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:*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, for example [[μ-recursion]], 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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"The primitive recursive functions are a subset of the total recursive functions, which are a subset of the partial recursive functions."
Sadly, the article never defines what it means by "total recursive" or "partial recursive" anywhere, despite "partial recursive function" redirecting here. Does "total recursive function" mean "general recursive total function" and "partial recursive function" mean "general recursive partial function"? If so, could this please be clarified and an example of a well-known "partial recursive" function which is not total be provided? [[User:TricksterWolf|TricksterWolf]] ([[User talk:TricksterWolf|talk]]) 13:07, 14 February 2021 (UTC)
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