Solving Higher-Order Equations

1. Front Matter

   Pages i-ix

   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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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

• Institut für Informatik, SB3, München, Germany

  Christian Prehofer

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