Programming Language Theory: Difference between revisions
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The integers (or any countably infinite set) can be represented via the [http://en.wikipedia.org/wiki/Church_encoding Church encoding]: | The integers (or any countably infinite set) can be represented via the [http://en.wikipedia.org/wiki/Church_encoding Church encoding]: | ||
* <tt>n ≡ λf . λx . f<sup>n</sup>x</tt> | * <tt>n ≡ λf . λx . f<sup>n</sup>x</tt> | ||
* <tt>plus ≡ λm . λn . λf . λx . m f (n f x)</tt> (from f<sup>(m + n)</sup>(x) = f<sup>m</sup>(f<sup>n</sup>(x))) | |||
Common syntactic sugar: | Common syntactic sugar: | ||