Is it correct to state that basic primitive recursive functions are in fact combinators?

Is it correct saying that the Zero, Successor and Projection functions can be seen as combinators?

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This question would probably have been more appropriate at math.stackexchange.com, since while it’s a good question, it’s not really reasearch-level. –  Peter LeFanu Lumsdaine Dec 2 '10 at 16:41
sorry, I didn't know about math.stackexchange.com; I found out about it a minute ago –  NoWhereMan Dec 2 '10 at 20:54

1 Answer

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 here, for instance, how the "Church numerals" (Zero among them, of course) can be introduced, along with Successor and various other primitive recursive functions.

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Your assumption is right. My question was terse because I'm very new to the subject, and it's still quite a lot confused in my head; I'm trying to understand by the help of something I think I'm more confident with (computability theory). Thank you! –  NoWhereMan Dec 2 '10 at 21:07