Proof in Context — Web Editing with Rich, Modeless Contextual Feedback

Abstract

The Agora system is a prototypical Wiki for formal mathematics: a web-based system for collaborating on formal mathematics, intended to support informal documentation of formal developments. This system requires a reusable proof editor component, both for collaborative editing of documents, and for embedding in the resulting documents. This paper describes the design of Agora's asynchronous editor, that is generic enough to support different tools working on editor content and providing contextual information, with interactive theorem proverss being a special, but important, case described in detail for the Coq theorem prover

Formal Mathematics on Display: A Wiki for Flyspeck

“…With Agora, we also want to lower the threshold for participating in formalization projects by providing an easy-to-use web interface to a proof assistant [8]. This allows people to cooperate on a project, the files of which are stored on the server.…”

“…Editing We can directly use the tools that turn text into frames for building the server backend of a (simple) web-based editor: the front end of this editor just gathers the entered text and sends it to the server, the server processes it into a list of frames and post-processes it: both by generating proof assistant (HOL Light) responses and by sending markup information based on the correctness of a part of the text. Because this processing is incremental, information can be returned on demand: after the text has been parsed into frames, the server can give the editor information as it is produced, using the protocols described in [8]. As also described in that paper, it remains an open question on how to properly deal with the impact of the formal text written in the editor, as this might invalidate the entire repository.…”

“…If an ATP proof is found, it is minimized and reconstructed by a number of reconstruction strategies described in [22]. In parallel to such AI/ATP 8 To help this, we also use the theorem names stored by the HOL Light processing in the "theorems" file, using the mechanisms from the file update database **.ml.…”