A Complete Equational Axiomatisation of Partial Differentiation

Q3 Computer Science

Electronic Notes in Theoretical Computer Science Pub Date : 2020-10-01 DOI:10.1016/j.entcs.2020.09.011

Gordon D. Plotkin

引用次数: 1

Abstract

We formalise the well-known rules of partial differentiation in a version of equational logic with function variables and binding constructs. We prove the resulting theory is complete with respect to polynomial interpretations. The proof makes use of Severi's interpolation theorem that all multivariate Hermite problems are solvable. We also present a number of related results, such as decidability and equational completeness.

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偏微分的完全等式公理化

我们将众所周知的偏微分规则形式化成一个带有函数变量和绑定构造的等式逻辑。我们用多项式解释证明了所得理论是完备的。利用塞维里插值定理证明了所有多元埃尔米特问题都是可解的。我们也给出了一些相关的结果，如可决性和等式完备性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Notes in Theoretical Computer Science Computer Science-Computer Science (all)

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