Programming Language Theory: Difference between revisions
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* Function definition: <tt>(λ''boundparam''. body)</tt> | * Function definition: <tt>(λ''boundparam''. body)</tt> | ||
* Function application: <tt>function(''actualparam'')</tt> | * Function application: <tt>function(''actualparam'')</tt> | ||
The body is made up of ''free'' and ''bound'' variables. Those not present in the λ's list of bound variables are free. A λ-expression with no free variables is ''closed'' | The body is made up of ''free'' and ''bound'' variables. Those not present in the λ's list of bound variables are free. A λ-expression with no free variables is ''closed'' (closed expressions are equivalent in power to [http://en.wikipedia.org/wiki/Combinatory_logic|combinatory logic]). | ||
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): | ||