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  "body": "\n## Summary\n\nThe lambda calculus is a formal system for describing functions by abstraction and application, with computation done by substituting arguments into function bodies.\nIn its untyped form it computes exactly the same functions on natural numbers as [[Turing machines|758EYCN27B]].\nIt was introduced by Alonzo Church and is the basis of functional programming languages and of type theory.\n\n## Explanations\n\n### L1 human\n\nIn the lambda calculus, $\\lambda x.\\, M$ means \"the function that sends $x$ to $M$\".\nTo apply a function to an argument, one replaces the variable by the argument.\nFor example, $(\\lambda x.\\, x)\\, y$ becomes $y$: the identity function applied to $y$ gives $y$.\nNothing else is built in, yet numbers, truth values and recursion can all be encoded as functions.\n",
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