Verification of attribute grammar

Verification of attribute grammar is discussed. As is widely recognized, attribute grammar of Knuth [8] is a very convenient device to describe semantics of programming languages, especially in automating compiler construction. Many efforts have been made to obtain efficient evaluators for attribute grammar [1,3,4,5,7,10] so that efficient compilers may be produced from the semantic specifications written in the attribute grammar.There is another important problem about the semantic specifications. This is how to verify the correctness of the specification and is essential in ascertaining the correctness of produced compilers. In contrast with the evaluation problem, this has not been studied well and only a few partial results have been reported up to now [2,9].In this paper we propose a verification procedure for proving the correctness of attribute grammar, which is applicable to the wide class of attribute grammars called absolutely noncircular ones [7]. Our method can be extended to accept any noncircular attribute grammar since it is shown that any noncircular attribute grammar is transformed into an equivalent absolutely noncircular one [5].Our verification procedure utilizes dependency relations among attributes and verification is performed by induction based on this order relation, according to which attributes are evaluated. This procedure consists of (1) assigning assertions to relevant pairs of a nonterminal symbol and a parallelly evaluable subset of its attributes, (2) generating a set of verification conditions for each production rule with the aid of dependency graph of the rule and (3) proving the verification conditions. Of course, verification is performed production-rule-wise.Our method can accept attribute grammars which contain both synthesized and inherited attributes and handle them in a well-formed way. This contrasts to the previous works where only the synthesized case is considered [2] or there seems no general and formal descriptions about how to verify general attribute grammars [9].In this paper we first give necessary definitions and notations for attribute grammar and then propose a verification procedure to prove its correctness. After giving some examples of verification, we establish consistency and completeness of our procedure.