Higher-order subtyping with intersection types

Acknowledgements Mariangiola Dezani is the most encouraging and enthusiastic computer scientist I have ever met. From her I learned to trust my intuition and follow it through to the very end. This research would not have been possible without her technical supervision and moral support. I would also like to thank my supervisor, Henk Barendregt. His lucid lectures on-calculus, his ability to hide irrelevant details, the clarity of his explanations, and his elegant technical prose have been constant guides. I thank the people in the Netherlands, especially Erik Barendsen and Jan Ku-per, for their help and friendship, and Steeen van Bakel and Paula Severi, for their comments on previous drafts of this thesis. Mieke Massink and Maria Fernn andez Ferreira started as colleagues and soon became two of my dearest friends. I am grateful to Benjamin Pierce, who suggested the study of a-calculus combining higher-order polymorphism and intersection types. He and I deened the system F ! ^ , whose study is, by and large, the theme of this thesis; together we wrote CP93], from which chapters 5 and 6 arose. His fertile mind and his passion for hard work make him inspiring company. I am indebted to Rod Burstall, who opened to me the doors of the Laboratory for Foundations of Computer Science. There I found a highly motivating research environment where I developed most of the results in this thesis, and a handful of friends who made my life in Edinburgh a beautifully rich experience. I enjoyed technical discussions with special thanks to Healfdene Goguen for many helpful comments on draft versions of this thesis. It has been an honour to have Jan Willem Klop, Giuseppe Longo, and Rob Nederpelt as members of the manuscript commission. From my watercolor teacher, Joost van Moll, I learned a technique which actually changed my way of doing research; it consists of carefully examining what has been done, learning from the successful ideas, and being brave enough to start over again regardless of the time invested in the previous try. In the non-academic world, I want to thank my parents, Mario Compagnoni and Susana Brunsch, for their unconditional love. I want to mention (in the order in which they appeared in my life)