Aldor is the result of the work of many people.
Here we outline the major contributors, both individuals and organizations.
While we have attempted to acknowledge all major contributors, we may have
made some inadvertent omissions. If you are aware of any,
please directed inform us at credits@aldor.org.
Pre-history: Scratchpad II
The Aldor project was initiated at
IBM Thomas J. Watson Research Center
in the 1980s as an outgrowth of the research work in symbolic mathematical
computation.
At IBM, the computer algebra group, led by
Richard D. Jenks and including
Robert S. Sutor,
Barry M. Trager,
Stephen M. Watt,
and others, were developing a research system for computer algebra
called Scratchpad II.
This system had its own programming language (compiled to Lisp) which
was a precursor to Aldor.
An early version of this language was described in the paper
A Language for Computational Algebra
(Jenks and Trager, pp 22-29
Proc. 1981 Symposium on Symbolic and Algebraic Manipulation, ACM Press).
The purpose of this language was to allow users to define their own algebraic
structures (e.g. rings, fields, modules...) in a general way.
The language provided run-time generics (templates) and used type categories
(interfaces) to restrict type parameters to satisfy interface requirements.
The language had several limitations and irregularities (e.g. one could
write expressions for which there was no well-defined type in the language)
and there was not a complete implementation.
A New Language: A#
An effort was initiated in 1984 to redesign the Scratchpad II extension
language and provide a complete implementation, sufficiently robust to
support a large, complex system. This was led by
Stephen Watt,
and a first, Lisp-based, implementation involved contributions from
Florian Bundshuh,
William Burge,
James Davenport,
Marc Gaëtano,
Michael Monagan,
Scott Morrison,
Simon Robinson,
Robert Sutor,
and Barry Trager.
In 1990 Stephen Watt initiated a second, C-based, implementation under
the name A# (A Sharp).
A First Deployment of A# in AXIOM
In 1991, Scratchpad II was adopted by the Numerical Algorithms Group Ltd,
a not-for-profit UK corporation. It was released by NAG under the
product name Axiom.
Work continued on A# for inclusion in the second (1994)
release of Axiom. This work was described in the paper
A First Report on the A# Compiler
(Watt, Broadbery, Dooley, Iglio, Steinbach and Sutor,
Proc. International Symposium on Symbolic and Algebraic Computation
(ISSAC 1994), pp 25-31, ACM Press).
This implementation first became publicly available at the end of 1994
as part of Axiom release 2.
Though this effort was led by Stephen Watt,
many people directly contributed to the compiler implementation at IBM,
including
Gerald Baumgartner,
Peter Broadbery,
Samuel Dooley,
Teresa Gomez Diaz,
Stephen Gortler,
Pietro Iglio,
Jonathan Steinbach,
and Knut Wolf.
Others contributed to the initial mathematical libraries, the documentation,
porting and testing, including
Dave Bayer (Columbia U),
Manuel Bronstein (ETH Zurich),
Ronnie Brown (University of Wales, Bangor),
Robert Corless (U Western Ontario and IBM),
Tim Daly (IBM),
Mike Dewar (NAG),
Patrizia Gianni (U Pisa and IBM),
Johannes Grabmeier (IBM),
Hans-Gert Gräbe (University of Leipzig),
Tony Kennedy (Supercomputer Computations Research Institute,
Florida State U),
Larry Lambe (IBM),
Mike Richardson (NAG),
Philip Santas (ETH Zurich),
Barry Trager (IBM),
and Themos Tsikas (NAG).
A number of executives and managers in both companies devoted many hours
to the transfer of A# from IBM to NAG. Thanks are
due in particular to
Brian Ford (NAG),
Steve Hague (NAG),
Richard Jenks (IBM),
Bill Pulleyblank (IBM),
Marshall Schor (IBM),
and Shmuel Winograd (IBM).
What's in a Name? A# to AXIOM-XL to Aldor
For trade-mark reasons, it was decided at IBM that the
name "A#" could not be used. Therefore,
in its first release with Axiom 2.0, the new language was
described as "the Axiom Extension Language", or Axiom XL.
Subsequently NAG established the product name Aldor for the
language and its compiler.
Use and Development in the Late 1990s: FRISCO and other projects
INRIA (Institut National de
Recherche en Informatique et en Automatique) and NAG, together with
the French CNRS and the Universities of Pisa and Cantabria
launched the ESPRIT Long Term Research Project
FRISCO (FRamework for Integrated Symbolic-numeric COmputation) to
further research and development in compiler technologies
(Aldor-based) and algebraic algorithms. Later, a group at the University of Western Ontario joined this effort. A
number of indiviuals enhanced the Aldor compiler and wrote significant
Aldor libraries under the auspices of FRISCO and the IBM/NAG
relationship, including
Yannis Chicha [Aldor/C++ interoperability] (U Western Ontario),
Florence Defaix [Aldor/C++ interoperability] (U Western Ontario),
Mike Dewar [Fortran interoperability] (NAG),
Sam Dooley [Compiler maintenance](IBM),
Martin Dunstan [Principal compiler maintainer] (NAG),
Marc Gaëtano [Openmath library] (INRIA),
Teresa Gomez-Diaz [Applications to Signal Processing] (NAG),
Vilya Harvey (NAG),
Peter Huerter (U Western Ontario),
Marc Moreno Maza [Basicmath] (NAG and U Lille I),
and Stephen Watt [Coordination and Aldor/C++ interoperability] (IBM, INRIA, and U Western Ontario).
At the same time, a number of other individuals made significant contributions
to the Aldor world, including
Manuel Bronstein (ETH Zurich and INRIA),
James Davenport (U Bath),
Martin Dunstan (University of St Andrews),
Robert Edwards (SCRI Florida State U),
Tom Kelsey (University of St Andrews),
Tony Kennedy (SCRI Florida State U),
Ralf Hemmecke (U Linz),
Niklaus Mannhart (ETH Zurich),
Simon Thompson (U Kent),
and Saul Youssef (SCRI Florida State U).
These efforts led to the creation of some significant packages, including
BasicMath [polynomial and matrix arithmetic] (Moreno Maza, et al.),
Delta [polynomial system solver] (Moreno Maza, et al.),
Piit [parallel computation] (Mannhart),
Sum^it [differential equations] (Bronstein, et al.),
and Paraldor [Aldor for super computers] (Edwards and Kennedy).
The FRISCO project ended in 1999, but the indivuals who had been contributing
to Aldor during this period continued to do so.
Participants at the University of Western Ontario wish to
acknowledge support from the
Canadian Natural Sciences and Engineering Research Council,
the Ontario Research and Development Challenge Fund,
and the Fields Institute.
Subsequently, a number of additional individuals have made significant
contributions to Aldor, including
Tom Ashby [Paraldor],
Greg Collins, [Run-time system experiments]
Laurentiu Dragan [Windows port],
Bálint Joó [Paraldor],
Bill Naylor [MathML],
and
Cosmin Oancea [Compiler debugging].
The Present Day
In 2001, NAG ceased distribution of Axiom (and hence Aldor).
Aldor.org was formed as an organization involving NAG
and the principal supporters of Aldor to distribute it freely. Work on
Aldor now continues:
- at the University of Western Ontario (in the group led by Stephen
Watt) to provide compiler and libraries development, support,
coordination,
- at INRIA (in the group led by Manuel Bronstein) to provide
library development (libaldor,
which was developped at INRIA under the name salli, is now
bundled with the Aldor compiler as the main library), and
- at the University of Edinburgh (in the group led by Tony Kennedy)
to develop the Paraldor project.
Aldor is used in projects at NAG, IBM
and Seagate as well as a number of universities.
There have been many others, not listed here, who have helped in various ways
and to them we offer our most sincere gratitude.