Solving Higher-Order Equations

From Logic to Programming

  • Christian Prehofer

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

Table of contents

  1. Front Matter
    Pages i-ix
  2. Christian Prehofer
    Pages 1-5
  3. Christian Prehofer
    Pages 7-23
  4. Christian Prehofer
    Pages 25-35
  5. Christian Prehofer
    Pages 37-53
  6. Christian Prehofer
    Pages 55-78
  7. Christian Prehofer
    Pages 79-120
  8. Christian Prehofer
    Pages 121-134
  9. Christian Prehofer
    Pages 135-152
  10. Christian Prehofer
    Pages 153-161
  11. Back Matter
    Pages 163-188

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.


Hardware Program Analysis Theorem Proving Variable calculus computer computer science declarative programming functional programming logic program transformation programming verification

Authors and affiliations

  • Christian Prehofer
    • 1
  1. 1.Institut für Informatik, SB3MünchenGermany

Bibliographic information