The development of first-order logic programming can be traced back to resolution theorem proving and further to the Skolem-Herbrand-Gödel Theorem, a fundamental theorem of first-order logic. This book proceeds by providing an extrapolation of this development to a higher-order setting. More precisely, it presents a largely theoretical foundation of a form of higher-order resolution, and combined functional and logic programming.

The Clausal Theory of Types is a higher-order logic for which the Skolem-Herbrand-Gödel Theorem and resolution can be generalized. It is a clausal extensional sub-logic of Church's formulation of the Simple Theory of Types which includes equality. It is “higher-order” in the sense that it allows quantification of variables of all types, embeddable predicates, representations of functions and predicates by λ-abstractions, and equations involving abstractions.

All of these features enable its Horn clause form to be a concise logic and functional programming language which has a sound and complete declarative and operational semantics. Clausal Theory of Types logic programs incorporate higher-order functional evaluation as an elementary operation through unification or conditional higher-order rewriting, higher-order relational proofs through backtrack search, and the separation of their declarative specifications.

This extrapolation entails largely self-contained discussions on the development of resolution and logic programming, the simply typed λ-calculus, higher-order logics and Henkin-Andrews general models, higher-order forms of term rewriting and equational unification, and higher-order versions of the Resolution Theorem and fixed point, model theoretic, and operational results in logic programming.