All posts by Makarius

Foundations of Higher-Order Logic at Curry Club Augsburg

On Thu 01-Dec-2016 there will be a presentation about “Foundations of Higher-Order Logic with Classical Reasoning and Hilbert-Choice” at Curry Club Augsburg.

Start: approximately 19:00
Duration: approximately 90min
Language of the talk: German

Overview:

  • History of Higher-Order Logic
  • Implementations of HOL
  • Quasi-programming in Isabelle/HOL
  • Isabelle foundations: primitive inferences, object-logic rules, rule composition, structured proofs
  • Foundations of Higher-Order Logic: actual Isabelle/HOL, Pure bootstrap of HOL
  • Isabelle theory with some exercises (for Isabelle2016-1)

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Release candidates for Isabelle2016-1

The coming Isabelle2016-1 release is scheduled for December 2016. This spot is continuously updated to inform about the ongoing process of testing release candidates.

  • On 07-Oct-2016 an informal snapshot Isabelle2016-1-RC0 was published.
  • On 28-Oct-2016 the release candidate Isabelle2016-1-RC1 was published. Serious testing by users is now required, to expose remaining problems.
  • On 06-Nov-2016 the release candidate Isabelle2016-1-RC2 was published. Various details have been consolidated.
  • On 22-Nov-2016 the release candidate Isabelle2016-1-RC3 was published. More fine points have been consolidated. A component for the new experimental Nunchaku tool has been included.
  • On 27-Nov-2016 the release candidate Isabelle2016-1-RC4 was published. It introduces the following important last-minute changes:
    1. Prover IDE: more aggressive flushing of machine-generated input
    2. Sledgehammer: MaSh is faster and less likely to hang seemingly forever
    3. fine-tuning of Isabelle/LaTeX typesetting
  • On 08-Dec-2016 the release candidate Isabelle2016-1-RC5 was published, presumably the last one. It introduces the following important last-minute changes:
    1. more uniform automatic indentation (empty vs. non-empty lines)
    2. fewer tracing/warning messages in some proof tools

The Isabelle release process is subject to the laws of causality: release candidates can be modified, but the final release remains final. Testing needs to happen in the weeks before the final release, not after it.

The main forum for discussion of Isabelle2016-1 release candidates is on isabelle-users mailing list.

Update 13-Dec-2016: The final release of Isabelle2016-1 (December 2016) is now available from the Isabelle website. The above release candidates will disappear eventually.

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Isabelle/PIDE as IDE for ML

On Friday 18-Nov-2016 10:00, I will give a presentation about PIDE at Laboratoire de Recherche en Informatique, Orsay (Paris Sud).

Abstract:

Isabelle is usually positioned as environment for interactive and automated theorem proving, but its Prover IDE (PIDE) may be used for regular program development as well. Standard ML is particularly important here, since it is the bootstrap language of Isabelle/ML (i.e. SML with many add-ons) and Isabelle/Pure (i.e. the logical framework).

The ML IDE functionality of Isabelle + Poly/ML is manifold:

  • Continuous feedback from static analysis and semantic evaluation is already available for years, e.g. Isabelle2014 (August 2014). It is a corollary of how PIDE interaction works, and of the integration of the Poly/ML compiler into that framework. 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.
  • Source-level debugging within the IDE is new in Poly/ML 5.6, which is bundled with Isabelle2016 (February 2016). The Prover IDE provides the Debugger dockable to connect to running ML threads, inspect the stack frame with local ML bindings, and evaluate ML expressions in a particular run-time context. See also here.
  • IDE support for the Isabelle/Pure bootstrap process is new technology for the coming release of Isabelle2016-1 (December 2016). The ROOT.ML file acts like a quasi-theory in the context of theory ML_Bootstrap: this allows continuous checking of all loaded ML files. The theory file is presented with a modified header to import Pure from the running Isabelle instance.
  • It is also possible to modify standalone SML projects, to edit the sources freely in the ML IDE. For example, MetiTarski can participate after some trivial changes of its ROOT.ML file.

Overall, we move more and more to an integrated framework for development of formal-reasoning tools, but other applications are admissible as well.

The Slides are available, together with their sources (which are required for the live system demo).

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Isabelle/PIDE — from Interactive Theorem Proving to Integrated Theorem Proving

On Tuesday 15-Nov-2016 14:00, I will give a presentation about PIDE at Laboratoire Spécification et Vérification, Cachan (Paris). See also the official announcement.

Abstract:

Interactive theorem proving was historically tied to the read-eval-print loop, with sequential and synchronous evaluation of prover commands given on the command-line. This user-interface technology was adequate when Robin Milner introduced his LCF proof assistant in the 1970s, but today it severely restricts the potential of multicore hardware and advanced IDE front-ends.

The Isabelle Prover IDE breaks this loop and retrofits the read-eval-print phases into an asynchronous model of document-oriented proof processing. Instead of feeding a sequence of commands into the prover process, the primary interface works via edits over immutable document versions. Execution is implicit and managed by the prover in a timeless and stateless manner, making adequate use of parallel hardware.

PIDE document content consists of the theory sources (with dependencies via theory imports), and auxiliary source files of arbitrary user-defined format: this allows to integrate other languages than Isabelle/Isar into the IDE. A notable application is the Isabelle/ML IDE, which can be also applied to the system itself, to support interactive bootstrapping of the Isabelle/Pure implementation.

Further tool integration works via “asynchronous print functions” that operate on already checked theory sources. Thus long-running or potentially non-terminating processes may provide spontaneous feedback while the user is editing. Applications range from traditional proof state output (which often consumes substantial run-time) to automated provers and dis-provers that report on existing proof document content (e.g. Sledgehammer, Nitpick, Quickcheck in Isabelle/HOL). It is also possible to integrate “query operations” via additional GUI panels with separate input and output (e.g. for manual Sledgehammer invocation or find-theorems).

Thus the Prover IDE orchestrates a suite of tools that help the user to write proofs. In particular, the classic distinction of ATP and ITP is overcome in this emerging paradigm of Integrated Theorem Proving.

The Slides are available.

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Grant Olney Passmore on Formal Verification of Financial Algorithms

On 25-Aug-2016, Grant Olney Passmore from Aesthetic Integration gave an invited talk at the ITP 2016 conference in Nancy, France. Here is the official announcement from the program:

Title: Formal Verification of Financial Algorithms, Progress and Prospects

Abstract:
Many deep issues plaguing today’s financial markets are symptoms of a fundamental problem: The complexity of algorithms underlying modern finance has significantly outpaced the power of traditional tools used to design and regulate them. At Aesthetic Integration, we’ve pioneered the use of formal verification for analysing the safety and fairness of financial algorithms. With a focus on financial infrastructure (e.g., the matching logics of exchanges and dark pools), we’ll describe the landscape, and illustrate our Imandra formal verification system on a number of real-world examples. We’ll sketch many open problems and future directions along the way.

The session chair introduced the speaker as a colleague from the prover community who managed to get his private life covered by the NY Times.

Passmore then started his presentation with a promotional video, which is intended for people from the Financial Industry – without a background in formal logic or software verification. He pointed out that this is his first talk about the subject before an audience with expertise in theorem proving, and promised that many odd terms and buzzwords from the world of Finance would become clear later.

From his many slides, Passmore could fit only a small portion into the 60min time slot. A key point was the following Stack of Financial Algorithms (from top to bottom):

  • Collateral Trading
  • Inventory Management
  • Algo Containers
  • Trading Algorithms
  • Smart Order Routers
  • Venues

So far, Aesthetic Integration has mainly worked at the bottom: “Venues” are virtual places where trading happens, e.g. a “dark pool” as in the UBS Future of Finance Challenge (see also the white paper).

Passmore invited the prover community to participate in formal treatment of the whole stack given above. For example, full formalization of Financial Mathematics in Isabelle/HOL could support the slot “Trading Algorithms”.

He also presented the present flagship tool environment: Imandra. Here is a quotation from the official website:

What is Imandra?

AI’s Imandra is breakthrough artificial intelligence technology for ensuring financial algorithms are designed and implemented safely and fairly.

Powered by major recent advances in formal verification, Imandra:

  • Verifies correctness and stability of system designs for regulatory compliance
  • Uncovers nontrivial bugs
  • Tests – creates high-coverage test-suites
  • Saves – radically reduces associated costs

The system was demonstrated in two versions: one running on the local machine, and one running on a server (i.e. “in the cloud”). The interaction model is still mainly command-line based, but Aesthetics Integration is interested to improve on that.

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The Isar proof language in 2016

At the Isabelle Workshop 2016 in Nancy, I presented a paper about recent renovations of the Isar proof language:

This is a description of the Isar proof language as it stands today in 2016. This means the official release Isabelle2016 (February 2016), and the next release that is presumably published towards the end of the year. Relevant NEWS entries and updated portions from the Isabelle/Isar Reference Manual are summarized in one comprehensive article.

See also the full paper and the slides.

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Video for Isabelle presentation at Curry Club Augsburg

Another Isabelle presentation at Curry Club Augsburg (19-May-2016) has been recorded and uploaded to Youtube.

Materials from the presentation:

  • Exercise from Haskell Workshop 1 + 2 (Dec-2015).
  • Solution produced during the presentation.
  • Slides that were briefly shown towards the end.

To try it interactively (with Prover IDE markup), it is possible to open the URL of the Solution directly in Isabelle/jEdit.

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PIDE as Standard ML IDE for bootstrapping Isabelle

Isabelle is usually advertized as environment for interactive and automated theorem proving, but its Prover IDE (PIDE) may be used for regular program development as well. Standard ML is particularly important here, since it is the bootstrap language of Isabelle/ML (i.e. SML with many add-ons) and Isabelle/Pure (i.e. the logical framework).

Using Isabelle/PIDE for bootstrapping Isabelle itself is now possible in recent repository versions, e.g. Isabelle/1c1f8531ca37 – see also README_REPOSITORY for general explanations how to build and run that. Here is the relevant NEWS entry from that version:

IDE support for the Isabelle/Pure bootstrap process. The initial files src/Pure/ROOT0.ML or src/Pure/ROOT.ML may be opened with Isabelle/jEdit: they act like independent quasi-theories in the context of theory ML_Bootstrap. This allows continuous checking of ML files as usual, but results are isolated from the actual Isabelle/Pure that runs the IDE
itself.

The ML project consists of a sequence of ML_file commands in ROOT.ML. Projects other than Isabelle can do the same with SML_file for official Standard ML. Afterwards, the following Poly/ML command line is able to build the project without the IDE: poly --eval "val SML_file = PolyML.use" --use ROOT.ML

What is also notable in the Isabelle/Pure bootstrap environment is the structure Thread_Data for global state variables within the current thread. There are two implementations: (1) physical and (2) virtual. The virtual version is used when Isabelle/Pure is loaded into itself: it allows to manage many versions of the load process with different intermediate states in a value-oriented manner.

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