Computation and Reasoning

The book develops a type theory, studies its properties, and explains its uses in applications to computer science. In particular, it shows how the study of type theory may offer a powerful and uniform language for programming, program specification and development, and logical reasoning. The type theory developed here reflects a conceptual distinction between logical propositions and computational data types. Starting from introducing the basic concepts, the author explains intuitively the meaning and use of the type-theoretic language with proof-theoretic justifications, and discusses various issues in the study of type theory. The pragmatic use of the language is illustrated by developing an approach to specification and data refinement in type theory, which supports modular development of spcdifications, programs and proofs.