Interactive Theorem Proving with Tasks

Interactive theorem proving systems for mathematics require user interfaces which allow for user interaction that is as natural as possible. However, this interaction is often limited by the traditional calculi underlying most theorem proving systems. This is particularly problematic with respect to the application of assertions and intuitive presentation of proof states. In this paper we show how a more flexible user interaction can be realized when traditional calculi for classical logic are replaced by a less restrictive reasoning engine, the recently developed CORE [2] system. We describe the task level which is built on top of the CORE system and combines the Proof by Pointing approach [5] with a flexible mechanism for the application of assertions that avoids decomposition and abstracts from the syntactical form of an assertion. We demonstrate how proof steps that are difficult to implement in other systems, like forward application of assertions, are quite naturally supported by the underlying CORE system and are therefore straightforward to realize at the task level.