Adding New Rules to an LCF-style Logic Implementation

Abstract

By encapsulating the primitive rules of inference as the constructors of the abstract type of theorems, LCF-style systems provide a successful answer to the problem of how to soundly add derived inference rules to a theorem prover. We suggest a supplementary method which uses formal proof of program equivalence to justify the dynamic addition of new primitive rules. The method does not increase the strength of the logic; rather, it is a means of increasing the computational strength of the implementation. The method can be used to enforce rigour in the process of iteratively improving the performance of a system. This work uses first class environments, a recent addition to the SML/NJ compiler.