## 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) 0See also von Neumann integer.

Last updated: 1994-11-29

Try this search on Wikipedia, OneLook, Google

**Nearby terms:**

**Church integer**» Church of the SubGenius » Church-Rosser Theorem » ci