2004 Workshop on Categorical Programming Languages

with an Emphasis on Aldor

Thursday 8 and Friday 9 July 2004
University of Cantabria, Santander Spain


The Aldor workshop has been a satellite event at previous ISSAC conferences.  This year's workshop will be the 3rd such event, held on July 8th and 9th following of the ISSAC 2004 meeting and the IAMC workshop. There is no registration fee for the workshop, and space is available on a first-come-first-serve basis.

Categorical Programming Languages and Aldor

The most successful current programming languages are based the paradigm of object orientation, where individual data objects have state that is modified by object-specific methods. These programming languages do not lend themselves to the natural expression of mathematical algorithms, which view computation more as a calculation of new values from multiple given values, which are left unchanged.

A number of programming languages have emerged that offer a more natural setting for mathematical algorithms, and which arguably have all of the benefits of object orientation. Of these languages, Aldor is of particular interest for the area of algorithmic mathematics because its type system is designed to support rich hierarchies of type categories corresponding to the categories of modern algebra.

Such "Categorical Programming Languages" allow the natural expression of algorithms in the most generic setting. Generalization of algorithms takes the form of weakening categorical constraints on arguments, or strengthening categorical statements about their return values. Far from being "abstract nonsense," this approach leads to highly configurable software with sufficient information to compile efficient code.

The Workshop

This workshop will focus on the Aldor programming language, its compiler, and libraries, within the more general context of theoretical and practical issues in the implementation and use of categorical programming languages.

Workshop participants are anticipated to fall into four groups:

  • those who have been central in the establishing the ideas in categorical programming languages for computer algebra,
  • those with experience using categorical programming languages in various settings
  • university researchers and students who might wish to use Aldor in their research projects or courses
  • those who might wish to contribute to Aldor

A list of confirmed participants will be made available at a later date.

Preliminary Program

Thursday July 8 (18h00-21h00 )

Friday July 9(9h00-12h00)

18h00  Tutorial Introduction to Aldor
            Stephen Watt



  9h00 New Developments
  • Aldor debugger
  • Maple interface
  • New ports
  • CVS repository
19h00  Break 10h00 Break
19h15 The Aldor Algebraic Libraries
            Manuel Bronstein and
            Marc Moreno Maza
  • The category hierarchy
  • Commutative Algebra
  • Algebraic Equation Solving
  • Differential Equation Solving
10h15 Open Discussion on Ongoing Topics
All participants
  • Documentation Support
  • Language Evolution
  • Current development of mathematical libraries
20h15 Contributed Presentations
11h15 Contributed Presentations

Call for Participation and Registration

Individuals wishing to participate in the workshop should send E-mail to by July 1, 2004.

Individuals wishing to make a presentation at the workshop are asked to contact Stephen Watt ( by June 15, 2004.

Web Pages

ISSAC 2004 home page:
CATLAN 2004 home page:
Aldor home page: