Home Articles FAQs XREF Games Software Instant Books BBS About FOLDOC RFCs Feedback Sitemap
irt.Org

Church integer

You are here: irt.org | FOLDOC | 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.

(1994-11-29)

Nearby terms: chug report « chunker « Church, Alonzo « Church integer » Church of the SubGenius » Church-Rosser Theorem » ci

FOLDOC, Topics, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, ?, ALL

©2018 Martin Webb