Abstract

We develop a calculus in which the computation steps required to execute a computer program can be separated into discrete stages. The calculus, denoted 2 , is embedded within the pure untyped -calculus. The main result of the paper is a characterization of sucient conditions for conuence for terms in the calculus. The condition can be taken as a correctness criterion for translators that perform reductions in one stage leaving residual redexes over for subsequent computation stages. As an application of the theory, we verify the correctness of a macro expansion algorithm. The expansion algorithm is of some interest in its own right since it solves the problem of desired variable capture using only the familiar capture avoiding substitutions. 1 Introduction The -calculus is widely used as a metalanguage for programming language semantics because most of the complexities of real programming languages can be modeled by relatively simple and well-understood aspects of the calculus. ...

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