@@ -34,7 +34,7 @@ In addition to that (what a calculated pun...), we have associativity which buys
Now, don't go confusing this with commutativity which allows us to rearrange the order. While that holds for addition, we're not particularly interested in that property at the moment - too specific for our abstraction needs.
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.
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 there 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 which acts as our associative binary operator.
