What is currying in F#? [duplicate]

Question

Possible Duplicate:
Functional programming: currying

I'm reading the free F# Wikibook here:

http://en.wikibooks.org/wiki/F_Sharp_Programming

There's a section explaining what Partial Functions are. It says that using F# you can partially use a function, but I just can't understand what's going on. Consider the following code snippet that is used an example:

#light
open System

let addTwoNumbers x y = x + y
let add5ToNumber = addTwoNumbers 5

Console.WriteLine(add5ToNumber 6)

The ouput is 11. But I'm not following. My function 'add5ToNumber' doesn't ask for a paramter so why can I invoke it and give it it one?

I really like learning about F# these days, baby steps!

Answer 1

Basically, every function in F# has one parameter and returns one value. That value can be of type unit, designated by (), which is similar in concept to void in some other languages.

When you have a function that appears to have more than one parameter, F# treats it as several functions, each with one parameter, that are then "curried" to come up with the result you want. So, in your example, you have:

let addTwoNumbers x y = x + y

That is really two different functions. One takes x and creates a new function that will add the value of x to the value of the new function's parameter. The new function takes the parameter y and returns an integer result.

So, addTwoNumbers 5 6 would indeed return 11. But, addTwoNumbers 5 is also syntactically valid and would return a function that adds 5 to its parameter. That is why add5ToNumber 6 is valid.

Answer 2

Currying is something like this:

addTwoNumbers is a function that takes a number and returns a function that takes a number that returns a number.

So addTwoNumbers 5 is in fact a function that takes a number and returns a number, which is how currying works. Since you assign addTwoNumbers 5 to add5ToNumber, that make add5ToNumber a function that takes a number an returns a number.

I don't know what type definition looks like in F# but in Haskell, the type definition of functions makes this clear:

addTwoNumbers :: (Num a) => a -> a -> a

On the other hand, if you wrote addTwonumbers to take a two tuple,

addTwoNumbers :: (Num a) => (a, a) -> a

then is would be a function that takes a two tuple and returns a number, so add5ToNumber would not be able to be created as you have it.