vorgelegt von

Prof. Dr. N. NavabTo my familyAcknowledgements I am deeply grateful that I had the opportunity to write this thesis while working at the Chair for Pattern Recognition within the project B6 of the Sonderforschungsbereich 603 (funded by Deutsche Forschungsgemeinschaft). Many people contributed to this work and I want to express my gratitude to all of them

Dekan der Naturwissenschaftlich-Technischen

Hiermit versichere ich an Eides statt, dass ich die vorliegende Arbeit selbständi

Acknowledgements

(Universität des Saarlandes

zur Erlangung des akademischen Grades des

tomyfatherVictorino, toLuis. Acknowledgments This work was only possible due to the help of many people. I would like to express my sincere thanks to some of them. My parents initiated me to doubt and reason. My teachers at the university supported me and my inquisitive questions; one who deserves special mention is Jorge “el Profe ” Aguirre, and Ugo Montanari escorted me at my first autonomous steps. Friendsassistedme in different ways, either emotionallyor technically (or both), among them Maribel Fernández, Gudrun Gruber, Andrea and Thom, Daniel Szyld, Max Vogl. Martin Wirsing showed extreme patience to guide me through the jungle of scientific activity. And of course Luis. Part of this work was performed while visiting John Crossley at Monash University. My PhD studywas funded by the DAAD (German Academic Exchange Office).

Program Verification in Synthetic Domain Theory

Synthetic Domain Theory provides a setting to consider domains as sets with certain closure properties for computing suprema of ascending chains. As a consequence the notion of domain can be internalized which allows one to construct and reason about solutions of recursive domain equations. Moreover, one can derive that all functions are continuous. In this thesis such a synthetic theory of domains (#-domains) is developed based on a few axioms formulated in an adequate intuitionistic higher-order logic. This leads to an elegant theory of domains. It integrates the positive features of several approaches in the literature. In contrast to those, however, it is model independent and can therefore be formalized. A complete formalization of the whole theory of #-domains has been coded into a proof-checker (Lego) for impredicative type theory. There one can exploit dependent types in order to express program modules and modular specifications. As an application of this theory an entirely fo..