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.
