Thirty-Three Years of Mathematicians and Software Engineers: A Case Study of Domain Expertise and Participation in Proof Assistant Ecosystems

As technical computing software, such as MATLAB and SciPy, has gained popularity, ecosystems of interdependent software solutions and communities have formed around these technologies. The development and maintenance of these technical computing ecosystems requires expertise in both software engineering and the underlying technical domain. The inherently interdisciplinary nature of these ecosystems presents unique challenges and opportunities that shape software development practices.Proof assistants, a type of technical computing software, aid users in the creation of formal proofs. In order to examine the influence of the underlying technical domain — mathematics — on the development of proof assistant ecosystems, we mined participant activity data from the code repositories and social channels of three popular proof assistants: Lean, Coq, Isabelle. Despite having a shared technical domain, we found little cross-pollination between contributors to the proof assistants. Additionally, we found that most long-term developers focused solely on technical work and did not participate in official social channels. We also found that proof assistant developers specialized into technical subfields. However, the proportion of specialists varied between ecosystems. We did not find evidence that these specialties contributed to fractures within the ecosystems. We discuss the implications of these results on the long-term health and sustainability of proof assistant ecosystems.