The Associative[A] type class describes an associative binary operator for a type A. For example, addition for integers, and string concatenation for strings.

Associative is at the top of the hierarchy for abstracting over operations to combine types because while there are some operations that are not associative but do obey other laws, it is generally difficult to combine more than two values in interesting ways with these operators, and thus to build solutions to more complicated problems out of solutions to simpler ones.

For example, the mean of two numbers is an operation that is commutative but not associative. However, the lack of associativity is an indication that we can't combine the means of multiple values in an interesting way with this definition. If we attempt to take the mean of three values we always place twice as much weight on one number as the others, which is rarely what we want.

If we instead define this operation using a StatsCounter object then means can be combined in ways that are associative, commutative, and have an identity element, supporting much more interesting modes of composition.