Combinators and the Story of Computation

TL;DR

This paper explores the historical development and significance of combinators in the evolution of computation, from formal logic to modern theories including physics and the computational universe.

Contribution

It provides a comprehensive overview of combinators' role across a century, linking formal logic, lambda calculus, and contemporary computational theories.

Findings

Combinators originated in 1920 as an extension of Nand logic.

They influenced the development of lambda calculus and symbolic computation.

Recent views connect combinators to the computational universe and fundamental physics.

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.