License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2016.15
URN: urn:nbn:de:0030-drops-59924
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5992/
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Breuvart, Flavien ; Manzonetto, Giulio ; Polonsky, Andrew ; Ruoppolo, Domenico

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

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LIPIcs-FSCD-2016-15.pdf (0.7 MB)

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.

BibTeX - Entry

@InProceedings{breuvart_et_al:LIPIcs:2016:5992,
  author =	{Flavien Breuvart and Giulio Manzonetto and Andrew Polonsky and Domenico Ruoppolo},
  title =	{{New Results on Morris's Observational Theory: The Benefits of Separating the Inseparable}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Delia Kesner and Brigitte Pientka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5992},
  URN =		{urn:nbn:de:0030-drops-59924},
  doi =		{10.4230/LIPIcs.FSCD.2016.15},
  annote =	{Keywords: Lambda calculus, relational models, fully abstract, B{\"o}hm-out, omega-rule}
}

Keywords: Lambda calculus, relational models, fully abstract, Böhm-out, omega-rule
Collection: 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)
Issue Date: 2016
Date of publication: 17.06.2016

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