A formalism for completely representing linear and two-dimensional computer languages
Robert J. Klerer · 1989
This dissertation presents a new formalism, called Logic-BNF (LBNF), which may be used to describe clearly and completely computer languages. LBNF is a notation that comes from a merger of BNF and Prolog. It will be shown that LBNF is appropriate and convenient for expressing such language structures as implied multiplication and implicit declarations more clearly than by other notations. It is also demonstrated that LBNF can completely describe computer languages that include features that make them not context free. This dissertation presents the new concept of geometric grammars and analyzes a special case, rectangular grammars. This class of geometric grammars, which is described as a two-dimensional form of LBNF, is shown to completely describe two-dimensional languages, such as mathematics. Additionally, it will be shown that such languages can be easily described in their natural two-dimensional form by using geometric grammars. Both LBNF and geometric grammars are capable of being used to prototype language designs via direct translation into a Prolog program. The prototyped language can accept linear or two-dimensional language strings and will provide a parse tree, which records the grammatical structures in the language string. Moreover, a semantic definition, which can be included in the grammar describing a language, will allow the execution of prototyped programs via a semantic representation corresponding to that program.