Category Archives: Isabelle

Intelligible semi-automatic reasoning in December 2015

A presentation on old and new aspects of Isabelle/Isar will happen 04-Dec-2015 10:00 at Univ. Bonn (Workgroup of Prof. Koepke). See also the web page of Oberseminar mathematische Logik.

Abstract:

Isabelle was introduced in 1989 (by L. Paulson) as a generic logical framework for higher-order natural deduction. Intelligible semi-automated reasoning (Isar) was introduced in 1999 (by M. Wenzel) as a structured proof language for human-readable formal proof documents. Today, in December 2015, we see large applications of Isabelle/Isar in the Isabelle/HOL object-logic, e.g. in the Archive of Formal Proofs with more than 240 entries.

After so many years, development of Isar is still not finished. Recent refinements of old concepts and additions of new concepts include: structured rule statements (Eigen-contexts), multi-branch elimination (case-splitting), structured backwards refinement. The new Eisbach language (by D. Matichuk et al) allows to define complex proof methods in their usual syntax, instead of traditional Isabelle/ML. Sledgehammer (by J. Blanchette et al) allows to generate semi-intelligible Isar proofs from machine-generated proofs (via external ATPs and SMTs).

The ultimate aim of Isabelle/Isar is to turn the results of formal proof production into mathematical documents with nice type-setting. Document source was mainly written in LaTeX in the past, but is now moving towards Markdown, with specific GUI support in the Prover IDE (Isabelle/jEdit).

The Slides are available.

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Isabelle Tutorial at Bonn

A tutorial on Isabelle for students of mathematics will happen 03/04-Dec-2015 at Univ. Bonn (Workgroup of Prof. Koepke). The detailed schedule is available on the web page of Praktikum Mathematische Logik. The main language of the tutorial is German; materials are in English.

Notable topics

  • Isabelle/Pure as logical framework for Natural Deduction
  • Isabelle/Isar as proof language for formalized mathematics
  • Isabelle/ML as environment for developing tools for logic applications (including Prover IDE support)

Prerequisites

The tutorial uses the following snapshot of the emerging winter release: Isabelle_01-Dec-2015.

Moreover, a full installation of LaTeX is required (Linux: TeX Live via package manager, Windows: MiKTeX, Mac OS X: MacTeX).

Materials

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Isabelle Tutorial at CADE-25

A full-day tutorial on Isabelle will happen Saturday 01-Aug-2015 in Berlin, as an associated event of the 25th International Conference on Automated Deduction (CADE-25). Here is some further organizational information about tutorials at CADE-25. Important materials for the tutorial are available at the bottom of this post.

More than 25 years ago, Isabelle was initiated by Larry Paulson as a logical framework for rapid prototyping of Natural-Deduction proof systems. Today, Isabelle is one of the major platforms for Interactive Theorem Proving (ITP), with notable support for automated reasoning tools (ATPs and SMTs). Isabelle/HOL is the main environment for applications; it is accompanied by the Archive of Formal Proofs (AFP) as repository for user-contributions. Isabelle supports logical tool development in Isabelle/ML and Isabelle/Scala, but it is also possible to connect external tools; this works routinely on Linux, Windows, and Mac OS X. The system presents itself to the end-user by an advanced Prover IDE: Isabelle/jEdit.

The purpose of the tutorial is to get acquainted with Isabelle, using the latest release Isabelle2015 (May 2015). Topics cover specifications in HOL, proofs in Isar, use of automated provers via Sledgehammer etc. The target audience are doctoral students or researchers with an interest in formalized reasoning, application of reasoning tools for interactive and automated proof development, maybe even with an interest to develop their own tools with/for Isabelle.

There will be presentations by Makarius Wenzel and Christian Sternagel, with hands-on tutoring and exercises done by the participants on their own computers (at least 2 cores and 4 GB memory).

Materials

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Release candidates for Isabelle2015

The release of Isabelle2015 is scheduled for this spring, presumably the end of May, or the start of June. As usual, there are several weeks for thorough testing of release candidates that are available here:

With ever increasing size and complexity of the system and its many add-on tools, it is important to take testing of release candidates seriously. Problems can be solved before the release, not after it!

The main forum for discussion is on isabelle-users mailing list.

The convergence towards the final release happens on the following repository.

Update: The final release of Isabelle2015 (May 2015) is now available from the Isabelle website. The above release candidates will disappear eventually.

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Proposal: document preparation improvements

(See also general notes on proposals.)

Isabelle/Isar is ultimately about beatiful proof documents, not profane “proof scripts”. This explains why high-quality rendering of theory files in PDF-LaTeX has been part of the game from early on. In the past 15 years, the Isabelle document preparation system has been applied to produce numerous articles, books, theses etc. based on content that is formally checked in the logic (usually Isabelle/HOL). Here is an arbitrary example from AFP.
The Isabelle manuals are usually produced as Isabelle documents as well, e.g. see the sources in the directory src/Doc of the Isabelle distribution.

Traditional Isabelle document preparation is a side-effect of a session build process that is run in batch-mode; see also the Isabelle System manual, chapters 2 and 3. The main command-line tools for session management with document preparation are isabelle mkroot and isabelle build. This edit-typeset-preview cycle works, but feels a bit awkward today, where interactive theory and proof development with continuous checking in the Prover IDE (PIDE) is used routinely. So it his high time for various renovations and reforms of Isabelle document preparation as sketched below.

Immediate build process of documents within the Prover IDE.
There is no particular reason why LaTeX should be run via batch-mode tools on the command-line. The Prover IDE could take care of that interactively, with much shorter turnaround cycles of the edit-typeset-preview cycle. To achieve that, parts of the document preparation in Isabelle/ML need to be moved to Isabelle/Scala, and slightly generalized to become stateless and applicable to partial/unfinished document sources.
GUI panel for document preparation in Isabelle/jEdit.
This should allow to control document preparation in the IDE, e.g. to specify which parts of the document are presently interesting, or to change options for LaTeX and add-on tools.
Improved error reporting from LaTeX

LaTeX error output should be parsed and presented within the Prover IDE adequately, with proper error positions over the original source text. The notoriously obscure LaTeX log files need to be overcome.
Light-weight document markup as in Markdown / Commonmark with approximative preview in the source.
Instead of old-fashioned LaTeX markup like \begin{itemize} \item ... \end{itemize} there could be more direct indication of itemization in the source (with actual bullets from the Isabelle symbol repertoire). Using conventions from Markdown, it would approximate a preview of the final typesetting already in the source text. Enumerations and description lists could be done similarly. Note that there is no need for sections (which are already supported via explicit Isar commands), nor for hyperlinks and other formal inserts (which are already supported via document antiquotations).
Improved HTML output
A subset of document markup that fits into the limited Markdown / Commonmark format sketched above could be taken as starting point for better HTML presentation, with relatively modest ambitions and technical requirements. It is important to recall that “HTML” as such is a huge and vaguely defined collection of standards: producing portable output that looks nice on most browsers requires significant expertise or special tools, or both.

A few improvements have already made it into the repository after Isabelle2014. For example, the repository version Isabelle/872f330a0f8a provides support for BibTeX files in Isabelle/jEdit. In Isabelle/9986fb541c87 there is also support for @{cite} antiquotations, with formal links etc.

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Proposal: remote prover connectivity for Isabelle/PIDE

(See also general notes on proposals.)

“Cloud computing” is one of these buzzwords without any particular meaning, but the idea to run heavy-duty computations remotely is rather old: some “big-iron” in the background provides the CPU and memory resources for substantial applications, while the user interacts with the system via some small local terminal. Already in the classic days of Proof General (around 1999) it was common-place to run Emacs locally on a workstation and the prover process remotely on a server (via rsh). Alternatively it was possible to run both the editor and the prover remotely and use X11 as display protocol, which was especially important for the rather heavy XEmacs of that time.

This normal mode of distributed computing was almost forgotten, when the performance of local laptops and remote servers were approaching the same order of magnitude (due to the demands of the gaming industry). This was only an episode over a single decade, though, and we are already back to the traditional situation where local and remote machines can differ significantly. In 2014, typical mobile devices were limited to 2–8 CPU cores and 2–8 GB RAM. This is very little compared to low-end workstations or high-end servers, with something like 8–36 CPU cores and 32–512 GB RAM, or more.

Note that some big Isabelle applications already go beyond the possibilities of small machines with only 4–8 GB RAM, but for more memory Poly/ML process needs to be switched from 32-bit to 64-bit mode, which also doubles the memory demands. Thus there is a discontinuity here: stepping out of the “small device” category means to go for 16–32 GB RAM minimum.

This motivates the demand for remote prover connectivity for Isabelle and its Prover IDE (PIDE). The most basic approach is to run the internal socket connection for the PIDE protocol between ML and Scala over ssh. This should be sufficient for fast and reliable local networks. For non-local networks, there are the usual questions about bandwidth, latency, and reliability of the connection. The PIDE protocol requires relatively high bandwidth (which is easily provided by common DSL connections), but can afford high latency due to its asynchronous nature. Lack of reliability might turn out a real problem, though: resetting a lost TCP/IP connection naively means to restart the prover process and recheck the whole session from start, which could take minutes or hours.

Thus a more advanced approach would keep both the ML and Scala side of PIDE together on the server. Remote access then works via a separate PIDE display protocol, which is postulated here and still needs to be defined and implemented. Depending on active buffers and open text areas in the editor, the remote side would provide continuous access to incoming PIDE document markup, without demanding persistent management of the whole PIDE state locally. Loosing the connection would merely mean to reconnect the IDE to the remote Isabelle/Scala/ML component, which keeps running indefinitely.

Thus the mode of operation becomes more like the re-connection facility of VNC or RDP (but not X11). Of course it is already possible today with Isabelle2014 to use VNC or RDP for a completely remote ML/Scala/IDE process, but remote ML/Scala and local IDE would make this more comfortable for the user, with better graphics performance and reactivity.

Taking this perspective of remote PIDE sessions one step further could mean to support low-bandwidth, high-latency, unreliable connections of mobile networks: sitting on a train with a laptop and local IDE, while re-connecting to a remote PIDE session on a big server, would really count as cloud computing. We should think here of editing whole libraries like AFP on the spot, with immediate feedback. A bit more efforts will be required to get there, though.

In summary, the following stages are possible, depending on the amount of resources spent on this subject:

  1. Simple remote PIDE socket connection via ssh, usable for fast and reliable local networks. (The jEdit text editor already provides some means to manage ssh, so this merely requires the usual study of sources with subsequent tinkering and polishing to make it work smoothly.)
  2. Separate PIDE display protocol where the editor is local and the Isabelle/Scala/ML session is remote. This should be usable for fast DSL network connections.
  3. Support for smooth disconnection and re-connection for mobile networks.
  4. Development of a completely different PIDE front-end that works on tablets or smart-phones (Android or iOS).

The last point is speculative: it merely sketches to horizon of what could eventually be targeted, if there were lots of resources and several enthusiastic people working on it.

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Isabelle Tutorial at CADE-25

(See also updated version with more details.)

A full-day tutorial on Isabelle is scheduled as associated event of the 25th International Conference on Automated Deduction (CADE-25), which will take place in Berlin at the start of August 2015.

More than 25 years ago, Isabelle was initiated by Larry Paulson as a logical framework for rapid prototyping of Natural-Deduction proof systems. Today, Isabelle is one of the major platforms for Interactive Theorem Proving (ITP), with notable support for automated reasoning tools (ATPs and SMTs). Isabelle/HOL is the main environment for applications; it is accompanied by the Archive of Formal Proofs (AFP) as repository for user-contributions. Isabelle supports logical tool development in Isabelle/ML and Isabelle/Scala, but it is also possible to connect external tools; this works routinely on Linux, Windows, and Mac OS X. The system presents itself to the end-user by an advanced Prover IDE: Isabelle/jEdit.

The purpose of the tutorial is to help participants to get acquainted with Isabelle: topics will cover specifications in HOL, proofs in Isar, use of automated provers via Sledgehammer etc. The target audience are doctoral students or researchers with an interest in formalized reasoning, application of reasoning tools for interactive and automated proof development, maybe even with an interest to develop their own tools with/for Isabelle.

There will be presentations by myself and one or two colleagues, with hands-on tutoring and exercises done by the participants on their own computers (with at least 2 cores and 4 GB memory).

Further organizational details will emerge sooner or later, as summer 2015 approaches. Watch this space, as well as the main CADE-25 website.

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Isabelle/PIDE as IDE for Standard ML

Strictly speaking the Isabelle environment is for interactive and automated theorem proving, but its SML IDE support is quite sophisticated: source files are statically checked and semantically evaluated while the user is editing. The annotated sources contain markup about inferred types, references to defining positions of items etc.

As a quick start, see the Documentation panel, section Examples, entry src/Tools/SML/Examples.thy (as of Isabelle2014).

SML-PIDE

The time where SML sources need to be edited with vi or emacs are over. See also this related thread on Stackoverflow.

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