Church encoding and Lambda calculus

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Difference between Church encoding and Lambda calculus

Church encoding vs. Lambda calculus

In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution.

Alonzo Church

Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science.

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Arithmetic

Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.

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Church–Turing thesis

In computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a hypothesis about the nature of computable functions.

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Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

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Extensionality

In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties.

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Haskell (programming language)

Haskell is a standardized, general-purpose compiled purely functional programming language, with non-strict semantics and strong static typing.

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Higher-order function

In mathematics and computer science, a higher-order function (also functional, functional form or functor) is a function that does at least one of the following.

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Lambda calculus

Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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MIT Press

The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States).

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Smalltalk

Smalltalk is an object-oriented, dynamically typed, reflective programming language.

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System F

System F, also known as the (Girard–Reynolds) polymorphic lambda calculus or the second-order lambda calculus, is a typed lambda calculus that differs from the simply typed lambda calculus by the introduction of a mechanism of universal quantification over types.

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Truth value

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.

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Turing completeness

In computability theory, a system of data-manipulation rules (such as a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing complete or computationally universal if it can be used to simulate any Turing machine.

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