## 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

### Nearby terms:

Church, Alonzo ♦ **Church integer** ♦ Church of the SubGenius ♦ Church-Rosser Theorem

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