Lambda calculus

Church encoding

In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation. The method is named for Alonzo Church, who first encoded data in the lambda calculus this way. Terms that are usually considered primitive in other notations (such as integers, booleans, pairs, lists, and tagged unions) are mapped to higher-order functions under Church encoding. The Church-Turing thesis asserts that any computable operator (and its operands) can be represented under Church encoding. In the untyped lambda calculus the only primitive data type is the function. (Wikipedia).

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Related pages

Exponentiation | Truth value | Lambda lifting | System F | Monus | Alonzo Church | Higher-order function | Lambda calculus | Scala (programming language) | Extensionality | Ordinal number | Division (mathematics) | Cons | Multiplication | Successor function | Natural number | Mathematics | Addition | Integer | Mogensen–Scott encoding | Computable number | Subtraction | Deductive lambda calculus | Fold (higher-order function) | Fixed-point combinator | Function composition | Algebraic data type | Arithmetic