DefiningFunctions.md

Defining functions

Named functions

We can define a function simply by naming it with its parameters:

isEvenLength: String -> Bool
isEvenLength s =
  modBy 2 (length s) == 0

Here it is in use, assuming we put the code in a module called DefiningFunctions and import the length function:

> import DefiningFunctions exposing (..)
> isEvenLength "Hello"
False : Bool
> isEvenLength "Hell"
True : Bool
>

Anonymous functions

Before the next part, here's a reminder that the filter function filters through just those elements of a list that pass a specific test - i.e. those that return True from a specific function.

> import DefiningFunctions exposing (..)
> import List exposing (filter)
> filter isEvenLength ["Once", "upon", "a", "time", "long", "ago"]
["Once","upon","time","long"] : List String
>

We can define a function anonymously using the backslash operator. Here the function we pass to filter is anonymous. It's usual not to have a space after the backslash, but we can.

ones: List String -> List String
ones li =
  filter (\s -> length s == 1) li

Here's the ones function in use:

> import DefiningFunctions exposing (..)
> ones ["a", "bb", "c", "d", "ee"]
["a","c","d"] : List String
>

We can define an anonymous function and then give it a name after.

concat : String -> String -> String
concat = (\a b -> a ++ b)

Here it is in use:

> import DefiningFunctions exposing (..)
> concat "elm" "o"
"elmo" : String
>

Simple type tags (constructors) are functions, too

If we've defined a type with a tag then the tag (the constructor) is a function, too.

Here we use map to convert a list of Int values into a list of Boxed values.

type Boxed = Boxed Int

box : List Int -> List Boxed
box li =
    map Boxed li

Here it is in use.

import DefiningFunctions exposing (..)
> box [7, 6, 5, 4]
[Boxed 7,Boxed 6,Boxed 5,Boxed 4]
    : List Boxed
>

Type tags for records are also functions

Next we define a type for a record called Point, and its associated tag/constructor (also called Point). But that tag is also a function from the plain record to a Point. This is exactly the same idea as with simple type tags. We can see this when we use it with the map function.

type Point = Point { x : Float, y : Float }

triangle1 : List { x : Float, y : Float }
triangle1 =
  [ { x = 0, y = 0 }
  , { x = 8, y = 1 }
  , { x = 5, y = 7 }
  ]

triangle2 : List Point
triangle2 =
  map Point triangle1

Here's how it looks in the REPL. Notice that we've converted from the type of triangle1 to the type of triangle2 thanks to the Point function.

> import DefiningFunctions exposing (..)
> triangle1
[{ x = 0, y = 0 },{ x = 8, y = 1 },{ x = 5, y = 7 }]
    : List { x : Float, y : Float }
> triangle2
[Point { x = 0, y = 0 },Point { x = 8, y = 1 },Point { x = 5, y = 7 }]
    : List Point
>

Type aliases for records act as multi-parameter functions

If we have a type alias for a record then that also acts as a function, but in a different way from a type declaration. Let's define a type alias...

type alias Person = { name : String, age : Int }

This gives us a Person function that takes several arguments, one for each field, and it will return a record with those fields. This means we need to know the order in which we originally defined the fields.

If we look at it in the REPL we see that Person is indeed a function:

> import DefiningFunctions exposing (..)
> Person
<function> : String -> Int -> Person
>

Now let's define a value using the Person function, passing in two arguments:

bob : { name : String, age : Int }
bob = Person "Robert" 55

And here we use the Person function to bring a list of names and a list of ages together:

people : List { name : String, age : Int }
people =
  map2 Person ["Alice", "Brian", "Coco"] [61, 23, 35]

Let's see what that looks like in the REPL:

> import DefiningFunctions exposing (..)
> bob
{ age = 55, name = "Robert" }
    : { age : Int, name : String }
> people
[{ age = 61, name = "Alice" },{ age = 23, name = "Brian" },{ age = 35, name = "Coco" }]
    : List { age : Int, name : String }
>

Record field names define functions

Any field name is a function if you precede it immediately with a dot (no whitespace). It is a function that takes any type of record with that field, and returns the value of that field. Here's what we can do in the Elm REPL:

> .name
<function> : { b | name : a } -> a
> .age
<function> : { b | age : a } -> a
> .totallyUnlikelyMadeUpField
<function> : { b | totallyUnlikelyMadeUpField : a } -> a
>