Validated Construction of Congruence Closures

It is by now well known that congruence closure (CC) algorithms can be viewed as implementing ground completion: given a set of ground equations, the CC algorithm computes a convergent rewrite system whose equational theory conservatively extends that of the original set of equations. We call such a rewrite system a CC for the original set. This paper describes work in progress to create an implementation of a CC algorithm which is validated, in the following sense. Any non-aborting, terminating run of the implementation is guaranteed to produce a CC for the input set of equations. Note that aborting or failing to terminate can happen for implementations of CC algorithms only due to bugs in code; the algorithms themselves are usually proved terminating and correct. Validation of an implementation of a CC algorithm is achieved by implementing the algorithm in RSP1, a dependently typed programming language. Type checking ensures that proofs of convergence and conservative extension are well-formed.