What is 'Currying'?

Question

I've seen references to curried functions in several articles and blogs but I can't find a good explanation (or at least one that makes sense!)

Answer 1

Currying is when you break down a function that takes multiple arguments into a series of functions that each take only one argument. Here's an example in JavaScript:

function add (a, b) {   return a + b; }  add(3, 4); // returns 7 

This is a function that takes two arguments, a and b, and returns their sum. We will now curry this function:

function add (a) {   return function (b) {     return a + b;   } } 

This is a function that takes one argument, a, and returns a function that takes another argument, b, and that function returns their sum.

add(3)(4);  var add3 = add(3);  add3(4); 

The first statement returns 7, like the add(3, 4) statement. The second statement defines a new function called add3 that will add 3 to its argument. (This is what some may call a closure.) The third statement uses the add3 operation to add 3 to 4, again producing 7 as a result.

Answer 2

In an algebra of functions, dealing with functions that take multiple arguments (or equivalent one argument that's an N-tuple) is somewhat inelegant -- but, as Moses Schönfinkel (and, independently, Haskell Curry) proved, it's not needed: all you need are functions that take one argument.

So how do you deal with something you'd naturally express as, say, f(x,y)? Well, you take that as equivalent to f(x)(y) -- f(x), call it g, is a function, and you apply that function to y. In other words, you only have functions that take one argument -- but some of those functions return other functions (which ALSO take one argument;-).

As usual, wikipedia has a nice summary entry about this, with many useful pointers (probably including ones regarding your favorite languages;-) as well as slightly more rigorous mathematical treatment.