Original language | English |
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Title of host publication | Stanford Encyclopedia of Philosophy |

Editors | Edward N. Zalta |

Place of Publication | Stanford, CA |

Publisher | The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University |

Edition | Fall 2018 Edition |

Publication status | Published - 21 Mar 2018 |

## Abstract

The λ-calculus is, at heart, a simple notation for functions and application. The main ideas are applying a function to an argument and forming functions by abstraction. The syntax of basic λ-calculus is quite sparse, making it an elegant, focused notation for representing functions. Functions and arguments are on a par with one another. The result is a non-extensional theory of functions as rules of computation, contrasting with an extensional theory of functions as sets of ordered pairs. Despite its sparse syntax, the expressiveness and flexibility of the λ-calculus make it a cornucopia of logic and mathematics. This entry develops some of the central highlights of the field and prepares the reader for further study of the subject and its applications in philosophy, linguistics, computer science, and logic.