Reflection in General Logics, Rewriting Logic, and Maude

Abstract

This paper is a summary of my PhD dissertation in which: general axiomatic notions of reflective logic and of strategy, based on the theory of general logics, are proposed; a detailed proof that rewriting logic satisfies the axiomatic definition of reflective logic is given; and the great practical importance of these concepts when a reflective logic becomes implemented as a reflective declarative language---as it is the case for a system such as Maude---is illustrated in a wide range of application areas through relevant examples.This work has been essentially carried out at SRI's Computer Science Laboratory where I developed my research project as an International Fellow during the years 1994/97 under the direction of José Meseguer. I am particularly grateful to my advisor, José Meseguer, and to the rest of my fellow members in the Maude team Steven Eker, Patrick Lincoln, and Francisco Durán with whom I have exchanged many ideas about this work, and with whom I have worked to realize them in the Maude language. I thank Narciso Martí-Oliet for very fruitful discussions that have contributed to the development of these ideas.