Currying Example in Scala

Question

Is the following a good example of currying?

def sum(a: Int, b: Int) : (Int => Int) = {
    def go(a: Int) : Int = {
        a + b;
    }
    go
}

I half understand the below results, but how could I write (or maybe how I should've written) sum() in a curried way?

scala> sum(3,4) res0: Int => Int = <function1>
scala> sum(3,4).apply(2) res1: Int = 6
scala> sum(3,4).apply(3) res2: Int = 7

Answer 1

In the lambda calculus, you have something called a lambda abstraction λx.term1 which when applied to another term (λx.term1)(term2), corresponds to the concept of applying a function to term2. The lambda calculus is the theoritical basis for functional programming. In lambda calculus, you don't have lambda abstraction taking multiple parameters. So how you do you represent functions of two arguments? The answer is to return a function that will take the other argument and then return the result on both argument.

So in Scala, if you have a var a in scope, you can return a function that will add its argument b to a:

scala> var a = 1
a: Int = 1

scala> val adda = (b: Int) => a + b
adda: Int => Int = <function1>

scala> adda(3)
res1: Int = 4

Now if you have an argument a in scope it works just as well:

scala> val sum = (a: Int) => (b: Int) => a + b
sum: Int => Int => Int = <function1>

scala> sum(3)(5)
res2: Int = 8

So without having access to a syntax that lets you define a function of two arguments, you just basically achieve that with a function sum taking an argument a returning a function equivalent to adda that takes a argument b and returns a + b. And that's called currying.

As an exercise, define a function using currying that will let you work on 3 arguments. For instance val sum3: Int => Int => Int => Int = ???, and fill in what goes into the question marks.

Answer 2

Disclaimer: I'm pretty new to Scala, so treat this with a grain of salt

In purely functional languages like Haskell currying plays very important role in function composition, e.g. if I want to find sum of squares I would write in Haskell (sorry for too much Haskell, but syntax has similarities with Scala and it's not that hard to guess)

without currying:

sum_of_squares xs = foldl (\x y -> x + y) 0 (map (\x -> x * x) xs)

with curring (. is a function composition):

sum_of_squares = (foldl (\x y -> x + y) 0) . (map (\x -> x * x))

which allows me to operate with functions instead of operating with arguments. It may not be that clear from previous example, but consider this:

sum_of_anything f = (foldl (\x y -> x + y) 0) . (map f)

here f is an arbitrary function and I can rewrite the first example as:

sum_of_squares = sum_of_anything (\x -> x * x)

Now let's go back to Scala. Scala is OO language, so usually xs will be a receiver:

def sum_of_squares(xs: List[Int]): Int = {
  xs.map(x => x * x).foldLeft(0)((x, y) => x + y)
}

sum_of_squares(List(1,2,3))

def sum_of_anything(f: (Int, Int) => Int)(xs: List[Int]): Int = {
  xs.map(x => x * x).foldLeft(0)(f)
}

sum_of_anything((x, y) => x + y)(List(1, 2, 3))

which means I can't omit xs. I can probably rewrite it with lambdas, but I won't be able to use map and foldLeft without adding more boilerplate. So as other people mentioned in Scala "currying" is probably mostly used to support type inference.

Meanwhile in your particular example I have a feeling that you don't need outer a, it's shadowed anyway, you probably meant:

def sum(b: Int) : (Int => Int) = {
    def go(a: Int) : Int = {
        a + b;
    }
    go
}

But in this simple example you can use partial application (given that you will probably pass sum to higher order functions):

List(1, 2, 3).map(sum(2))   //> res0: List[Int] = List(3, 4, 5)
List(1, 2, 3).map(_ + 2)    //> res1: List[Int] = List(3, 4, 5)

For this kind of application sum can be shorter because sum(2) will be implicitly expanded to Int => Int:

def sum(b: Int)(a: Int): Int = a + b

This form is not valid for val sum2 = sum(2) though, you will have to write val sum2 = sum(2) _.

Answer 3

Currying mechanism was introduced in Scala to support type inference. For example foldLeft function in the standard lib:

def foldLeft[B](z: B)(op: (B, A) => B): B

Without currying you must provide types explicitly:

def foldLeft[B](z: B, op: (B, A) => B): B
List("").foldLeft(0, (b: Int, a: String) => a + b.length)
List("").foldLeft[Int](0, _ + _.length)

There are three ways to write a curried function:

1) Write it in currying form:

def sum(a: Int)(b: Int) = a + b

which is just syntactic sugar for:

def sum(a: Int): Int => Int = b => a + b

2) Call curried on the function object (sum _).curried and check the types:

sum: (a: Int, b: Int)Int
res10: Int => (Int => Int) = <function1>

In your example, you can use Scala type inference to reduce the amount of code and change your code:

def sum(a: Int, b: Int) : (Int => Int) = {
    def go(a: Int) : Int = {
        a + b;
    }
    go
}

into:

def sum(a: Int, b: Int) : (Int => Int) = c => a + b + c

semantically these are the same, because you explicitly provided the return type, so Scala knows that you will return a function wich takes an Int argument and return an Int

Also a more complete answer about curring was given by retronym