Lambda Calculi with Types

Abstract

Abstract The lambda calculus was originally conceived by Church [Church, 193233] as part of a general theory of functions and logic, intended as a foundation for mathematics. Although the full system turned out to be inconsistent, as shown in [Kleene and Rosser, 1935], the subsystem dealing with functions only became a successful model for the computable functions. This system is called now the lambda calculus. Books on this subject e.g. are [Church, 1941], [Curry and Feys, 1958], [Curry et al., 1972], [Barendregt, 1984], [Hindley and Seldin, 1986) and [Krivine, 1990].