Pages tagged monoid:

Monoids and Finger Trees

"A very powerful application of monoids are 2-3 finger trees, first described by Ralf Hinze and Ross Patterson. Basically, they allow you to write fast implementations for pretty much every abstract data type mentioned in Okasaki's book on purely functional data structures. For example, you can do sequences, priority queues, search trees and priority search queues. Moreover, any fancy and custom data structures like interval trees or something for stock trading are likely to be implementable in this framework as well. How can one tree be useful for so many different data structures? The answer: monoids! Namely, the finger tree works with elements that are related to a monoid, and all the different data structures mentioned above arise by different choices for this monoid. Let me explain how this monoid magic works."