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As the concept described in the article is known either as "general recursive function" or "μ-recursive function" but has no commonly used other names, the article title must be one of these two names, and changing it would be [[WP:OR]]. My move from the latter title to the former one could be discussed, but the former name seems more common, specially when used outside the theory of recursive functions. Also, the latter title appears in the search engine as
"M-recursive function", which is confusing, as it may be difficult for the reader to understand that "M" means "μ". [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 11:59, 24 February 2020 (UTC)
:This is a bit of a multithreaded discussion with a lot of facets, which is always hard to keep track of. Let me try a bulleted list and see if that helps.
:*Thanks {{u|Jochen Burghardt}} for pointing out the redirect [[μ recursion]]. I think that's a better title for this article than any so far proposed (though there might be still better options; e.g. I would probably prefer [[μ-recursion]] with the hyphen). The reason is that we seem to be agreed that this article is about a model of computation, and μ-recursion is a model of computation.
:*I agree with {{u|D.Lazard}} that we can't make up our own names for things; if a name is standard in the literature then we use it. However I am skeptical that "general recursive function" truly standardly refers to the model of computation we're discussing, as opposed to the functions thereby computed. I also think that anywhere "general recursive function" is likely to be linked from, or most of the searches for it, will be more usefully served by finding an article about the functions rather than the model of computation.
:*Therefore [[general recursive function]], [[total recursive function]], and all similar phrases with "function" as the [[head (linguistics)|head]], should point to [[computable function]].
:*The fact that the μ gets capitalized in lists is unfortunate, but the damage is limited by the fact that this article is very rarely the first one a reader should be searching for. ''Most'' times, the reader will be better served by reading [[computable function]] first. Only if he/she truly wants to know ''specifically'' about this model of computation is this the right article, and in that case hopefully he/she can find it via a link from another article.
:*I agree that we aren't talking about set theory — for "class of functions" substitute "kind of function", if you like. The kind of function computed by the various models are all the same, and are treated at [[computable function]]. The differences in model of computation are "implementation details", like different programming languages if you will.
:*The point about including the computation as part of the function in some sense is generally well-taken, but doesn't really change anything in this discussion. The computation that computes a given function can be effectively translated between different models of computation in a completely stereotyped way, and you can prove using very mild assumptions (and I'm pretty sure, even in intuitionistic logic) that they compute the same function. Therefore we can still speak of whether a computable function is provably total (for example) without worrying about which model of computation is used.
:Well, that's a lot, better stop here. The big takeaway is we should move this content to a name that clearly names a model of computation, and all the "function" links should point at [[computable function]]. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 21:18, 24 February 2020 (UTC)
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