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Automated Mathematical Induction

  • Hantao Zhang

Table of contents

  1. Front Matter
    Pages i-1
  2. Francois Bronsard, Uday S. Reddy, Robert W. Hasker
    Pages 3-37
  3. Andrew Ireland, Alan Bundy
    Pages 79-111
  4. Ina Kraan, David Basin, Alan Bundy
    Pages 113-145
  5. David A. Basin, Toby Walsh
    Pages 147-180

About this book

Introduction

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.

Keywords

Arithmetic automated theorem proving formal method proof proving

Editors and affiliations

  • Hantao Zhang
    • 1
  1. 1.University of IowaIowa CityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-1675-3
  • Copyright Information Springer Science+Business Media B.V. 1996
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-7250-2
  • Online ISBN 978-94-009-1675-3
  • Buy this book on publisher's site