AMBIT: A PROGRAMMING LANGUAGE FOR ALGEBRAIC SYMBOL MANIPULATION.

Abstract : This paper defines a programming language system called AMBIT (Algebraic Manipulation By Identity Translation). The AMBIT language is intended for the precise description of the operations of mathematics in general, and programs in the languages are suitable for efficient compilation and execution by an automatic computer. The language is distinguished by its adherence to an important portion of the conventional notation of algebra, the 'identity'. AMBIT uses the 'identity' to express in a single linguistic structure an arbitrarily complex sequence of elementary symbol-manipulation operations, just as FORTRAN and ALGOL use the 'formula' to express in a single linguistic structure an arbitrarily complex sequence of arithmetic operations. Thus AMBIT attempts to serve algebra as FORTRAN and ALGOL serve arithmetic. (Author)