Formalizing Moessner's theorem and generalizations in Nuprl

Moessner's theorem describes a procedure for generating a sequence of n integer sequences that lead unexpectedly to the sequence of nth powers 1n, 2n, 3n, … . Several generalizations of Moessner's theorem exist. Recently, Kozen and Silva gave an algebraic proof of a general theorem that su...

Full description

Saved in:
Bibliographic Details
Published inJournal of logical and algebraic methods in programming Vol. 124; p. 100713
Main Authors Bickford, Mark, Kozen, Dexter, Silva, Alexandra
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2022
Subjects
Formalization
Moessner's theorem
Nuprl
Pascal triangle
Nuprl
Formalization
Moessner's theorem
Pascal triangle
Online AccessGet full text

Cover

More Information
Summary:Moessner's theorem describes a procedure for generating a sequence of n integer sequences that lead unexpectedly to the sequence of nth powers 1n, 2n, 3n, … . Several generalizations of Moessner's theorem exist. Recently, Kozen and Silva gave an algebraic proof of a general theorem that subsumes Moessner's original theorem and its known generalizations. In this note, we describe the formalization of this theorem that the first author did in Nuprl. On the one hand, the formalization remains remarkably close to the original proof. On the other hand, it leads to new insights in the proof, pointing to small gaps and ambiguities that would never raise any objections in pen and pencil proofs, but which must be resolved in machine formalization.
ISSN:2352-2208
DOI:10.1016/j.jlamp.2021.100713