The Use of Proof Planning for Co-operative Theorem Proving

We describe BARNACLE: a cooperative interface to an inductive theorem prover. The cooperative nature of the BARNACLE interface is made possible by proof planning. Proof planning is a technique for guiding the search for a proof in automatic theorem proving. Common patterns of reasoning in proofs are identified and represented computationa.lly as proof plans. These proof plans are then used to guide the search for proofs of new conjectures. Where a proof requires more than common patterns of reasoning, proof planning needs to be supplemented by human interaction. Proof planning makes new kinds of user interaction possible. Proof plans structure proofs hierarchica.lly. This can be used to present partial proofs to users without overwhelming them with detail. Proof plans use a meta-logic to relate each chunk of a proof to its parents and daughters in the hierarchy and to its subparts. Proof plans sometimes annotate the proof steps to display the rationale behind them. The relations between proof chunks and the annotations can both be used to help users understand the state of proof attempts. This improved understanding can help them find patches to failed proofs and the metalogic provides a high-level language for specifying the patch. J\"ey words and phrases" Proof Planning, Co-operative Theorem Proving, Explanations.