Idempotent relations in Isabelle/HOL

Authors:
Florian Kammüller;J. W. Sanders
Affiliations:
Institute for Software Engineering and Theoretical Computer Science, Technische Universität Berlin;Institute for Software Engineering and Theoretical Computer Science, Technische Universität Berlin
Venue:
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
Year:
2004

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Mechanical Analysis of Finite Idempotent Relations

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Abstract

A characterization of idempotent relations is presented first as a paper-style proof, then by its formalization in Isabelle/HOL. The novel characterization gives rise to the construction of idempotent relations by an abstract algorithm. This algorithm is rigorously developed inside Isabelle/HOL using primitive recursive function definitions. Whilst the characterisation and algorithm appear to be new, we regard this as an interesting demonstration of the interplay between mathematical reasoning and program development, in particular using Isabelle/HOL.