Add Gen.fix to make recursive generators cleaner

[johnynek]

same idea as typelevel/cats#3208 but particular to Gen.

Gen and Parsers are what motivated the 3208 PR.

[ashawley]

What's the example do? It's building lists that terminate with numbers higher than 5?

val fixGen =
  Gen.fix[List[Int]] { recurse =>
    Gen.choose(0, 10).flatMap { idx =>
      if (idx < 5) recurse.map(idx :: _)
      else Gen.const(idx :: Nil)
    }
  }

[johnynek]

Yes. I didn’t want to make a longer example such as a tree or JSON or something in the comment and I wanted to test the same thing that I put in the comment.

It’s probably not a great example because in this case there are ways to do this without recursion.

[ashawley]

Yeah, I was also wondering if there was a better example to use. I do like this example for one reason: Writing with existing combinators is clunky, because I tried:

val fixGen = {
  Gen.nonEmptyListOf(Gen.choose(0, 9)).map { ns =>
    val idx = ns.indexWhere(_ >= 5)
    ns.take(if (idx == -1) ns.size - 1 else idx + 1)
  }
}

Maybe there is a built-in generator that could be rewritten using this syntax as an example?

[ashawley]

This construct seems pretty useful. Should we elevate it by giving it a better name for visibility sake? Could we rename to something like from, of, until or continually?:

val listGen = Gen.of { lists: Gen[List[Int]] =>
  ...
}

The best name I came up with is Gen.fromRecursion but it's disqualified for being too long.

[johnynek]

Fix is the name for this traditionally: fix(f) = f(fix(f)).

I think the name should explain something about recursion. If you aren’t doing recursion you don’t need this.

What about def recursive?

[ashawley]

I agree. I guess I prefer a verb or an adverb, so even just recur. We can stew on it for a few days. This could be part of 1.15.0 which should be ready soon.

PS. I'm familiar with fixed point since I used to Scheme occasionally. I won't suggest Gen.y, though.

[ashawley]

After some time, I haven't had any strong feelings about a better name, so should we go with Gen.recursive? It works for me.

[larsrh]

fast-check calls it letrec

[ashawley]

That would seem to give evidence for naming it recursive then. I'm going to merge and follow-up with a commit that renames it.