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Automated Mathematical Induction

Editors: Hantao Zhang (Ed.)

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About this book

It has been shown how the common structure that defines a family of proofs can be expressed as a proof plan [5]. This common structure can be exploited in the search for particular proofs. A proof plan has two complementary components: a proof method and a proof tactic. By prescribing the structure of a proof at the level of primitive inferences, a tactic [11] provides the guarantee part of the proof. In contrast, a method provides a more declarative explanation of the proof by means of preconditions. Each method has associated effects. The execution of the effects simulates the application of the corresponding tactic. Theorem proving in the proof planning framework is a two-phase process: 1. Tactic construction is by a process of method composition: Given a goal, an applicable method is selected. The applicability of a method is determined by evaluating the method's preconditions. The method effects are then used to calculate subgoals. This process is applied recursively until no more subgoals remain. Because of the one-to-one correspondence between methods and tactics, the output from this process is a composite tactic tailored to the given goal. 2. Tactic execution generates a proof in the object-level logic. Note that no search is involved in the execution of the tactic. All the search is taken care of during the planning process. The real benefits of having separate planning and execution phases become appar­ ent when a proof attempt fails.

Table of contents (6 chapters)

  • Induction Using Term Orders

    Bronsard, Francois (et al.)

    Pages 3-37

  • New Uses of Linear Arithmetic in Automated Theorem Proving by Induction

    Kapur, Deepak (et al.)

    Pages 39-78

  • Productive Use of Failure in Inductive Proof

    Ireland, Andrew (et al.)

    Pages 79-111

  • Middle-Out Reasoning for Synthesis and Induction

    Kraan, Ina (et al.)

    Pages 113-145

  • A Calculus for and Termination of Rippling

    Basin, David A. (et al.)

    Pages 147-180

Buy this book

eBook $129.00
price for USA in USD (gross)
  • ISBN 978-94-009-1675-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA in USD
  • ISBN 978-0-7923-4010-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.99
price for USA in USD
  • ISBN 978-94-010-7250-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Automated Mathematical Induction
Editors
  • Hantao Zhang
Copyright
1996
Publisher
Springer Netherlands
Copyright Holder
Kluwer Academic Publishers
eBook ISBN
978-94-009-1675-3
DOI
10.1007/978-94-009-1675-3
Hardcover ISBN
978-0-7923-4010-2
Softcover ISBN
978-94-010-7250-2
Edition Number
1
Number of Pages
VI, 222
Topics