Church integer

A representation of integers as functions invented by AlonzoChurch, 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 purelambda-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.

(1994-11-29)