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Mathematica's help on SyntaxInformation does not rule out syntax information for pure functions.

SyntaxInformation[f] gives information used to generate syntax coloring and other advisories when f[…] is entered as input.

The naive code

f = # &;
SyntaxInformation[f] = {"ArgumentsPattern" -> {_}}

fails with a message about the first argument. Using the string instead of the symbol

SyntaxInformation["f"] = {"ArgumentsPattern" -> {_}}

does not throw a message but it does not produce the expected red parameters in f[a,b].

Is there any way to specify syntax information on pure functions?

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    $\begingroup$ SyntaxInformation works at the Symbol level. Call it before assigning to f. $\endgroup$ – b3m2a1 Jan 17 '18 at 20:11
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    $\begingroup$ Although the solution is quite simple, it is far from trivial. Write it as an answer, I will accept it. $\endgroup$ – Hector Jan 17 '18 at 20:15
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SyntaxInformation does not hold its arguments so you can hold it:

f // ClearAll
f = # &;
f // Unevaluated // SyntaxInformation = {"ArgumentsPattern" -> {_}};

as an alternative to altering the order:

f // ClearAll
f // SyntaxInformation = {"ArgumentsPattern" -> {_}};
f = # &;
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