Use laws to explain why there is no e.g. Monad[Validated]

[armanbilge]

H/t @TonioGela, seems we could improve the Parallel docs https://typelevel.org/cats/typeclasses/parallel.html

[TonioGela]

The Validated doc talks precisely about the example in the title, demonstrating that implementing Monad the ap function will get overridden and the new implementation is a short-circuiting one. What's your idea for the Parallel doc exactly?

[armanbilge]

Thanks for that pointer! I think it would be great if the documentation could specifically reference a law that relates flatMap to ap. It's the law that specifies the correct behavior, the override default implementation is merely a convenience.

However, at this moment I am struggling to find said law, or appreciate why it doesn't need to exist 🤔

cats/laws/src/main/scala/cats/laws/MonadLaws.scala

Line 31 in fe9afb5

trait MonadLaws[F[_]] extends ApplicativeLaws[F] with FlatMapLaws[F] {

[johnynek]

I believe this is the law:

cats/laws/src/main/scala/cats/laws/FlatMapLaws.scala

Line 51 in fe9afb5

def mproductConsistency[A, B](fa: F[A], fb: A => F[B]): IsEq[F[(A, B)]] =

[TonioGela]

I believe this is the law:

cats/laws/src/main/scala/cats/laws/FlatMapLaws.scala

Line 51 in fe9afb5

def mproductConsistency[A, B](fa: F[A], fb: A => F[B]): IsEq[F[(A, B)]] =

Thanks @johnynek! I'll try it and I'll submit an idea asap.

[TonioGela]

I opened a PR for this. BTW @johnynek I showed that overriding ap in a Validated[Monad] instance would not satisfy this law:

def flatMapConsistentApply[A, B](fa: F[A], fab: F[A => B]): IsEq[F[B]] =
  fab.ap(fa) <-> fab.flatMap(f => fa.map(f))

but since mproduct is defined in FlatMap it had no point demonstrating its faultiness. Am I right?