APPLICATIONS OF INDUCTIVE DEFINITIONS AND CHOICE PRINCIPLES TO PROGRAM SYNTHESIS [chapter]

Ulrich Berger, Monika Seisenberger
2005 From Sets and Types to Topology and Analysis  
We describe two methods of extracting constructive content from classical proofs, focusing on theorems involving infinite sequences and nonconstructive choice principles. The first method removes any reference to infinite sequences and transforms the theorem into a system of inductive definitions, the other applies a combination of Gödel's negativeand Friedman's A-translation. Both approaches are explained by means of a case study on Higman's Lemma and its well-known classical proof due to
more » ... Williams. We also discuss some proof-theoretic optimizations that were crucial for the formalization and implementation of this work in the interactive proof system Minlog. 1 Higman's lemma is used, for example, in term rewriting theory for termination proofs [CTB94,Tou02].
doi:10.1093/acprof:oso/9780198566519.003.0008 fatcat:n4z453pujrenfgte7abt4tkjhi