Advances in Equational Theorem Proving

time wall-clock time [d] m em or y [G B y te ] Figure 7.7: Memory requirements over time for ROB001-1: bottom axis denotes abstract time, top axis denotes wall-clock time in days 7.4 Further benefits Besides the smaller memory footprint and some simplifications (e. g. for interreduction) there are some other benefits of the new loop design that are worth discussing. Not all of them are completely implemented yet. Advantages of the compact search state representation When we analyze the new representations of A and P, we see that not only are they much more compact than the old ones, they are much simpler as well. For both, we can distinguish between the administrative data structures (the index of A and the priority queues of P) and the actual contents. Given the contents, the administrative data structures are easy to construct. Hence, we can consider A as a collection of rules and equations annotated with activation and deactivation timestamps; and the whole set P consists only of tuples of numbers. It is therefore much easier than with the old representation to develop routines that allow us to save proof states to disk and to restore them when necessary. With the old representation, this is simply not feasible because of the amount of data that would have to be written or read. Such a save/restore-facility is not only useful to protect long running proof searches against power failures, machine crashes, and kernel updates. They also give the further option to migrate to a different machine, or simply to stop the proof search with the option to resume it later. Often, the completion of some (sub-)set of equations to a convergent rewrite system