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Publication Detail
Moessner’s theorem: An exercise in coinductive reasoning in COQ
  • Publication Type:
    Conference
  • Authors:
    Krebbers R, Parlant L, Silva A
  • Publication date:
    01/01/2016
  • Pagination:
    309, 324
  • Published proceedings:
    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
  • Volume:
    9660
  • ISBN-13:
    9783319307336
  • Status:
    Published
  • Print ISSN:
    0302-9743
Abstract
© Springer International Publishing Switzerland 2016. Moessner’s Theorem describes a construction of the sequence of powers (1 n , 2 n , 3 n ,…), by repeatedly dropping and summing elements from the sequence of positive natural numbers. The theorem was presented by Moessner in 1951 without a proof and later proved and generalized in several directions. More recently, a coinductive proof of the original theorem was given by Niqui and Rutten. We present a formalization of their proof in the Coq proof assistant. This formalization serves as a non-trivial illustration of the use of coinduction in Coq. During the formalization, we discovered that Long and Salié’s generalizations could also be proved using (almost) the same bisimulation.
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