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Outline

Title
Abstract
Introduction 1.SUBJECT Area
Expectations and Importance of Future Progress
Possible Way to Future Progress -Overall Thesis
(Hypotheses Task)
Recursion Analysis and Induction Variables
The Hypotheses Problem
Discussion
The Rôle of Recursion Analysis in Descente Infinie
(Task of Case Analysis on Induction Variables)
Conclusion
Summary
References

Progress in Computer-Assisted Inductive

Profile image of Claus-Peter WirthClaus-Peter Wirth

2006

Abstract

In this position paper we briefly review the development history of automated inductive theorem proving and computer-assisted mathematical induction. We think that the current low expectations on progress in this field result from a faulty narrow-scope historical projection. Our main motivation is to explain-on an abstract but hopefully sufficiently descriptive level-why we believe that future progress in the field is to result from human-orientedness and descente infinie.

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  112. Claus-Peter Wirth (2005). History and Future of Implicit and Inductionless Induction: Beware the old jade and the zombie!. In: [53], pp. 192-203. http://www.ags. uni-sb.de/~cp/p/zombie/welcome.html (Dec. 02, 2002).
  113. Claus-Peter Wirth (2006). lim +, δ + , and Non-Permutability of β-Steps. SEKI-Report SR-2005-01, ISSN 1437-4447, rev. ed. of July 30, 2006. http://www.ags. uni-sb.de/~cp/p/nonpermut/welcome.html (July 30, 2006).
  114. Claus-Peter Wirth (2006). A Self-Contained Discussion of Fermat's Only Explicitly Known Proof by Descente Infinie. SEKI-Working-Paper SWP-2006-02, ISSN 1860-5931. http://www.ags.uni-sb.de/~cp/p/fermatsproof/welcome.html (Aug. 25, 2006).
  115. Claus-Peter Wirth (2007). Thomas S. Kuhn: The Structure of Scientific Revolu- tions -Zweisprachige Auszüge mit Deutschem Kommentar. SEKI-Working-Paper SWP-2007-01, ISSN 1860-5931. http://www.ags.uni-sb.de/~cp/p/kuhn (June 20, 2008).
  116. Claus-Peter Wirth (2008). Hilbert's epsilon as an Operator of Indefinite Committed Choice. J. Applied Logic, Elsevier, http://dx.doi.org/10.1016/j.jal. 2007.07.009. http://www.ags.uni-sb.de/~cp/p/epsi (Oct. 15, 2007).
  117. Claus-Peter Wirth (2008). Shallow Confluence of Conditional Term Rewriting Sys- tems. J. Symbolic Computation, Elsevier, http://dx.doi.org/10.1016/j.jsc. 2008.05.005. http://www.ags.uni-sb.de/~cp/p/shallow/welcome. html (May 31, 2008).
  118. Claus-Peter Wirth, Bernhard Gramlich (1994). On Notions of Inductive Validity for First- Order Equational Clauses. 12 th CADE 1994, LNAI 814, pp. 162-176, Springer. http: //www.ags.uni-sb.de/~cp/p/cade94/welcome.html (Aug. 05, 2001).
  119. Claus-Peter Wirth, Christoph Benzmüller, Armin Fiedler, Andreas Meier, Serge Autex- ier, Martin Pollet, Carsten Schürmann (2003). Human-Oriented Theorem Proving - Foundations and Applications. Lecture course at Saarland Univ., WS 2003/4. http: //www.ags.uni-sb.de/~cp/teaching/hotp (Sept. 12, 2003).

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