Fridays are investment days at thoughtbot, so I decided to use the day to explore Elm, a functional programming language for the browser. I was able to pair program on making a Select2 implementation in Elm with my mentor Joël, and it was a fantastic experience. One of the most interesting aspects that I learned was about Currying and Partial Application.

Currying

Currying is the process of taking a function with multiple arguments and turning it into a series of functions with one argument. So, for example, for making the select library we wanted a filtering aspect, so we had a function optionContainsTerm that takes two arguments, a String (the search term), and an Option, one of the elements in the dropdown, and returns a boolean that says whether that option contains the search term or not. In Elm, that looks like this

optionContainsTerm : String -> Option -> Bool

This syntax threw me off a lot at first. When we were dealing with functions that take one argument, this syntax made sense to me. myFunc : String -> String means the function myFunc takes in a string and returns a string. With multiple arguments though the arrows suddenly stopped making sense. It takes in a String and then returns an Option and then returns a Bool? Well, turns out through the magic of currying, that’s exactly what’s happening!

In Elm, all functions are curried under the hood. So, if a function has n arguments, it will be transformed into n functions with one argument each.

This then leads us into partial application.

Partial Application

Arity is the number of arguments a function takes. If it takes 2 arguments, the function is said to have an arity of 2. To partially apply a function is to call a function with less arguments then it’s arity. So, if a function has an arity of 2, and you call it with only 1 argument, then the function is “partially applied.” As a result, you’ll get back an anonymous function that takes in the second argument. Knowing this makes Elm’s error messages make a lot more sense. Oftentimes you’ll get an error that looks something like this:

-- TYPE MISMATCH -------------------------------------------------- src/Main.elm

The type annotation for `initialSelect` does not match its definition.

25| initialSelect : Select
                    ^^^^^^
The type annotation is saying:

    { options : List Option
    , searchTerm : String
    }

But I am inferring that the definition has this type:

    String -> Select

What this is saying is that I’m expecting Select to be a record with two keys, options, which is a List of Options and searchTerm, which is a string. Instead, I’m getting back a function that takes in a String and returns a Select.

If you see an error like this, 99% of the time what it’s trying to say is that you’ve passed in less arguments than you were supposed to, so the function has been partially applied. In this case, since I only passed in one argument when it was expecting two, it returned an anonymous function that takes in the second argument (a String) and returns a Select.

To recap, currying is breaking down a function with n arguments into n functions with one argument each. Partial Application is calling a function with fewer arguments then it’s arity, which will then return an anonymous function that will expect to receive the missing arguments. These are concepts that always sounded scary to me, but one day of working with Elm and seeing how they’re applied in practice and they make a lot more sense. Hopefully this explanation helps them make sense to someone else!