Was (wer) ist Church integer - definition
REPRESENTATION OF THE NATURAL NUMBERS AS HIGHER-ORDER FUNCTIONS
Church numeral; Church number; Church boolean; Church booleans; Church numerals; Church integer; Church numbers
Church integer
<theory> A representation of integers as functions invented by
Alonzo Church, inventor of lambda-calculus. The integer N
is represented as a higher-order function which applies a
given function N times to a given expression. In the {pure
lambda-calculus} there are no constants but numbers can be
represented by Church integers.
A Haskell function to return a given Church integer could be
written:
church n = c
where
c f x = if n == 0 then x else c' f (f x)
where
c' = church (n-1)
A function to turn a Church integer into an ordinary integer:
unchurch c = c (+1) 0
See also von Neumann integer.
(1994-11-29)
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.
Almost integer
![[[Ed Pegg Jr.]] noted that the length ''d'' equals <math>\frac{1}{2}\sqrt{\frac{1}{30}(61421-23\sqrt{5831385})} </math> that is very close to 7 (7.0000000857 ca.)<ref name="MathWorld"/>](https://commons.wikimedia.org/wiki/Special:FilePath/Almost integer in triangle.svg?width=200 "[[Ed Pegg Jr.]] noted that the length ''d'' equals <math>\frac{1}{2}\sqrt{\frac{1}{30}(61421-23\sqrt{5831385})} </math> that is very close to 7 (7.0000000857 ca.)<ref name=\"MathWorld\"/>")
ANY NUMBER THAT IS NOT AN INTEGER BUT IS VERY CLOSE TO ONE
Near integer; Near-integer
In recreational mathematics, an almost integer (or near-integer) is any number that is not an integer but is very close to one. Almost integers are considered interesting when they arise in some context in which they are unexpected.
Wikipedia
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.
