Invited Lectures

Mathematical Foundations of Computer Science 1993

Volume 711 of the series Lecture Notes in Computer Science pp 84-104

Date:

Some results on the full abstraction problem for restricted lambda calculi

  • Furio HonsellAffiliated withDipartimento di Matematica e Informatica, Università di Udine
  • , Marina LenisaAffiliated withDipartimento di Matematica e Informatica, Università di Udine

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Abstract

Issues in the mathematical semantics of two restrictions of the λ-calculus, i.e. λI-calculus and λv-calculus, are discussed. A fully abstract model for the natural evaluation of the former is defined using complete partial orders and strict Scott-continuous functions. A correct, albeit non-fully abstract, model for the SECD evaluation of the latter is denned using Girard's coherence spaces and stable functions. These results are used to illustrate the interest of the analysis of the fine structure of mathematical models of programming languages.