## TL;DR

Lambda calculus (Alonzo Church, 1936) is a formal system for expressing computation via function abstraction and application. It is Turing-complete and the theoretical foundation of functional programming (Lisp, Haskell, ML, Clojure, JavaScript's arrow functions).

## Core Explanation

Three constructs: variables (x), abstraction (λx.M — function definition), application (M N — function call). Church numerals encode natural numbers: 0 = λf.λx.x, 1 = λf.λx.f x, 2 = λf.λx.f(f x). Y combinator enables recursion in untyped lambda calculus. Church-Turing thesis: lambda calculus and Turing machines are equivalent in computational power.

## Further Reading

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