PLMMS 2010

The scope of this workshop is the intersection of programming languages (PL) and mechanized mathematics systems (MMS). The latter category subsumes present-day computer algebra systems (CAS), interactive proof assistants (PA), and automated theorem provers (ATP), all heading towards fully integrated mechanized mathematical assistants.

The program committee welcomes submissions on all aspects of programming languages and mechanised mathematics.

See the call for papers.

The topics of interest meet at, but are not limited to, the following:

• Input languages for MMS: all aspects of languages for the user to deploy or extend the system, both algorithmic and declarative. Typical examples are tactic languages such as Ltac in Coq, mathematical proof languages as in Mizar or Isar, and specialized programming languages built into CA systems.
• Mathematical modelling languages used for programming: the relation of logical descriptions vs. algorithmic content. For instance the logic of ACL2 extends a version of Lisp, that of Coq is close to Haskell, and some portions of HOL are similar to ML and Haskell, while Maple tries to do both simultaneously. Such mathematical languages offer rich specification capabilities, which are rarely available in regular programming languages. How can programming benefit from mathematical concepts, without limiting mathematics to the computational worldview?
• Programming languages and mathematical specifications: advanced mathematical concepts in programming languages that improve the expressive power of functional specifications, type systems, module systems etc. Programming languages with dependent types are of particular interest here, as is intentionality vs extensionality.
• Language elements for program verification: specific means built into a language to facilitate correctness proofs using MMS. For example, logical annotations within programs may be turned into verification conditions to be solved in a proof assistant eventually. How can MMS and PL be improved to make verification more convenient and mathematically appealing?

only the programme on one page

• Jacques Carette -- Mechanized Mathematics
  If one were designing an entirely new mathematical assistant, what might it look like? Problems and some favoured solutions are presented.
  [Joint invited talk with Calculemus; extended abstract (pdf)]


• Brigitte Pientka -- Beluga: programming with contextual data, contexts, and ...
  The logical framework LF provides an elegant foundation for specifying formal systems and proofs and it is used successfully in a wide range of applications such as certifying code and mechanizing meta-theory of programming languages. However, incorporating LF technology into functional programming to allow programmers to specify and reason about formal guarantees of their programs from within the programming language itself has been a major challenge.
  An overview of Beluga, will be presented. This is a framework for programming and reasoning with formal systems. It supports specifying formal systems in LF and it also provides a dependently typed functional language that supports analyzing and manipulating LF data via pattern matching. A distinct feature of Beluga is its direct support for reasoning with contexts and contextual objects. Taken together these features lead to powerful language which supports writing compact and elegant proofs.
  See the Beluga website for more information.


• Andrew Gacek -- The Abella Theorem Prover and Two-level Logic Reasoning
  The Abella theorem prover uses both a specification logic and a reasoning logic. This two-level logic approach is particularly fruitful in the domain of formalizing systems with binding structure. In this talk, we discuss the structure and consequences of this approach and explore possible extensions.
  See the Abella website for more information.


• Pierre Cartier -- Can we make Mathematics universal as well as fully reliable ?
  [Joint invited talk with MKM]
  These are times of change for the mathematical profession and for the practice of mathematics, with, for instance, the advent of powerful computing machinery and the extraordinary immediacy of communication all over the world. If the concept of globalization has any meaning, this is now the time of globalization in mathematics. The pretense of mathematics of being universal can now be made real, and mathematical knowledge be shared by people from many different background. In addition, there are now mechanical help in reasoning, digitization of large parts of the traditional mathematical literature, and amazing amounts of scientific data and problems begging analysis which all help to offer a change in the role of mathematics. Checking proofs by computers is just one of the many new possibilities. A new paradigm is needed to understand a world of TERABYTES, where the frontier between "proof" and "guess" is quite fuzzy. Between "finite" and "infinite", we have to introduce in our axiomatics the world of "very very large".

Abstract submission:	Tue 6 April 2010
Paper submission:	Fri 9 April 2010 (by PLMMS 2010 easychair)
Reviews sent to authors:	Mon 10 May 2010
Author's rebuttal deadline:	Mon 17 May 2010
Submission of demo and presentation proposals:	Mon 17 May 2010 (by PLMMS 2010 easychair)
Notification of acceptance:	Mon 24 May 2010
Camera ready copy due:	Mon 7 June 2010
Workshop:	Thu 8 July 2010

We welcome submission of proposals to present a demo, as well as submissions of papers presenting original unpublished work which is not been submitted for publication elsewhere.

Selected papers will appear in the ACM Communications in Computer Algebra. All accepted papers and system demos will be presented at the workshop, and the extended abstracts will be made available online.

Papers and demo proposals should be submitted via PLMMS 2010 easychair.

Papers should be no more than 8 pages in length and are to be submitted in PDF format. They must conform to the ACM SIGPLAN style guidelines.

At least one author of each accepted paper/demo is expected to attend PLMMS 2010 and presents her or his paper/demo.

• Thorsten Altenkirch (University of Nottingham, UK)
• Serge Autexier (DFKI, Germany)
• David Delahaye (CNAM, Paris, France)
• James Davenport [PC co-chair] (University of Bath, UK)
• Lucas Dixon [PC co-chair] (University of Edinburgh, UK)
• Gudmund Grov (University of Edinburgh, UK)
• Ewen Maclean (University of Herriot Watt, UK)
• Dale Miller (INRIA, France)
• Gabriel Dos Reis (Texas A&M University, USA)
• Carsten Schuermann (IT University of Copenhagen, Denmark)
• Tim Sheard (Portland State University, USA)
• Sergei Soloviev (IRIT, Toulouse, France)
• Stephen Watt (The University of Western Ontario, Canada)
• Makarius Wenzel (ITU Munich, Germany)
• Freek Wiedijk (Radboud University Nijmegen, Netherlands)

The 2009 PLMMS workshop, Munich, Germany. With TPHOLs

The 2008 PLMMS workshop, Birmingham, UK. With CICM

The 2007 PLMMS workshop, Hagenberg, Austria. With Calculemus