Solving Higher-Order Equations

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.