@@ -36,7 +36,7 @@ Now, don't go confusing this with commutativity which allows us to rearrange the
Come to think of it, what properties should be in our abstract superclass anyways? What traits are specific to addition and what ones can be generalized? Are the other abstractions amidst this hierarchy or is it all one chunk? It's this kind of thinking that our mathematical forefathers applied when conceiving the interfaces in abstract algebra.
As it happens, those old school abstractionists landed on the concept of a *group* when abstracting addition. A *group* has all the bells and whistles including the concept of negative numbers. Here, we're only interested in that associative binary operator so we'll choose the less specific interface *Semigroup*. A *Semigroup* is a type with a `concat` method with acts as our associative binary operator.
As it happens, those old school abstractionists landed on the concept of a *group* when abstracting addition. A *group* has all the bells and whistles including the concept of negative numbers. Here, we're only interested in that associative binary operator so we'll choose the less specific interface *Semigroup*. A *Semigroup* is a type with a `concat` method which acts as our associative binary operator.
Let's implement it for addition and call it `Sum`:
