Category Archives: ML

Scaling Isabelle Proof Document Processing

Isabelle applications (e.g. from AFP) are growing steadily in size and number. To outline requirements and possibilities of the technology, I have produced a document on Scaling Isabelle Proof Document Processing.

Abstract:

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).

Future Prospects of Isabelle Technology

On 23-Nov-2017, I will give a presentation about Future Prospects of Isabelle Technology at DTU (Danmarks Tekniske Universitet), Copenhagen – thanks to an invitation by Jørgen Villadsen. More information on the meeting is available on the website.

Abstract:

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.

Sources for the presentation: Copenhagen2017.tar.gz

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).

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.

Isabelle no longer supports SML/NJ

17-Feb-2016 marks the historic day when support for SML/NJ was removed from the Isabelle code base, see the main changeset and another changeset concerning ML multithreading.

The changes of the source illustrate the amount of conditional compilation that has accumulated in the past decades of Isabelle development. In the future, we will be able to proceed faster in just one direction, and pick up more advanced features of Poly/ML.

Already ten years ago, SML/NJ had little practical relevance for Isabelle users. It was occasionally used by tool developers to figure out difficult situations of type-inference, at a time when the SML/NJ compiler errors were better than the ones of Poly/ML. This has changed dramatically in recent years, with fairly good compiler errors and full IDE support in Poly/ML.

Performance of SML/NJ had always been a problem (after 1993): growing with the total heap size of Isabelle applications. This is inherent in the “CPS approach” of SML/NJ, see also this brief discussion on Stackoverflow.

The reason for giving up these tons of extra weight right after shipping Isabelle2016 are rather profane: in the routine tests of SML/NJ for the release, many basic Isabelle sessions (e.g. HOL-Library) no longer worked, running out of memory (within 32bit address space) after many hours.

ML debugging within the Prover IDE

Isabelle/ML is based on Poly/ML and thus benefits from the source-level debugger of that implementation of Standard ML. 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. A typical debugger session is shown in the screenshot below.

[ML debugger]

ML debugging depends on the following pre-requisites.

  1. ML source needs to be compiled with debugging enabled. This may be controlled for particular chunks of ML sources using any of the subsequent facilities.

    1. The system option ML_debugger as implicit state of the Isabelle process. It may be changed in the menu Plugins / Plugin Options / Isabelle / General. ML modules need to be reloaded and recompiled to pick up that option as intended.
    2. The configuration option ML_debugger, with an attribute of the same name, to update a global or local context (e.g. with the declare command).
    3. Commands that modify ML_debugger state for individual files: ML_file_debug, ML_file_no_debug, SML_file_debug, SML_file_no_debug.

    The instrumentation of ML code for debugging causes minor run-time overhead. ML modules that implement critical system infrastructure may lead to deadlocks or other undefined behaviour, when put under debugger control!

  2. The Debugger panel needs to be active, otherwise the program ignores debugger instrumentation of the compiler and runs unmanaged. It is also possible to start debugging with the panel open, and later undock it, to let the program continue unhindered.

  3. The ML program needs to be stopped at a suitable breakpoint, which may be activated individually or globally as follows.

    For ML sources that have been compiled with debugger support, the IDE visualizes possible breakpoints in the text. A breakpoint may be toggled by pointing accurately with the mouse, with a right-click to activate jEdit’s context menu and its Toggle Breakpoint item. Alternatively, the Break checkbox in the Debugger panel may be enabled to stop ML threads always at the next possible breakpoint.

Note that the state of individual breakpoints gets lost when the coresponding ML source is re-compiled! This may happen unintentionally, e.g. when following hyperlinks into ML modules that have not been loaded into the IDE before.

The debugger panel (see screenshot) shows a list of all threads that are presently stopped. Each thread shows a stack of all function invocations that lead to the current breakpoint at the top.

It is possible to jump between stack positions freely, by clicking on this list. The current situation is displayed in the big output window, as a local ML environment with names and printed values.

ML expressions may be evaluated in the current context by entering snippets of source into the text fields labeled Context and ML, and pushing the Eval button. By default, the source is interpreted as Isabelle/ML with the usual support for antiquotations (like ML, ML_file). Alternatively, strict Standard ML may be enforced via the SML checkbox (like SML_file).

The context for Isabelle/ML is optional, it may evaluate to a value of type theory, Proof.context, Context.generic. Thus the given ML expression (with its antiquotations) may be subject to the intended dynamic run-time context, instead of the static compile-time context.

The buttons labeled Continue, Step, Step over, Step out recommence execution of the program, with different policies concerning nested function invocations. The debugger always moves the cursor within the ML source to the next breakpoint position, and offers new stack frames as before.

Release of Poly/ML 5.6

David Matthews has released Poly/ML 5.6 on 25-Jan-2016. Poly/ML is one of the oldest and most sophisticated implementations of Standard ML. It routinely supports multi-threading with true parallelism on multicore hardware, fast incremental compilation, source-level debugging. The latest release is also notable for native support on Windows (32/64 bit).

Poly/ML 5.6 is used for Isabelle2016 (February 2016).

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.