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Zbl 0971.68098
Crole, Roy L.
Encoding FIX in object calculi. (English)
[J] Theor. Inform. Appl. 34, No.1, 15-38 (2000). ISSN 0988-3754; ISSN 1290-385X/e

Summary: We show that the FIX type theory introduced by {\it R. L. Crole} and {\it A. M. Pitts} [Inf. Comput. 98, No. 2, 171-210 (1992; Zbl 0763.03031)] 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 metalanguage 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.

MSC 2000:: *68Q55 Semantics

Keywords: FIX type theory

Citations: Zbl 0763.03031

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