Category Archives: Science

Isabelle, Science

Invited talk at Malinca Kickoff-Meeting in Paris

I have attended the Malinca project Kickoff-Meeting from 01..03-Oct-2025, and delivered an invited talk about Human-readable Proof Documents and Embedded Sublanguages in Isabelle/Isar.

Abtract:

Isabelle/Pure was originally introduced by Paulson (1986/1989) as a Logical Framework to specify object-logics declaratively, based on Higher-order Natural Deduction. Isabelle/HOL emerged soon as main object-logic and Isabelle application, with many tools for specifications and proofs written in Isabelle/ML.

Isabelle/Isar was added by Wenzel (1999) as a structured language for Human-readable formal proof documents: it works with Isabelle/Pure and regular object-logics. The proof language has been reworked over the decades, with notable extensions in 2015/2016, including the Eisbach language for Isar Proof Methods. Already, from the beginning, Isar had been accompanied by the Isabelle Document language, to write mathematical texts with high-quality typesetting in LaTeX.

So today we may see Isabelle as an agglomeration of many languages for different purposes, all integrated into a single System Framework in Isabelle/Scala. That includes the Isabelle/PIDE Prover IDE with parallel and asynchronous processing of formal documents, and the Isabelle build system (with its distributed cluster manager). Thus we can carry the weight and gravity of large proof documents, as e.g. seen in the Archive of Formal Proofs (AFP).

Isabelle, Scala, Science

Isabelle as System Platform for the Archive of Formal Proofs (AFP)

At the Dagstuhl-Seminar 23401 Automated mathematics: integrating proofs, algorithms and data (01..06-Oct-2023), I delivered a talk on Isabelle as System Platform for the Archive of Formal Proofs (AFP) .

Abstract:

Isabelle is usually seen as an interactive proof assistant, mostly for Higher-Order Logic (HOL), but that is somehow accidental. In reality, Isabelle is a system platform for functional programming and formal proofs, with sufficient infrastructure to carry its own weight and gravity. The Archive of Formal Proofs (AFP) is the official collection of Isabelle applications that is maintained together with the base system. That poses ever growing demands on the Isabelle platform. This talk gives an overviewof Isabelle software technology, with specific focus on Programming and Scaling, e.g. distributed build clusters for AFP.

See also the slides, which contain further links to relevant materials.

Isabelle, Science

Isabelle Workshop 2022 at FLoC

Following our usual 2-years cycle, we have another Isabelle Workshop on Thu 11-Aug-2022. This will be a truly hybrid event: the organizers of the FLoC multiconference will provide local facilities at the Technion Haifa; this will include a digital projector and network connection. We will use that to provide our own virtual facilities on top, to accommodate remote participants via BigBlueButton hosted at TU Munich.

The remote organizers of the workshop, including myself, are very grateful to the few heroic colleagues who will be there in Haifa, despite these confused times of plague and war – and rather expensive conference registration.

Isabelle, Science

Talk on Export of formal theory content

On 22-Nov-2019 I have delivered the following talk at TUM (Garching bei München):

Title:
Export of formal theory content in Isabelle/Scala
Abstract:
This is an overview of the state of affairs of systematic export of formal theory content. The general motivation is to provide semantically enriched views on the Isabelle/AFP library, without requiring a running Isabelle process. A typical application could be search over a database of digested theories, e.g. for an AFP web service.
Materials:
Slides with sources, which include practically relevant links and examples.
Isabelle, PIDE, Science

MMT as component for Isabelle2019

MMT is a language, system and library (in Scala) to represent a broad range of languages in the OMDoc format: this supports formal, informal, semi-formal content. The MMT repository includes
general APIs to operate on OMDoc theories, together with various tools and applications. There are several MMT sub-projects to connect to other systems. This includes Isabelle/MMT, which appeared as preliminary version already in Nov-2018.

The release of Isabelle2019 (June 2019) is an opportunity to distribute MMT version 17.0.0 (May 2019) as Isabelle application. An alternative is to incorporate the underlying Isabelle component manually into Isabelle2019 in $ISABELLE_HOME_USER/etc/settings like this: init_component ".../mmt-20190611" — where the three dots refer to the directory where the component tar.gz has been unpacked.

In either case, the mmt.jar of the MMT distribution is included in the Isabelle/Scala package name space. The component provides Isabelle command-line tools as follows:

  • isabelle mmt_build to (re)build the MMT project inside the Isabelle system environment (only required after change of the Scala sources)
  • isabelle mmt_import to import the content of a headless Isabelle/PIDE session into MMT (OMDoc and RDF/XML triples)
  • isabelle mmt_server to present imported content using the built-in HTTP server of MMT
  • isabelle mmt to run the interactive MMT shell inside the Isabelle system environment, e.g. for experimentation within the Isabelle + MMT package namespace, using the scala sub-shell.

The main functionality is provided by isabelle mmt_import: that is a medium-sized Scala module (57KB) within the MMT code-base (file src/mmt-isabelle/src/info/kwarc/mmt/isabelle/Importer.scala). It refers to general export facilities of Isabelle/Scala, which are part of the Isabelle2019 distribution (file src/Pure/Thy/export_theory.scala). The latter may be studied independently of MMT in the implementation of the isabelle dump tool (file src/Pure/Tools/dump.scala); see also the Isabelle System Manual, section 2.6.

The following papers provide further explanations on Isabelle/MMT:

Isabelle, PIDE, Science

Isabelle/Naproche for Automatic Proof-Checking of Ordinary Mathematical Texts

Naproche-SAD is a recent tool by Frerix and Koepke, based on the original System for Automated Deduction (SAD) by Paskevich and others. It processes the Formal Theory Language (ForTheL), which is designed to look like mathematical text, but it is restricted to a small subset of natural language.

The tool is implemented in Haskell as a plain function from input text to output messages. A file is like a chapter of mathematical text, with a nested tree-structure of elements and sub-elements (for signatures, axiomatizations, statements, proofs). Output messages inform about the translation of mathematical text to problems of first-order logic, and indicate success or failure of external proof checking; the latter is delegated to the E Prover by Stephan Schulz and can take several seconds for each proof obligation.

To integrate Naproche-SAD into PIDE, Frerix and Wenzel have reworked the Haskell program over 2 months in 2018, to turn the command-line tool into a service for reactive checking of ForTheL texts. Isabelle integration was done via the new Isabelle/Haskell library and some glue code in Isabelle/Scala to register ForTheL as auxiliary file-format (extension .ftl).

[Isabelle/Naproche screenshot]

The resulting Isabelle/Naproche application is available as multi-platform download. A running instance is shown in the screenshot: users can directly open ForTheL files (e.g. from Documentation / Examples) and wait briefly to see output messages attached to the text in the usual IDE manner. Further edits produce a new version of the text, which is sent in total to Naproche-SAD again. The back-end is sufficiently smart to avoid redundant checking of unchanged sub-elements: it keeps a global state with results of old versions: this is easy to implement as the program keeps running until shutdown of Isabelle/PIDE.

(Cited from section 1.2 of the paper Interaction with Formal Mathematical Documents in Isabelle/PIDE.)

Isabelle, PIDE, Science

Isabelle presentations at LSV Paris/Cachan

During the two weeks of 17..28-Jun-2019, I will be visiting Deducteam at LSV, Paris/Cachan. There will be two presentations about Isabelle technology for formal documents and libraries:

  1. Interaction with Formal Mathematical Documents in Isabelle/PIDE (with slides) – Tuesday 18-Jun-2019, 11:00, Pavillon du Jardin, ENS Cachan.
  2. Isabelle technology for the Archive of Formal Proofs (with slides) – Thursday 20-Jun-2019, 14:00, LSV library.

See also the official announcement of Deducteam.

Note: These talks will be repeated at the Conference on Intelligent Computer Mathematics (CICM 2019), Prague (CZ), 08..12-Jul-2019.

Isabelle, PIDE, Science

Interaction with Formal Mathematical Documents in Isabelle/PIDE (at CICM 2019, Prague)

At the Conference for Intelligent Computer Mathematics (CICM 2019) in Prague (08..12-Jul-2019), I will give a keynote presentation on the track Mathematical Knowledge Management (MKM).

Title:
Interaction with Formal Mathematical Documents in Isabelle/PIDE
Abstract:
Isabelle/PIDE has emerged over more than 10 years as the standard Prover IDE for interactive theorem proving in Isabelle. The well-established Archive of Formal Proofs (AFP) testifies the success of such applications of formalized mathematics in Isabelle/HOL. More recently, the scope of PIDE has widened towards languages that are not connected to logic and proof in Isabelle, but taken from a broader repertoire of mathematics on the computer. The present paper provides a general overview of the PIDE project and its underlying document model, with built-in parallel evaluation and asynchronous interaction. There is also some discussion of original aims and approaches, successes and failures, later changes to the plan, and ideas for the future.
Paper:
Preprint from ArXiv