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DOI: 10.4230/LIPIcs.CSL.2011.470
URN: urn:nbn:de:0030-drops-32509
URL: https://drops.dagstuhl.de/opus/volltexte/2011/3250/
Reus, Bernhard ; Streicher, Thomas
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 = {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: | 31.08.2011 |
