What does the `<<` operator mean in elm?

Question

In the following code taken from Elm Form Example, line 122, what does the << operator mean?

Field.field Field.defaultStyle (Signal.send updat         


        

Answer 1

<< is a function composition - returns function.

Composition creates a pipe of computations, chain of functions. This pipe waits for input, and when provided, first function starts computation, sends output to next etc.

import Html

add x y =
    Debug.log "x" x + Debug.log "y" y

add9 =
    add 4 << add 5

main =
    Html.text <| toString <| add9 2

Note: In the above example I use partial application. It means that I don't provide all parameters to function and as a result I get function.

If you run above example in web browser and look at the console output, you will see:

x: 5
y: 2
x: 4
y: 7

If we write it as math operations it will look like this:

4 + (5 + 2)
4 + 7

Note: We can also use forward version >>.

Reading signatures

Looking at signature of this operator:

(<<) : (b -> c) -> (a -> b) -> a -> c

For << operator, there is a function b -> c as the first parameter, and a function a -> b as the second:

(b -> c) << (a -> b)

But there is also a third parameter a. Because -> is right-associative, then

(<<) : (b -> c) -> (a -> b) -> a -> c

is equivalent to:

(<<) : (b -> c) -> (a -> b) -> (a -> c).

So that << returns function a -> c.

Associativity

In programming languages, the associativity (or fixity) of an operator is a property that determines how operators of the same precedence are grouped in the absence of parentheses; i.e. in what order each operator is evaluated:

a = b = c is parsed as a = (b = c)

• What is associativity of operators and why is it important?
• https://www.quora.com/How-does-one-explain-the-right-to-left-associativity-of-the-conditional-operator-in-C

Infix operator

Here I use << as infix operator, but we can also use it as a prefix operator enclosing it with parenthesis: (<<) (b -> c) (a -> b) or (<|) (add 4) (add 5).

elm < 0.18 used to let you take normal functions and use them as infix operators.

A word about <| operator

<| is a function application - returns value

We basically use it instead of parentheses.

text (something ++ something)

can be written as

text <| something ++ something

So looking at signature of this operator:

(<|) : (a -> b) -> a -> b

we can see that for <| operator, there is a function a -> b as the first parameter, and value a as the second:

(a -> b) <| a

and it returns b.

We can get the same value with function application <|:

v1 = add 4 <| add 5 <| 4
v2 = (add 4 << add 5) 4

• There is also forward version of this operator |>.
• https://elm-community.github.io/elm-faq/#what-good-is-the--operator-if-it-is-just-function-application
• For clarity don't mix <| and <<