lambda calculus

Coined by Alonzo Church after the use of the Greek letter lambda (λ) as the basic abstraction operator in the calculus.

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lambda calculus (countable and uncountable, plural lambda calculi)

1. (computing theory) Any of a family of functionally complete algebraic systems in which lambda expressions are evaluated according to a fixed set of rules to produce values, which may themselves be lambda expressions.
   • 2009 March 2, John C. Baez with Mike Stay, “Physics, Topology, Logic and Computation: A Rosetta Stone”, in (Please provide the book title or journal name)‎^[1], page 50:

     In the 1930s, while Turing was developing what are now called ‘Turing machines’ as a model for computation, Church and his student Kleene were developing a different model, called the ‘lambda calculus’ [29, 63]. While a Turing machine can be seen as an idealized, simplified model of computer hardware, the lambda calculus is more like a simple model of software.

• When referring to lambda calculus, it is often prefixed with the definite article. I.e., both "lambda calculus" (without a definite article) and "the lambda calculus" are commonly used, and mean the same thing.

• alpha conversion
• beta reduction
• eta conversion
• lambda term

• simply typed lambda calculus
• typed lambda calculus

• calculus
• lambda
• lambda abstraction
• lambda expression

• combinator
• functionally complete
• recursive function
• Turing machine