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 mega [Benzm uller et al., 1997]. Tps can be called from mega 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 inTps; in interactive mode, all features of theTps-system are available to the user. If the subproblem which is passed to Tps contains concepts de ned in mega's database of mathematical theories, these de nitions 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 mega, any complete or partial proof generated in Tps can be translated one to one into an mega proof plan. Proof transformation is realised by proof plan expansion in mega's 3-dimensional proof data structure, and remains transparent to the user.