Proof pearl: defining functions over finite sets

Authors:
Tobias Nipkow;Lawrence C. Paulson
Affiliations:
Institut für Informatik, Technische Universität München, Germany;Computer Laboratory, University of Cambridge, England
Venue:
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Year:
2005

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Abstract

Structural recursion over sets is meaningful only if the result is independent of the order in which the set's elements are enumerated. This paper outlines a theory of function definition for finite sets, based on the fold functionals often used with lists. The fold functional is introduced as a relation, which is then shown to denote a function under certain conditions. Applications include summation and maximum. The theory has been formalized using Isabelle/HOL .