一种基于模式匹配的(面向机器的)逻辑

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS Mathematical Structures in Computer Science Pub Date : 2023-07-05 DOI:10.1017/s0960129523000191
Tim Lethen
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引用次数: 0

摘要

Robinson的统一算法可以被认为是命题逻辑中的C. Meredith规则D(凝聚分离)以及lambda演算和组合逻辑中主类型构造的基础机制。在组合逻辑中,它在Meyer, Bunder & Powers的Fool模型的构建中也起着至关重要的作用。本文现在考虑模式匹配,即统一的单向变体,作为逻辑推理、类型化和无类型化组合逻辑的一个非常简单和自然的模型的基础。对新类型方案的分析将使我们能够描述一大类组合逻辑项,它们在弱约简时不会改变其主类型。我们还考虑了应该使用大前提还是小前提作为固定模式的问题。
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A (machine-oriented) logic based on pattern matching
Robinson’s unification algorithm can be identified as the underlying machinery of both C. Meredith’s rule D (condensed detachment) in propositional logic and of the construction of principal types in lambda calculus and combinatory logic. In combinatory logic, it also plays a crucial role in the construction of Meyer, Bunder & Powers’ Fool’s model. This paper now considers pattern matching, the unidirectional variant of unification, as a basis for logical inference, typing, and a very simple and natural model for untyped combinatory logic. An analysis of the new typing scheme will enable us to characterize a large class of terms of combinatory logic which do not change their principal type when being weakly reduced. We also consider the question whether the major or the minor premisse should be used as the fixed pattern.
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来源期刊
Mathematical Structures in Computer Science
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
30
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.
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