Integrating Tps and Omega

This paper reports on the integration of the higher-order theorem proving environment Tps [Andrews et al., 1996] into the mathematical assistant Omega [Benzmueller et al., 1997] . Tps can be called from Omega either as a black box or as an interactive system. In black box mode, the user has control over the parameters which control proof search in Tps, in interactive mode, all features of the Tps-system are available to the user. If the subproblem which is passed to Tps contains concepts defined in Omega's database of mathematical theories, these definitions are not instantiated but are also passed to Tps. Using a special theory which contains proof tactics that model the ND-calculus variant of Tps within Omega, any complete or partial proof generated in Tps can be translated one to one into an Omega proof plan. Proof transformation is realised by proof plan expansion in Omega's 3-dimensional proof data structure, and remains transparent to the user.