What is Disjoint Union, Sum Type?

What is Disjoint Union? (aka Tagged Union, Variant, Discriminated Union, Sum Type)

let's explain by a example.

suppose you have 2 sets:

• set 1, {a,b}
• set 2, {c,d,b}

They have a common element “b”.

The disjoint union of them is a new set, this:

{
(a,1),
(b,1),
(b,2),
(c,2),
(d,2),
}

Notice that each element is a pair, first part is the element from a set, second part is a index that tells us where this element came from. If a element came from multiple places, it is repeated, such as our b here, we have (b,1) and (b,2).

So, what does it all mean?

As you can see, disjoint union, is somewhat like a union, but not really, because we have repeated things, and each new element has a added “index”. This “index”, serves the purpose of a “tag”, that's why it's also called tagged union

you can also see why it's called sum type, because the result is kinda a sum of the sets. Compare this to the “Cartesian Product” of set, nice contrast.