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Church, Alonzo

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

Church of the SubGenius

<body, humour>

A mutant offshoot of Discordianism launched in 1981 as a spoof of fundamentalist Christianity by the "Reverend" Ivan Stang, a brilliant satirist with a gift for promotion. Popular among hackers as a rich source of bizarre imagery and references such as "Bob" the divine drilling-equipment salesman, the Benevolent Space Xists, and the Stark Fist of Removal. Much SubGenius theory is concerned with the acquisition of the mystical substance or quality of slack.

http://sunsite.unc.edu/subgenius/slack.html.

Last updated: 1996-01-02

Church-Rosser Theorem

<theory>

A property of a reduction system that states that if an expression can be reduced by zero or more reduction steps to either expression M or expression N then there exists some other expression to which both M and N can be reduced. This implies that there is a unique normal form for any expression since M and N cannot be different normal forms because the theorem says they can be reduced to some other expression and normal forms are irreducible by definition. It does not imply that a normal form is reachable, only that if reduction terminates it will reach a unique normal form.

Last updated: 1995-01-25

Nearby terms:

chunker ♦ Church, Alonzo ♦ Church integer ♦ Church of the SubGenius

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