Partiality and recursion in interactive theorem provers – an overview
Journal article, 2016

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.


Ana Bove

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Alexander Krauss

Technical University of Munich

Matthieu Sozeau

Institut National de Recherche en Informatique et en Automatique (INRIA)

Mathematical Structures in Computer Science

0960-1295 (ISSN) 1469-8072 (eISSN)

Vol. 26 1 38-88

Areas of Advance

Information and Communication Technology

Subject Categories

Computer and Information Science

Computer Science



More information

Latest update