Tableau Method Implementation Using Laziness

Abstract

A few lines long reasonably efficient implementation of the (asymmetric) tableau method for the NP-complete boolean satisfiability problem is presented. The tableau method, also called the semantic tree method, for propositional calculus is a method for finding models to propositional formulas, i.e. a method for finding truth value assignments to the variables of propositional formulas such that the formulas become true. The tableau method can be implemented quite elegantly and reasonably efficiently in a lazy language by using the list of successes technique. Instead of searching for just one solution to a problem, the idea of the list of successes technique is to search for all the solutions, returning a list of successes [BW88]. In a lazy language, where only that which is needed is computed, this technique can be efficient. If e.g. just the first solution in the list of solutions is used --- as is often the case --- the rest of the solutions are never explicitly calculated. Th...