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...
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| Published in | Journal of logical and algebraic methods in programming Vol. 124; p. 100713 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
01.01.2022
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 100713 |
| Author | Kozen, Dexter Bickford, Mark Silva, Alexandra |
| Author_xml | – sequence: 1 givenname: Mark surname: Bickford fullname: Bickford, Mark email: markb@cs.cornell.edu organization: Computer Science Department, Cornell University, Ithaca, NY, USA – sequence: 2 givenname: Dexter surname: Kozen fullname: Kozen, Dexter email: kozen@cs.cornell.edu organization: Computer Science Department, Cornell University, Ithaca, NY, USA – sequence: 3 givenname: Alexandra surname: Silva fullname: Silva, Alexandra email: alexandra.silva@ucl.ac.uk organization: Computer Science Department, University College London, London, United Kingdom |
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| References | Long (br0070) October 1966; 73 Niqui, Rutten (br0100) 2011 Conway, Guy (br0010) 1996 Honsberger (br0030) 1991 Hinze (br0020) 2009; vol. 5836 Jackson (br0040) 1995 Long (br0080) December 1982; 66 Paasche (br0110) 1954; 12 Krebbers, Parlant, Silva (br0060) Kozen, Silva (br0050) February 2013; 120 Perron (br0120) May 1951; 4 Moessner (br0090) March 1951 Honsberger (10.1016/j.jlamp.2021.100713_br0030) 1991 Long (10.1016/j.jlamp.2021.100713_br0080) 1982; 66 Hinze (10.1016/j.jlamp.2021.100713_br0020) 2009; vol. 5836 Krebbers (10.1016/j.jlamp.2021.100713_br0060) Long (10.1016/j.jlamp.2021.100713_br0070) 1966; 73 Niqui (10.1016/j.jlamp.2021.100713_br0100) 2011 Jackson (10.1016/j.jlamp.2021.100713_br0040) 1995 Moessner (10.1016/j.jlamp.2021.100713_br0090) 1951 Perron (10.1016/j.jlamp.2021.100713_br0120) 1951; 4 Kozen (10.1016/j.jlamp.2021.100713_br0050) 2013; 120 Conway (10.1016/j.jlamp.2021.100713_br0010) 1996 Paasche (10.1016/j.jlamp.2021.100713_br0110) 1954; 12 |
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| Title | Formalizing Moessner's theorem and generalizations in Nuprl |
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