As discussed on Discourse, it would be nice to have !foo return a ComposedFunction, which would

1. allow dispatch and specialized methods for !foo
2. allow nicer pretty printing of !foo as "!foo" rather than as "#xx (generic function with 1 method)" (by overloading show for ComposedFunction{typeof(!)})
3. allow !!foo === foo

Although !foo and f ∘ g were introduced at the same time in #17155, when ∘ was subsequently updated in Julia 1.6 to return a special ComposedFunction type (#37517), the ! implementation was not correspondingly updated, which seems like an oversight.

On a related note, it would also be good to fix the ComposedFunction show method to put parentheses around operators (or other composed functions), as this is currently broken:

julia> (!) ∘ isnan
! ∘ isnan

julia> ! ∘ isnan
ERROR: syntax: "∘" is not a unary operator
Stacktrace:
 [1] top-level scope
   @ none:1

Should be a fairly easy PR.