Purging in an Equality Data Base

Equality data bases are important in facilitating proofs of equality between terns. They are useful in the implementation of code optimizers [2], program verifiers [7,9], theorem provers [I], and symbolic execution systems [S]. In these applications the typical operations are determining whether or not two terms are known to be equal and updating the data base to include a new equality. Some solutions include [3,4, 8,101. In this paper we discuss the problem of removing information (‘purging’) from an equality data base and describe an algorithm for carrying this out. A natural example where purging is useful is symbolic machine execution where register values are changing. As an example of the type of operations that we wish to handle, suppose we are given the set of equalities following from a z b, g(a) f h(c), and f(b) E h(d), and we wish to remove all information about f(b). One possible interpretation will result in eliminating the equation f(a) E h(d), since f(b) E f(a) by a E b. Another interpretation will be given later.