If an operation is can combine two elements, and there is a clearly defined empty empty version that can be used to keep the same element when used on an element.

In Category Theory, something that is Combinable is called a Monoid.

By doing use FunLand.Combinable you get an implementation of the Collectable protocol for free. If you want to implement your own version of Collectable, add Combinable with use FunLand.Combinable, auto_collectable: false.

Examples

• Integer-addition with 0 as empty element forms a Monoid, also known as the Sum.
• Integer-multiplication with 1 as empty element forms a Monoid, also known as the Product.
• List concatenation with [] as empty element.
• String concatenation with the empty string "" as empty element.
• Set union with the empty set as empty element.

Fruit Salad Example

Bowls that you can use to mix fruits in, are a monoid:

The combine operation would be to put the fruits from Bowl A into Bowl B, keeping that one. The empty operation would be to take an emtpy bowl.

As can be seen, this follows the Combinable laws:

• left-identity: putting the contents of an empty bowl into a bowl with apples, would be the same as doing nothing (you still have 'a bowl with apples')
• right-identity: putting the contents a bowl filled with apples into an empty bowl, would be the same as doing nothing (you still have 'a bowl with apples')