On the use of syntax-based translators for symbolic and algebraic manipulation

In this paper two well known formalisms, due to Irons and Knuth, for mapping syntactic tree structures into appropriate target strings or structures are considered. Their utility as general purpose tools for symbolic and algebraic manipulation is illustrated by applying them to a symbolic diferentiation exercise. A few of the existing syntax-based translation systems and the uses to which they have been put are discussed. Finally, attempts to mathematically model syntax-based translators are reviewed.