Should factories like Semigroup.instance be provided for other typeclasses?

[morgen-peschke]

While Semigroup has cats.kernel.Semigroup#instance, Monoid has no equivalent, which could be implemented as:

object Monoid {
  /**
   * Create a `Monoid` instance from the given function and constant
   */
  @inline def instance[A](emptyVal: A, cmb: (A, A) => A): Monoid[A] = new Monoid[A] {
    override val empty: A = emptyVal
    override def combine(x: A, y: A): A = cmb(x,y)
}

Looking at the various typeclasses in cats.kernel, there doesn't seem to be a pattern for which ones have factories, and which don't:

Typeclass	Has Factory	Commentary
Band	No	Should be identical to Semigroup.instance
BoundedSemilattice	No	Should be identical to Monoid.instance
CommutativeGroup	No	See note for parent type Group
CommutativeMonoid	No	Should be identical to Monoid.instance
CommutativeSemigroup	No	Should be identical to Semigroup.instance
Eq	Yes
Group	No	Group.instance(A, A => A, (A, A) => A) might be a bit much
Hash	Yes
Monoid	No	Monoid.instance(A, (A, A) => A) should be easy to understand
Order	Yes
PartialOrder	Yes
Semigroup	Yes
Semilattice	No	Should be identical to Semigroup.instance

Would a PR adding these be useful?

It doesn't look like factories for the typeclasses in cats.core would be possible, as they'd require accepting higher-order lambdas, which I don't think can be encoded as parameters in Scala.

[kailuowang]

Thanks for identifying these potential factory methods. I think there are value in them. On the other hand, it raises a question in my head, will such methods gives user the false impression that implementing these instances is as simple as calling these methods? Maybe a more interesting question is how do we make it obvious to users that the instances must obey the laws and there are tests they can write to ensure their lawfulness? Admittedly it's not obvious in the current setup, but will these methods make it even less so?

[morgen-peschke]

As cats-laws depends on cats-kernel, rather than the other way around, is it possible to include a link in the scaladoc to the laws it would need to conform to?

For example, would it compile to have a link to cats.laws.discipline.FunctorTests in the scaladoc for cats.Functor?