Grammar formalisms for design come in a large variety, requiring different representations of the objects being generated, and different interpretative mechanisms for this generation. At the same time, all grammars share certain definitions and characteristics. Building on these commonalities, we consider a component-based approach for building grammar systems, utilizing a uniform characterization of grammars.
representations constitute the components for this approach. They implement a model for representations, termed
, that defines formal operations on
and recognizes formal relationships between
defines an algebra over its elements; formal compositions of sorts derive their algebraic properties from their component sorts. This algebraic framework makes
representations particularly suited for defining grammar formalisms considering a variety of algebra, and match relations (or interpretative mechanisms). For urban design and simulation,
grammars may include, among others, descriptive grammars, shape grammars, GIS-based grammars and any combination thereof.