7 Conclusion Plan Formation and Execution in a Uniform Architecture of Declarative Metatheories

A. Bundy and B. Welham. Using meta-level inference for selective application of multiple rewrite rules in algebraic manipulation. In this paper we have shown how a metatheory of a mechanized logic can be deened and used to reason about proof plans. In particular proof plans can be built by theorem proving. Doing so we are guaranteed that, provided that the metatheory is correct and truthful proof plans are built correct. executed without adding or modifying the underlying code. The resulting system is thus able to acquire new theorem proving capabilities without any addition and/ or modiication of the underlying code. The resulting architecture is uniform in the sense that a tower of metatheories can be deened, each using the same code and the same commands (natural deduction and derived inference rules), each such that plan formation at one level can be obtained by plan execution one level up. Note that the commands are used to reason about the code that implements them. Currently, work is in progress to prove the correctness (we have a proof of this) and other properties of the system using the reeection principle, but without considering the issue of mechanization. A truthful metatheory of a mechanized logic is currently being studied. Possible extensions of the work described in this paper are to study how proof plans can be compiled down into the code; how to optimize the planning part (a related issue is to consider proof plans representing possibly failing tactics) and how to take advantage (if possible and feasible) of the tower of metatheories by reasoning at an arbitrary level. Acknowledgements This work started when the rst author was at the AI Department of Edinburgh University. The research described in this paper owes a lot to the openess and sharing of ideas which exists in the Mathematical Reasoning group in Edinburgh and Mechanized Reasoning group in Trento. Alan Bundy and Richard Weyhrauch have provided, in diierent moments, invaluable support; without them the research described in this paper could have never been done. References BM81] R.S. Boyer and J.S. Moore. Metafunctions: proving them correct and using them eeciently as new proof procedures. predicates (such as Prov) and terms (such as de) GSnt]; the explicit link in the code does not exist. As Boyer and Moore do BM81], we use functions deened in the underlying code. On the other hand, in our approach the underlying code is …