# Church integer

Computing Dictionary

### Church integer definition

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
(1994-11-29)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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