Monoids: Theme and Variations (Functional Pearl)

Monoids: Theme and Variations (Functional Pearl)

http://repository.upenn.edu/cis_papers/762/

Presented by Jesse Williamson, Developer of soft wares, Scripter of Javas.

Abstract

The monoid is a humble algebraic structure, at first glance even downright boring. However, there’s much more to monoids than meets the eye. Using examples taken from the diagrams vector graphics framework as a case study, I demonstrate the power and beauty of monoids for library design. The paper begins with an extremely simple model of diagrams and proceeds through a series of incremental variations, all related somehow to the central theme of monoids. Along the way, I illustrate the power of compositional semantics; why you should also pay attention to the monoid’s even humbler cousin, the semigroup; monoid homomorphisms; and monoid actions.

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