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The long-standing problem of adequate formalization of local names in mathematical formulas and semantics of references in object-oriented languages taken on their own without objects, is discussed. Reasons why the existing approaches cannot be considered suitable solutions, are explained. An introduction is given to the relatively recent works on the theories of names and references of the group lead by Andrew Pitts. The concept of referential transparency, in which contextual equivalence is used instead of the usual equality of values, is analyzed. It is the main property, which these theories are based upon: such modified referential transparency is preserved when a purely functional language is extended with names and references as data. An outline of a constructive denotational semantics of the extended functional language is given. It is argued that the modified referential transparency, along with many other valuable properties, can be also 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.

On Theory of Names to be Used in Semantics of References in Functional and Object-Oriented Languages