Transformations of Languages of Designs: Part 2

A formal model for defining transformations of languages of designs in terms of the grammars which generate them is described in detail. First, a normal form for grammars is presented which distinguishes two basic determinants of the compositional structure of designs in a language: spatial relations and the order in which they are employed to generate designs. These two constructive mechanisms are used to specify each rule in a normal form grammar. An internal formal property of a normal form grammar called its recursive structure is also characterized. Rules of transformation are then defined which map the rules of a given normal form grammar onto rules of new grammars by changing independently the two components of rules in the original grammar. The new grammars produced specify new languages of designs. Of particular interest are those transformations which preserve the recursive structure of the original grammar.