Equational Speci cations : 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 deened, consistent, and suuciently complete speciications. Direct implementations of speciications as term rewriting systems serve as software prototypes of systems. We use prototypes to determine that speciications are consistent with our intuitive expectations during design and with more eecient implementations during testing. We describe an automated tool for reasoning about both the properties a speciication and the cor-rectness of its implementation. Our approach is applicable to a relatively small class of speciications, but within this class it appears to be eeective for designing high quality speciications and for eeectively using these speciications for a variety of other tasks arising during the software lifecycle.