Is it correct to state that basic primitive recursive functions are in fact combinators? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T07:42:39Z http://mathoverflow.net/feeds/question/48006 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/48006/is-it-correct-to-state-that-basic-primitive-recursive-functions-are-in-fact-combi Is it correct to state that basic primitive recursive functions are in fact combinators? NoWhereMan 2010-12-02T07:05:06Z 2010-12-02T21:03:03Z <p>Is it correct saying that the Zero, Successor and Projection functions can be seen as combinators?</p> http://mathoverflow.net/questions/48006/is-it-correct-to-state-that-basic-primitive-recursive-functions-are-in-fact-combi/48008#48008 Answer by Ed Dean for Is it correct to state that basic primitive recursive functions are in fact combinators? Ed Dean 2010-12-02T07:35:38Z 2010-12-02T07:35:38Z <p>Yes, if I'm right in assuming you mean to ask whether these can be construed without free variables in the lambda calculus. (If my assumption is wrong, I apologize; your question is rather terse.) You can see <a href="http://en.wikipedia.org/wiki/Church_encoding" rel="nofollow">here</a>, for instance, how the "Church numerals" (Zero among them, of course) can be introduced, along with Successor and various other primitive recursive functions.</p>