单型λ微积分中λβ约简的证明理论研究

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-09-23 DOI:10.1016/j.apal.2025.103657

William Stirton

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引用次数: 0

摘要

本文定义了一个由单型λ项到自然数的函数f，并证明了，如果M是由任意λβ-索引缩并到另一项M内形成的单型λ项，则f(M) <f(M)。与之前类似定理的证明不同，收缩的索引可以是完全任意的，即不受规则（ξ）的任何限制。函数f本身与sch特的证明理论（1977）中定义的一个类似的函数相关，并且在计算上并不困难。

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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Proof-theoretic investigation of λβ-reduction in the simply typed λ-calculus

The paper defines a function f from simply typed λ-terms to natural numbers and proves that, if

M^{⁎}

is a simply typed λ-term formed by contracting an arbitrary λβ-redex within another term M, then

f (M^{⁎}) < f (M)

. Unlike previous proofs of similar theorems, the redex contracted may be completely arbitrary, i.e. without any restriction on rule (ξ). The function f itself is related to, and no more computationally difficult than, a similar-looking function defined in Schütte's Proof Theory (1977).

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.