Proof Theory in Computer Science : International Seminar PTCS 2001 Dagstuhl Castle Germany October 7–12 2001 Proceedings This book constitutes the refereed proceedings of the International Seminar on Proof Theory in Computer Science PTCS 2001 held in Dagstuhl Castle Germany in October 2001. The 13 thoroughly revised full papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are higher type recursion lambda calculus complexity theory transfinite induction categories induction recursion post Turing analysis natural deduction implicit characterization iterate logic and Java programming