Programming Languages for Mechanized Mathematics Workshop
As part of Calculemus 2007
<http://www.risc.uni-linz.ac.at/about/conferences/Calculemus2007/>
Hagenberg, Austria
[http://www.cas.mcmaster.ca/plmms07/]
The intent of this workshop is to examine more closely the intersection
between programming languages and mechanized mathematics systems (MMS).
By MMS, we understand computer algebra systems (CAS), [automated]
theorem provers (TP/ATP), all heading towards the development of fully
unified systems (the MMS), sometimes also called universal mathematical
assistant systems (MAS) (see Calculemus 2007
<http://www.risc.uni-linz.ac.at/about/conferences/Calculemus2007/>).
There are various ways in which these two subjects of /programming
languages/ and /systems for mathematics/ meet:
* Many systems for mathematics contain a dedicated programming
language. For instance, most computer algebra systems contain a
dedicated language (and are frequently built in that same
language); some proof assistants (like the Ltac language for Coq)
also have an embedded programming language. Note that in many
instances this language captures only algorithmic content, and
/declarative/ or /representational/ issues are avoided.
* The /mathematical languages/ of many systems for mathematics are
very close to a functional programming language. For instance the
language of ACL2 is just Lisp, and the language of Coq is very
close to Haskell. But even the mathematical language of the HOL
system can be used as a functional programming language that is
very close to ML and Haskell. On the other hand, these languages
also contain very rich specification capabilities, which are
rarely available in most computation-oriented programming
languages. And even then, many specification languages ((B, Z,
Maude, OBJ3, CASL, etc) can still teach MMSes a trick or two
regarding representational power.
* Conversely, functional programming languages have been getting
"more mathematical" all the time. For instance, they seem to have
discovered the value of dependent types rather recently. But they
are still not quite ready to 'host' mathematics (the non-success
of docon <http://www.haskell.org/docon/> being typical). There are
some promising languages on the horizon (Epigram
<http://www.e-pig.org/>, Omega
<http://web.cecs.pdx.edu/%7Esheard/Omega/index.html>) as well as
some hybrid systems (Agda <http://agda.sourceforge.net/>, Focal
<http://focal.inria.fr/site/index.php>), although it is unclear if
they are truly capable of expressing the full range of ideas
present in mathematics.
* Systems for mathematics are used to prove programs correct. (One
method is to generate "correctness conditions" from a program that
has been annotated in the style of Hoare logic and then prove
those conditions in a proof assistant.) An interesting question is
what improvements are needed for this both on the side of the
mathematical systems and on the side of the programming languages.
We are interested in all these issues. We hope that a certain synergy
will develop between those issues by having them explored in parallel.
These issues have a very colourful history. Many programming language
innovations first appeared in either CASes or Proof Assistants, before
migrating towards more mainstream languages. One can cite (in no
particular order) type inference, dependent types, generics,
term-rewriting, first-class types, first-class expressions, first-class
modules, code extraction, and so on. However, a number of these
innovations were never aggressively pursued by system builders, letting
them instead be developped (slowly) by programming language researchers.
Some, like type inference and generics have flourished. Others, like
first-class types and first-class expressions, are not seemingly being
researched by anyone.
We want to critically examine what has worked, and what has not. Why are
all the current ``popular'' computer algebra systems untyped? Why are
the (strongly typed) proof assistants so much harder to use than a
typical CAS? But also look at question like what forms of polymorphism
exists in mathematics? What forms of dependent types exist in
mathematics? How can MMS regain the upper hand on issues of
'genericity'? What are the biggest barriers to using a more mainstream
language as a host language for a CAS or an ATP?
This workshop will accept two kinds of submissions: full research papers
as well as position papers. Research papers should be nore more than 15
pages in length, and positions papers no more than 3 pages. Submission
will be through _EasyChair_. An informal version of the proceedings will
be available at the workshop, with a more formal version to appear
later. We are looking into having the best papers completed into full
papers and published as a special issue of a Journal (details to follow).
Important Dates
April 25, 2007: Submission Deadline
June 29-30, 2007: Workshop
Program Committee
Lennart Augustsson <http://www.cs.chalmers.se/%7Eaugustss> [Credit Suisse]
Wieb Bosma <http://www.math.ru.nl/%7Ebosma/>[Radboud University
Nijmegen, Netherlands]
Jacques Carette <http://www.cas.mcmaster.ca/%7Ecarette> (co-Chair)
[McMaster University, Canada]
David Delahaye <http://cedric.cnam.fr/%7Edelahaye/> [CNAM, France]
Jean-Christophe Filliâtre <http://www.lri.fr/%7Efilliatr/> [CNRS and
Université de Paris-Sud, France]
John Harrison <http://www.cl.cam.ac.uk/%7Ejrh13/> [Intel Corporation, USA]
Markus (Makarius) Wenzel <http://www4.in.tum.de/%7Ewenzelm/> [Technische
Universität München, Germany]
Freek Wiedijk <http://www.cs.ru.nl/%7Efreek/> (co-Chair) [Radboud
University Nijmegen, Netherlands]
Wolfgang Windsteiger <http://www.risc.uni-linz.ac.at/people/wwindste/>
[University of Linz, Austria]
Location and Registration
Location and registration information can be found on the Calculemus
<http://www.risc.uni-linz.ac.at/about/conferences/Calculemus2007/> web
site.
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