Proviola: A Tool for Proof Re-animation

Abstract

To improve on existing models of interaction with a proof assistant (PA), in particular for storage and replay of proofs, we introduce three related concepts, those of: a proof movie, consisting of frames which record both user input and the corresponding PA response; a camera, which films a user's interactive session with a PA as a movie; and a proviola, which replays a movie frame-by-frame to a third party. In this paper we describe the movie data structure and we discuss a prototype implementation of the camera and proviola based on the ProofWeb system [7]. ProofWeb uncouples the interaction with a PA via a webinterface (the client) from the actual PA that resides on the server. Our camera films a movie by "listening" to the ProofWeb communication. The first reason for developing movies is to uncouple the reviewing of a formal proof from the PA used to develop it: the movie concept enables users to discuss small code fragments without the need to install the PA or to load a whole library into it. Other advantages include the possibility to develop a separate commentary track to discuss or explain the PA interaction. We assert that a combined camera+proviola provides a generic layer between a client (user) and a server (PA). Finally we claim that movies are the right type of data to be stored in an encyclopedia of formalized mathematics, based on our experience in filming the Coq standard library. ⋆ The final publication of this paper is available at www.springerlink.com

jsCoq: Towards Hybrid Theorem Proving Interfaces

“…Also, support for interactive elements -think of a "Coq box", i.e., an HTML div that is filled with the result of the execution of some Coq program -is a must. We are also very close to providing Proviola-like [27] functionality, that is to say, a system where the user can interactively perform proof replay.…”

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

“…The client and the server share the proof's state in a proof movie [14], but each represents the model differently. This section describes the different models, including the model used to communicate changes from the server to the client.…”

“…Taken together, these commands form a proof script, which can be distributed to other users of the theorem prover. Because the script is meaningless without the proof states, a system that wants to give readers stand-alone access to the proofs should provide the proof states as well, a model which we explored with the Proviola tool [14].…”

Communicating Formal Proofs: The Case of Flyspeck

“…Moreover, these publications hardly give access to the formalization, but describe the project on a rather high level of abstraction. The Journal of Formalized Reasoning 4 , the Archive of Formal Proofs 5 and the Journal of Formalized Mathematics 6 try to improve on this by explicitly giving a platform for formalizations (the latter for Mizar), but that is not really taking off.…”

“…When hovering over the formal proofs, one sees the proof state at that point, so a reader can observe what the action of the proof commands is. This uses the Proviola technology that we have previously developed and described [4]. 3.…”