Church integer

A Church integer is a representation of integers as functions, invented by Alonzo Church. An integer N is represented as a higher-order function, which applies a given function to a given expression N times.

For example, in the programming language Haskell, a function that returns a particular Church integer might be

church0 =fxx
churchn =c

The transformation from a Church integer to an integer might be

unchurch n = n (+1) 0

Thus we can generate the integers–the (+1) function would be applied to an initial value of 0 n times, yielding the ordinary integer n.

Title Church integer
Canonical name ChurchInteger
Date of creation 2013-03-22 12:32:31
Last modified on 2013-03-22 12:32:31
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 8
Author mathcam (2727)
Entry type Definition
Classification msc 03B40
Classification msc 68N18
Related topic LambdaCalculus