Equational Specifications: Design, Implementation, and Reasoning∗

Sets of equations can be used to specify, implement, and reason about software. We discuss how to automate these tasks for constructor-based, convergent rewrite systems. Using incremental design strategies, we obtain completely defined, consistent, and sufficiently complete specifications. Direct implementations of specifications as term rewriting systems serve as software prototypes of systems. We use prototypes to determine that specifications are consistent with our intuitive expectations during design and with more efficient implementations during testing. We describe an automated tool for reasoning about both the properties a specification and the correctness of its implementation. Our approach is applicable to a relatively small class of specifications, but within this class it appears to be effective for designing high quality specifications and for effectively using these specifications for a variety of other tasks arising during the software lifecycle. ∗This work has been partially supported by the C.N.R. “Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo” under grant n.90.00750.69, by the National Science Foundation grant CCR-9196023 and CCR-9406751, and by the Office of Naval Research grants N00014-87-K-0307 and N0014-90-J4091.