Mining the Archive of Formal Proofs

Abstract

International audienceThe Archive of Formal Proofs is a vast collection of computer-checked proofs developed using the proof assistant Isabelle. We perform an in-depth analysis of the archive, looking at various properties of the proof developments, including size, dependencies, and proof style. This gives some insights into the nature of formal proofs

Exploration of neural machine translation in autoformalization of mathematics in Mizar

“…This is the largest formal library that the ITP community can provide that has a comparable size to a natural language corpus. The only contender is the Isabelle library and its Archive of Formal Proofs [9], which has more formalized computer science knowledge, but less mathematics that can be overlayed with LaTeX texts. It is mainly because of the library size that we chose Mizar as our formal language.…”

QED at Large: A Survey of Engineering of Formally Verified Software

“…While most proof languages were designed with mathematics in mind, their use has not been confined to mathematics. For example, using Isar is recommended style for submission to the Isabelle Archive of Formal Proofs (Klein et al, 2004(Klein et al, -2019, which consists of more computer science than mathematics formalizations (Blanchette et al, 2015).…”

“…Proof assistants projects are software artifacts, and can thus be packaged and distributed in a similar way. For Isabelle/HOL, the venue for distribution is the Archive of Formal Proofs (Klein et al, 2004(Klein et al, -2019Blanchette et al, 2015). Coq uses the OCaml infrastructure around the OPAM package manager to provide a similar collection of packages (Coq development team, 2018).…”

Topological structures as a tool for formal modelling of rough sets

“…But the real properties of the topology (both ∅ and the whole universe should be open; the family should be closed for finite intersections and arbitrary unions) is given by the Mizar attribute which is in fact an adjective (TopSpace-like). Making appropriate hierarchy for well-established notions is really crucial for the repository of formal texts; if we are interested only in pure predicates and computer-generated proofs, readability is something which does not really matters (and this is the case of the part of Isabelle's Archive of Formal Proofs [3] devoted to software verification), however from a viewpoint of reusability of adjectives, when large databases are involved, this is a question of efficiency. As a simple nontrivial example, we can mention the net of cross-linked properties of rough approximation operators under various conditions as reflexivity, symmetry, transitivity -as canonical examples, but also with seriality, positive and negative alliance as less straightforward ones.…”