Polymorphic Syntax Deenition

Context-free grammars are used in several algebraic speciication formalisms instead of rst-order signatures for the deenition of the structure of algebras , because grammars provide better notation than signatures. The rigidity of these rst-order structures enforces a choice between strongly typed structures with little genericity or generic operations over untyped structures. In two-level signatures level 1 deenes the algebra of types used at level 0 providing the possibility to deene polymorphic abstract data types. Two-level grammars are the grammatical counterpart of two-level signatures. This paper discusses the correspondence between context-free grammars and rst-order signatures, the extension of this correspondence to two-level grammars and signatures, examples of the usage of two-level grammars for polymorphic syntax deenition, a restriction of the class of two-level grammars for which the parsing problem is decidable, a parsing algorithm that yields a minimal and nite set of most general parse trees for this class of grammars, and a proof of its correctness.