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This text is an outgrowth of notes prepared by J.-Y. Girard for a course at the University of Paris VII. It deals with the mathematical background of the application to computer science of aspects of logic (namely the correspondence between proposition and types). Combined with the conceptual perspectives of Girard's ideas, this sheds light on both the traditional logic material and its prospective applications to computer science. The book covers a very active and exciting research area, and it will be essential reading for all those working in logic and computer science.
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