---
id:"kb-2026-00198"
title:"Lambda Calculus"
schema_type:"TechArticle"
category:"computer-science"
language:"en"
confidence:"high"
last_verified:"2026-05-22"
generation_method: "human_only"
ai_models:["claude-opus"]
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known_gaps:
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completeness: 0.88
ai_citations:
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primary_sources:
- title: "ACM Digital Library"
    type: "repository"
    year: 2026
    url: "https://dl.acm.org/"
    institution: "ACM"
secondary_sources:
  - title: "ACM Digital Library"
    type: "repository"
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    url: "https://dl.acm.org/"
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---

## 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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