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Meaning of CHURCH INTEGER

 
Computing Dictionary
 
 Definition: 

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.

 

 

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