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Functional Programming in Scheme
Expressions, Types, and Functions
Lambda calculus

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.

Lambda calculus is a more dense notation than the similar Scheme notation

Lambda calculusScheme
Abstractionλ v . E(lambda (v) E)
CombinationE1 E2(E1 E2)

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.