Modules

Loading modules

An Elm module is a collection of related functions and types. An Elm program is a collection of modules where the main module loads up the other modules and then uses the functions defined in them to do something. Having code split up into several modules has quite a lot of advantages. If a module is generic enough, the functions it exports can be used in a multitude of different programs. If your own code is separated into self-contained modules which don’t rely on each other too much (we also say they are loosely coupled), you can reuse them later on. It makes the whole deal of writing code more manageable by having it split into several parts, each of which has some sort of purpose.

The Elm core library is split into modules, each of them contains functions and types that are somehow related and serve some common purpose. There’s a module for manipulating lists, a module for concurrent programming, a module for dealing with dates, etc. All the functions and types that we’ve dealt with so far were from modules which are imported by default. In this chapter, we’re going to examine a few useful modules and the functions that they have. But first, we’re going to see how to import modules.

The syntax for importing modules in an Elm script is import <module name>, which will make the entire module accessible under the module name namespace (e.g. if we import the List module, we can access everything exposed by the module as long as you put List. before it… like List.map, List.filter, etc.). These are called qualified imports. The functions you’re importing are qualified by the module name, like Dict.map or String.toList You can also import specific functions from a module like this: import List exposing (map, filter) or import Dict exposing (..) (which exposes everything in the Dict module). These are unqualified imports. This can make your code more concise, but since many modules export functions with identical names (e.g. map and filter), you may need to take care not to import multiple identically named functions into the same module (but don’t worry too much, if you do the compiler will let you know), Importing must be done before defining any functions, so imports are usually done at the top of the file. One script can, of course, import several modules. Just put each import statement into a separate line. Let’s import the List module, which has a bunch of useful functions for working with lists and use a function that it exports to create a function that tells us how many odd elements a list has. We’ll also import the Tuple module to work with the results produced by List.partition. List and Tuple are imported qualified by default, so the following is intended just to give you an idea of how importing works. You wouldn’t necessarily need to do the following in real life.

import List exposing (length, partition)
import Tuple

numOdds : List Int -> Int
numOdds = 
    let
        odd n = n % 2 == 1
    in
    length << Tuple.first << partition odd

When you do import Tuple, all the functions that Tuple exports become available under the Tuple namespace, meaning that you can call them from wherever in the script. And when you do import List exposing (length, partition), you pull length and partition into the module unqalified. partition is a function defined in List that takes a predicate and a list and produces a tuple of two lists. The first list being those elements for which the predicate evaluated to True, and the second list being those elements for which the predicate evaluated to False. Composing length, Tuple.first, and partition we produce a function that’s the equivalent of \xs -> length (Tuple.first (partition (\n -> n % 2 == 1) xs))

We can also import modules using the as keyword to provide a shorter name. For example,

import Json.Decode as Decode

Decode.string "JSON string"

This makes it so that if we want to reference Json.Decode’s string function, we don’t have to type out Json.Decode.string every time.

Use this handy reference to see which modules are in the standard library. A great way to pick up new Elm knowledge is to just click through the standard library reference and explore the modules and their functions. You can also view the Elm source code for each module. Reading the source code of some modules is a really good way to learn Elm and get a solid feel for it.

List

The List module is all about lists, obviously. It provides some very useful functions for dealing with them. We’ve already met some of its functions (like map and filter) because the List module is imported by default. Let’s take a look at some of the functions that we haven’t met before.

intersperse takes an element and a list and then puts that element in between each pair of elements in the list. Here’s a demonstration:

> List.intersperse "on" ["turtles","turtles","turtles"]
["turtles","on","turtles","on","turtles"] : List String
> intersperse 0 [1,2,3,4,5,6]
[1,0,2,0,3,0,4,0,5,0,6] : List number

concat flattens a list of lists into just a list of elements.

> List.concat [["foo", "bar"],["baz","qux"]]
["foo","bar","baz","qux"] : List String
> List.concat [[3,4,5],[2,3,4],[2,1,1]]
[3,4,5,2,3,4,2,1,1] : List number

It will just remove one level of nesting. So if you want to completely flatten [[[2,3],[3,4,5],[2]],[[2,3],[3,4]]], which is a list of lists of lists, you have to concatenate it twice.

Doing concatMap is the same as first mapping a function to a list and then concatenating the list with concat.

> List.concatMap (List.repeat 4) [1,2,3]
[1,1,1,1,2,2,2,2,3,3,3,3] : List number

any and all take a predicate and then check if any or all the elements in a list satisfy the predicate, respectively.

> List.any ((==) 4) [2,3,5,6,1,4]
True : Bool
> List.all ((>) 4) [6,9,10]
True : Bool
> List.all (\n -> n % 2 == 1) [1,2,3,4,5]
False : Bool
> List.any (\n -> n % 2 == 1) [1,2,3,4,5]
True : Bool

sort simply sorts a list. The type of the elements in the list has to be part of the comparable typeclass, because if the elements of a list can’t be compared in some way, then the list can’t be sorted.

> List.sort [8,5,3,2,1,6,4,2]
[1,2,2,3,4,5,6,8]
> List.sort ["foo", "bar", "baz", "qux"]
["bar","baz","foo","qux"] : List String

member checks if an element is inside a list.

partition takes a list and a predicate and returns a pair of lists. The first list in the result contains all the elements that satisfy the predicate, the second contains all the ones that don’t.

> List.partition (\n -> n % 2 == 1) [1,2,3,4,5,6]
([1,3,5],[2,4,6]) : ( List Int, List Int )
> List.partition (flip (>) 3) [1,3,5,6,3,2,1,0,3,7]
([5,6,7],[1,3,3,2,1,0,3]) : ( List number, List number )

What length, take, drop, repeat have in common is that they take an Int as one of their parameters (or return an Int). For instance, length has a type signature of length : List a -> Int. If we try to get the average of a list of numbers by doing let xs = List.range 1 6 in List.sum xs / List.length xs, we get a type error, because you can’t use / with an Int.

The sort function also has a more general equivalent. sortWith take a function that determines if one element is greater, smaller or equal to the other. The type signature of sortWith is sortWith : (a -> a -> Order) -> List a -> List a. If you remember from before, the Order type can have a value of LT, EQ or GT. sort is the equivalent of List.sortWith compare, because compare just takes two elements whose type is in the comparable typeclass and returns their ordering relationship.

Lists can be compared, but when they are, they are compared lexicographically. What if we have a list of lists and we want to sort it not based on the inner lists’ contents but on their lengths? Well, as you’ve probably guessed, we’ll use the sortWith function. First we’ll define the on function, like this, to act as a helper:

on : (b -> b -> c) -> (a -> b) -> a -> a -> c
on f g = \x y -> f (g x) (g y)

So doing on (==) (> 0) returns an equality function that looks like \x y -> (x > 0) == (y > 0). on is useful with the By/With functions because with it, we can do:

> xs = [[5,4,5,4,4],[1,2,3],[3,5,4,3],[],[2],[2,2]]
[[5,4,5,4,4],[1,2,3],[3,5,4,3],[],[2],[2,2]] : List (List number)
> List.sortWith (on compare List.length) xs
[[],[2],[2,2],[1,2,3],[3,5,4,3],[5,4,5,4,4]]

Awesome! on compare List.length… man, that reads almost like real English! If you’re not sure how exactly the on works here, on compare List.length is the equivalent of \x y -> compare (List.length x) (List.length y). When you’re dealing with By/With functions that take an equality function, you might do something like on (==) something and when you’re dealing with By/With functions that take an ordering function, you might do on compare something.

Char

The Char module does what its name suggests. It exports functions that deal with characters.

Char exports a bunch of predicates over characters. That is, functions that take a character and tell us whether some assumption about it is true or false. Here’s what they are:

isUpper checks whether a character is an upper case ASCII letter.

isLower checks whether a character is a lower case ASCII letter.

isDigit checks whether a character is an ASCII digit [0-9].

isOctDigit checks whether a character is an ASCII octal digit [0-7].

isHexDigit checks whether a character is an ASCII hexadecimal digit [0-9a-fA-F].

All these predicates have a type signature of Char -> Bool. Most of the time you’ll use this to filter out strings or something like that. For instance, let’s say we’re making a program that takes a username and the username can only be comprised of lowercase characters. We can use the List function all and the String function toList in combination with the Char predicates to determine if the username is alright.

> List.all Char.isLower <| String.toList "bobby"
True : Bool
> List.all Char.isLower <| String.toList "Bobbyå"
False : False

Kewl. In case you don’t remember, all takes a predicate and a list and returns True only if that predicate holds for every element in the list.

toUpper converts a character to upper-case. Spaces, numbers, and the like remain unchanged.

toLower converts a character to lower-case.

toCode converts a character to a KeyCode (a type alias for Int).

> List.map Char.toCode <| String.toList "34538"
[51,52,53,51,56] : List Char.KeyCode
> List.map Char.toCode <| String.toList "FF85AB"
[70,70,56,53,65,66] : List Char.KeyCode

fromCode is the inverse function of toCode. It takes a KeyCode and converts it to a character.

> Char.fromCode 70
'F' : Char
> Char.toCode 51
'3'

The Caesar cipher is a primitive method of encoding messages by shifting each character in them by a fixed number of positions in the alphabet. We can easily create a sort of Caesar cipher of our own, only we won’t constrict ourselves to the alphabet.

encode : Int -> String -> String
encode shift msg =
    let
        ords = List.map Char.toCode <| String.toList msg
        shifted = List.map ((+) shift) ords
    in
    String.fromList <| List.map Char.fromCode shifted

Here, we first convert the string to a list of Char, then map it to a list of KeyCode’s (which, again, are just a type alias to Int). Then we add the shift amount to each number before converting the list of numbers back to characters, then back to a string. If you’re a composition cowboy, you could write the body of this function as String.fromList <| List.map (Char.fromCode << ((+) shift) << Char.toCode) <| String.toList msg. Let’s try encoding a few messages.

> encode 3 "Heeeeey"
"Khhhhh|" : String
> encode 4 "Heeeeey"
"Liiiii}" : String
> encode 1 "abcd"
"bcde" : String
> encode 5 "Marry Christmas! Ho ho ho!"
"Rfww~%Hmwnxyrfx&%Mt%mt%mt&" : String

That’s encoded alright. Decoding a message is basically just shifting it back by the number of places it was shifted by in the first place.

decode : Int -> String -> String
decode shift msg = encode (negate shift) msg

> encode 3 "Im a little teapot"
"Lp#d#olwwoh#whdsrw"
> decode 3 "Lp#d#olwwoh#whdsrw"
"Im a little teapot"
> decode 5 << encode 5 <| "This is a sentence"
"This is a sentence"

Dict

Association lists (also called dictionaries) are lists that are used to store key-value pairs where ordering doesn’t matter. For instance, we might use an association list to store phone numbers, where phone numbers would be the values and people’s names would be the keys. We don’t care in which order they’re stored, we just want to get the right phone number for the right person.

The most obvious way to represent association lists in Elm would be by having a list of pairs. The first component in the pair would be the key, the second component the value. Here’s an example of an association list with phone numbers:

phoneBook =
    [("betty","555-2938")
    ,("bonnie","452-2928")
    ,("patsy","493-2928")
    ,("lucille","205-2928")
    ,("wendy","939-8282")
    ,("penny","853-2492")
    ]

Despite this seemingly odd indentation, this is just a list of pairs of strings. The most common task when dealing with association lists is looking up some value by key. Let’s make a function that looks up some value given a key.

findKey : k -> List (k,v) -> Maybe v
findKey key xs = Maybe.map Tuple.second << List.head << List.filter (\(k,v) -> key == k) <| xs

Pretty simple. The function that takes a key and a list, filters the list so that only matching keys remain, gets the first key-value that matches and returns the value. But what happens if the key we’re looking for isn’t in the association list? Hmm. Well, our old friend Maybe is here to help. If we don’t find the key, we’ll return a Nothing. If we find it, we’ll return Just something, where something is the value corresponding to that key.

This is a textbook recursive function that operates on a list. Edge case, splitting a list into a head and a tail, recursive calls, they’re all there. This is the classic fold pattern, so let’s see how this would be implemented as a fold.

findKey : k -> List (k,v) -> Maybe v
findKey key = List.foldr (\(k,v) acc -> if key == k then Just v else acc) Nothing

Note: It’s usually better to use folds for this standard list recursion pattern instead of explicitly writing the recursion because they’re easier to read and identify. Everyone knows it’s a fold when they see the foldr call, but it takes some more thinking to read explicit recursion.

> findKey "penny" phoneBook
Just "853-2492" : Maybe.Maybe String
> findKey "betty" phoneBook
Just "555-2938" : Maybe.Maybe String
> findKey "wilma" phoneBook
Nothing : Maybe.Maybe String

Works like a charm! If we have the girl’s phone number, we Just get the number, otherwise we get Nothing.

If we want to find the corresponding value to a key, we have to traverse all the elements of the list until we find it. The Dict module offers association lists that are much faster (because they’re internally implemented with trees) and also it provides a lot of utility functions. From now on, we’ll say we’re working with dictionaries instead of association lists.

Let’s go ahead and see what Dict has in store for us! Here’s the basic rundown of its functions.

The fromList function takes an association list (in the form of a list) and returns a dictionary with the same associations.

> Dict.fromList [("betty","555-2938"),("bonnie","452-2928"),("lucille","205-2928")]
Dict.fromList [("betty","555-2938"),("bonnie","452-2928"),("lucille","205-2928")] : Dict.Dict String String
> Dict.fromList [(1,2),(3,4),(3,2),(5,5)]
Dict.fromList [(1,2),(3,2),(5,5)] : Dict.Dict number number1

If there are duplicate keys in the original association list, the duplicates are just discarded. This is the type signature of fromList

Dict.fromList : List (comparable, v) -> Dict.Dict comparable v

It says that it takes a list of pairs of type comparable and v and returns a dictionary that maps from keys of type comparable to type v. Notice here that the keys have to be comparable. That’s an essential constraint in the Dict module. It needs the keys to be comparable so it can arrange them in a tree.

You should always use Dict for key-value associations unless you have keys that aren’t part of the comparable typeclass.

Let’s back up for a moment. Did notice anything unusual with our dictionary’s type signature? Dict.Dict number number1. We’ve seen number before, so what is number1? Well, number in Elm is a typeclass consisting of either Int or Float. So what the type system is telling us is that we have a dictionary with keys of type number and values also of type number, but we should not assume that these types are equivalent! It could turn out that our keys are Int’s, but our values are Float’s (or vice versa), so the type system is helping us out here by keeping these two types distinct. Alright, let’s continue.

empty represents an empty dictionary. It takes no arguments, it just returns an empty dictionary.

> Dict.empty
Dict.fromList [] : Dict.Dict k v

insert takes a key, a value and a dictionary and returns a new dictionary that’s just like the old one, only with the key and value inserted.

> Dict.empty
Dict.fromList [] : Dict.Dict k v
> Dict.insert 3 100 Dict.empty
Dict.fromList [(3,100)] : Dict.Dict number number1
> Dict.insert 5 600 (Dict.insert 4 200 ( Dict.insert 3 100  Dict.empty))
fromList [(3,100),(4,200),(5,600)] : Dict.Dict number number1
> Dict.insert 5 600 << Dict.insert 4 200 << Dict.insert 3 100 <| Dict.empty
fromList [(3,100),(4,200),(5,600)] : Dict.Dict number number1

We can implement our own fromList by using the empty dictionary, insert and a fold. Watch:

fromList : List (comparable,v) -> Dict.Dict comparable v
fromList = List.foldr (\(k, v) acc -> Dict.insert k v acc) Dict.empty

It’s a pretty straightforward fold. We start of with an empty dictionary and we fold it up from the right, inserting the key value pairs into the accumulator as we go along.

isEmpty checks if a dictionary is empty.

> Dict.isEmpty Dict.empty
True : Bool
> Dict.isEmpty <| Dict.fromList [(2,3),(5,5)]
False : Bool

size reports the size of a dictionary.

> Dict.size Dict.empty
0 : Int
> Dict.size <| Dict.fromList [(2,4),(3,3),(4,2),(5,4),(6,4)]
5 : Int

singleton takes a key and a value and creates a dictionary that has exactly one mapping.

> Dict.singleton 3 9
fromList [(3,9)] : Dict.Dict number number1
> Dict.insert 5 9 <| Dict.singleton 3 9
fromList [(3,9),(5,9)] : Dict.Dict number number1

get returns Just something if it finds something for the key and Nothing if it doesn’t.

member is a predicate that takes a key and a dictionary and reports whether the key is in the dictionary or not.

> Dict.member 3 <| Dict.fromList [(3,6),(4,3),(6,9)]
True : Bool
> Dict.member 3 <| Dict.fromList [(2,5),(4,5)]
False : Bool

map and filter work much like their list equivalents, although the functions you pass to them will need to have a slightly different signature to account for both the key and the value which they will be passed.

> Dict.map (\k v -> (k, v * 100)) <| Dict.fromList [(1,1),(2,4),(3,9)]
fromList [(1,100),(2,400),(3,900)] : Dict.Dict number number1
> Dict.filter (\_ v -> Char.isUpper v) <| Dict.fromList [(1,'a'),(2,'A'),(3,'b'),(4,'B')]
fromList [(2,'A'),(4,'B')] : Dict.Dict number Char

toList is the inverse of fromList.

> Dict.toList << Dict.insert 9 2 <| Dict.singleton 4 3
[(4,3),(9,2)] : List (number, number)

keys and values return lists of keys and values respectively. keys is the equivalent of List.map Tuple.first << Dict.toList and values is the equivalent of List.map Tuple.second << Dict.toList

These were just a few functions from Dict. You can see a complete list of functions in the documentation.

Set

The Set module offers us, well, sets. Like sets from mathematics. Sets are kind of like a cross between lists and dictionaries. All the elements in a set are unique. And because they’re internally implemented with trees (much like dictionaries in Dict), they’re ordered. Checking for membership, inserting, deleting, etc. is much faster than doing the same thing with lists. The most common operation when dealing with sets are inserting into a set, checking for membership and converting a set to a list.

Let’s say we have two pieces of text. We want to find out which characters were used in both of them.

text1 = "I just had an anime dream. Anime... Reality... Are they so different?"
text2 = "The old man left his garbage can out and now his trash is all over my lawn!"

The fromList function works much like you would expect. It takes a list and converts it into a set.

> set1 = Set.fromList <| String.toList text1
Set.fromList [' ','.','?','A','I','R','a','d','e','f','h','i','j','l','m','n','o','r','s','t','u','y']
    : Set.Set Char
> set2 = Set.fromList <| String.toList text2
Set.fromList [' ','!','T','a','b','c','d','e','f','g','h','i','l','m','n','o','r','s','t','u','v','w','y']
    : Set.Set Char

As you can see, the items are ordered and each element is unique. Now let’s use the intersect function to see which elements they both share.

> Set.intersect set1 set2
Set.fromList [' ','a','d','e','f','h','i','l','m','n','o','r','s','t','u','y']
    : Set.Set Char

We can use the diff function to see which letters are in the first set but aren’t in the second one and vice versa.

> Set.diff set1 set2
Set.fromList ['.','?','A','I','R','j'] : Set.Set Char
> Set.diff set2 set1
Set.fromList ['!','T','b','c','g','v','w'] : Set.Set Char

Or we can see all the unique letters used in both sentences by using union.

> Set.union set1 set2
Set.fromList [' ','!','.','?','A','I','R','T','a','b','c','d','e','f','g','h','i','j','l','m','n','o','r','s','t','u','v','w','y']
    : Set.Set Char

The isEmpty, size, member, empty, singleton, insert and remove functions all work like you’d expect them to.

> Set.isEmpty Set.empty
True : Bool
> Set.isEmpty <| Set.fromList [3,4,5,5,4,3]
False : Bool
> Set.size <| Set.fromList [3,4,5,3,4,5]
3 : Int
> Set.singleton 9
Set.fromList [9] : Set.Set number
> Set.insert 4 <| Set.fromList [9,3,8,1]
Set.fromList [1,3,4,8,9] : Set.Set number
> Set.insert 8 <| Set.fromList <| List.range 5 10
Set.fromList [5,6,7,8,9,10] : Set.Set Int
> Set.remove 4 <| Set.fromList [3,4,5,4,3,4,5]
Set.fromList [3,5] : Set.Set number

We can also map over sets and filter them.

> odd n = n % 2 == 1
<function> : Int -> Bool
> Set.filter odd <| Set.fromList [3,4,5,6,7,2,3,4]
Set.fromList [3,5,7] : Set.Set Int
> Set.map ((+) 1) <| Set.fromList [3,4,5,6,7,2,3,4]
Set.fromList [3,4,5,6,7,8] : Set.Set number

Sets are often used to weed a list of duplicates from a list by first making it into a set with fromList and then converting it back to a list with toList.

> setDedup xs = Set.toList <| Set.fromList xs
<function> : List comparable -> List comparable
> String.fromList <| setDedup <| String.toList "HEY WHATS CRACKALACKIN"
" ACEHIKLNRSTWY" : String

Keep in mind, though, that the order of the original list likely will not be preserved.

Making our own modules

We’ve looked at some cool modules so far, but how do we make our own module? Almost every programming language enables you to split your code up into several files and Elm is no different. When making programs, it’s good practice to take functions and types that work towards a similar purpose and put them in a module. That way, you can easily reuse those functions in other programs by just importing your module.

Let’s see how we can make our own modules by making a little module that provides some functions for calculating the volume and area of a few geometrical objects. We’ll start by creating a file called Geometry.elm.

We say that a module exports functions. What that means is that when I import a module, I can use the functions that it exports. It can define functions that its functions call internally, but we can only see and use the ones that it exports.

At the beginning of a module, we specify the module name. If we have a file called Geometry.elm, then we should name our module Geometry. Then, we specify the functions that it exports and after that, we can start writing the functions. So we’ll start with this.

module Geometry
    exposing
        ( sphereVolume
        , sphereArea
        , cubeVolume
        , cubeArea
        , cuboidArea
        , cuboidVolume
        )

As you can see, we’ll be doing areas and volumes for spheres, cubes and cuboids. Let’s go ahead and define our functions then:

module Geometry
    exposing
        ( cubeArea
        , cubeVolume
        , cuboidArea
        , cuboidVolume
        , sphereArea
        , sphereVolume
        )


sphereVolume : Float -> Float
sphereVolume radius =
    (4.0 / 3.0) * pi * (radius ^ 3)


sphereArea : Float -> Float
sphereArea radius =
    4 * pi * (radius ^ 2)


cubeVolume : Float -> Float
cubeVolume side =
    cuboidVolume side side side


cubeArea : Float -> Float
cubeArea side =
    cuboidArea side side side


cuboidVolume : Float -> Float -> Float -> Float
cuboidVolume a b c =
    rectangleArea a b * c


cuboidArea : Float -> Float -> Float -> Float
cuboidArea a b c =
    rectangleArea a b * 2 + rectangleArea a c * 2 + rectangleArea c b * 2


rectangleArea : Float -> Float -> Float
rectangleArea a b =
    a * b

Pretty standard geometry right here. There are a few things to take note of though. Because a cube is only a special case of a cuboid, we defined its area and volume by treating it as a cuboid whose sides are all of the same length. We also defined a helper function called rectangleArea, which calculates a rectangle’s area based on the lenghts of its sides. It’s rather trivial because it’s just multiplication. Notice that we used it in our functions in the module (namely cuboidArea and cuboidVolume) but we didn’t export it! Because we want our module to just present functions for dealing with three dimensional objects, we used rectangleArea but we didn’t export it.

When making a module, we usually export only those functions that act as a sort of interface to our module so that the implementation is hidden. If someone is using our Geometry module, they don’t have to concern themselves with functions that we don’t export. We can decide to change those functions completely or delete them in a newer version (we could delete rectangleArea and just use * instead) and no one will mind because we weren’t exporting them in the first place.

To use our module, we just do:

import Geometry

Geometry.elm has to be in the same folder that the program that’s importing it is in, though.

Modules can also be given a hierarchical structures. Each module can have a number of sub-modules and they can have sub-modules of their own. Let’s section these functions off so that Geometry is a module that has three sub-modules, one for each type of object.

First, we’ll make a folder called Geometry. Mind the capital G. In it, we’ll place three files: Sphere.elm, Cuboid.elm, and Cube.elm. Here’s what the files will contain:

Sphere.elm

module Geometry.Sphere
    exposing
        ( area
        , volume
        )


volume : Float -> Float
volume radius =
    (4.0 / 3.0) * pi * (radius ^ 3)


area : Float -> Float
area radius =
    4 * pi * (radius ^ 2)

Cuboid.elm

module Geometry.Cuboid
    exposing
        ( area
        , volume
        )


volume : Float -> Float -> Float -> Float
volume a b c =
    rectangleArea a b * c


area : Float -> Float -> Float -> Float
area a b c =
    rectangleArea a b * 2 + rectangleArea a c * 2 + rectangleArea c b * 2


rectangleArea : Float -> Float -> Float
rectangleArea a b =
    a * b

Cube.elm

module Geometry.Cube
    exposing
        ( area
        , volume
        )

import Geometry.Cuboid as Cuboid


volume : Float -> Float
volume side =
    Cuboid.volume side side side


area : Float -> Float
area side =
    Cuboid.area side side side

Alright! So first is Geometry.Sphere. Notice how we placed it in a folder called Geometry and then defined the module name as Geometry.Sphere. We did the same for the cuboid. Also notice how in all three sub-modules, we defined functions with the same names. We can do this because they’re separate modules.

So now if we’re in a file that’s on the same level as the Geometry folder, we can do, say:

import Geometry.Sphere

And then we can call area and volume and they’ll give us the area and volume for a sphere.

The next time you find yourself writing a file that’s really big and has a lot of functions, try to see which functions serve some common purpose and then see if you can put them in their own module. You’ll be able to just import your module the next time you’re writing a program that requires some of the same functionality.