Lambda Calculus A fairly simple system for representing functions The base of typed functional programming languages such as ML and Haskell

The theory of lambda calculus was developed by Alonzo Church as a foundation for mathematics in 1930s, years before computers were invented. In 1920s Moses Schonfinkel developed a theory of functions called combinators. In the 1930s Haskell Curry rediscovered Schonfinkel’s theory and showed that it was equivalent to lambda calculus In the 1950s John McCarthy inspired by the lambda calculus invented the programming language Lisp.

During the 1970’s Henderson and Morris wrote some influentional papers discussing the advantages of functional programming for software engineering. In the 1980s several groups started working on architectures to support functional programming.

Example Squaring function in lambda calculus λx.x*x λx means that we take a value x and the rest of the definition says that we multiply x by itself. The λ is called lambda abstraction.

Lambda has one parameter. If we wanted to take two numbers, double the first and add it to the second we would write λx λy.2*x+y