2005 | OriginalPaper | Buchkapitel
Proof Pearl: Defining Functions over Finite Sets
verfasst von : Tobias Nipkow, Lawrence C. Paulson
Erschienen in: Theorem Proving in Higher Order Logics
Verlag: Springer Berlin Heidelberg
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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 .