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happened to need Type Two Theory of Effectivity
For computable function, I understand this to be a synonym for partial recursive function; the trend seems to be to use “computable” more in modern texts and “partial recursive” in older ones. Anyway, one might consider a renaming or redirect or something.
Quick comment: We wrote an overview article some time ago. The page should be merged with computable analysis.
This was quick.
Actually, I should merge with exact analysis, then. Give me just a minute…
Ah, I don’t have the energy to merge the entries now, and you would be more expert than me to do so anyway. All I did was add that survey and cross-link constructive analysis and computable analysis.
Todd, there is essentially nothing in that entry. You should go and fill in whatever you deem appropriate.
Well, no, what I think I’d rather do (instead of “filling in”) is merge into partial recursive function. So I’ll do that.
Does “computable function” mean the same in computable analysis? Does it matter to distinguish between “number realizability” and “function realizability”?
Okay, I see. If in computable analysis, a computable function has domain $\mathbb{R}$ (for instance), then the answer would have to be ’no’. In that case, I think it makes sense to write an article titled, e.g., computable function (analysis). The Wikipedia article that had been linked to in the earlier article you wrote up gives the notion involving partial recursive functions whose domain is a subset of $\mathbb{N}^k$, so I assumed that was meant, hence the merge.
All right, let’s have computable function (analysis), eventually. Have added the disambiguation now at partial recursive function.
BTW, in that entry and maybe elsewhere, “Church-Turing thesis” should eventually hyperlink to somewhere…
Todd, looking at p. 4 of Andrej Bauer’s lecture notes (pdf) makes me feel that we should have a standalone entry “computable function” after all, with some general discussion along such lines and then pointing to the various special incarnations.
Would you object?
Urs, that seems sensible to me.
Okay, please check out computable function now. Please edit as you see the need.
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