Encoding FIX in Object Calculi

Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH, U.K.; (Roy.Crole@mcs.le.ac.uk)

Received: 15 November 1998
Accepted: 14 March 2000

Abstract

We show that the FIX type theory introduced by Crole and Pitts [3] can be encoded in variants of Abadi and Cardelli's object calculi. More precisely, we show that the FIX type theory presented with judgements of both equality and operational reduction can be translated into object calculi, and the translation proved sound. The translations we give can be seen as using object calculi as a metalanguge within which FIX can be represented; an analogy can be drawn with Martin Löf's Theory of Arities and Expressions. As well as providing a description of certain interesting recursive objects in terms of rather simpler expressions found in the FIX type theory, the translations will be of interest to those involved with the automation of operational semantics.