Partial Functions in a Total Setting

  • Authors:

  • Simon Finn;Michael P. Fourman;John Longley

  • Affiliations:

  • Abstract Hardware Limited, Uxbridge, Middlesex;The University of Edinburgh, Edinburgh, UK;The University of Edinburgh, Edinburgh, UK

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 1997

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Abstract

We discuss a scheme for defining and reasoning about partial recursive functions within a classical two-valued logic in which all terms denote. We show how a total extension of the partial function introduced by a recursive declaration may be axiomatized within a classical logic, and illustrate by an example the kind of reasoning that our scheme supports. By presenting a naive set-theoretic semantics, we show that the system we propose is logically consistent. Our work is motivated largely by the pragmatic issues arising from mechanical theorem proving – we discuss some of the practical benefits and limitations of our scheme for mechanical verification of software and hardware systems.