Acknowledgments

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Readers who find value in this book owe their biggest debt of gratitude to four mentors—Luca Cardelli, Bob Harper, Robin Milner, and John Reynolds—who taught me most of what I know about programming languages and types.

The rest I have learned mostly through collaborations; besides Luca, Bob, Robin, and John, my partners in these investigations have included MartínAbadi, Gordon Plotkin, Randy Pollack, David N. Turner, Didier Rémy, Davide Sangiorgi, Adriana Compagnoni, Martin Hofmann, Giuseppe Castagna, Martin Steffen, Kim Bruce, Naoki Kobayashi, Haruo Hosoya, Atsushi Igarashi, Philip Wadler, Peter Buneman, Vladimir Gapeyev, Michael Levin, Peter Sewell, Jérôme Vouillon, and Eijiro Sumii. These collaborations are the foundation not only of my understanding, but also of my pleasure in the topic.

The structure and organization of this text have been improved by discussions on pedagogy with Thorsten Altenkirch, Bob Harper, and John Reynolds, and the text itself by corrections and comments from Jim Alexander, Penny Anderson, Josh Berdine, Tony Bonner, John Tang Boyland, Dave Clarke, Diego Dainese, Olivier Danvy, Matthew Davis, Vladimir Gapeyev, Bob Harper, Eric Hilsdale, Haruo Hosoya, Atsushi Igarashi, Robert Irwin, Takayasu Ito, Assaf Kfoury, Michael Levin, Vassily Litvinov, Pablo López Olivas, Dave MacQueen, Narciso Marti-Oliet, Philippe Meunier, Robin Milner, Matti Nykänen, Gordon Plotkin, John Prevost, Fermin Reig, Didier Rémy, John Reynolds, James Riely, Ohad Rodeh, Jürgen Schlegelmilch, Alan Schmitt, Andrew Schoonmaker, Olin Shivers, Perdita Stevens, Chris Stone, Eijiro Sumii, Val Tannen, Jérôme Vouillon, and Philip Wadler. (I apologize if I've inadvertently omitted anybody from this list.) Luca Cardelli, Roger Hindley, Dave MacQueen, John Reynolds, and Jonathan Seldin offered insiders' perspectives on some tangled historical points.

The participants in my graduate seminars at Indiana University in 1997 and 1998 and at the University of Pennsylvania in 1999 and 2000 soldiered through early versions of the manuscript; their reactions and comments gave me crucial guidance in shaping the book as you see it. Bob Prior and his team from The MIT Press expertly guided the manuscript through the many phases of the publication process. The book's design is based on macros developed by Christopher Manning for The MIT Press.

Proofs of programs are too boring for the social process of mathematics to work. —Richard DeMillo, Richard Lipton, and Alan Perlis, 1979

… So don't rely on social processes for verification. —David Dill, 1999

Formal methods will never have a significant impact until they can be used by people that don't understand them. —attributed to Tom Melham

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