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DOI: 10.4230/LIPIcs.CSL.2011.470

Relative Completeness for Logics of Functional Programs

Authors: Bernhard Reus and Thomas Streicher

Published in: LIPIcs, Volume 12, Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (2011)

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.

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Bernhard Reus and Thomas Streicher. Relative Completeness for Logics of Functional Programs. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 470-480, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{reus_et_al:LIPIcs.CSL.2011.470,
  author =	{Reus, Bernhard and Streicher, Thomas},
  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 =	{Bezem, Marc},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.470},
  URN =		{urn:nbn:de:0030-drops-32509},
  doi =		{10.4230/LIPIcs.CSL.2011.470},
  annote =	{Keywords: completeness, program logics, LCF}
}

Document

DOI: 10.4230/DagSemRep.303

Semantic Foundations of Proof-search (Dagstuhl Seminar 01141)

Authors: David Pym, Eike Ritter, and Thomas Streicher

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract

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David Pym, Eike Ritter, and Thomas Streicher. Semantic Foundations of Proof-search (Dagstuhl Seminar 01141). Dagstuhl Seminar Report 303, pp. 1-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2001)

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@TechReport{pym_et_al:DagSemRep.303,
  author =	{Pym, David and Ritter, Eike and Streicher, Thomas},
  title =	{{Semantic Foundations of Proof-search (Dagstuhl Seminar 01141)}},
  pages =	{1--16},
  ISSN =	{1619-0203},
  year =	{2001},
  type = 	{Dagstuhl Seminar Report},
  number =	{303},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.303},
  URN =		{urn:nbn:de:0030-drops-151879},
  doi =		{10.4230/DagSemRep.303},
}

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Documents authored by Streicher, Thomas

Relative Completeness for Logics of Functional Programs

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Semantic Foundations of Proof-search (Dagstuhl Seminar 01141)

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