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Relative Completeness for Logics of Functional Programs
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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Publication status
- Published
ISSN
1868-8969Publisher
LIPIcs 12 Schloss DagstuhlPublisher URL
Volume
12Pages
10.0Presentation Type
- paper
Event name
Computer Science Logic, 25th International Workshop / 20th Annual Conference of the EACSL, CSL 2011Event location
Bergen (Norway)Event type
conferenceISBN
978-3-939897-32-3Department affiliated with
- Informatics Publications
Full text available
- No
Peer reviewed?
- Yes
Editors
B MarcLegacy Posted Date
2012-02-06Usage metrics
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