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In this paper we outline a language belonging to the domain-specific class of algebraic programming languages. The problem domain we are concerned with is that of the theory of discrete groups and related structures. In 1971, Neübuser in Aachen and Cannon in Sydney, commenced the development of a general purpose group theory system called GROUP, the great majority of which is coded in ANSI Standard FORTRAN. For a discussion of the group theory algorithms planned for the system see Cannon [1]. Two driver languages are planned, Galois, a language with explicit type declarations intended for batch processing, and Cayley, a language where types are determined at run time and hence suitable both for batch processing and interactive computing. An interpreter for Cayley has been implemented at Sydney for the CDC6000 and CYBER series machines. The interpreter is coded in ANSI Standard FORTRAN and experience indicates that the entire system (some 50,000 lines of FORTRAN at present) can be implemented on a new machine with less than 2 months programming effort.

A draft description of the group theory language Cayley