On theories of names and references in formal languages and implications for functional and object-oriented programming

Abstract

The long-standing problem of adequate formalization of local names in mathematical formulae and semantics of references in object-oriented languages taken “as is” without objects, is discussed. Reasons why the existing approaches cannot be considered suitable solutions, are explained. An introduction to the relatively recent works on the theories of names and references of the group headed by Andrew Pitts, is given. The notion of referential transparency, in which contextual equivalence is used instead of the usual equality of values, is analyzed. This is the main property, which these theories are based upon: it is preserved when a purely functional language is extended with names and references as data. It is argued that such referential transparency, along with many others, can be preserved for mutable objects that change to a limited extent. This leads to a model of computation between functional and object-oriented ones, allowing for a deterministic parallel implementation.