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. |