2016
DOI: 10.1007/978-3-319-30734-3_21
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Moessner’s Theorem: An Exercise in Coinductive Reasoning in Coq

Abstract: Dedicated to Frank de Boer on the occasion of his 60th birthday.Abstract. 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… Show more

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Cited by 3 publications
(7 citation statements)
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“…Being blind scientists ourselves, but with the benefit of hindsight, we try not to cover the whole elephant but instead try to characterize the elephant. As such, we conclude that the articles by van Yzeren [44], Long [22,23], Niqui and Rutten [29], Danvy et al [7], and Krebbers et al [19] are the pieces of related work most relevant to our goals, since they span several generalizations of -and connections to -Moessner's sieve with a focus on machine-assisted theorem proving. In particular, we share the same perspective as Long of wanting to explore the intrinsic beauty of simple mathematical concepts, which we do on top of the foundation laid by Danvy et al…”
Section: Discussionmentioning
confidence: 83%
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“…Being blind scientists ourselves, but with the benefit of hindsight, we try not to cover the whole elephant but instead try to characterize the elephant. As such, we conclude that the articles by van Yzeren [44], Long [22,23], Niqui and Rutten [29], Danvy et al [7], and Krebbers et al [19] are the pieces of related work most relevant to our goals, since they span several generalizations of -and connections to -Moessner's sieve with a focus on machine-assisted theorem proving. In particular, we share the same perspective as Long of wanting to explore the intrinsic beauty of simple mathematical concepts, which we do on top of the foundation laid by Danvy et al…”
Section: Discussionmentioning
confidence: 83%
“…Further work with the framework of stream calculus was done in collaboration with Milad Niqui [28,31], where they studied various operations for partitioning, projecting and merging streams, and later used them to develop precise proofs for Moessner's theorem using coinductive proof techniques [29,30]. Subsequently, the proofs by Niqui and Rutten of Moessner's theorem have been formalized in the Coq proof assistant [1] by Krebbers et al [19]. Besides proving Moessner's theorem, their formalization made them able to create a foundation of proved properties that abstracted away the often brittle reasoning associated with Coq's guardedness condition for corecursive definitions.…”
Section: Coinductive Contributionsmentioning
confidence: 99%
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