title: Handbook of Proof Theory, Volume 137 (Studies in Logic and the Foundations of Mathematics)
author: S.R. Buss
description: Toshiyasu Arai<br>The Handbook is most welcome in the logic community. I recommend the Handbook to researchers and graduate students in logic, mathematics, computer science, philosophy, linguistics, artificial intelligence, automated reasoning and cognitive sciences.<br>Bulletin of Symbolic Logic<br>
zlib_text: An Introduction to Formal Language Theory that
  Integrates Experimentation and Proof
  Allen Stoughton
  Kansas State University
  Draft of Fall 2004
  
  Copyright c⃝ 2003–2004 Allen Stoughton
  Permission is granted to copy, distribute and/or modify this document under
  the terms of the GNU Free Documentation License, Version 1.2 or any later
  version published by the Free Software Foundation; with no Invariant Sec-
  tions, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license
  is included in the section entitled “GNU Free Documentation License”.
  The LATEX source of this book and associated lecture slides, and the
  distribution of the Forlan toolset are available on the WWW at http:
  //www.cis.ksu.edu/~allen/forlan/.
  
  Contents
  Preface
  v
  1
  Mathematical Background
  1
  1.1
  Basic Set Theory . . . . . . . . . . . . . . . . . . . . . . . . .
  1
  1.2
  Induction Principles for the Natural Numbers . . . . . . . . .
  11
  1.3
  Trees and Inductive Deﬁnitions . . . . . . . . . . . . . . . . .
  16
  2
  Formal Lan