CLU reference manual
The treatment of data types in EL1
Communications of the ACM
MODLISP -- an introduction (invited)
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Design of algebraic data structures with the approach of abstract data types
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
LFP '80 Proceedings of the 1980 ACM conference on LISP and functional programming
Data type specification: Parameterization and the power of specification techniques
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The definition and use of data structures in REDUCE
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Proceedings of the ACM SIGPLAN symposium on Very high level languages
Toward a formal implementation of computer algebra
ACM SIGSAM Bulletin
A knowledge-based system for computer algebra
ACM SIGSAM Bulletin
A Smalltalk system for algebraic manipulation
OOPLSA '86 Conference proceedings on Object-oriented programming systems, languages and applications
The type inference and coercion facilities in the scratchpad II interpreter
SIGPLAN '87 Papers of the Symposium on Interpreters and interpretive techniques
An object-oriented approach to algebra system design
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Object-oriented programming for linear algebra
OOPSLA '89 Conference proceedings on Object-oriented programming systems, languages and applications
LFP '92 Proceedings of the 1992 ACM conference on LISP and functional programming
How to make AXIOM into a scratchpad
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
FPCA '95 Proceedings of the seventh international conference on Functional programming languages and computer architecture
Abstract Data Types in Computer Algebra
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Operators and algebraic structures
FPCA '81 Proceedings of the 1981 conference on Functional programming languages and computer architecture
Evaluating logarithms in GF(2n)
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Computer algebra handbook
Fast reduce: the trade-off between efficiency and generality
ACM SIGSAM Bulletin
What do we want from a high-level language?
ACM SIGSAM Bulletin
SSGIP'10 Proceedings of the 2010 international spring school conference on Generic and Indexed Programming
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This paper reports ongoing research at the IBM Research Center on the development of a language with extensible parameterized types and generic operators for computational algebra. The language provides an abstract data type mechanism for defining algorithms which work in as general a setting as possible. The language is based on the notions of domains and categories. Domains represent algebraic structures. Categories designate collections of domains having common operations with stated mathematical properties. Domains and categories are computed objects which may be dynamically assigned to variables, passed as arguments, and returned by functions. Although the language has been carefully tailored for the application of algebraic computation, it actually provides a very general abstract data type mechanism. Our notion of a category to group domains with common properties appears novel among programming languages (cf. image functor of RUSSELL) and leads to a very powerful notion of abstract algorithms missing from other work on data types known to the authors.