Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general. In programming language theory, a branch of computer science, type theory can refer to the design, analysis and study of type systems, although some computer scientists limit the term''s meaning to the study of abstract formalisms such as typed -calculi.