Special issue on Programming Languages and Mechanized Mathematics Systems
Journal of Automated Reasoning
This special issue is focused on 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 that are expected to emerge
The two subjects of PL and MMS meet in many interesting ways, in particular
in the following main topics of this journal issue.
- Dedicated input languages for MMS: covers all aspects of
languages intended for the user to deploy or extend the system, both
algorithmic and declarative ones. Typical examples are tactic definition
languages such as Ltac in Coq, mathematical proof languages as in Mizar or
Isar, or specialized programming languages built into CA systems. Of
particular interest are the semantics of those languages, especially when
current ones are untyped.
- Mathematical modeling languages used for programming: covers 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 with mathematical specifications: covers
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 intensionality vs extensionality.
- Language elements for program verification: covers 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 need MMS and PL to be
improved to make this work conveniently and in a mathematically appealing
These topics have been addressed in the PLMMS 2007
workshops (associated with Calculemus
). While the journal issue
emerges from that community, submission is open to everyone interested in any of
Manuscripts should not have been previously published in archival journals
nor have been submitted to, or be in consideration for, any journal or
conference. Significantly revised and enhanced papers published in workshop or
conference proceedings are welcome. All submissions will be reviewed according
to scholarly standards for scientific journal publications. See also the general
JAR submission policies.
We suggest a page limit of approximately 25 pages, using the LaTeX macros
provided by Springer. Instead of using the Springer online submission system,
please submit papers in PDF through EasyChair.
- Submission deadline: 10th November 2008.
- Notification: January 16th 2009.
- Final versions: March 30th 2009.
Editors of the special issue