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I know that there are partial binary operations and partial unary operations, but is there such a thing as a partial $0$-ary function (which is not total, of course)?

user107952
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    To me, "a 0-ary function" sounds like a pretentious way to say "a constant". – Brian Moehring Feb 29 '24 at 01:02
  • @BrianMoehring I'd say not just any constant, but a constant that has for domain $X^\emptyset$, i.e. a constant that has for domain ${\emptyset}$. ;) – Sassatelli Giulio Feb 29 '24 at 01:20
  • I think a partial 0-ary function makes sense. I don't think anything stops the $n$-ary definition from working when $n = 0$. If you use $0$-ary functions to implement constants, then it's pretty much required to allow them to be partial if you want to define compositions for arbitrary partial functions! A $0$-ary function which is not total then basically represents an "undefined value". See also eg the Maybe monad from functional programming. – Izaak van Dongen Feb 29 '24 at 16:18
  • @peterwhy Why? Isn't the empty function a partial function on any domain (in particular, the domain with a single element)? – Alex Kruckman Mar 22 '24 at 22:10
  • @AlexKruckman It seems that I misunderstood when I commented; I might have read the "partial" with "not total" conditions, and disregarded partial functions that are undefined for every argument. – peterwhy Mar 22 '24 at 22:32

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