On the Transformational Derivation of an Efficient Recognizer for Algol 68

During the sixties two level van Wijngaarden grammars (2vwg) were introduced for the formal definition of Algol 68. Two level van Wijngaarden grammars provide a formalism suited for writing rigorous formal definitions which read like human prose. Both the context free and context sensitive syntax of Algol 68 are defined in 2vwg. However, the specification is not executable. The Extended Affix Grammar (eag) formalism is closely related to 2vwg. Any 2vwg can be simulated in eag. From a given eag an exact recognizer for the language defined by the eag can be derived automatically. Termination of such a recognizer is guaranteed if certain liberal well-formedness conditions are satisfied. However, in general some effort is necessary to enforce well-formedness. cdl3 is a programming language which rides the borderline between affix grammars and programs. It can be seen as a deterministic version of eag. From a grammar in cdl3 efficient parsers can be generated. Specifications in 2vwg and eag often are of a declarative nature. Our purpose is to derive efficient parsers from such a language specification in a transformational way. We have generalized well known transformations techniques for making context free grammars top down parsable to two level grammars. Furthermore, we have defined transformations for applying the well-known unfold/rearrange/fold-technique on specifications which are formulated as a two level grammar. These transformations can be used for imposing stronger well-formedness conditions on a two level grammar and for operationalizing declarative constructs in the grammar. As a case study, we have undertaken an attempt to derive a new specification for Algol 68 in eag by applying language preserving transformations to the original grammar. Secondly, we have tried to make the resulting eag deterministic in order to obtain an efficient recognizer in cdl3.