Bottom-up grammar analysis : a functional formulation

Abstract

This paper discusses bottom-up grammar analysis problems such as te EMPTY problem and the FIRST problem. It defines a general class of bottom-up grammar analysis problems, and from this definition it derives a functional program for performing bottom-up grammar analysis. The derivation is purely calculational, using theorems from lattice therory, the Bird-Meertens calculus, and laws for list-comprehensions. Sufficient conditions guaranteeing the existence of a solution emerge as a byproduct of the calculation. The resulting program is used to construct programs for the EMPTY problem and the FIRST problem.