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Functions in lambda calculus don't have a name, so that statement is nonsensical in the context of lambda calculus. To make some sense you need to specify some formal language where you can/must have names for some functions. But the example that is supposed to clarify the meaning of "anonymous" (as opposed to named) is in lambda calculus, where all functions are anonymous! The anonymous (like all other!) function returned by Y (i.e. factorial) is indeed a [[primitive recursive function]], but all [[μ-recursive function]]s are [[Lambda_calculus#Computable_functions_and_lambda_calculus|lambda definable]] (see a theory book for proof, e.g. [http://books.google.com/books?q=lectures+on+the+curry+howard+isomorphism&btnG=Search+Books]), so what are you trying to say here? [[User:Pohta ce-am pohtit|Pcap]] [[User_talk:Pohta ce-am pohtit|<small>ping</small>]] 05:38, 21 August 2009 (UTC)
: I think I've [http://en.wikipedia.org/w/index.php?title=Fixed_point_combinator&diff=309207132&oldid=309194153 clarified] the matter. [[User:Pohta ce-am pohtit|Pcap]] [[User_talk:Pohta ce-am pohtit|<small>ping</small>]] 07:22, 21 August 2009 (UTC)
: It is true that the only form of recursion in lambda calculus is anonymous recursion (since there are no functions names). But for most people in other languages, they are only familiar with recursion by explicitly using the function name. The very concept of anonymous recursion is surprising to many people. It is therefore informative to tell them that fixed point combinators is the mechanism by which anonymous recursion is done (and specifically "anonymous" recursion, to distinguish it from the recursion that they are familiar with). Fixed point combinators are not just for lambda calculus, but also other languages too. --[[Special:Contributions/76.173.203.32|76.173.203.32]] ([[User talk:76.173.203.32|talk]]) 04:31, 22 August 2009 (UTC)
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