We will here introduce the notation of the lambda calculus, mainly in order to understand the inspiration which led to the concept of lambda expressions in Lisp and Scheme.

A comparison of the notations of abstraction and combination (application) in the lambda calculus and Lisp. In some variants of lambda calculus there are more parentheses than shown here: (λ v . E). However, mathematicians tend to like ultra brief notation, and they often eliminate the parentheses. This stands as a contrast to Lisp and Scheme programmers.