Journal of Logical and Algebraic Methods in Programming ( IF 0.9 ) Pub Date : 2021-08-23 , DOI: 10.1016/j.jlamp.2021.100713 Mark Bickford 1 , Dexter Kozen 1 , Alexandra Silva 2
Moessner's theorem describes a procedure for generating a sequence of n integer sequences that lead unexpectedly to the sequence of nth powers , , , … . 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.
中文翻译:
在 Nuprl 中形式化 Moessner 定理和推广
Moessner 定理描述了生成n 个整数序列的序列的过程,这些序列意外地导致了n次幂的序列, , ,……。存在 Moessner 定理的几种推广。最近,Kozen 和 Silva 给出了包含 Moessner 原始定理及其已知概括的一般定理的代数证明。在这篇笔记中,我们描述了第一作者在Nuprl 中所做的这个定理的形式化。一方面,形式化仍然非常接近原始证明。另一方面,它在证明中带来了新的见解,指出了在钢笔和铅笔证明中永远不会引起任何反对意见但必须在机器形式化中解决的小差距和歧义。