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Relative Completeness for Logics of Functional Programs

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posted on 2023-06-08, 00:17 authored by Bernhard ReusBernhard Reus, Thomas Streicher
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.

History

Publication status

  • Published

ISSN

1868-8969

Publisher

LIPIcs 12 Schloss Dagstuhl

Volume

12

Pages

10.0

Presentation Type

  • paper

Event name

Computer Science Logic, 25th International Workshop / 20th Annual Conference of the EACSL, CSL 2011

Event location

Bergen (Norway)

Event type

conference

ISBN

978-3-939897-32-3

Department affiliated with

  • Informatics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Editors

B Marc

Legacy Posted Date

2012-02-06

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