English

A Note on Shortest Developments

Logic in Computer Science 2015-07-01 v2

Abstract

De Vrijer has presented a proof of the finite developments theorem which, in addition to showing that all developments are finite, gives an effective reduction strategy computing longest developments as well as a simple formula computing their length. We show that by applying a rather simple and intuitive principle of duality to de Vrijer's approach one arrives at a proof that some developments are finite which in addition yields an effective reduction strategy computing shortest developments as well as a simple formula computing their length. The duality fails for general beta-reduction. Our results simplify previous work by Khasidashvili.

Cite

@article{arxiv.0708.0200,
  title  = {A Note on Shortest Developments},
  author = {Morten Heine Sørensen},
  journal= {arXiv preprint arXiv:0708.0200},
  year   = {2015}
}
R2 v1 2026-06-21T09:04:01.220Z