Operators and algebraic structures

Authors:
D. Kapur;D. R. Musser;A. A. Stepanov
Affiliations:
Computer Science Branch, Corporate Research and Development, General Electric Company;Computer Science Branch, Corporate Research and Development, General Electric Company;Computer Science Branch, Corporate Research and Development, General Electric Company
Venue:
FPCA '81 Proceedings of the 1981 conference on Functional programming languages and computer architecture
Year:
1981

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Abstract

Operators in functional languages such as APL and FFP are a useful programming concept. However, this concept cannot be fully exploited in these languages because of certain constraints. It is proposed that an operator should be associated with a structure having the algebraic properties on which the operator's behavior depends. This is illustrated by introducing a language that provides mechanisms for defining structures and operators on them. Using this language, it is possible to describe algorithms abstractly, thus emphasizing the algebraic properties on which the algorithms depend. The role that formal representation of mathematical knowledge can play in the development of programs is illustrated through an example. An approach for associating complexity measures with a structure and operators is also suggested. This approach is useful in analyzing the complexity of algorithms in an abstract setting.