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
Enlarging the REDUCE domain of computation
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
The Bath algebraic number package
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Semantics in algebraic computation
Proceedings of the third conference on Computers and mathematics
A rewrite-based type discipline for a subset of computer algebra
Journal of Symbolic Computation
Scratchpad's view of algebra II: A categorical view of factorization
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
AXIOM: the scientific computation system
AXIOM: the scientific computation system
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Larch: languages and tools for formal specification
Larch: languages and tools for formal specification
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
Programming with algebraic structures: design of the MAGMA language
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Algorithms for type inference with coercions
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Lightweight formal methods for computer algebra systems
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Exact real arithmetic: a case study in higher order programming
LFP '86 Proceedings of the 1986 ACM conference on LISP and functional programming
Initial Algebra Semantics and Continuous Algebras
Journal of the ACM (JACM)
On the Theory of Specification, Implementation, and Parametrization of Abstract Data Types
Journal of the ACM (JACM)
An exact real algebraic arithmetic with equality determination
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Data Type Specification: Parameterization and the Power of Specification Techniques
ACM Transactions on Programming Languages and Systems (TOPLAS)
Fundamentals of Algebraic Specification I
Fundamentals of Algebraic Specification I
An Extended Polymorphic Type System for Applicative Languages
MFCS '80 Proceedings of the 9th Symposium on Mathematical Foundations of Computer Science
Efficient Type Inference and Coercion in Computer Algebra
DISCO '90 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Putting Algebraic Components Together: A Dependent Type Approach
DISCO '90 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Scratchpad's View of Algebra I: Basic Commutative Algebra
DISCO '90 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
The Weyl Computer Algebra Substrate
DISCO '93 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Gauss: A Parameterized Domain of Computation System with Support for Signature Functions
DISCO '93 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
An Order-Sorted Approach to Algebraic Computation
DISCO '93 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Rewrite Rule Theory and Abstract Data Type Analysis
EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra
Completeness in Data Type Specifications
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Correctness Proofs of the Implementation of Abstract Data Types
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Integrating Computer Algebra and Reasoning through the Type System of Aldor
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
Using category theory to design implicit conversions and generic operators
Semantics-Directed Compiler Generation, Proceedings of a Workshop
A language for computational algebra
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Generic, type-safe and object oriented computer algebra software
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
| Hi-index | 0.01 |
The theory of abstract data types was developed in the late 1970s and the 1980s by several people, including the "ADJ" group, whose work influenced the design of Axiom. One practical manifestation of this theory was the OBJ-3 system. An area of computing that cries out for this approach is computer algebra, where the objects of discourse are mathematical, generally satisfying various algebraic rules. There have been various theoretical studies of this in the literature: [36, 42, 45] to name but a few. The aim of this paper is to report on the practical applications of this theory within computer algebra, and also to outline some of the theoretical issues raised by this practical application. We also give a substantial bibliography.