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.

Last updated: 1994-11-29

Nearby terms:

Church, AlonzoChurch integerChurch of the SubGeniusChurch-Rosser Theorem

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