Church integer
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Church integer
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)