Simple precedence grammar explained

A simple precedence grammar is a context-free formal grammar that can be parsed with a simple precedence parser.^[1] The concept was first created in 1964 by Claude Pair,^[2] and was later rediscovered, from ideas due to Robert Floyd, by Niklaus Wirth and Helmut Weber who published a paper, entitled EULER: a generalization of ALGOL, and its formal definition, published in 1966 in the Communications of the ACM.

Formal definition

G = (N, Σ, P, S) is a simple precedence grammar if all the production rules in P comply with the following constraints:

• There are no erasing rules (ε-productions)
• There are no useless rules (unreachable symbols or unproductive rules)
• For each pair of symbols X, Y (X, Y

\in (N ∪ Σ)) there is only one Wirth–Weber precedence relation.

• G is uniquely inversible

Examples

S \to aSSb | c

precedence table:

\begin{array}{c|ccccc} & S& a& b& c & \$ \\ \hline S& • = & \lessdot & • = & \lessdot& \\ a& • = & \lessdot& & \lessdot& \\ b& & \gtrdot& & \gtrdot& \gtrdot \\ c& & \gtrdot& \gtrdot& \gtrdot& \gtrdot \\ \$& & \lessdot& & \lessdot& \end{array}

References

• Alfred V. Aho, Jeffrey D. Ullman (1977). Principles of Compiler Design. 1st Edition. Addison–Wesley.
• William A. Barrett, John D. Couch (1979). Compiler construction: Theory and Practice. Science Research Associate.
• Jean-Paul Tremblay, P. G. Sorenson (1985). The Theory and Practice of Compiler Writing. McGraw–Hill.

External links

• "Simple Precedence Relations" at Clemson University

Notes and References

1. The Theory of Parsing, Translation, and Compiling: Compiling, Alfred V. Aho, Jeffrey D. Ullman, Prentice–Hall, 1972.
2. Claude Pair . Arbres, piles et compilation. 1964. Revue française de traitement de l'information., in English Trees, stacks and compiling