Concept
Lambda calculus
Overview
In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and application using variable binding and substitution. Untyped lambda calculus, the topic of this article, is a universal machine, i.e. a model of computation that can be used to simulate any Turing machine (and vice versa). It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics. In 1936, Church found a formulation which was logically consistent, and documented it in 1940.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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The nature of abstract mathematics (the general division of which will be examined in the following chapter) is clearly and exactly determined. It is composed of what is called the _Calculus_,[2] taking this word in its greatest extent, which reaches from the most simple numerical operations to the most sublime combinations of transcendental analysis. The _Calculus_ has the solution of all questions relating to…
Auguste Comte, The philosophy of mathematics
States what Lambda calculus is.
Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.
Alfred North Whitehead, Science and the modern world
States what Lambda calculus is.
There are nevertheless, in mathematics, some examples of so-called Induction, in which the conclusion does bear the appearance of a generalization grounded on some of the particular cases included in it. A mathematician, when he has calculated a sufficient number of the terms of an algebraical or arithmetical series to have ascertained what is called the _law_ of the series, does not hesitate to fill up any number…
John Stuart Mill, A System of Logic
States what Lambda calculus is.
Related ideas
- Computable function
- Tuple
- Philosophy
- Free variables and bound variables
- Dana Scott
- Formalism (philosophy of mathematics)
- Foundations of mathematics
- Proof theory
- Function (mathematics)
- Mathematics
- Mathematical logic
- Model theory
- Natural number
- Linguistics
- Principia Mathematica
- Recursion
- Curry–Howard correspondence
- Self-reference
- Semantics
- Turing machine
- Arithmetic
- Formal system
- Alonzo Church
- Computer science
Place in the tradition
Part of Outline of logic.