A Linear Applicative Solution for the Set Union Problem

This paper is about an applicative solution to the IMPERATIVE Set Union Problem, as posed by Peyton-Jones [3]. The adjectivisation is used here to emphasise that the problem was thought to pose significant questions in finding an applicative solution of the same order of complexity as the imperative version. We show one such solution, written in the style of KRC [5]. The same reasoning, when applied to the Set Intersection and Difference problems will yield solutions with the same order of complexity of the imperative counterparts. The complexity of the solution, or rather of one of the functions in it, depends on the implementation's capability of destructively overwriting objects if that does not affect the referential transparency property of a purely applicative language. Such a system is described elsewhere [2].