Solving Higher-Order Equations From Logic to Programming [Hardcover]

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.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 l&