Simplifying transformations for type-alpha certificates

Abstract

This paper presents an algorithm for simplifying NDL deductions. An array of simplifying transformations are rigorously defined. They are shown to be terminating, and to respect the formal semantis of the language. We also show that the transformations never increase the size or complexity of a deduction---in the worst case, they produce deductions of the same size and complexity as the original. We present several examples of proofs containing various types of "detours", and explain how our procedure eliminates them, resulting in smaller and cleaner deductions. All of the given transformations are fully implemented in SML-NJ. The complete code listing is presented, along with explanatory comments. Finally, although the transformations given here are defined for NDL, we point out that they can be applied to any type-alpha DPL that satisfies a few simple conditions.