Find out all the function properties in JavaScript [duplicate]

How could I find out all the function properties in JavaScript?

Here is what I tried:

var a = function(a, b, c) {};
a.length;
Object.keys(a);

So, the a definitely has the length property (with the value of 3), but for some reasons there is no "length" in the array produced by the Object.keys(a);. Why? How could I see all the function properties? I am interested to know both personal and inherited (using the proto) properties.

I am interested in this purely due to desire to learn and explore the intricacies of JavaScript. I do not have any real world application for this knowledge right now.