What is 'Currying'?

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!)

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.

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.

Here's a concrete example:

Suppose you have a function that calculates the gravitational force acting on an object. If you don't know the formula, you can find it here. This function takes in the three necessary parameters as arguments.

Now, being on the earth, you only want to calculate forces for objects on this planet. In a functional language, you could pass in the mass of the earth to the function and then partially evaluate it. What you'd get back is another function that takes only two arguments and calculates the gravitational force of objects on earth. This is called currying.

It can be a way to use functions to make other functions.

In javascript:

let add = function(x){
  return function(y){ 
   return x + y
  };
};

Would allow us to call it like so:

let addTen = add(10);

When this runs the 10 is passed in as x;

let add = function(10){
  return function(y){
    return 10 + y 
  };
};

which means we are returned this function:

function(y) { return 10 + y };

So when you call

 addTen();

you are really calling:

 function(y) { return 10 + y };

So if you do this:

 addTen(4)

it's the same as:

function(4) { return 10 + 4} // 14

So our addTen() always adds ten to whatever we pass in. We can make similar functions in the same way:

let addTwo = add(2)       // addTwo(); will add two to whatever you pass in
let addSeventy = add(70)  // ... and so on...

Now the obvious follow up question is why on earth would you ever want to do that? It turns what was an eager operation x + y into one that can be stepped through lazily, meaning we can do at least two things

1. cache expensive operations
2. achieve abstractions in the functional paradigm.

Imagine our curried function looked like this:

let doTheHardStuff = function(x) {
  let z = doSomethingComputationallyExpensive(x)
  return function (y){
    z + y
  }
}

We could call this function once, then pass around the result to be used in lots of places, meaning we only do the computationally expensive stuff once:

let finishTheJob = doTheHardStuff(10)
finishTheJob(20)
finishTheJob(30)

We can get abstractions in a similar way.

Currying is a transformation that can be applied to functions to allow them to take one less argument than previously.

For example, in F# you can define a function thus:-

let f x y z = x + y + z

Here function f takes parameters x, y and z and sums them together so:-

f 1 2 3

Returns 6.

From our definition we can can therefore define the curry function for f:-

let curry f = fun x -> f x

Where 'fun x -> f x' is a lambda function equivilent to x => f(x) in C#. This function inputs the function you wish to curry and returns a function which takes a single argument and returns the specified function with the first argument set to the input argument.

Using our previous example we can obtain a curry of f thus:-

let curryf = curry f

We can then do the following:-

let f1 = curryf 1

Which provides us with a function f1 which is equivilent to f1 y z = 1 + y + z. This means we can do the following:-

f1 2 3

Which returns 6.

This process is often confused with 'partial function application' which can be defined thus:-

let papply f x = f x

Though we can extend it to more than one parameter, i.e.:-

let papply2 f x y = f x y
let papply3 f x y z = f x y z
etc.

A partial application will take the function and parameter(s) and return a function that requires one or more less parameters, and as the previous two examples show is implemented directly in the standard F# function definition so we could achieve the previous result thus:-

let f1 = f 1
f1 2 3

Which will return a result of 6.

In conclusion:-

The difference between currying and partial function application is that:-

Currying takes a function and provides a new function accepting a single argument, and returning the specified function with its first argument set to that argument. This allows us to represent functions with multiple parameters as a series of single argument functions. Example:-

let f x y z = x + y + z
let curryf = curry f
let f1 = curryf 1
let f2 = curryf 2
f1 2 3
6
f2 1 3
6

Partial function application is more direct - it takes a function and one or more arguments and returns a function with the first n arguments set to the n arguments specified. Example:-

let f x y z = x + y + z
let f1 = f 1
let f2 = f 2
f1 2 3
6
f2 1 3
6

A curried function is a function of several arguments rewritten such that it accepts the first argument and returns a function that accepts the second argument and so on. This allows functions of several arguments to have some of their initial arguments partially applied.

Currying means to convert a function of N arity into N functions of arity 1. The arity of the function is the number of arguments it requires.

Here is the formal definition:

 curry(f) :: (a,b,c) -> f(a) -> f(b)-> f(c)

Here is a real world example that makes sense:

You go to ATM to get some money. You swipe your card, enter pin number and make your selection and then press enter to submit the "amount" alongside the request.

here is the normal function for withdrawing money.

const withdraw=(cardInfo,pinNumber,request){
    // process it
       return request.amount
}

In this implementation function expects us entering all arguments at once. We were going to swipe the card, enter the pin and make the request, then function would run. If any of those steps had issue, you would find out after you enter all the arguments. With curried function, we would create higher arity, pure and simple functions. Pure functions will help us easily debug our code.

this is Atm with curried function:

const withdraw=(cardInfo)=>(pinNumber)=>(request)=>request.amount

ATM, takes the card as input and returns a function that expects pinNumber and this function returns a function that accepts the request object and after the successful process, you get the amount that you requested. Each step, if you had an error, you will easily predict what went wrong. Let's say you enter the card and got error, you know that it is either related to the card or machine but not the pin number. Or if you entered the pin and if it does not get accepted you know that you entered the pin number wrong. You will easily debug the error.

Also, each function here is reusable, so you can use the same functions in different parts of your project.

Currying is translating a function from callable as f(a, b, c) into callable as f(a)(b)(c).

Otherwise currying is when you break down a function that takes multiple arguments into a series of functions that take part of the arguments.

Literally, currying is a transformation of functions: from one way of calling into another. In JavaScript, we usually make a wrapper to keep the original function.

Currying doesn’t call a function. It just transforms it.

Let’s make curry function that performs currying for two-argument functions. In other words, curry(f) for two-argument f(a, b) translates it into f(a)(b)

function curry(f) { // curry(f) does the currying transform
  return function(a) {
    return function(b) {
      return f(a, b);
    };
  };
}

// usage
function sum(a, b) {
  return a + b;
}

let carriedSum = curry(sum);

alert( carriedSum(1)(2) ); // 3

As you can see, the implementation is a series of wrappers.

• The result of curry(func) is a wrapper function(a).
• When it is called like sum(1), the argument is saved in the Lexical Environment, and a new wrapper is returned function(b).
• Then sum(1)(2) finally calls function(b) providing 2, and it passes the call to the original multi-argument sum.

Here's a toy example in Python:

>>> from functools import partial as curry

>>> # Original function taking three parameters:
>>> def display_quote(who, subject, quote):
        print who, 'said regarding', subject + ':'
        print '"' + quote + '"'

        
>>> display_quote("hoohoo", "functional languages",
	       "I like Erlang, not sure yet about Haskell.")
hoohoo said regarding functional languages:
"I like Erlang, not sure yet about Haskell."

>>> # Let's curry the function to get another that always quotes Alex...
>>> am_quote = curry(display_quote, "Alex Martelli")

>>> am_quote("currying", "As usual, wikipedia has a nice summary...")
Alex Martelli said regarding currying:
"As usual, wikipedia has a nice summary..."

(Just using concatenation via + to avoid distraction for non-Python programmers.)

Editing to add:

See http://docs.python.org/library/functools.html?highlight=partial#functools.partial, which also shows the partial object vs. function distinction in the way Python implements this.

Here is the example of generic and the shortest version for function currying with n no. of params.

const add = a => b => b ? add(a + b) : a; 

const add = a => b => b ? add(a + b) : a; 
console.log(add(1)(2)(3)(4)());

Currying is one of the higher-order functions of Java Script.

Currying is a function of many arguments which is rewritten such that it takes the first argument and return a function which in turns uses the remaining arguments and returns the value.

Confused?

Let see an example,

function add(a,b)
	{
		return a+b;
	}
add(5,6);

This is similar to the following currying function,

function add(a)
	{
		return function(b){
			return a+b;
		}
	}
var curryAdd = add(5);
curryAdd(6);

So what does this code means?

Now read the definition again,

Currying is a function of many arguments which is rewritten such that it takes first argument and return a function which in turns uses the remaining arguments and returns the value.

Still, Confused? Let me explain in deep!

When you call this function,

var curryAdd = add(5);

It will return you a function like this,

curryAdd=function(y){return 5+y;}

So, this is called higher-order functions. Meaning, Invoking one function in turns returns another function is an exact definition for higher-order function. This is the greatest advantage for the legend, Java Script. So come back to the currying,

This line will pass the second argument to the curryAdd function.

curryAdd(6);

which in turns results,

curryAdd=function(6){return 5+6;}
// Which results in 11

Hope you understand the usage of currying here. So, Coming to the advantages,

Why Currying?

It makes use of code reusability. Less code, Less Error. You may ask how it is less code?

I can prove it with ECMA script 6 new feature arrow functions.

Yes! ECMA 6, provide us with the wonderful feature called arrow functions,

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

With the help of the arrow function, we can write the above function as follows,

x=>y=>x+y

Cool right?

So, Less Code and Fewer bugs!!

With the help of these higher-order function one can easily develop a bug-free code.

I challenge you!

Hope, you understood what is currying. Please feel free to comment over here if you need any clarifications.

Thanks, Have a nice day!

If you understand partial you're halfway there. The idea of partial is to preapply arguments to a function and give back a new function that wants only the remaining arguments. When this new function is called it includes the preloaded arguments along with whatever arguments were supplied to it.

In Clojure + is a function but to make things starkly clear:

(defn add [a b] (+ a b))

You may be aware that the inc function simply adds 1 to whatever number it's passed.

(inc 7) # => 8

Let's build it ourselves using partial:

(def inc (partial add 1))

Here we return another function that has 1 loaded into the first argument of add. As add takes two arguments the new inc function wants only the b argument -- not 2 arguments as before since 1 has already been partially applied. Thus partial is a tool from which to create new functions with default values presupplied. That is why in a functional language functions often order arguments from general to specific. This makes it easier to reuse such functions from which to construct other functions.

Now imagine if the language were smart enough to understand introspectively that add wanted two arguments. When we passed it one argument, rather than balking, what if the function partially applied the argument we passed it on our behalf understanding that we probably meant to provide the other argument later? We could then define inc without explicitly using partial.

(def inc (add 1)) #partial is implied

This is the way some languages behave. It is exceptionally useful when one wishes to compose functions into larger transformations. This would lead one to transducers.

Curry can simplify your code. This is one of the main reasons to use this. Currying is a process of converting a function that accepts n arguments into n functions that accept only one argument.

The principle is to pass the arguments of the passed function, using the closure (closure) property, to store them in another function and treat it as a return value, and these functions form a chain, and the final arguments are passed in to complete the operation.

The benefit of this is that it can simplify the processing of parameters by dealing with one parameter at a time, which can also improve the flexibility and readability of the program. This also makes the program more manageable. Also dividing the code into smaller pieces would make it reuse-friendly.

For example:

function curryMinus(x) 
{
  return function(y) 
  {
    return x - y;
  }
}

var minus5 = curryMinus(1);
minus5(3);
minus5(5);

I can also do...

var minus7 = curryMinus(7);
minus7(3);
minus7(5);

This is very great for making complex code neat and handling of unsynchronized methods etc.

I found this article, and the article it references, useful, to better understand currying: http://blogs.msdn.com/wesdyer/archive/2007/01/29/currying-and-partial-function-application.aspx

As the others mentioned, it is just a way to have a one parameter function.

This is useful in that you don't have to assume how many parameters will be passed in, so you don't need a 2 parameter, 3 parameter and 4 parameter functions.

As all other answers currying helps to create partially applied functions. Javascript does not provide native support for automatic currying. So the examples provided above may not help in practical coding. There is some excellent example in livescript (Which essentially compiles to js) http://livescript.net/

times = (x, y) --> x * y
times 2, 3       #=> 6 (normal use works as expected)
double = times 2
double 5         #=> 10

In above example when you have given less no of arguments livescript generates new curried function for you (double)

A curried function is applied to multiple argument lists, instead of just one.

Here is a regular, non-curried function, which adds two Int parameters, x and y:

scala> def plainOldSum(x: Int, y: Int) = x + y
plainOldSum: (x: Int,y: Int)Int
scala> plainOldSum(1, 2)
res4: Int = 3

Here is similar function that’s curried. Instead of one list of two Int parameters, you apply this function to two lists of one Int parameter each:

scala> def curriedSum(x: Int)(y: Int) = x + y
curriedSum: (x: Int)(y: Int)Intscala> second(2)
res6: Int = 3
scala> curriedSum(1)(2)
res5: Int = 3

What’s happening here is that when you invoke curriedSum, you actually get two traditional function invocations back to back. The first function invocation takes a single Int parameter named x , and returns a function value for the second function. This second function takes the Int parameter y.

Here’s a function named first that does in spirit what the first traditional function invocation of curriedSum would do:

scala> def first(x: Int) = (y: Int) => x + y
first: (x: Int)(Int) => Int

Applying 1 to the first function—in other words, invoking the first function and passing in 1 —yields the second function:

scala> val second = first(1)
second: (Int) => Int = <function1>

Applying 2 to the second function yields the result:

scala> second(2)
res6: Int = 3

An example of currying would be when having functions you only know one of the parameters at the moment:

For example:

func aFunction(str: String) {
    let callback = callback(str) // signature now is `NSData -> ()`
    performAsyncRequest(callback)
}

func callback(str: String, data: NSData) {
    // Callback code
}

func performAsyncRequest(callback: NSData -> ()) {
    // Async code that will call callback with NSData as parameter
}

Here, since you don't know the second parameter for callback when sending it to performAsyncRequest(_:) you would have to create another lambda / closure to send that one to the function.

Here you can find a simple explanation of currying implementation in C#. In the comments, I have tried to show how currying can be useful:

public static class FuncExtensions {
    public static Func<T1, Func<T2, TResult>> Curry<T1, T2, TResult>(this Func<T1, T2, TResult> func)
    {
        return x1 => x2 => func(x1, x2);
    }
}

//Usage
var add = new Func<int, int, int>((x, y) => x + y).Curry();
var func = add(1);

//Obtaining the next parameter here, calling later the func with next parameter.
//Or you can prepare some base calculations at the previous step and then
//use the result of those calculations when calling the func multiple times 
//with different input parameters.

int result = func(1);

"Currying" is the process of taking the function of multiple arguments and converting it into a series of functions that each take a single argument and return a function of a single argument, or in the case of the final function, return the actual result.

The other answers have said what currying is: passing fewer arguments to a curried function than it expects is not an error, but instead returns a function that expects the rest of the arguments and returns the same result as if you had passed them all in at once.

I’ll try to motivate why it’s useful. It’s one of those tools that you never realized you needed until you do. Currying is above all a way to make your programs more expressive - you can combine operations together with less code.

For example, if you have a curried function add, you can write the equivalent of JS x => k + x (or Python lambda x: k + x or Ruby { |x| k + x } or Lisp (lambda (x) (+ k x)) or …) as just add(k). In Haskelll you can even use the operator: (k +) or (+ k) (The two forms let you curry either way for non-commutative operators: (/ 9) is a function that divides a number by 9, which is probably the more common use case, but you also have (9 /) for a function that divides 9 by its argument.) Besides being shorter, the curried version contains no made-up parameter name like the x found in all the other versions. It’s not needed. You’re defining a function that adds some constant k to a number, and you don’t need to give that number a name just to talk about the function. Or even to define it. This is an example of what’s called “point-free style”. You can combine operations together given nothing but the operations themselves. You don’t have to declare anonymous functions that do nothing but apply some operation to their argument, because *that’s what the operations already are.

This becomes very handy with higher-order functions when they’re defined in a currying-friendly way. For instance, a curried map(fn, list) let’s you define a mapper with just map(fn) that can be applied it to any list later. But currying a map defined instead as map(list, fn) just lets you define a function that will apply some other function to a constant list, which is probably less generally useful.

Currying reduces the need for things like pipes and threading. In Clojure, you might define a temperature conversion function using the threading macro ->: (defn f2c (deg) (-> deg (- 32) (* 5) (/ 9)). That’s cool, it reads nicely left to right (“subtract 32, multiply by 5 and divide by 9.”) and you only have to mention the parameter twice instead of once for every suboperation… but it only works because -> is a macro that transforms the whole form syntactically before anything is evaluated. It turns into a regular nested expression behind the scenes: (/ (* (- deg 32) 5) 9). If the math ops were curried, you wouldn’t need a macro to combine them so nicely, as in Haskell let f2c = (subtract 32) & (* 5) & (/ 9). (Although it would admittedly be more idiomatic to use function composition, which reads right to left: (/ 9) . (* 5) . (subtract 32).)

Again, it’s hard to find good demo examples; currying is most useful in complex cases where it really helps the readability of the solution, but those take so much explanation just to get you to understand the problem that the overall lesson about currying can get lost in the noise.

There is an example of "Currying in ReasonML".

let run = () => {
    Js.log("Curryed function: ");
    let sum = (x, y) => x + y;
    Printf.printf("sum(2, 3) : %d\n", sum(2, 3));
    let per2 = sum(2);
    Printf.printf("per2(3) : %d\n", per2(3));
  };

Below is one of currying example in JavaScript, here the multiply return the function which is used to multiply x by two.

const multiply = (presetConstant) => {
  return (x) => {
    return presetConstant * x;
  };
};

const multiplyByTwo = multiply(2);

// now multiplyByTwo is like below function & due to closure property in JavaScript it will always be able to access 'presetConstant' value
// const multiplyByTwo = (x) => {
//   return presetConstant * x;
// };

console.log(`multiplyByTwo(8) : ${multiplyByTwo(8)}`);

Output

multiplyByTwo(8) : 16