We use G\"odel'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.Comment: In Proceedings CL&C 2012, arXiv:1210.289
