Sets as anti-chains

Abstract

In this paper we present a theory of anti-chains as data representations for sets in circumstances where sets of interest satisfy properties such as being upward-closed or convex relative to a partial ordering. Our goal is to provide an interface for supplying an implementation of the necessary primitives in a reusable manner and a theory that will facilitate algebraic reasoning about correctness. We present an algebra of anti-chains and illustrate its use in programming and reasoning about a machine learning algorithm.