A Pragmatic Approach to Reuse in Tactical Theorem Proving

In interactive theorem proving, tactics and tacticals have been introduced to automate proof search. In this scenario, user interaction traditionally is restricted to the mode in which the user decides which tactic to apply on the top-level, without being able to interact with the tactic once it has begun running. We propose a technique to allow the implementation of derivational analogy in tactical theorem proving. Instead of replaying tactics including backtracked dead ends our framework makes choice points in tactics explicit and thus avoids dead ends when reusing tactics. Additionally users can override choices a tactic has made or add additional steps to a derivation without terminating the tactic. The technique depends on an eÆcient replay of tactic executions without repeating search that the original computation may have involved.