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I saw this question asking about the Listable. The accepted answer did a good explanation on the poor performance of user defined function with Listable. However the answer didn't clarify why the f function in following code doesn't show Listable feature.

f = #[[1]] + #[[2]]^#[[3]] &;
SetAttributes[f, Listable];
f@{{1, 2, 3}, {4, 5, 6}}

output: enter image description here I Know why the code above cannot achieve its goal, and I know how to fix it. I just don't think the above wrong code should produce the above specific output. According to my understanding of how Listable thread function arguments, it should produce the following output:

{{f[1], f[2], f[3]}, {f[4], f[5], f[6]}}

Because the list {{1, 2, 3}, {4, 5, 6}} as argument should be threaded to the innermost level, which in the end is {{f[1], f[2], f[3]}, {f[4], f[5], f[6]}} and stop with some error message since f has Part on the argument.

However, in the reality, the real output shows that actually no Listable is in effect. The List {{1, 2, 3}, {4, 5, 6}} is passed to f as one whole arguments, which can also be proved by running a Trace on it.

Someone please help me?

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    $\begingroup$ Here are a few hints: SetAttributes[] will only work if you had defined f as f[v_] := v[[1]] + v[[2]]^v[[3]]. Otherwise, an anonymous function with attributes has to be declared this way: f = Function[Null, #[[1]] + #[[2]]^#[[3]], {Listable}]. Now, try your examples again with this in mind. $\endgroup$ May 5, 2020 at 18:40
  • $\begingroup$ Wolfram surprised me again! I've recently read tons of articles on Documentation website , nowhere had I ever seen it says that SetAttributes work differently for f=Function[x, ...] and f[x_]! $\endgroup$
    – Murphy Ng
    May 6, 2020 at 7:18

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