Church integer

(theory)A representation of integers as functions invented byAlonzo Church, inventor of lambda-calculus. The integer Nis represented as a higher-order function which applies agiven function N times to a given expression. In the pure lambda-calculus there are no constants but numbers can berepresented by Church integers.

A Haskell function to return a given Church integer could bewritten:

church n = cwherec f x = if n == 0 then x else c' f (f x)wherec' = church (n-1)

A function to turn a Church integer into an ordinary integer:

unchurch c = c (+1) 0

See also von Neumann integer.

单词	church integer
释义	Church integer Church integer (theory)A representation of integers as functions invented byAlonzo Church, inventor of lambda-calculus. The integer Nis represented as a higher-order function which applies agiven function N times to a given expression. In the pure lambda-calculus there are no constants but numbers can berepresented by Church integers. A Haskell function to return a given Church integer could bewritten: church n = cwherec f x = if n == 0 then x else c' f (f x)wherec' = 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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