Reflection, the capacity to represent our ideas and to make them the object of our own thoughts, has for many centuries been recognized as a key mark of human intelligence. Clavel's book proposes a general theory of reflective logics and reflective declarative programming languages, that provides a conceptual foundation for judging the extent to which a computational system is reflective. Applying this general framework, Clavel makes an in depth study of reflection in rewriting logic. This book presents examples of the powerful potential for reflective programming in a number of novel computer applications.

The very success and extension of reflective ideas in logic and computer science underscores the need for conceptual foundations. In this book, Clavel proposes axiomatic notions for reflective logics and reflective declarative programming languages. The key concept is the notion of a “universal theory” that can simulate the deductions of all other theories in a logic. This axiomatization unifies different strands of research in reflection, including reflective functional, equational, Horn logic, and rewriting logic programming languages. Based on these universal metalogical axioms, Clavel investigates reflection in rewriting logic at both the theoretical and at the practical level. Providing a fully detailed proof of the reflective nature of rewriting logic, Clavel then gives examples of the useful and powerful properties of this reflective nature in a wide range of computer applications.

All these applications are developed using the Maude language, a reflective programming language and environment that implements rewriting logic and supports its reflective capabilities. These examples demonstrate the power of Maude to define and execute mappings of logics, and to represent and execute different languages and models of computation. Clavel also proposes a general method to easily build theorem proving tools in Maude, with examples.