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DOI: 10.4230/LIPIcs.FSCD.2016.15
New Results on Morris's Observational Theory: The Benefits of Separating the Inseparable

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

Published in: LIPIcs, Volume 52, 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)

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.
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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)

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@InProceedings{breuvart_et_al:LIPIcs.FSCD.2016.15,
  author =	{Breuvart, Flavien and Manzonetto, Giulio and Polonsky, Andrew and Ruoppolo, Domenico},
  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 =	{Kesner, Delia and Pientka, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.15},
  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}
}
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