A Characterisation of Multiply Recursive Functions with Higman's Lemma

Multiply-Recursive Upper Bounds with Higman's Lemma

We develop a new analysis for the length of controlled bad sequences in well-quasi-orderings based on Higman’s Lemma. This leads to tight multiply-recursive upper bounds that readily apply to several verification algorithms for well-structured systems.

An Inductive Version of Nash-Williams' Minimal-Bad-Sequence Argument for Higman's Lemma

Higman’s lemma has a very elegant, non-constructive proof due to Nash-Williams [NW63] using the so-called minimal-bad-sequence argument. The objective of the present paper is to give a proof that uses the same combinatorial idea, but is constructive. For a two letter alphabet this was done by Coquand and Fridlender [CF94]. Here we present a proof in a theory of inductive definitions that works ...

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

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.

From Proofs to Programs in the Minlog System the Warshall Algorithm and Higman's Lemma

The Warshall algorithm computing the transitive closure of a relation is extracted from a constructive proof that repetitions in a path can always be avoided. Secondly a nonconstructive proof of a special case of Higman's lemma is transformed into a constructive proof. From the latter an eecient program is extracted. Both examples are implemented in the interactive theorem prover Minlog develop...

A proof of Higman's lemma by structural induction