Partiality and recursion in interactive theorem provers – an overview

Author:

BOVE ANA,KRAUSS ALEXANDER,SOZEAU MATTHIEU

Abstract

The use of interactive theorem provers to establish the correctness of critical parts of a software development or for formalizing mathematics is becoming more common and feasible in practice. However, most mature theorem provers lack a direct treatment of partial and general recursive functions; overcoming this weakness has been the objective of intensive research during the last decades. In this article, we review several techniques that have been proposed in the literature to simplify the formalization of partial and general recursive functions in interactive theorem provers. Moreover, we classify the techniques according to their theoretical basis and their practical use. This uniform presentation of the different techniques facilitates the comparison and highlights their commonalities and differences, as well as their relative advantages and limitations. We focus on theorem provers based on constructive type theory (in particular, Agda and Coq) and higher-order logic (in particular Isabelle/HOL). Other systems and logics are covered to a certain extent, but not exhaustively. In addition to the description of the techniques, we also demonstrate tools which facilitate working with the problematic functions in particular theorem provers.

Publisher

Cambridge University Press (CUP)

Subject

Computer Science Applications,Mathematics (miscellaneous)

Cited by 9 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Formal definitions and proofs for partial (co)recursive functions;Journal of Logical and Algebraic Methods in Programming;2024-10

2. A Type-Based Approach to Divide-and-Conquer Recursion in Coq;Proceedings of the ACM on Programming Languages;2023-01-09

3. Strong functional pearl: Harper’s regular-expression matcher in Cedille;Proceedings of the ACM on Programming Languages;2020-08-02

4. Fundamental Proof Methods in Computer Science: A Computer-Based Approach, by Arkoudas and Musser, The MIT Press, Cambridge, USA, ISBN 978-0-262-03553-8;Theory and Practice of Logic Programming;2020-06-10

5. Partial type constructors: or, making ad hoc datatypes less ad hoc;Proceedings of the ACM on Programming Languages;2020-01

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