Monoid type annotation

Question

In the book Functional Programming in Scala I see the following signature:

def productMonoid[A,B](A: Monoid[A], B: Monoid[B]): Monoid[(A,B)]

The description says that:

if types A and B are monoids, then the tuple type (A, B) is also a monoid

I have a difficulty in understanding the following part:

A: Monoid[A]

A is of type Monoid which takes itself as a type parameter? How to understand that?

Answer 1

Here: A: Monoid[A] the is just a variable name, it can also be written as a: Monoid[A] or param1: Monoid[A]. It it a bit of convention to give such variable names, for example in most cases variable name for a functor is F - F: Function[A] and M for a Monad - M: Monad[A]:

abstract class SomeClass[TC[_], A](param: TC[A]) {
  implicit val M: Monad[TC]
  ... // other code
}

It's more readable and clear if you see something like M.point[TC] where M is an instance of a Monad.

Added

And A: Monoid[A] is not a type annotation at all. Type parameters are written in square brackets:

def productMonoid [A,B] (params...), so in this variant:

def productMonoid[A: Monoid,B](params...)

Yes Monoid[A] is a type class for A type, it's desugared into:

def productMonoid[A,B](params...)(implicit val $ev: Monoid[A])

This means that Monoid is a type constructor which takes a type A and constructs a type Monoid[A] for $ev.