Proof Pearl: a Formal Proof of Higman's Lemma in ACL2

Authors:
Francisco Jesús Martín-Mateos;José Luis Ruiz-Reina;José Antonio Alonso;María José Hidalgo
Affiliations:
Computational Logic Group, Department of Computer Science and Artificial Intelligence, University of Seville, E.T.S.I. Informática, Sevilla, Spain 41012;Computational Logic Group, Department of Computer Science and Artificial Intelligence, University of Seville, E.T.S.I. Informática, Sevilla, Spain 41012;Computational Logic Group, Department of Computer Science and Artificial Intelligence, University of Seville, E.T.S.I. Informática, Sevilla, Spain 41012;Computational Logic Group, Department of Computer Science and Artificial Intelligence, University of Seville, E.T.S.I. Informática, Sevilla, Spain 41012
Venue:
Journal of Automated Reasoning
Year:
2011

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Abstract

Higman's lemma is an important result in infinitary combinatorics, which has been formalized in several theorem provers. In this paper we present a formalization and proof of Higman's Lemma in the ACL2 theorem prover. Our formalization is based on a proof by Murthy and Russell, where the key termination argument is justified by the multiset relation induced by a well-founded relation. To our knowledge, this is the first mechanization of this proof.