The logic and expressibility of simply-typed call-by-value and lazy languages

We study the operational, denotational, and axiomatic semantics of lazy and call-by-value functional languages, and use these semantics to build a new expressiveness theory for comparing functional languages. The rst part of the thesis develops the theory of lazy and call-by-value languages separately, following paradigmatic studies of call-by-name functional languages. We rst describe the operational semantics of two simply-typed languages, lazy PCF and call-by-value PCF. These two languages provide enough intuition to describe general deenitions of denotational models and logics for lazy and call-by-value languages. We prove, via a completeness theorem, that the deenitions of models and logic coincide for both the lazy and call-by-value theories. The second part of the thesis compares the two kinds of languages via translations. Speciically, we develop the idea of a fully abstract translation and deene new fully abstract translations from call-by-value PCF to lazy PCF, and vice versa. We then use the ideas to develop an expressiveness theory for languages. The theory shows that call-by-value PCF and lazy PCF are equally expressive, and another language, call-by-name PCF, is strictly less expressive than either of the other two. iii iv v Acknowledgements I owe a great debt to my advisor, Albert R. Meyer. It was his initial question that set me working on logics and translations for the two languages in this thesis, and his technical help and encouragement along the way were invaluable. My only regret of the time I spent at MIT was not having more time to work on research with Albert. His enthusiasm, philosophical wisdom, and good taste have made a deep impression on me, and I hope, through his example, to develop these qualities in myself. It has also been a pleasure working with two other coauthors: Bard Bloom, once a student at MIT and now a faculty member at Cornell, and Stavros Cosmadakis of IBM Research. I learned a lot from Bard and Stavros, including facts not always connected to computer science! I would also like to thank the members of my thesis committee, David Giiord and Rishiyur Nikhil, who provided good comments on a draft of this thesis and during the defense, and Carl Gunter of the University of Pennsylvania, who gave me time to nish the thesis during the rst months of a postdoctoral position. My fellow semantics students (many of whom are now elsewhere) deserve my warmest thanks: They have all, at one time or …