Developing Deduction Systems: The Toolbox Style

Abstract

Implementing an automated theorem proving system poses practical problems of an order of magnitude a naive implementor hardly expects. Even an experimental version requires the solution of numerous technical problems each of which may not be too difficult (although some are), but whose mere number is frightening, such as defining basic data structures and implementing the algorithms for fundamental tasks like parsing input, or copying terms. Furthermore, the engineering discipline of building deduction systems is — after twenty years of experience — rather advanced, and many tasks such as indexing techniques for very large sets of formulae (cf. the article by Graf on indexing), fast first order unification algorithms (Paterson and Wegman, 1978; Martelli and Montanan, 1982; Corbin and Bidoit, 1983; Dowek et al., 1995) or the implementation of higher order constructs require an amount of experience and know-how that may take several years to develop. The effect is that the effort spent on the really interesting part of the experiment, namely testing a new calculus or the modification of a given one, is forced to take a back seat. Furthermore, even moderate efficiency — which may be enough for most experimental versions — depends on the particular encoding of the data structures and algorithms involved.