Earlier quoted context omitted.
I'm not trying to dodge your question, but the answer to your question is that until you work with it for a while you're not going to understand it. Any blog-sized, bite-sized snippet isn't impressive. You have to work with it for a while. I speak many computer languages, and one of the ways I measure them is, "what do I miss from X when using Y?" The answers will often surprise you; the thing you'd swear up and down…
Couldn't I "curry" a function f(x,y) to "partially apply" it on x=3 with just: function(y) { return f(3,y); } ? And then I've "partially applied" f. Is this what currying is? The syntax I posted is ambivalent about which arguments you're partially applying, isn't that superior to only being able to provide the first argument?
f(x,y) = ... // arity 2
f = \x -> \y -> ... // sequence of two unary functions
f x y = ... // more compact representation of the above
f x y = ...
fByThree = f 3
fByThree y = f 3 y
And the Haskell version is more general, since it doesn't require a unique function to be written for each possible partial application. Of course, you can do this in languages with closures:
function fByX(x) {
return y => f(x,y);
}
fByThree = fByX(3);
fXbyThree = flip f 3
// equivalent to:
fXByThree x = f x 3
// JS
function fXByThree(x) { return f(x,3); }
// or
function fXByFixedY(y) { return x => f(x,y); }
fXByThree = fXByFixedY(3);