Monoid instance for A => A in Cats

Question

Functions A => A are monoid with identity as empty and composition as combine. Unfortunately I did not find it in cats library. Does the library provide a monoid instance for these functions ?

What about A => M[A], where M is a monad or applicative ?

score 2 · Accepted Answer · answered Mar 18 '17 at 09:43

2

Cats has a Monoid instance of A => A in instances/function.scala.

A => M[A] for a Monad M seams to form form a Monoid with a => M.pure(a) as empty the following combine op:

def compose(f1 = A => M[A], f2 = A => M[A]): A => M[A] =
  a => f1(a).flatMap { e => f2(e) }

This does does not apeart to be implemented in the library.
Proof of Monoid laws left as an exersise for the reader.

answered Mar 18 '17 at 09:43

OlivierBlanvillain

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Thanks a lot. Is `X => A[X]`, where is `A` is Applicative, a monoid ? – Michael Mar 18 '17 at 09:46
A monad is just a monoid in the category of endofunctors, what's the problem? – n. m. could be an AI Mar 18 '17 at 09:49
@Michael Can you write a `combine` op without `flatMap`? – OlivierBlanvillain Mar 18 '17 at 10:13
Maybe not. I should think about it. – Michael Mar 18 '17 at 10:15

Monoid instance for A => A in Cats

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