Semigroup

A semigroup for some given type A has a single operation (which we will call combine), which takes two values of type A, and returns a value of type A. This operation must be guaranteed to be associative. That is to say that,

(a.combine(b)).combine(c)

must be the same as

a.combine(b.combine(c))

for all possible values of a, b, c.

There are instances of Semigroup defined for many types found in Arrow and the Kotlin std lib. For example, Int values are combined using addition by default, but multiplication is also associative and forms another Semigroup.

Examples

Now that you’ve learned about the Semigroup instance for Int, try to guess how it works in the following examples:

import arrow.typeclasses.Semigroup

Semigroup.int().run { 1.combine(2) }

import arrow.typeclasses.Semigroup

Semigroup.list<Int>().run {
    listOf(1, 2, 3).combine(listOf(4, 5, 6))
}

import arrow.core.Option
import arrow.typeclasses.Semigroup

Semigroup.option(Semigroup.int()).run {
    Option(1).combine(Option(2))
}

import arrow.core.Option
import arrow.core.None
import arrow.typeclasses.Semigroup

Semigroup.option(Semigroup.int()).run {
    Option(1).combine(None)
}

Many of these types have methods defined directly on them, which allow for this example of combining: + on List. But the value of having a Semigroup typeclass available is that these compose.

Additionally, Semigroup adds + syntax to all types for which a Semigroup instance exists:

Semigroup.option(Semigroup.int()).run {
    Option(1) + Option(2)
}

Contents partially adapted from Scala Exercises Cat’s Semigroup Tutorial