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<*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) 0See also von Neumann integer.

(1994-11-29)

Nearby terms: chug report « chunker « Church, Alonzo « **Church integer** » Church of the SubGenius » Church-Rosser Theorem » ci

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