Sure you can - just not anonymously. Kind of like how you can have "higher order functions" and "closures" in Java with anonymous classes - roughly equivalent, but awkward and not quite what the language was designed for. C is probably better in this regard than Java, but the lack of managed memory is a major drawback.

Right. SO you can program 'functionally' in those languages, but they are not 'functional programming languages' because they don't support it natively.

"just not anonymously"

Just not depending on anything in the environment either except globals, which is a huge limitation. So writing a function inc by = \x -> x + by becomes unnecessarily difficult for example.

then you just have a void* / fn ptr couple that you pass around..