I want to be able to define a function that behaves like, for example, the intrinsic SIZE function, where the kind of the output is specified by an optional input. Am I correct that this currently isn't possible?

Maybe using something similar to @cmacmackin's parameterized function syntax from #4, combined with a better way to specify the default value of optional arguments (see also #22):

function my_class_size(me, kind=INT32) result(s) class(my_class) :: me integer,intent(in),optional,kind :: kind integer(kind) :: s ... end function my_class_size

See also #78, and also the various issues about generic programming and templates.