The nu-calculus of Pitts and Stark is a typed lambda-calculus, extended with state in the form of dynamically-generated names. These names can be created locally, passed around, and compared with one another. Through the interaction between names and functions, the language can capture notions of scope, visibility and sharing. Originally motivated by the study of references in Standard ML, the nu-calculus has connections to other kinds of local declaration, and to the mobile processes of the -calculus.

In this paper we describe some of our progress towards an operational implementation of a modern programming logic. The logic is inspired by the variable type systems of Feferman, and is designed for reasoning about imperative functional programs. The logic goes well beyond traditional programming logics, such as Hoare's logic and Dynamic logic in its expressibility, yet is less problematic to encode into higher order logics. The main focus of the paper is too present an axiomatization of the base first order theory. 1 Introduction VTLoE [34, 23, 35, 37, 24] is a logic for reasoning about imperative functional programs, inspired by the variable type systems of Feferman. These systems are two sorted theories of operations and classes initially developed for the formalization of constructive mathematics [12, 13] and later applied to the study of purely functional languages [14, 15]. VTLoE builds upon recent advances in the semantics of languages with effects [16, 19, 28, 32, 33] and go...

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iancaglini, and S. Ronchi Della Rocca, editors, Automata, Languages and Programming, volume 372 of Lecture Notes in Computer Science, pages 704--722, Stresa, Italy, 1989. Springer-Verlag, Berlin. [RV95] J. G. Riecke and R. Viswanathan. Isolating side effects in sequential languages. In Conf. Record 22nd ACM Symp. on Principles of Programming Languages, pages ??--??, San Francisco, 1995. ACM, New York. [Sie94] K. Sieber. Full abstraction for the second order subset of an Algol-like language (preliminary report). Technischer Bericht A 01/94, Universitaet des Saarlandes, February, 1994. [SRI91] V. Swarup, U.S. Reddy, and E. Ireland. Assignments for applicative languages. In Hughes, editor, Functional Programming Languages and Computer Architecture, pages 193--214, 1991. LNCS 523, Springer Verlag. [Ten89] R. D. Tennent. Elementary data structures in Algol-like languages. Science of Computer Programming, 13:73-