The Semantics of Plurals

Abstract

Inside many software languages lives an expression language that caters for the computation of single values from single values. These languages' fixation on single-valuedness is often at odds with their application domains, in which many values, or plurals, regularly occur in the places of single. While the classical mathematical means of dealing with plurals is the set, in computing, other representations have evolved, notably strings and the much lesser known bunches. We review bunch theory in the context of expression languages including non-recursive functions, and show how giving bunches set semantics suggests that evaluating bunch functions amounts to computing with relations. We maintain that the ensuing seamless integration of relations in expression languages that otherwise know only functions makes a worthwhile contribution in a field in which the difference between modeling, with its preference for relations, and programming, with its preference for functions, is increasingly considered accidental.