When people say that Python, for instance, has first class functions, it makes it sound like Python also has second class functions. However, I've never yet (knowingly) encountered a second class function in Python. When we say this, does it really mean "All Python functions are first class?" Or is there an example of a second class function in Python?
2 Answers
First, to clarify the nomenclature.
The term "first class functions" means that it is "first class" in the type system: that is, that functions themselves are values. In languages where functions are not first class, functions are defined as a relationship between values, which makes them "second class".
Put another way, "first class" functions implies that you can use a function as a value, which means (among other things) that you can pass functions into functions. You couldn't do this in Java before Java 7 (reflection doesn't count), so that's an example of a programming language only having "second class" functions. In order to "pass a function", you had to define a type where that function could live (as a method), and then pass an instance of that type.
So, in Python, all functions are first class, because all functions can be used as a value.
Now, there is another concept which you might be getting confused with. There is also a concept of a "higher order function". A higher order function is a function that takes a function as an argument. Not all functions in Pythons are higher-order, because not all functions take another function as an argument. But even the functions that are not higher-order are first class. (It's a square/rectangle thing.)
Usually, when we say "language X has first-class functions", we actually mean that "language X treats functions as first-class" (just like it does with other types). It usually means that you can pass functions as arguments, store them in arrays, etc.
I don't see any reason why a particular language (that treated functions as first-class) would also have second-class functions (i.e. those that couldn't be passed as arguments), but can't say whether Python does or doesn't.
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