The Clausal Theory of Types

This book presents the theoretical foundation of a higher-order logic programming language with equality based on the clausal theory of types. A long-sought goal of logic programming the clausal theory of types is a logic programming language that allows functional computation as a primitive operation while having rigorous sound and complete declarative and operational semantics. The language is very powerful supporting higher-order equational deduction and functional computation. Its higher order syntax makes it concise and expressive abstract data types can be expressed in it and searching for multiple solutions is a basic operation. The author proves a number of important and surprising results: a Skolem-Herbrand-Gdel theorem for higher-order logic; a Higher-Order Resolution Theorem which includes as special cases some previously unproven conjectures about equational matching and higher-order matching.