A classification of noncircular attribute grammars based on the look-ahead behavior

We propose a family of static evaluators for subclasses of the well-defined (i.e., noncircular) attribute grammars. These evaluators augment the evaluator for the absolutely noncircular attribute grammars with look-ahead behaviors. Because this family covers exactly the set of all well-defined attribute grammars, well-defined attribute grammars may be classified into a hierarchy, called the NC hierarchy, according to their evaluators in the family. The location of a noncircular attribute grammar in the NC hierarchy is an intrinsic property of the grammar. The NC hierarchy confirms a result of Riis and Skyum (1981), which says that all well-defined attribute grammars allow a (static) pure multivisit evaluator by actually constructing such an evaluator. We also show that, for any finite m, an NC(m) attribute grammar can be transformed to an equivalent NC(0) grammar.