2, as in the last few years I've only worked with Scala 3 and I became fluent with that instead, so I'm not confident anymore with taking this task.

Let me know