Program transformation is used to show the correspondence between two known algorithms for translating parenthesized expressions into their polish counterparts. The first algorithm is a syntax-directed translator which produces output upon the recognition of predefined syntactic rules. The second one, suggested by Dijkstra, is of empirical nature: it performs the translation by simulating the operation of a railyard shunt. The second algorithm is more efficient than the first, but less general. This work enables one 1) to assert the correctness of the empirical algorithm, 2) to compare the relative efficiencies of the two algorithms, and 3) to gain insight into the circumstances in which syntax-directed translation may be improved by generalizing the ideas involved in Dijkstra's algorithm.

Time formulas are symbolic formulas which express the execution time of a program as a function of its input data and of variables representing the time to execute individual operations (e.g., push, pop, transfer, etc.). It is shown that in many cases the time formulas for recursive descent parsers may be generated automatically by a simple inspection of the parser code. These time formulas are instrumental in estimating the gains attained by various types of optimizations. Several of these optimizations are presented and their efficiency gains are estimated. A parser for a simple programming language is generated, optimized, and evaluated using the proposed techniques.