A Class of Rewriting Rules and Reverse Transformation for Rule-based Equivalent Transformation

In the rule-based equivalent transformation (RBET) paradigm, where computation is based on meaning-preserving transformation of declarative descriptions, a set of rewriting rules is regarded as a program. The syntax for a large class of rewriting rules is determined. The incorporation of meta-variables of two different kinds enables precise control of rewriting-rule instantiations. As a result, the applicability of rewriting rules and the results of rule applications can be rigorously specified. A theoretical basis for justifying the correctness of rewriting rules is established. Reverse transformation operation in the RBET framework is discussed, and it is shown that a correct rewriting rule is reversible, i.e., a correct rewriting rule can in general be constructed by syntactically reversing another correct rewriting rule. 1 Akama was partly supported by Grant-in-Aid for Scientific Research (B)(2) #12480076. 2 Email: [email protected] 3 Nantajeewarawat was supported partially by the Thailand Research Fund. 4 Email: [email protected] 5 Email: [email protected] c ©2001 Published by Elsevier Science B. V. Akama, Nantajeewarawat and Koike