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One can specify the second argument of SortBy not to sub-sort ties, i.e. cases that have identical values according to the main sorting function. SortBy[list, {First}] ensures that sublists are sorted by the first (real) element, and ties are not resolved but left in the order they appear in the original list.

list = {{.1, {0, 1, 2}}, {.4, {1}}, {.1, {0, 1}}, {.7, {0}}};

Column /@ {list, SortBy[list, First], SortBy[list, {First}], SortBy[list, {}], SortBy[list, Identity]}

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How can I specify a second argument for SortBy that leaves list as is, without actually sorting it? Clearly, {} or Identity, {Identity}, etc. do not achieve this.

While I strongly believe this cannot be done, as SortBy is a function specifically designed to sort, I nevertheless post this as there may be some undocumented way to do it simply.

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2 Answers 2

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I would have expected SortBy[list,{}] to also work, but at least the following seems to do the trick:

SortBy[list, {0 &}] === list
(* True *)

This is effectively using the "stable-sort" property of SortBy[...,{func}] with a "useless" sorting function that always returns the same value (0 in this case)

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    $\begingroup$ This is surprising. Where do you learn about the "stable-sort" property? This doesn't seem to be mentioned in document of SortBy. $\endgroup$
    – xzczd
    Nov 30, 2022 at 8:38
  • $\begingroup$ @xzczd I can't recall how I first learned about it, but it's mentioned a few times on this site, e.g. here it is explicitly called out. I think I also saw a question about being documented or not, but I can't find it now... $\endgroup$
    – Lukas Lang
    Nov 30, 2022 at 8:50
  • $\begingroup$ I also assumed that sorting is stable, and I am surprised that I cannot find this in the docs. $\endgroup$
    – Szabolcs
    Nov 30, 2022 at 9:23
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How about:

i = 0; SortBy[list, i++&]

Or skip SortBy with upvalue:

SortBy[l_, nosort] ^:= l
SortBy[list, nosort]
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  • $\begingroup$ These are nice, but in my case I need a solution that only involves the 2nd argument of SortBy. For context: I define sorting as an option to a higher level function that is internally passed on as the 2nd arg to SortBy, without modification. I rather not have users specify contrived sorting functions by meddling with either global variables or upvalues just to pass it on as an option. $\endgroup$
    – István Zachar
    Nov 30, 2022 at 11:45
  • $\begingroup$ @IstvánZachar How about including the nosort as a symbol in the package? (I guess it's a package?) $\endgroup$
    – xzczd
    Nov 30, 2022 at 13:46
  • $\begingroup$ That could work, but then again the user has to remember another custom symbol (I already have 300+). For the case at hand, Lukas's answer is exactly what I was looking for. $\endgroup$
    – István Zachar
    Dec 1, 2022 at 9:11

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