Extraction of redundancy-free programs from constructive natural deduction proofs

Abstract

Executable codes can be extracted from constructive proofs by using realizability interpretation. However, realizability also generates redundant codes that have no significant computational meaning. This redundancy causes heavy runtime overheads and is one of the obstacles in applying realizability to practical systems that realize the mathematical programming paradigm. This paper presents a method to eliminate redundancy by analysing proof trees as preprocessing of realizability interpretation. According to the declaration given to the theorem that is proved, each node of the proof tree is marked automatically to show which part of the realizer is needed. This procedure does not always work well. This paper also gives an analysis of the procedure and techniques to resolve critical cases. The method is studied in simple constructive logic with primitive types, mathematical induction and its q -realizability interpretation. As an example, the extraction of a prime number checker program is given.