An order-sorted approach to algebraic computation
This paper presents the prototype design of an algebraic computation system that manipulates algebraic quantities as generic objects using order-sorted algebra as the underlying model. The resulting programs have a form that is closely related to the algorithmic description of a problem, but with the security of full type checking in a compact, natural style.
KeywordsAlgebraic Computation Type Domain Default Representation Symbolic Mode Current Prototype
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- 1.S.K. Abdali, G.W. Cherry, N. Soiffer, An Object Oriented Approach to Algebra System Design, Proc. 1986 Sym. on Symbolic and Algebraic Computation, pp. 24–30, ACM (1986)Google Scholar
- 2.G. Birkhoff and J.D. Lipson, Heterogeneous Algebras, Journal of Combinatorial Theory, 8:115–133, 1970Google Scholar
- 3.R.J. Bradford, A.C. Hearn, J.A. Padget, E. Schrüfer, Enlarging the Reduce Domain of Computation, Proc. 1986 Sym. on Symbolic and Algebraic Computation, pp. 100–106, ACM (1986)Google Scholar
- 4.R. J. Fateman, Advances and Trends in the Design and Construction of Algebraic Manipulation Systems, Proc. International Sym. on Symbolic and Algebraic Computation, Tokyo, pp. 60–67, ACM (1990)Google Scholar
- 5.A. Fortenbacher, Efficient Type Inference and Coercion in Computer Algebra, Proc. International Sym. DISCO '90, pp. 56–60, Springer, Lecture Notes in Computer Science, vol. 429Google Scholar
- 6.J. Meseguer and J. Goguen, Order-sorted Algebra Solves the Constructor-selector, Multiple Representation and Coercion Problems, Technical Report SRI-CSL-90-06, SRI International, Computer Science Laboratory, 1990Google Scholar
- 7.J.A. Goguen, D.A. Wolfram, On Types and FOOPS, in W.K.R. Meersman, S. Khosla (editors), Object Oriented Databases: Analysis, Design and Construction, pp. 1–22, North Holland (1991), Proc, IFIP TC2 Conference, Windermere, UKGoogle Scholar
- 9.A.C. Hearn, A Mode Analyzing Algebraic Manipulation Program, Proc. ACM '74, pp. 722–724, ACM (1974)Google Scholar
- 10.R. Jenks, R. Sutor, AXIOM The Scientific Computation System, Springer (1992)Google Scholar
- 12.D.A. Wolfram, J.A. Goguen, A Sheaf Semantics for FOOPS Expressions, Proc. ECOOP'91 Workshop on Object-based Concurrent Computation Springer (1992), Lecture Notes in Computer Science, vol. 612Google Scholar
- 13.R. E. Zippel. The Weyl Computer Algebra Substrate, Technical Report 90-1077, Dept. Computer Science, Cornell University, Ithaca, NY, 1990Google Scholar