Analysing Logic Programs by Reasoning Backwards

One recent advance in program development has been the application of abstract interpretation to verify the partial correctness of a (constraint) logic program. Traditionally forwards analysis has been applied that starts with an initial goal and traces the execution in the direction of the control-flow to approximate the program state at each program point. This is often enough to verify assertions that a property holds. The dual approach is to apply backwards analysis to propagate properties of the allowable states against the control-flow to infer queries for which the program will not violate any assertion. Backwards analysis also underpins other program development tasks such as verifying the termination of a logic program or proving that a logic program with a delay mechanism cannot reduce to a state that contains sub-goals which suspend indefinitely. This paper reviews various backwards analyses that have been proposed for logic programs, identifying common threads in these techniques. The analyses are explained through a series of worked examples. The paper concludes with some suggestions for research in backwards analysis for logic program development.