Partial Application and Function Composition in

About Partial Application and Function Composition

Partial application

All functions in Elm are curried, which means that if you call a function without passing all of the arguments, it returns a new function.

The result of doing this is called partial-application (you are not passing all the arugments to the function, but are partially applying some of them).

add: Int -> Int -> Int
add a b = a + b

add2: Int -> Int
add2 = add 2

eight: Int
eight = add2 6
--> 8

Partial application always applies the arguments in order.

contains: String -> String -> Bool
contains first second =
--> This function is in the standard library, and returns True if the second string contains the first one

containsCedd: String -> Bool
containsCedd = contains "Cedd"
--> (partial application always applies the arguments in order, so "Cedd" becomes the first argument to contains
--> This is a function that takes a string, and returns True if that string contains Cedd)

ceddBurgeContainsCedd: Bool
ceddBurgeContainsCedd = containsCedd "Cedd Burge"
--> True
--> ("Cedd Burge" ends up being the second argument to contains, and it does include "Cedd", the first argument)

Pipe operator (|>)

Saying x |> f is exactly the same as f x. A concrete example is "5" |> String.toInt is the same as String.toInt "5".

This doesn't sound very useful at first, but it is called the pipe operator because it lets you write “pipelined” code.

For example, say we have a sanitize function for turning user input into integers:

sanitize : String -> Maybe Int
sanitize input =
    String.toInt (String.trim input)

We can rewrite it like this:

sanitize : String -> Maybe Int
sanitize input =
    input
    |> String.trim
    |> String.toInt

This avoids the use of brackets, and shows the functions in the order that they are applied (first String.trim, then String.toInt), which aids readability.

There is also a reverse pipe operator (<|). Saying x <| f is exactly the same as f x. This doesn't look very useful at first glance either, and is definitely not used as much as the pipe operator, but it helps to avoid brackets in some situations.

Function composition / point free style

The (>>) operator has the type (a -> b) -> (b -> c) -> (a -> c) and creates a function of type a -> c by composing two compatible functions of type a -> b and b -> c. It does this by taking the output (of type b) from the first function and using it as the first argument to the second function (which must be of the same type b). The created function will take the same input (of type a) first function, and will return whatever c the second function returns.

A concrete example is String.trim >> String.toInt. String.trim takes a string as its only parameter, so this is what the created function takes. String.toInt returns a Maybe Int, so this is what the created function returns. String.trim returns a String, which String.toInt accepts as a parameter, so the example compiles.

We can now rewrite our sanitize function as follows:

sanitize : String -> Maybe Int
sanitize =
    String.trim >> String.toInt

Note that we no longer use the input parameter that you can see the original example, even though the functionality is identical. This way of creating functions that make no reference to their parameters is called "Point Free Style". The advantage of this style is that the code is more concise, the disadvantage is that it can be harder to understand, especially for beginners.

It is worth remembering that all functions are curried in Elm, so String.length >> max compiles, and results in the following:

• A function (1) that has a string parameter (the input to String.length)
• max is a function that has two Int parameters, but function 1 passes a single Int to it (the return from String.length) so max is partially applied.
• The return value of the partially applied max function, is another function (2) that takes an Int, and returns the largest of this Int and the partially applied Int from String.length
• Hence function 1 (String -> Int) returns function 2 (Int -> Int)
• So ((String.length >> max) "123") 2 returns 3, because "123" has a length of 3, which is greater than the 2 from the Int argument.

Function design

To make it easy to write elegant code in Elm, you should make the main data structure the last parameter of functions. All the common functions in the standard library do this, such as List.map (type signature below).

map : (a -> b) -> List a -> List b

Here we can see that the last parameter to the map function is List a and it returns List b, so the main data structure (List) is the last parameter.

This makes it possible to write elegant pipelined code, such as below.

trimAndUpperCase : List String -> List String
trimAndUpperCase names =
    names
    |> List.map String.trim
    |> List.map String.toUpper

It also makes it convenient to use function composition and point free style, as an alternative to pipelining.

trimAndUpperCase : List String -> List String
trimAndUpperCase =
    List.map String.trim
    >> List.map String.toUpper

Function composition also allows you to reduce this example to a single call to List.map.

trimAndUpperCase : List String -> List String
trimAndUpperCase =
    List.map (String.trim >> String.toUpper)