# Some results on the full abstraction problem for restricted lambda calculi

Invited Lectures

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## Abstract

Issues in the mathematical semantics of two restrictions of the λ-calculus, i.e. λ*I*-calculus and λ*v*-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.

## Keywords

Normal Form Stable Function Operational Semantic Denotational Semantic Coherence Model
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