Over 32 years, Isabelle has made a long way from a small experimental proof assistant to a versatile platform for proof document development and maintenance. There has always been a challenge to keep up with the natural growth of applications, notably the Archive of Formal Proofs (AFP).
Can we scale this technology further, towards really big libraries of formalized mathematics?
Can the underlying Scala/JVM and Poly/ML platforms cope with the demands?
Can we eventually do 10 times more and better?
I will revisit these questions from the perspectives of
Editing: Prover IDE,
Building: batch-mode tools and background services,
Browsing: HTML views and client-server applications.
This is a study of performance requirements, technological side-conditions, and possibilities for scaling of formal proof document processing in Isabelle and The Archive of Formal Proofs (AFP). The approaches range from simple changes of system parameters and basic system programming with standard APIs to more ambitious reforms of Isabelle and the underlying Poly/ML system. The running examples for typical scalability issues are existing formalizations of classical analysis and differential equations. Such applications can be further extrapolated towards a development of Financial Mathematics (e.g. Itô calculus).
In the past 3 decades, Isabelle has made a long way from a modest LCF-style proof assistant (with copy-paste of proof scripts written in ML) to the current Isabelle/PIDE editor-environment (with its timeless and stateless processing of proof documents). In this presentation, I will try to extrapolate this into the future: How far can we scale proof documents and libraries, e.g. via moving Isabelle into the “cloud”? How can we reduce system resource requirements on the client side? How can we upgrade interactive edits produced by a single author, towards versioned changesets by multiple or distributed authors? What are suitable frameworks for the next generation of Isabelle document preparation? What can we make out of Isabelle/ML as ultra-clean environment for functional programming? Etc. etc.
The new Isabelle2017 release includes support for VSCode as alternative Prover IDE front-end. This continues earlier experiments and is released as Isabelle/VSCode 1.0. Note that Isabelle/jEdit had its 1.0 release in October 2011 and is presently at version 9.0.
Isabelle2017 provides the main Isabelle/Scala/PIDE functionality to connect to VSCode, using the official Language Server Protocol (with some PIDE add-ons). The front-end requires the extension called “Isabelle2017” from the VSCode marketplace: its README provides more information and installation instructions.
The Isabelle/VSCode project has been made possible thanks to funding by Aesthetic Integration (Grant Passmore and Denis Ignatovich).
The Docker image contains Ubuntu Linux with Isabelle2017. It can be used, e.g. on another Linux host like this:
docker pull makarius/isabelle:Isabelle2017
docker run makarius/isabelle:Isabelle2017
That provides command-line access to the regular isabelle tool wrapper, with indirection through the Docker container infrastructure.
The image already contains ML heaps for Isabelle/Pure and Isabelle/HOL. Here is an example to build more:
docker run makarius/isabelle:Isabelle2017 -s -b HOL-Library
Note that Docker is mainly for command-line tools on the “Cloud”. There is presently no Isabelle Prover IDE support, although very old-fashioned X11 connections can be made to work with extra tinkering.
As usual, the Isabelle release process is subject to the laws of causality: release candidates can be modified, but the final release is unchangeable. This means that testing needs to happen in the weeks before the final release, not after it.
The main ideas around Isabelle/PIDE go back to summer 2008. This is an overview of what has been achieved in the past 9 years, with some prospects for the future. Where can we go from here as Isabelle community? (E.g. towards alternative front-ends like Visual Studio Code; remote prover sessions “in the cloud”; support for collaborative editing of large formal libraries.) Where can we go as greater ITP community (Lean, Coq, HOL family)?
Here are some notable VSCode projects that were briefly mentioned in the talk:
Here is an interesting (draft) paper about Social Network structures in the Isabelle and Coq community, based on the main mailing lists of the two systems:
J. Fleuriot, S. Obua, Ph. Scott: Social Network Processes in the Isabelle and Coq Theorem Proving Communities.arXiv:1609.07127, September 2016.
Just a few comments of mine:
The isabelle-users mailing list is still the main forum for Isabelle users, but Stackoverflow is gaining more and more importance. Note that I helped to bring it in form in Mar-2013 (earning a badge for 30 days of continuous activity :-), but I am rarely participating there now, because I am too busy with the classic mailing lists.
The seasonal peaks on isabelle-users in Fig. 1 are due to the release process, which happens approx. every 8-10 months. In 2012, I started to make discussion of release candidates fully public on isabelle-users; before it was confined to isabelle-dev, which is also open to everyone, but has fewer participants.
Page 12: “This seems to indicate that there is some clear separation of expertise when it comes to the tool.” This is correct and follows a general principle of Isabelle development: there are areas of undisputed “experts” for certain parts of the system. Thus there is a clear responsibility to make that thrive in the long term. Often this assignment is a consequence of starting that area in the first place, or investing significant work in upgrading it (e.g. by a designated PhD or research project). My recurring appearance on Sledgehammer threads is mainly technological: I am responsible for underlying infrastructure for parallel ML programming and the Prover IDE; it also overlaps with overall system integration and release management due to the add-on ATP and SMT systems.
In recent years, I have economized my appearance on isabelle-users as follows:
Incoming messages are marked as important, when the topic overlaps with my areas of expertise. I rarely answer on the spot.
After some days, weeks, or months, I revisit marked message and make sure that questions are actually answered, or add a few remarks to discussion threads.
During the release candidate phases, I revisit all marked messages back to the previous release (or even one before that), to make sure that old technical problems are solved or remain in a reasonably well-defined state.
This means the mailing list also serves as an “issue tracker”. I’ve made some experiments with an explicit tracker just for the release process, but there was very little participation. Trackers tend to become a long-term storage for well-known and unresolved problems.
Microsoft is more and more becoming an Open Source company, e.g. it has joined the Linux foundation as Platinum member in November 2016. A notable Open Source project by Microsoft is Visual Studio Code: under the slogans “Code editing. Redefined. Free. Open Source. Runs everywhere.” it provides a very interesting editor framework, as a desktop application based on Node.js and TypeScript.
Isabelle/VSCode is now following this trend: I have spent some weeks in December 2016 / January 2017 with VSCode, using a little bit of TypeScript and implementing the new Language Server Protocol in Isabelle/Scala. The subsequent screenshot shows formal annotations produced by Isabelle/PIDE in the usual manner, while the editor rendering is all done by VSCode. For more information, see the report Isabelle/VSCode in January 2017.