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.CSL.2015.582
URN: urn:nbn:de:0030-drops-54402
URL: https://drops.dagstuhl.de/opus/volltexte/2015/5440/
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Amini, Shahin ; Erhard, Thomas

On Classical PCF, Linear Logic and the MIX Rule

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Abstract

We study a classical version of PCF from a semantical point of view. We define a general notion of model based on categorical models of Linear Logic, in the spirit of earlier work by Girard, Regnier and Laurent. We give a concrete example based on the relational model of Linear Logic, that we present as a non-idempotents intersection type system, and we prove an Adequacy Theorem using ideas introduced by Krivine. Following Danos and Krivine, we also consider an extension of this language with a MIX construction introducing a form of must non-determinism; in this language, a program of type integer can have more than one value (or no value at all, raising an error). We propose a refinement of the relational model of classical PCF in which programs of type integer are single valued; this model rejects the MIX syntactical constructs (and the MIX rule of Linear Logic).

BibTeX - Entry

@InProceedings{amini_et_al:LIPIcs:2015:5440,
  author =	{Shahin Amini and Thomas Erhard},
  title =	{{On Classical PCF, Linear Logic and the MIX Rule}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{582--596},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Stephan Kreutzer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5440},
  URN =		{urn:nbn:de:0030-drops-54402},
  doi =		{10.4230/LIPIcs.CSL.2015.582},
  annote =	{Keywords: lambda-calculus, linear logic, classical logic, denotational semantics}
}

Keywords: lambda-calculus, linear logic, classical logic, denotational semantics
Collection: 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)
Issue Date: 2015
Date of publication: 07.09.2015

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