Solving Higher-Order Equations: From Logic to Programming (Progress in Theoretical Computer Science) - Hardcover

Prehofer, Christian

Hardcover

ISBN 10: 0817640320 ISBN 13: 9780817640323

Publisher: Birkhäuser, 1997

Synopsis

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.

About this title

Synopsis

This monograph develops techniques for equational reasoning and declarative programming based on higher-order logic. The author presents a framework for the full integration of declarative programming models and shows its application. On the technical side, he integrates the main results of both worlds. The book presents completeness results as common in logic programming and also generalizes evaluation strategies found in current functional programming languages to this setting. The book includes a thorough introduction to higher-order equational logic, higher-order rewriting, and unification. This followed by a stepwise development from general equational reasoning toward effective methods for declarative programming in higher-order logic and lambda-calculus. Another important, complementing, result shows that higher order unification, the basic inference engine in logic programming, is decidable for programming applications. The text is aimed at researchers and advanced students in computer science and mathematics with interests in declarative programming, symbolic computation, term rewriting, equational reasoning, and theorem proving.

It can provide a firm basis for a variety of graduate course in logic and theoretical computer science.

Edition details

• Publisher: Birkhäuser
• Publication date: 1997
• Language: English
• ISBN 10: 0817640320
• ISBN 13: 9780817640323
• Binding: Hardcover
• Number of pages: 197