A quantitative model for simply typed λ-calculus

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Mathematical Structures in Computer Science Pub Date : 2021-11-29 DOI:10.1017/S0960129521000256

M. Hofmann, J. Ledent

引用次数: 0

Abstract

Abstract We use a simplified version of the framework of resource monoids, introduced by Dal Lago and Hofmann, to interpret simply typed λ-calculus with constants zero and successor. We then use this model to prove a simple quantitative result about bounding the size of the normal form of λ-terms. While the bound itself is already known, this is to our knowledge the first semantic proof of this fact. Our use of resource monoids differs from the other instances found in the literature, in that it measures the size of λ-terms rather than time complexity.

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单型λ微积分的定量模型

摘要利用Dal Lago和Hofmann引入的资源模群框架的简化版本来解释具有常数为零和后继的简单型λ-微积分。然后，我们用这个模型证明了一个简单的定量结果，关于λ-项的正规形式的大小边界。虽然界限本身是已知的，但据我们所知，这是对这一事实的第一个语义证明。我们对资源单群的使用不同于文献中发现的其他实例，因为它测量的是λ项的大小，而不是时间复杂度。

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

Mathematical Structures in Computer Science 工程技术-计算机：理论方法

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.