Cayley, version 4: The user language

Abstract

Cayley, version 4, is a proposed knowledge-based system for modern algebra. The proposal integrates the existing powerful algorithm base of Cayley with modest deductive facilities and large sophisticated databases of groups and related algebraic structures. The outcome will be a revolutionary computer algebra system.

The user language of Cayley, version 4, is the first stage of the project to develop a computer algebra system which integrates algorithmic, deductive, and factual knowledge. The language plays an important role in shaping the users' communication of their knowledge to the system, and in presenting the results to the user. The very survival of a system depends upon its acceptance by the users, so the language must be natural, extensible, and powerful. The major changes in the language (over version 3) are the definitions of algebraic structures, set constructors and associated control structures, the definitions of maps and homomorphisms, the provision of packages for procedural abstraction and encapsulation, database facilities, and other input/output. The motivation for these changes has been the need to provide facilities for a knowledge-based system; to allow sets to be defined by properties; and to remove semantic ambiguities of structure definitions.

The language design is complete and the implementation of an interpreter is well under way. A prototype database containing information about the small simple groups (that is, those of order less than one million) is being implemented in Prolog. The integration of the database with Cayley remains to be done, as does the provision of an inference engine. However, the language design does accommodate the future needs of the database and the inference engine.