Optional Keyword arguments

General Usage
2

Your first example definition uses a optional positional argument and not a keyword argument. Your second example definition uses a keyword argument named tl. In Julia, when you call a function with a keyword argument you must use this name, as you discovered (either g(x; tl=y) or g(x; tl) which is just a shorthand for g(x; tl=tl).

Now, to the question about defaults: A common way is to use nothing as a default, and check for that inside the function body, for example:

function g(ti::AbstractVector; tl = nothing) # or tl::Union{Timelimits,Nothing} = nothing
    if tl === nothing
        tl = Timelimits(ti[begin],ti[end])
    end
    # ...
end
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