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URN: urn:nbn:de:0030-drops-32509
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Relative Completeness for Logics of Functional Programs

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Abstract

We prove a relative completeness result for a logic of functional programs extending D. Scott's LCF. For such a logic, contrary to results for Hoare logic, it does not make sense to ask whether it is complete relative to the full theory of its first-order part, since the first order part does not determine uniquely the model at higher-order types. Therefore, one has to fix a model and choose an appropriate data theory w.r.t. which the logic is relatively complete. We establish relative completeness for two models: for the Scott model we use the theory of Baire Space as data theory, and for the effective Scott model we take first-order arithmetic. In both cases we need to extend traditional LCF in order to capture a sufficient amount of domain theory.

BibTeX - Entry

@InProceedings{reus_et_al:LIPIcs:2011:3250,
  author =	{Bernhard Reus and Thomas Streicher},
  title =	{{Relative Completeness for Logics of Functional Programs}},
  booktitle =	{Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL},
  pages =	{470--480},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-32-3},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{12},
  editor =	{Marc Bezem},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3250},
  URN =		{urn:nbn:de:0030-drops-32509},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.CSL.2011.470},
  annote =	{Keywords: completeness, program logics, LCF}
}

Keywords: completeness, program logics, LCF
Seminar: Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL
Issue date: 2011
Date of publication: 2011


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