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New Results on Morris's Observational Theory: The Benefits of Separating the Inseparable

Authors Flavien Breuvart, Giulio Manzonetto, Andrew Polonsky, Domenico Ruoppolo

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Flavien Breuvart
Giulio Manzonetto
Andrew Polonsky
Domenico Ruoppolo

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Flavien Breuvart, Giulio Manzonetto, Andrew Polonsky, and Domenico Ruoppolo. New Results on Morris's Observational Theory: The Benefits of Separating the Inseparable. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.FSCD.2016.15

Abstract

Working in the untyped lambda calculus, we study Morris's
lambda-theory H+. Introduced in 1968, this is the original
extensional theory of contextual equivalence. On the syntactic side,
we show that this lambda-theory validates the omega-rule, thus
settling a long-standing open problem.On the semantic side, we
provide sufficient and necessary conditions for relational graph
models to be fully abstract for H+. We show that a relational graph
model captures Morris's observational preorder exactly when it is
extensional and lambda-Konig. Intuitively, a model is lambda-Konig
when every lambda-definable tree has an infinite path which is
witnessed by some element of the model.

Both results follow from a weak separability property enjoyed by
terms differing only because of some infinite eta-expansion,
which is proved through a refined version of the Böhm-out technique.

Subject Classification

Keywords
  • Lambda calculus
  • relational models
  • fully abstract
  • Böhm-out
  • omega-rule

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