Realizability for Monotone and Clausular (Co)inductive Definitions

Authors:
Favio E. Miranda-Perea
Affiliations:
Institut für Informatik Ludwig-Maximillians-Universität Oettingenstr. 67, D-80538 München, Germany
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2005

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Abstract

We develop an extension of second order logic (AF2) with monotone, and not only positive, (co)inductive definitions and a clausular feature which simplifies considerably the defining mechanism. A sound realizability interpretation, where the extracted programs are untyped, but typable, terms of a strongly normalizing Curry-style system of monotone (co)inductive types makes our logic into a logical framework suitable for programming with proofs.