Combinators and the Story of Computation

Abstract: We discuss the role of combinators in the development of the modern conception of computation over the course of the past century. We describe how ideas about formalism and mathematical logic led to the introduction of combinators in 1920 as an extension of the discovery of Nand as a basis for basic logic. We then discuss how combinators informed lambda calculus and symbolic computation, and their relationship to the development of practical computation. We finally describe recent views of combinators in terms of the computational universe of possible programs, and a recent approach to the fundamental theory of physics.