Siddharth, are you aware that the question whether a given element belongs to the domain of a given computable function is algorithmically undecidable? Alexey. On Tue, 2017-12-19 at 16:51 +0000, Siddharth Bhat wrote:

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So, I have two opinions to share on this: Regarding the plane example, it is wrong to attempt to graph it on a plane, precisely because the domain is not the plane. I am confused by your assertion that it is impossible to avoid divergence in mathematics: we do not define division as a *partial* function. Rather we define it as a *total* function on a *restricted domain*. So, what one would need is the ability to create these restricted domains, which certain languages have as far as I am aware. At that point, now that we track our domains and codomains correctly, all should work out? I would still like an answer to interesting transformations that are enabled by having purity and laziness and are not encumbered by the presence of bottoms. Cheers, Siddharth