Lazy techniques for fully expansive theorem proving

Abstract

The HOL system is afully expansive theorem prover: proofs generated in the system are composed of applications of the primitive inference rules of the underlying logic. One can have a high degree of confidence that such systems are sound, but they are far slower than theorem provers that exploit metatheoretic or derived properties.

This paper presents techniques for postponing part of the computation so that the user of a fully expansive theorem prover can be more productive. The notions oflazy theorem andlazy conversion are introduced. These not only allow part of the computation to be delayed, but also permit nonlocal optimizations that are only possible because the primitive inferences are not performed immediately. The approach also opens the way to proof procedures that exploit metatheoretic properties without sacrificing security; the primitive inferences still have to be performed in order to generate a theorem, but during the proof development the user is free of the overheads they entail.