Twenty-five years of Automath research

Publisher Summary This chapter provides a historical overview of proof systems, leading to a short survey of the Automath project, and a description of recent developments. A proof system which is based on typed lambda calculus but does not treat proofs as formal objects is Higher Order Logic (HOL). The system is not a framework, but supports a version of classical higher order predicate logic. There are also systems for proof development that do not use type theory at all. This chapter presents selected papers for the survey of the contents which are divided in six groups, in accordance with the global character of the topics treated namely motivation and exposition, language definition and special subjects, theory, text examples, verification, and some related topics. It provides some insight in the contents of the different papers, with a view to the aims and ideas of the Automath project. The chapter discusses the contributions of Alonzo Church, the founder of type theory. The Automath project, the related type systems, and the recent developments are discussed.