The Lambda Calculus

Johannes Korbmacher

The Lambda Calculus

OFR - Theoretical Philosophy

Research output: Chapter in Book/Report/Conference proceeding › Entry for encyclopedia/dictionary › Academic › peer-review

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.

Original language	English
Title of host publication	Stanford Encyclopedia of Philosophy
Publisher	The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University
Edition	Fall 2023 Edition
Publication status	Published - 2023

Bibliographical note

substantive revision of earlier version, published Tue Jul 25, 2023

Access to Document

The Lambda Calculus (Stanford Encyclopedia of Philosophy)Accepted author manuscript, 944 KB

https://plato.stanford.edu/entries/lambda-calculus/

Cite this

@inbook{0978c27b3b6543b981838f2bb3c80ef9,

title = "The Lambda Calculus",

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.",

author = "Johannes Korbmacher",

note = "substantive revision of earlier version, published Tue Jul 25, 2023",

year = "2023",

language = "English",

booktitle = "Stanford Encyclopedia of Philosophy",

publisher = "The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University",

edition = "Fall 2023 Edition",

}

TY - CHAP

T1 - The Lambda Calculus

AU - Korbmacher, Johannes

N1 - substantive revision of earlier version, published Tue Jul 25, 2023

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

M3 - Entry for encyclopedia/dictionary

BT - Stanford Encyclopedia of Philosophy

PB - The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University

ER -

The Lambda Calculus

Abstract

Bibliographical note

Access to Document

Fingerprint

Cite this