Applying Gödel's Dialectica Interpretation to Obtain a Constructive Proof of Higman's Lemma

Abstract

We use Gödel's Dialectica interpretation to analyse Nash-Williams' elegant but non-constructive "minimal bad sequence" proof of Higman's Lemma. The result is a concise constructive proof of the lemma (for arbitrary decidable well-quasi-orders) in which Nash-Williams' combinatorial idea is clearly present, along with an explicit program for finding an embedded pair in sequences of words.

In Proceedings CL&C 2012, arXiv:1210.2890

References in corpus (1)

• A Game-Theoretic Computational Interpretation of Proofs in Classical Analysis