Automated Improving of Proof Legibility in the Mizar System

Both easily readable and obscure proof scripts can be found in the bodies of formalisations around formal proof checking environments such as Mizar. The communities that use this system try to encourage writing legible texts by making available various solutions, e.g., by introduction of phrases and constructs that make formal deductions look closer to the informal ones. Still, many authors do not want to invest additional efforts in enhancing readability of their scripts and assume this can be handled automatically for them. Therefore, it is desirable to create a tool that can automatically improve legibility of proofs. It turns out that this goal is non-trivial since improving features of text that enhance legibility is in general NP-complete.

The successful application of SMT technology to solving computationally difficult problems suggests that available SMT solvers can give progress in legibility enhancement. In this paper we present the first experimental results obtained with automated legibility improving tools for the Mizar system that use Z3 solver in the backend.