Relative Completeness for Logics of Functional Programs

Reus, Bernhard and Streicher, Thomas (2011) Relative Completeness for Logics of Functional Programs. In: Computer Science Logic, 25th International Workshop / 20th Annual Conference of the EACSL, CSL 2011, Bergen (Norway).

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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.

Item Type: Conference or Workshop Item (Paper)
Schools and Departments: School of Engineering and Informatics > Informatics
Depositing User: Bernhard Reus
Date Deposited: 06 Feb 2012 19:51
Last Modified: 13 Apr 2012 09:48
URI: http://sro.sussex.ac.uk/id/eprint/22582
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