Running Programs Backwards : The Logical Inversion of Imperative

The feasibility of inverting imperative computations using logic programming technology is informally explored. Program inversion is the process of determining the possible input values that will produce a given output for a program. The relational semantics of imperative computations treats programs as logical relations over the observable environment, which is usually taken to be the state of the variables in memory. The declarative semantics of program relations implicitly denote both forward and inverse computations. This view of computation has practical applications when logic programming technology is considered. An imperative program has a logic program derived for it which abductively describes its inverted behaviour. Depending on the inference strategy used, execution of this relational program can compute the inverse of the imperative program. It is shown how a number of nontrivial imperative computations can be inverted with minimal logic programming tools. The advantage of this approach is that nondeterministic inversions are possible, which permits sets of inputs to be computed for a particular output. This should prove to be a useful tool in imperative program testing and debugging.