非标准分析的有状态实现器

IF 0.6 4区 数学 Q4 COMPUTER SCIENCE, THEORY & METHODS Logical Methods in Computer Science Pub Date : 2023-04-25 DOI:10.46298/lmcs-19(2:7)2023
Bruno Dinis, Étienne Miquey
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引用次数: 0

摘要

本文提出了一种非标准算术可实现性解释的新方法。我们在(半)直觉可实现的背景下处理非标准分析,重点讨论了Lightstone-Robinson通过超幂的非标准分析模型的构造。特别地,我们考虑将$\lambda$-演算扩展为包含一个整数(状态)的内存单元,以指示在超功率$\cal{M}^{\mathbb{N}}$的哪个切片中进行计算。我们关注在这种情况下可获得的非标准原理(及其计算内容)。特别是,我们给出了理想化的非平凡实现器和LLPO原理的非标准版本。然后,我们讨论了如何对这个乘积进行商,以模拟Lightstone-Robinson结构。
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Stateful Realizers for Nonstandard Analysis
In this paper we propose a new approach to realizability interpretations for nonstandard arithmetic. We deal with nonstandard analysis in the context of (semi)intuitionistic realizability, focusing on the Lightstone-Robinson construction of a model for nonstandard analysis through an ultrapower. In particular, we consider an extension of the $\lambda$-calculus with a memory cell, that contains an integer (the state), in order to indicate in which slice of the ultrapower $\cal{M}^{\mathbb{N}}$ the computation is being done. We pay attention to the nonstandard principles (and their computational content) obtainable in this setting. In particular, we give non-trivial realizers to Idealization and a non-standard version of the LLPO principle. We then discuss how to quotient this product to mimic the Lightstone-Robinson construction.
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来源期刊
Logical Methods in Computer Science
Logical Methods in Computer Science 工程技术-计算机:理论方法
CiteScore
1.80
自引率
0.00%
发文量
105
审稿时长
6-12 weeks
期刊介绍: Logical Methods in Computer Science is a fully refereed, open access, free, electronic journal. It welcomes papers on theoretical and practical areas in computer science involving logical methods, taken in a broad sense; some particular areas within its scope are listed below. Papers are refereed in the traditional way, with two or more referees per paper. Copyright is retained by the author. Topics of Logical Methods in Computer Science: Algebraic methods Automata and logic Automated deduction Categorical models and logic Coalgebraic methods Computability and Logic Computer-aided verification Concurrency theory Constraint programming Cyber-physical systems Database theory Defeasible reasoning Domain theory Emerging topics: Computational systems in biology Emerging topics: Quantum computation and logic Finite model theory Formalized mathematics Functional programming and lambda calculus Inductive logic and learning Interactive proof checking Logic and algorithms Logic and complexity Logic and games Logic and probability Logic for knowledge representation Logic programming Logics of programs Modal and temporal logics Program analysis and type checking Program development and specification Proof complexity Real time and hybrid systems Reasoning about actions and planning Satisfiability Security Semantics of programming languages Term rewriting and equational logic Type theory and constructive mathematics.
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