# Lambda Calculus

A Lambda Calculus is a logic calculus similar to first-order logic but that allows the binding of Variables using the lambda operator.

**Context:**- It can range from being a Deterministic Lambda Calculus to being a Stochastic Lambda Calculus.
- It can range from being a Typed Lambda Calculus to being an Untyped Lambda Calculus.
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**Counter-Example(s):****See:**Alonzo Church, Turing Machine.

## References

### 2013

- (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/Lambda_calculus
**Lambda calculus**(also written as λ-calculus or called “**the lambda calculus**") is a formal system in mathematical logic and computer science for expressing computation by way of variable binding and substitution. First formulated by Alonzo Church, lambda calculus found early successes in the area of computability theory, such as a negative answer to Hilbert's Entscheidungsproblem.Because of the importance of the notion of variable binding and substitution, there is not just one system of lambda calculus, and in particular there are

*typed*and*untyped*variants. Historically, the most important system was the untyped lambda calculus, in which function application has no restrictions (so the notion of the domain of a function is not built into the system). In the Church–Turing Thesis, the untyped lambda calculus is claimed to be capable of computing all effectively calculable functions. The typed lambda calculus is a variety that restricts function application, so that functions can only be applied if they are capable of accepting the given input's "type" of data.Today, the lambda calculus has applications in many different areas in mathematics, philosophy, linguistics, and computer science. It is still used in the area of computability theory, although Turing machines are also an important model for computation. Lambda calculus has played an important role in the development of the theory of programming languages. Counterparts to lambda calculus in computer science are functional programming languages, which essentially implement the calculus (augmented with some constants and datatypes). Beyond programming languages, the lambda calculus also has many applications in proof theory. A major example of this is the Curry–Howard correspondence, which gives a correspondence between different systems of typed lambda calculus and systems of formal logic.

### 2009

- http://en.wiktionary.org/wiki/lambda_calculus
- Etymology: Coined by Alonzo Church after the use of the Greek letter lambda (λ) as the basic abstraction operator in the calculus.
- Noun
- 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.