Formal Mathematics on Display: A Wiki

Abstract. The Agora system is a prototype “Wiki for Formal Math-ematics”, with an aim to support developing and documenting large formalizations of mathematics in a proof assistant. The functions imple-mented in Agora include in-browser editing, strong AI/ATP proof advice, verification, and HTML rendering. The HTML rendering contains hy-perlinks and provides on-demand explanation of the proof state for each proof step. In the present paper we show the prototype Flyspeck Wiki as an instance of Agora for HOL Light formalizations. The wiki can be used for formalizations of mathematics and for writing informal wiki pages about mathematics. Such informal pages may contain islands of formal text, which is used here for providing an initial cross-linking between Hales’s informal Flyspeck book, and the formal Flyspeck development. The Agora platform intends to address distributed wiki-style collabo-ration on large formalization projects, in particular both the aspect of immediate editing, verification and rendering of formal code, and the aspect of gradual and mutual refactoring and correspondence of the ini-tial informal text and its formalization. Here, we highlight these features within the Flyspeck Wiki.