Programming Language Theory: Difference between revisions
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====Numerics==== | ====Numerics==== | ||
The integers (or any countably infinite set) can be represented via the [http://en.wikipedia.org/wiki/Church_encoding Church encoding] (or [http://en.wikipedia.org/wiki/Mogensen-Scott_encoding Mogensen-Scott], or others): | The integers (or any countably infinite set) can be represented via the [http://en.wikipedia.org/wiki/Church_encoding Church encoding] (or [http://en.wikipedia.org/wiki/Mogensen-Scott_encoding Mogensen-Scott], or others): | ||
* <tt>0 ≡ λf. λx. x</tt> (referred to as <tt>c<sub>0</sub></tt>) | * <tt>0 ≡ λf. λx. x</tt> (referred to as <tt>c<sub>0</sub></tt>, and ɑ-equivalent to <tt>false</tt> [[Programming_Language_Theory#Logic|below]]) | ||
* <tt>1 ≡ λf. λx. f x</tt> | * <tt>1 ≡ λf. λx. f x</tt> | ||
* <tt>2 ≡ λf. λx. f (f x)</tt> | * <tt>2 ≡ λf. λx. f (f x)</tt> | ||