Abstraction of types which support a binary addition operator x + y. For numeric types, this is just familiar numeric addition. For String, it is string concatenation.

Integer next = current + 1;
String helloWorld = "hello" + " " + "world";

A concrete class that implements this interface should be a mathematical semigroup. That is, the addition operation should be associative, satisfying:

• (x+y)+z == x+(y+z)

A Summable type might be a monoid, that is, a semigroup with an additive identity element, usually denoted 0, but this is not required. For example:

• String is a monoid with identity element "",
• Float is a monoid with identity element 0.0, and
• Integer is a monoid with identity element 0.

For any monoid, the addition operation must satisfy:

• x + 0 == x