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Solving Higher-Order Equations

From Logic to Programming

  • Book
  • © 1998

Overview

Authors:
  1. Christian Prehofer

    1. Institut für Informatik, SB3, München, Germany

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Part of the book series: Progress in Theoretical Computer Science (PTCS)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • Christian Prehofer
    Pages 1-5

  3. Preview

    • Christian Prehofer
    Pages 7-23

  4. Preliminaries

    • Christian Prehofer
    Pages 25-35

  5. Higher-Order Equational Reasoning

    • Christian Prehofer
    Pages 37-53

  6. Decidability of Higher-Order Unification

    • Christian Prehofer
    Pages 55-78

  7. Higher-Order Lazy Narrowing

    • Christian Prehofer
    Pages 79-120

  8. Variations of Higher-Order Narrowing

    • Christian Prehofer
    Pages 121-134

  9. Applications of Higher-Order Narrowing

    • Christian Prehofer
    Pages 135-152

  10. Concluding Remarks

    • Christian Prehofer
    Pages 153-161

  11. Back Matter

    Pages 163-188
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Keywords

About this book

This monograph develops techniques for equational reasoning in higher-order logic. Due to its expressiveness, higher-order logic is used for specification and verification of hardware, software, and mathematics. In these applica­ tions, higher-order logic provides the necessary level of abstraction for con­ cise and natural formulations. The main assets of higher-order logic are quan­ tification over functions or predicates and its abstraction mechanism. These allow one to represent quantification in formulas and other variable-binding constructs. In this book, we focus on equational logic as a fundamental and natural concept in computer science and mathematics. We present calculi for equa­ tional reasoning modulo higher-order equations presented as rewrite rules. This is followed by a systematic development from general equational rea­ soning towards effective calculi for declarative programming in higher-order logic and A-calculus. This aims at integrating and generalizing declarative programming models such as functional and logic programming. In these two prominent declarative computation models we can view a program as a logical theory and a computation as a deduction.

Authors and Affiliations

  • Institut für Informatik, SB3, München, Germany

    Christian Prehofer

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