LFCS; Dept. of Comp. Sci.; University of Edinburgh
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EH9 3JZ Edinburgh, UK
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The -calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with -terms. However, if one goes further and uses fij-conversion to prove equivalence of programs, then a gross simplification 1 is introduced, that may jeopardise the applicability of theoretical results to real situations. In this paper we introduce a new calculus based on a categorical semantics for computations. This calculus provides a correct basis for proving equivalence of programs, independent from any specific computational model. 1 Introduction This paper is about logics for reasoning about programs, in particular for proving equivalence of programs. Following a consolidated tradition in theoretical computer science we identify programs with the closed -terms, possibly containing extra constants, corresponding to some features of the programming language under consideration. There are three approaches to proving equivalence of programs: ffl T...