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Tutorial

This is a tutorial for how to build Roc applications. It covers the REPL, basic types (strings, lists, tags, and functions), syntax (when, if then else) and more!

Enjoy!

Getting started

Learn how to install roc on your machine here.

Strings and Numbers

Let’s start by getting acquainted with Roc’s Read Eval Print Loop, or REPL for short. Run this in a terminal:

$ roc repl

You should see this:

The rockin’ roc repl

Try typing this in and pressing enter:

>> "Hello, World!"
"Hello, World!" : Str

Congratulations! You've just written your first Roc code!

Specifically, you entered the expression "Hello, World!" into the REPL, and the REPL printed it back out. It also printed : Str, which is the expression's type. We'll talk about types later; for now, we'll ignore the : and whatever comes after it whenever the REPL prints them.

Let's try putting in a more complicated expression:

>> 1 + 1
2 : Num *

According to the Roc REPL, one plus one equals two. Checks out!

Roc will respect order of operations when using multiple arithmetic operators like + and -, but you can use parentheses to specify exactly how they should be grouped.

>> 1 + 2 * (3 - 4)
-1 : Num *

Let's try calling a function:

>> Str.concat "Hi " "there!"
"Hi there!" : Str

In this expression, we're calling the Str.concat function passing two arguments: the string "Hi " and the string "there!". The Str.concat function concatenates two strings together (that is, it puts one after the other) and returns the resulting combined string of "Hi there!".

Note that in Roc, we don't need parentheses or commas to call functions. We don't write Str.concat("Hi ", "there!") but rather Str.concat "Hi " "there!".

Just like in the arithmetic example above, we can use parentheses to specify how nested function calls should work. For example, we could write this:

>> Str.concat "Birds: " (Num.toStr 42)
"Birds: 42" : Str

This calls Num.toStr on the number 42, which converts it into the string "42", and then passes that string as the second argument to Str.concat. The parentheses are important here to specify how the function calls nest! Try removing them, and see what happens:

>> Str.concat "Birds: " Num.toStr 42
<error>

This error message says that we've given Str.concat too many arguments. Indeed we have! We've passed it three arguments: the string "Birds", the function Num.toStr, and the number 42. That's not what we wanted to do. Putting parentheses around the Num.toStr 42 call clarifies that we want it to be evaluated as its own expression, rather than being two arguments to Str.concat.

Both the Str.concat function and the Num.toStr function have a . in their names. In Str.concat, Str is the name of a module, and concat is the name of a function inside that module. Similarly, Num is a different module, and toStr is a function inside that module.

We'll get into more depth about modules later, but for now you can think of a module as a named collection of functions. It'll be awhile before we want to use them for more than that anyway!

Building an Application

Let's move out of the REPL and create our first Roc application.

Create a new file called Hello.roc and put this inside it:

app "hello"
    packages { pf: "examples/interactive/cli-platform" }
    imports [pf.Stdout]
    provides [main] to pf

main = Stdout.line "I'm a Roc application!"

NOTE: This assumes you've put Hello.roc in the root directory of the Roc source code. If you'd like to put it somewhere else, you'll need to replace "examples/interactive/cli-platform" with the path to the examples/interactive/cli-platform folder in that source code. In the future, Roc will have the tutorial built in, and this aside will no longer be necessary!

Try running this with:

$ roc Hello.roc

You should see this:

I'm a Roc application!

Congratulations - you've now written your first Roc application! We'll go over what the parts of this file above main do later, but first let's play around a bit. Try replacing the main line with this:

main = Stdout.line "There are \(total) animals."

birds = 3

iguanas = 2

total = Num.toStr (birds + iguanas)

Now if you run roc Hello.roc, you should see this:

There are 5 animals.

Hello.roc now has four definitions - or defs for short - namely, main, birds, iguanas, and total.

A definition names an expression.

The first def assigns the name main to the expression Stdout.line "I have \(numDefs) definitions.". The Stdout.line function takes a string and prints it as a line to [stdout] (the terminal's standard output device).
The next two defs assign the names birds and iguanas to the expressions 3 and 2.
The last def assigns the name total to the expression Num.toStr (birds + iguanas).

Once we have a def, we can use its name in other expressions. For example, the total expression refers to birds and iguanas.

We can also refer to defs inside strings using string interpolation. The string "There are \(total) animals." evaluates to the same thing as calling Str.concat "There are " (Str.concat total " animals.") directly.

You can name a def using any combination of letters and numbers, but they have to start with a letter. Note that definitions are constant; once we've assigned a name to an expression, we can't reassign it! We'd get an error if we wrote this:

birds = 3

birds = 2

Order of defs doesn't matter. We defined birds and iguanas before total (which uses both of them), but we defined main before total even though it uses total. If you like, you can change the order of these defs to anything you like, and everything will still work the same way!

This works because Roc expressions don't have side effects. We'll talk more about side effects later.

Functions and `if`

So far we've called functions like Num.toStr, Str.concat, and Stdout.line. Next let's try defining a function of our own.

main = Stdout.line "There are \(total) animals."

birds = 3

iguanas = 2

total = addAndStringify birds iguanas

addAndStringify = \num1, num2 ->
    Num.toStr (num1 + num2)

This new addAndStringify function we've defined takes two numbers, adds them, calls Num.toStr on the result, and returns that. The \num1, num2 -> syntax defines a function's arguments, and the expression after the -> is the body of the function. The expression at the end of the body (Num.toStr (num1 + num2) in this case) is returned automatically.

Let's modify the function to return an empty string if the numbers add to zero.

addAndStringify = \num1, num2 ->
    sum = num1 + num2

    if sum == 0 then
        ""
    else
        Num.toStr sum

We did two things here:

We introduced a local def named sum, and set it equal to num1 + num2. Because we defined sum inside addAndStringify, it will not be accessible outside that function.
We added an if / then / else conditional to return either "" or Num.toStr sum depending on whether sum == 0.

Of note, we couldn't have done total = num1 + num2 because that would be redefining total in the global scope, and defs can't be redefined. (However, we could use the name sum for a def in a different function, because then they'd be in completely different scopes and wouldn't affect each other.)

Also note that every if must be accompanied by both then and also else. Having an if without an else is an error, because in Roc, everything is an expression - which means it must evaluate to a value. If there were ever an if without an else, that would be an expression that might not evaluate to a value!

We can combine if and else to get else if, like so:

addAndStringify = \num1, num2 ->
    sum = num1 + num2

    if sum == 0 then
        ""
    else if sum < 0 then
        "negative"
    else
        Num.toStr sum

Note that else if is not a separate language keyword! It's just an if/else where the else branch contains another if/else. This is easier to see with different indentation:

addAndStringify = \num1, num2 ->
    sum = num1 + num2

    if sum == 0 then
        ""
    else
        if sum < 0 then
            "negative"
        else
            Num.toStr sum

This code is equivalent to writing else if sum < 0 then on one line, although the stylistic convention is to write else if on the same line.

Records

Currently our addAndStringify function takes two arguments. We can instead make it take one argument like so:

total = addAndStringify { birds: 5, iguanas: 7 }

addAndStringify = \counts ->
    Num.toStr (counts.birds + counts.iguanas)

The function now takes a record, which is a group of values that travel together. Records are not objects; they don't have methods or inheritance, they just store values.

We create the record when we write { birds: 5, iguanas: 7 }. This defines a record with two fields - namely, the birds field and the iguanas field - and then assigns the number 5 to the birds field and the number 7 to the iguanas field. Order doesn't matter with record fields; we could have also specified iguanas first and birds second, and Roc would consider it the exact same record.

When we write counts.birds, it accesses the birds field of the counts record, and when we write counts.iguanas it accesses the iguanas field. When we use == on records, it compares all the fields in both records with ==, and only returns true if all fields on both records return true for their == comparisons. If one record has more fields than the other, or if the types associated with a given field are different between one field and the other, the Roc compiler will give an error at build time.

Note: Some other languages have a concept of "identity equality" that's separate from the "structural equality" we just described. Roc does not have a concept of identity equality; this is the only way equality works!

The addAndStringify function will accept any record with at least the fields birds and iguanas, but it will also accept records with more fields. For example:

total = addAndStringify { birds: 5, iguanas: 7 }

totalWithNote = addAndStringify { birds: 4, iguanas: 3, note: "Whee!" }

addAndStringify = \counts ->
    Num.toStr (counts.birds + counts.iguanas)

This works because addAndStringify only uses counts.birds and counts.iguanas. If we were to use counts.note inside addAndStringify, then we would get an error because total is calling addAndStringify passing a record that doesn't have a note field.

Record fields can have any combination of types we want. totalWithNote uses a record that has a mixture of numbers and strings, but we can also have record fields with other types of values - including other records, or even functions!

{ birds: 4, nestedRecord: { someFunction: (\arg -> arg + 1), name: "Sam" } }

Record shorthands

Roc has a couple of shorthands you can use to express some record-related operations more concisely.

Instead of writing \record -> record.x we can write .x and it will evaluate to the same thing: a function that takes a record and returns its x field. You can do this with any field you want. For example:

returnFoo = .foo

returnFoo { foo: "hi!", bar: "blah" }
# returns "hi!"

Whenever we're setting a field to be a def that has the same name as the field - for example, { x: x } - we can shorten it to just writing the name of the def alone - for example, { x }. We can do this with as many fields as we like, e.g. { x: x, y: y } can alternately be written { x, y }, { x: x, y }, or { x, y: y }.

Record destructuring

We can use destructuring to avoid naming a record in a function argument, instead giving names to its individual fields:

addAndStringify = \{ birds, iguanas } ->
    Num.toStr (birds + iguanas)

Here, we've destructured the record to create a birds def that's assigned to its birds field, and an iguanas def that's assigned to its iguanas field. We can customize this if we like:

addAndStringify = \{ birds, iguanas: lizards } ->
    Num.toStr (birds + lizards)

In this version, we created a lizards def that's assigned to the record's iguanas field. (We could also do something similar with the birds field if we like.)

It's possible to destructure a record while still naming it. Here's an example where we use the as keyword to name the record counts while also destructuring its fields:

addAndStringify = \{ iguanas: lizards } as counts ->
    Num.toStr (counts.birds + lizards)

Notice that here we didn't bother destructuring the birds field. You can always omit fields from a destructure if you aren't going to use them!

Finally, destructuring can be used in defs too:

{ x, y } = { x: 5, y: 10 }

Building records from other records

So far we've only constructed records from scratch, by specifying all of their fields. We can also construct new records by using another record to use as a starting point, and then specifying only the fields we want to be different. For example, here are two ways to get the same record:

original = { birds: 5, iguanas: 7, zebras: 2, goats: 1 }

fromScratch = { birds: 4, iguanas: 3, zebras: 2, goats: 1 }
fromOriginal = { original & birds: 4, iguanas: 3 }

The fromScratch and fromOriginal records are equal, although they're assembled in different ways.

fromScratch was built using the same record syntax we've been using up to this point.
fromOriginal created a new record using the contents of original as defaults for fields that it didn't specify after the &.

Note that when we do this, the fields you're overriding must all be present on the original record, and their values must have the same type as the corresponding values in the original record.

Lists

Another thing we can do in Roc is to make a list of values. Here's an example:

names = ["Sam", "Lee", "Ari"]

This is a list with three elements in it, all strings. We can add a fourth element using List.append like so:

List.append names "Jess"

This returns a new list with "Jess" after "Ari", and doesn't modify the original list at all. All values in Roc (including lists, but also records, strings, numbers, and so on) are immutable, meaning whenever we want to "change" them, we want to instead pass them to a function which returns some variation of what was passed in.

List.map

A common way to transform one list into another is to use List.map. Here's an example of how to use it:

List.map [1, 2, 3] \num -> num * 2

This returns [2, 4, 6]. List.map takes two arguments:

An input list
A function that will be called on each element of that list

It then returns a list which it creates by calling the given function on each element in the input list. In this example, List.map calls the function \num -> num * 2 on each element in [1, 2, 3] to get a new list of [2, 4, 6].

We can also give List.map a named function, instead of an anonymous one:

For example, the Num.isOdd function returns True if it's given an odd number, and False otherwise. So Num.isOdd 5 returns True and Num.isOdd 2 returns False.

So calling List.map [1, 2, 3] Num.isOdd returns a new list of [True, False, True].

List element type compatibility

If we tried to give List.map a function that didn't work on the elements in the list, then we'd get an error at compile time. Here's a valid, and then an invalid example:

# working example
List.map [-1, 2, 3, -4] Num.isNegative
# returns [True, False, False, True]

# invalid example
List.map ["A", "B", "C"] Num.isNegative
# error: isNegative doesn't work on strings!

Because Num.isNegative works on numbers and not strings, calling List.map with Num.isNegative and a list of numbers works, but doing the same with a list of strings doesn't work.

This wouldn't work either:

List.map ["A", "B", "C", 1, 2, 3] Num.isNegative

In fact, this wouldn't work for a more fundamental reason: every element in a Roc list has to share the same type. For example, we can have a list of strings like ["Sam", "Lee", "Ari"], or a list of numbers like [1, 2, 3, 4, 5] but we can't have a list which mixes strings and numbers like ["Sam", 1, "Lee", 2, 3] - that would be a compile-time error.

Ensuring all elements in a list share a type eliminates entire categories of problems. For example, it means that whenever you use List.append to add elements to a list, as long as you don't have any compile-time errors, you won't get any runtime errors from calling List.map afterwards - no matter what you appended to the list! More generally, it's safe to assume that unless you run out of memory, List.map will run successfully unless you got a compile-time error about an incompatibility (like Num.negate on a list of strings).

Lists that hold elements of different types

We can use tags with payloads to make a list that contains a mixture of different types. For example:

List.map [StrElem "A", StrElem "b", NumElem 1, StrElem "c", NumElem -3] \elem ->
    when elem is
        NumElem num -> Num.isNegative num
        StrElem str -> Str.isCapitalized str

# returns [True, False, False, False, True]

Compare this with the example from earlier, which caused a compile-time error:

List.map ["A", "B", "C", 1, 2, 3] Num.isNegative

The version that uses tags works because we aren't trying to call Num.isNegative on each element. Instead, we're using a when to tell when we've got a string or a number, and then calling either Num.isNegative or Str.isCapitalized depending on which type we have.

We could take this as far as we like, adding more different tags (e.g. BoolElem True) and then adding more branches to the when to handle them appropriately.

Using tags as functions

Let's say I want to apply a tag to a bunch of elements in a list. For example:

List.map ["a", "b", "c"] \str -> Foo str

This is a perfectly reasonable way to write it, but I can also write it like this:

List.map ["a", "b", "c"] Foo

These two versions compile to the same thing. As a convenience, Roc lets you specify a tag name where a function is expected; when you do this, the compiler infers that you want a function which uses all of its arguments as the payload to the given tag.

`List.any` and `List.all`

There are several functions that work like List.map - they walk through each element of a list and do something with it. Another is List.any, which returns True if calling the given function on any element in the list returns True:

List.any [1, 2, 3] Num.isOdd
# returns True because 1 and 3 are odd

List.any [1, 2, 3] Num.isNegative
# returns False because none of these is negative

There's also List.all which only returns True if all the elements in the list pass the test:

List.all [1, 2, 3] Num.isOdd
# returns False because 2 is not odd

List.all [1, 2, 3] Num.isPositive
# returns True because all of these are positive

Removing elements from a list

You can also drop elements from a list. One way is List.dropAt - for example:

List.dropAt ["Sam", "Lee", "Ari"] 1
# drops the element at offset 1 ("Lee") and returns ["Sam", "Ari"]

Another way is to use List.keepIf, which passes each of the list's elements to the given function, and then keeps them only if that function returns True.

List.keepIf [1, 2, 3, 4, 5] Num.isEven
# returns [2, 4]

There's also List.dropIf, which does the reverse:

List.dropIf [1, 2, 3, 4, 5] Num.isEven
# returns [1, 3, 5]

Custom operations that walk over a list

You can make your own custom operations that walk over all the elements in a list, using List.walk. Let's look at an example and then walk (ha!) through it.

List.walk [1, 2, 3, 4, 5] { evens: [], odds: [] } \state, elem ->
    if Num.isEven elem then
        { state & evens: List.append state.evens elem }
    else
        { state & odds: List.append state.odds elem }

# returns { evens: [2, 4], odds: [1, 3, 5] }

List.walk walks through each element of the list, building up a state as it goes. At the end, it returns the final state - whatever it ended up being after processing the last element. The \state, elem -> function it takes as its last argument accepts both the current state as well as the current list element it's looking at, and then returns the new state based on whatever it decides to do with that element.

In this example, we walk over the list [1, 2, 3, 4, 5] and add each element to either the evens or odds field of a state record { evens, odds }. By the end, that record has a list of all the even numbers in the list as well as a list of all the odd numbers.

The state doesn't have to be a record; it can be anything you want. For example, if you made it a boolean, you could implement List.any using List.walk. You could also make the state be a list, and implement List.map, List.keepIf, or List.dropIf. There are a lot of things you can do with List.walk - it's very flexible!

It can be tricky to remember the argument order for List.walk at first. A helpful trick is that the arguments follow the same pattern as what we've seen with List.map, List.any, List.keepIf, and List.dropIf: the first argument is a list, and the last argument is a function. The difference here is that List.walk has one more argument than those other functions; the only place it could go while preserving that pattern is the middle!

That third argument specifies the initial state - what it's set to before the \state, elem -> function has been called on it even once. (If the list is empty, the \state, elem -> function will never get called and the initial state gets returned immediately.)

Note: Other languages give this operation different names, such as "fold," "reduce," "accumulate," "aggregate," "compress," and "inject."

Getting an individual element from a list

Another thing we can do with a list is to get an individual element out of it. List.get is a common way to do this; it takes a list and an index, and then returns the element at that index...if there is one. But what if there isn't?

For example, what do each of these return?

List.get ["a", "b", "c"] 1

List.get ["a", "b", "c"] 100

The answer is that the first one returns Ok "b" and the second one returns Err OutOfBounds. They both return tags! This is done so that the caller becomes responsible for handling the possibility that the index is outside the bounds of that particular list.

Here's how calling List.get can look in practice:

when List.get ["a", "b", "c"] index is
    Ok str -> "I got this string: \(str)"
    Err OutOfBounds -> "That index was out of bounds, sorry!"

There's also List.first, which always gets the first element, and List.last which always gets the last. They return Err ListWasEmpty instead of Err OutOfBounds, because the only way they can fail is if you pass them an empty list!

These functions demonstrate a common pattern in Roc: operations that can fail returning either an Ok tag with the answer (if successful), or an Err tag with another tag describing what went wrong (if unsuccessful). In fact, it's such a common pattern that there's a whole module called Result which deals with these two tags. Here are some examples of Result functions:

Result.withDefault (List.get ["a", "b", "c"] 100) ""
# returns "" because that's the default we said to use if List.get returned an Err

Result.isOk (List.get ["a", "b", "c"] 1)
# returns True because `List.get` returned an `Ok` tag. (The payload gets ignored.)

# Note: There's a Result.isErr function that works similarly.

The pipe operator

When you have nested function calls, sometimes it can be clearer to write them in a "pipelined" style using the |> operator. Here are three examples of writing the same expression; they all compile to exactly the same thing, but two of them use the |> operator to change how the calls look.

Result.withDefault (List.get ["a", "b", "c"] 1) ""

List.get ["a", "b", "c"] 1
    |> Result.withDefault ""

The |> operator takes the value that comes before the |> and passes it as the first argument to whatever comes after the |> - so in the example above, the |> takes List.get ["a", "b", "c"] 1 and passes that value as the first argument to Result.withDefault - making "" the second argument to Result.withDefault.

We can take this a step further like so:

["a", "b", "c"]
    |> List.get 1
    |> Result.withDefault ""

This is still equivalent to the first expression. Since |> is known as the "pipe operator," we can read this as "start with ["a", "b", "c"], then pipe it to List.get, then pipe it to Result.withDefault."

One reason the |> operator injects the value as the first argument is to make it work better with functions where argument order matters. For example, these two uses of List.append are equivalent:

List.append ["a", "b", "c"] "d"

["a", "b", "c"]
    |> List.append "d"

Another example is Num.div. All three of the following do the same thing, because a / b in Roc is syntax sugar for Num.div a b:

first / second

Num.div first second

first
    |> Num.div second

All operators in Roc are syntax sugar for normal function calls. See the "Operator Desugaring Table" at the end of this tutorial for a complete list of them.

Types

Sometimes you may want to document the type of a definition. For example, you might write:

# Takes a firstName string and a lastName string, and returns a string
fullName = \firstName, lastName ->
    "\(firstName) \(lastName)"

Comments can be valuable documentation, but they can also get out of date and become misleading. If someone changes this function and forgets to update the comment, it will no longer be accurate.

Type annotations

Here's another way to document this function's type, which doesn't have that problem:

fullName : Str, Str -> Str
fullName = \firstName, lastName ->
    "\(firstName) \(lastName)"

The fullName : line is a type annotation. It's a strictly optional piece of metadata we can add above a def to describe its type. Unlike a comment, the Roc compiler will check type annotations for accuracy. If the annotation ever doesn't fit with the implementation, we'll get a compile-time error.

The annotation fullName : Str, Str -> Str says "fullName is a function that takes two strings as arguments and returns a string."

We can give type annotations to any value, not just functions. For example:

firstName : Str
firstName = "Amy"

lastName : Str
lastName = "Lee"

These annotations say that both firstName and lastName have the type Str.

We can annotate records similarly. For example, we could move firstName and lastName into a record like so:

amy : { firstName : Str, lastName : Str }
amy = { firstName: "Amy", lastName: "Lee" }

jen : { firstName : Str, lastName : Str }
jen = { firstName: "Jen", lastName: "Majura" }

When we have a recurring type annotation like this, it can be nice to give it its own name. We do this like so:

Musician : { firstName : Str, lastName : Str }

amy : Musician
amy = { firstName: "Amy", lastName: "Lee" }

simone : Musician
simone = { firstName: "Simone", lastName: "Simons" }

Here, Musician is a type alias. A type alias is like a def, except it gives a name to a type instead of to a value. Just like how you can read name : Str as "name has the type Str," you can also read Musician : { firstName : Str, lastName : Str } as "Musician has the type { firstName : Str, lastName : Str }."

We can also give type annotations to tag unions:

colorFromStr : Str -> [Red, Green, Yellow]
colorFromStr = \string ->
    when string is
        "red" -> Red
        "green" -> Green
        _ -> Yellow

You can read the type [Red, Green, Yellow] as "a tag union of the tags Red, Green, and Yellow."

When we annotate a list type, we have to specify the type of its elements:

names : List Str
names = ["Amy", "Simone", "Tarja"]

You can read List Str as "a list of strings." Here, Str is a type parameter that tells us what type of List we're dealing with. List is a parameterized type, which means it's a type that requires a type parameter; there's no way to give something a type of List without a type parameter - you have to specify what type of list it is, such as List Str or List Bool or List { firstName : Str, lastName : Str }.

There are some functions that work on any list, regardless of its type parameter. For example, List.isEmpty has this type:

isEmpty : List * -> Bool

The * is a wildcard type - that is, a type that's compatible with any other type. List * is compatible with any type of List - so, List Str, List Bool, and so on. So you can call List.isEmpty ["I am a List Str"] as well as List.isEmpty [True], and they will both work fine.

The wildcard type also comes up with empty lists. Suppose we have one function that takes a List Str and another function that takes a List Bool. We might reasonably expect to be able to pass an empty list (that is, []) to either of these functions. And so we can! This is because a [] value has the type List * - that is, "a list with a wildcard type parameter," or "a list whose element type could be anything."

List.reverse works similarly to List.isEmpty, but with an important distinction. As with isEmpty, we can call List.reverse on any list, regardless of its type parameter. However, consider these calls:

strings : List Str
strings = List.reverse ["a", "b"]

bools : List Bool
bools = List.reverse [True, False]

In the strings example, we have List.reverse returning a List Str. In the bools example, it's returning a List Bool. So what's the type of List.reverse?

We saw that List.isEmpty has the type List * -> Bool, so we might think the type of List.reverse would be reverse : List * -> List *. However, remember that we also saw that the type of the empty list is List *? List * -> List * is actually the type of a function that always returns empty lists! That's not what we want.

What we want is something like one of these:

reverse : List elem -> List elem

reverse : List value -> List value

reverse : List a -> List a

Any of these will work, because elem, value, and a are all type variables. A type variable connects two or more types in the same annotation. So you can read List elem -> List elem as "takes a list and returns a list that has the same element type." Just like List.reverse does!

You can choose any name you like for a type variable, but it has to be lowercase. (You may have noticed all the types we've used until now are uppercase; that is no accident! Lowercase types are always type variables, so all other named types have to be uppercase.) All three of the above type annotations are equivalent; the only difference is that we chose different names (elem, value, and a) for their type variables.

You can tell some interesting things about functions based on the type parameters involved. For example, any function that returns List * definitely always returns an empty list. You don't need to look at the rest of the type annotation, or even the function's implementation! The only way to have a function that returns List * is if it returns an empty list.

Similarly, the only way to have a function whose type is a -> a is if the function's implementation returns its argument without modifying it in any way. This is known as the identity function.

Numeric types

Roc has different numeric types that each have different tradeoffs. They can all be broken down into two categories: fractions, and integers. In Roc we call these Frac and Int for short.

Integers

Roc's integer types have two important characteristics: their size and their signedness. Together, these two characteristics determine the range of numbers the integer type can represent.

For example, the Roc type U8 can represent the numbers 0 through 255, whereas the I16 type can represent the numbers -32768 through 32767. You can actually infer these ranges from their names (U8 and I16) alone!

The U in U8 indicates that it's unsigned, meaning that it can't have a minus sign, and therefore can't be negative. The fact that it's unsigned tells us immediately that its lowest value is zero. The 8 in U8 means it is 8 bits in size, which means it has room to represent 2⁸ (which is equal to 256) different numbers. Since one of those 256 different numbers is 0, we can look at U8 and know that it goes from 0 (since it's unsigned) to 255 (2⁸ - 1, since it's 8 bits).

If we change U8 to I8, making it a signed 8-bit integer, the range changes. Because it's still 8 bits, it still has room to represent 2⁸ (that is, 256) different numbers. However, now in addition to one of those 256 numbers being zero, about half of the rest will be negative, and the others positive. So instead of ranging from, say -255 to 255 (which, counting zero, would represent 511 different numbers; too many to fit in 8 bits!) an I8 value ranges from -128 to 127.

Notice that the negative extreme is -128 versus 127 (not 128) on the positive side. That's because of needing room for zero; the slot for zero is taken from the positive range because zero doesn't have a minus sign. So in general, you can find the lowest signed number by taking its total range (256 different numbers in the case of an 8-bit integer) and dividing it in half (half of 256 is 128, so -128 is I8's lowest number). To find the highest number, take the positive version of the lowest number (so, convert -128 to 128) and then subtract 1 to make room for zero (so, 128 becomes 127; I8 ranges from -128 to 127).

Following this pattern, the 16 in I16 means that it's a signed 16-bit integer. That tells us it has room to represent 2¹⁶ (which is equal to 65536) different numbers. Half of 65536 is 32768, so the lowest I16 would be -32768, and the highest would be 32767. Knowing that, we can also quickly tell that the lowest U16 would be zero (since it always is for unsigned integers), and the highest U16 would be 65535.

Choosing a size depends on your performance needs and the range of numbers you want to represent. Consider:

Larger integer sizes can represent a wider range of numbers. If you absolutely need to represent numbers in a certain range, make sure to pick an integer size that can hold them!
Smaller integer sizes take up less memory. These savings rarely matters in variables and function arguments, but the sizes of integers that you use in data structures can add up. This can also affect whether those data structures fit in cache lines, which can easily be a performance bottleneck.
Certain processors work faster on some numeric sizes than others. There isn't even a general rule like "larger numeric sizes run slower" (or the reverse, for that matter) that applies to all processors. In fact, if the CPU is taking too long to run numeric calculations, you may find a performance improvement by experimenting with numeric sizes that are larger than otherwise necessary. However, in practice, doing this typically degrades overall performance, so be careful to measure properly!

Here are the different fixed-size integer types that Roc supports:

Range	Type	Size
`-128` `127`	`I8`	1 Byte
`0` `255`	`U8`	1 Byte
`-32_768` `32_767`	`I16`	2 Bytes
`0` `65_535`	`U16`	2 Bytes
`-2_147_483_648` `2_147_483_647`	`I32`	4 Bytes
`0` (over 4 billion) `4_294_967_295`	`U32`	4 Bytes
`-9_223_372_036_854_775_808` `9_223_372_036_854_775_807`	`I64`	8 Bytes
`0` (over 18 quintillion) `18_446_744_073_709_551_615`	`U64`	8 Bytes
`-170_141_183_460_469_231_731_687_303_715_884_105_728` `170_141_183_460_469_231_731_687_303_715_884_105_727`	`I128`	16 Bytes
`0` (over 340 undecillion) `340_282_366_920_938_463_463_374_607_431_768_211_455`	`U128`	16 Bytes

Roc also has one variable-size integer type: Nat (short for "natural number"). The size of Nat is equal to the size of a memory address, which varies by system. For example, when compiling for a 64-bit system, Nat works the same way as U64. When compiling for a 32-bit system, it works the same way as U32. Most popular computing devices today are 64-bit, so Nat is usually the same as U64, but Web Assembly is typically 32-bit - so when running a Roc program built for Web Assembly, Nat will work like a U32 in that program.

A common use for Nat is to store the length of a collection like a List; there's a function List.len : List * -> Nat which returns the length of the given list. 64-bit systems can represent longer lists in memory than 32-bit systems can, which is why the length of a list is represented as a Nat.

If any operation would result in an integer that is either too big or too small to fit in that range (e.g. calling Int.maxI32 + 1, which adds 1 to the highest possible 32-bit integer), then the operation will overflow. When an overflow occurs, the program will crash.

As such, it's very important to design your integer operations not to exceed these bounds!

Fractions

Roc has three fractional types:

F32, a 32-bit floating-point number
F64, a 64-bit floating-point number
Dec, a 128-bit decimal fixed-point number

These are different from integers in that they can represent numbers with fractional components, such as 1.5 and -0.123.

Dec is the best default choice for representing base-10 decimal numbers like currency, because it is base-10 under the hood. In contrast, F64 and F32 are base-2 under the hood, which can lead to decimal precision loss even when doing addition and subtraction. For example, when using F64, running 0.1 + 0.2 returns 0.3000000000000000444089209850062616169452667236328125, whereas when using Dec, 0.1 + 0.2 returns 0.3.

F32 and F64 have direct hardware support on common processors today. There is no hardware support for fixed-point decimals, so under the hood, a Dec is an I128; operations on it perform base-10 fixed-point arithmetic with 18 decimal places of precision.

This means a Dec can represent whole numbers up to slightly over 170 quintillion, along with 18 decimal places. (To be precise, it can store numbers between -170_141_183_460_469_231_731.687303715884105728 and 170_141_183_460_469_231_731.687303715884105727.) Why 18 decimal places? It's the highest number of decimal places where you can still convert any U64 to a Dec without losing information.

While the fixed-point Dec has a fixed range, the floating-point F32 and F64 do not. Instead, outside of a certain range they start to lose precision instead of immediately overflowing the way integers and Dec do. F64 can represent between 15 and 17 significant digits before losing precision, whereas F32 can only represent between 6 and 9.

There are some use cases where F64 and F32 can be better choices than Dec despite their precision drawbacks. For example, in graphical applications they can be a better choice for representing coordinates because they take up less memory, various relevant calculations run faster, and decimal precision loss isn't as big a concern when dealing with screen coordinates as it is when dealing with something like currency.

Num, Int, and Frac

Some operations work on specific numeric types - such as I64 or Dec - but operations support multiple numeric types. For example, the Num.abs function works on any number, since you can take the absolute value of integers and fractions alike. Its type is:

abs : Num a -> Num a

This type says abs takes a number and then returns a number of the same type. That's because the Num type is compatible with both integers and fractions.

There's also an Int type which is only compatible with integers, and a Frac type which is only compatible with fractions. For example:

Num.xor : Int a, Int a -> Int a

Num.cos : Frac a -> Frac a

When you write a number literal in Roc, it has the type Num *. So you could call Num.xor 1 1 and also Num.cos 1 and have them all work as expected; the number literal 1 has the type Num *, which is compatible with the more constrained types Int and Frac. For the same reason, you can pass number literals to functions expecting even more constrained types, like I32 or F64.

Typed Number Literals

When writing a number literal in Roc you can specify the numeric type as a suffix of the literal. 1u8 specifies 1 as an unsigned 8-bit integer, 5i32 specifies 5 as a signed 32-bit integer, etc. The full list of possible suffixes includes: i8, u8, i16, u16, i32, u32, i64, u64, i128, u128, nat, f32, f64, dec

Hexadecimal Integer Literals

Integer literals can be written in hexadecimal form by prefixing with 0x followed by hexadecimal characters. 0xFE evaluates to decimal 254 The integer type can be specified as a suffix to the hexadecimal literal, so 0xC8u8 evaluates to decimal 200 as an unsigned 8-bit integer.

Binary Integer Literals

Integer literals can be written in binary form by prefixing with 0b followed by the 1's and 0's representing each bit. 0b0000_1000 evaluates to decimal 8 The integer type can be specified as a suffix to the binary literal, so 0b0100u8 evaluates to decimal 4 as an unsigned 8-bit integer.

Interface modules

[This part of the tutorial has not been written yet. Coming soon!]

Builtin modules

There are several modules that are built into the Roc compiler, which are imported automatically into every Roc module. They are:

Bool
Str
Num
List
Result
Dict
Set

You may have noticed that we already used the first five - for example, when we wrote Str.concat and Num.isEven, we were referencing functions stored in the Str and Num modules.

These modules are not ordinary .roc files that live on your filesystem. Rather, they are built directly into the Roc compiler. That's why they're called "builtins!"

Besides being built into the compiler, the builtin modules are different from other modules in that:

They are always imported. You never need to add them to imports.
All their types are imported unqualified automatically. So you never need to write Num.Nat, because it's as if the Num module was imported using imports [Num.{ Nat }] (and the same for all the other types in the Num module).

The app module header

Let's take a closer look at the part of Hello.roc above main:

app "hello"
    packages { pf: "examples/interactive/cli-platform" }
    imports [pf.Stdout]
    provides main to pf

This is known as a module header. Every .roc file is a module, and there are different types of modules. We know this particular one is an application module (or app module for short) because it begins with the app keyword.

The line app "hello" states that this module defines a Roc application, and that building this application should produce an executable named hello. This means when you run roc Hello.roc, the Roc compiler will build an executable named hello (or hello.exe on Windows) and run it. You can also build the executable without running it by running roc build Hello.roc.

The remaining lines all involve the platform this application is built on:

packages { pf: "examples/interactive/cli-platform" }
imports [pf.Stdout]
provides main to pf

The packages { pf: "examples/interactive/cli-platform" } part says two things:

We're going to be using a package (that is, a collection of modules) called "examples/interactive/cli-platform"
We're going to name that package pf so we can refer to it more concisely in the future.

The imports [pf.Stdout] line says that we want to import the Stdout module from the pf package, and make it available in the current module.

This import has a direct interaction with our definition of main. Let's look at that again:

main = Stdout.line "I'm a Roc application!"

Here, main is calling a function called Stdout.line. More specifically, it's calling a function named line which is exposed by a module named Stdout.

When we write imports [pf.Stdout], it specifies that the Stdout module comes from the pf package.

Since pf was the name we chose for the examples/interactive/cli-platform package (when we wrote packages { pf: "examples/interactive/cli-platform" }), this imports line tells the Roc compiler that when we call Stdout.line, it should look for that line function in the Stdout module of the examples/interactive/cli-platform package.

Building a Command-Line Interface (CLI)

Tasks

Tasks are technically not part of the Roc language, but they're very common in platforms. Let's use the CLI platform in examples/interactive/cli-platform as an example!

In the CLI platform, we have four operations we can do:

Write a string to the console
Read a string from user input
Write a string to a file
Read a string from a file

We'll use these four operations to learn about tasks.

First, let's do a basic "Hello World" using the tutorial app.

app "cli-tutorial"
    packages { pf: "examples/interactive/cli-platform" }
    imports [pf.Stdout]
    provides [main] to pf

main =
    Stdout.line "Hello, World!"

The Stdout.line function takes a Str and writes it to standard output. It has this type:

Stdout.line : Str -> Task {} *

A Task represents an effect - that is, an interaction with state outside your Roc program, such as the console's standard output, or a file.

When we set main to be a Task, the task will get run when we run our program. Here, we've set main to be a task that writes "Hello, World!" to stdout when it gets run, so that's what our program does!

Task has two type parameters: the type of value it produces when it finishes running, and any errors that might happen when running it. Stdout.line has the type Task {} * because it doesn't produce any values when it finishes (hence the {}) and there aren't any errors that can happen when it runs (hence the *).

In contrast, Stdin.line produces a Str when it finishes reading from standard input. That Str is reflected in its type:

Stdin.line : Task Str *

Let's change main to read a line from stdin, and then print it back out again:

app "cli-tutorial"
    packages { pf: "examples/interactive/cli-platform" }
    imports [pf.Stdout, pf.Stdin, pf.Task]
    provides [main] to pf

main =
    Task.await Stdin.line \text ->
        Stdout.line "You just entered: \(text)"

If you run this program, at first it won't do anything. It's waiting for you to type something in and press Enter! Once you do, it should print back out what you entered.

The Task.await function combines two tasks into one bigger Task which first runs one of the given tasks and then the other. In this case, it's combining a Stdin.line task with a Stdout.line task into one bigger Task, and then setting main to be that bigger task.

The type of Task.await is:

Task.await : Task a err, (a -> Task b err) -> Task b err

The second argument to Task.await is a "callback function" which runs after the first task completes. This callback function receives the output of that first task, and then returns the second task. This means the second task can make use of output from the first task, like we did in our \text -> … callback function here:

\text ->
    Stdout.line "You just entered: \(text)"

Notice that, just like before, we're still setting main to be a single Task. This is how we'll always do it! We'll keep building up bigger and bigger Tasks out of smaller tasks, and then setting main to be that one big Task.

For example, we can print a prompt before we pause to read from stdin, so it no longer looks like the program isn't doing anything when we start it up:

main =
    Task.await (Stdout.line "Type something press Enter:") \_ ->
        Task.await Stdin.line \text ->
            Stdout.line "You just entered: \(text)"

This works, but we can make it a little nicer to read. Let's change it to the following:

app "cli-tutorial"
    packages { pf: "examples/interactive/cli-platform" }
    imports [pf.Stdout, pf.Stdin, pf.Task.{ await }]
    provides [main] to pf

main =
    await (Stdout.line "Type something press Enter:") \_ ->
        await Stdin.line \text ->
            Stdout.line "You just entered: \(text)"

Here we've changed how we're importing the Task module. Before it was pf.Task and now it's pf.Task.{ await }. The difference is that we're importing await in an unqualified way, meaning now whenever we write await in this module, it will refer to Task.await - so we no longer need to write Task. every time we want to await.

It's most common in Roc to call functions from other modules in a qualified way (Task.await) rather than unqualified (await) like this, but it can be nice for a function with an uncommon name (like "await") which often gets called repeatedly across a small number of lines of code.

Speaking of calling await repeatedly, if we keep calling it more and more on this code, we'll end up doing a lot of indenting. If we'd rather not indent so much, we can rewrite main into this style which looks different but does the same thing:

main =
    _ <- await (Stdout.line "Type something press Enter:")
    text <- await Stdin.line

    Stdout.line "You just entered: \(text)"

This <- syntax is called backpassing. The <- is a way to define an anonymous function, just like \ … -> is.

Here, we're using backpassing to define two anonymous functions. Here's one of them:

text <-

Stdout.line "You just entered: \(text)"

It may not look like it, but this code is defining an anonymous function! You might remember it as the anonymous function we previously defined like this:

\text ->
    Stdout.line "You just entered: \(text)"

These two anonymous functions are the same, just defined using different syntax.

The reason the <- syntax is called backpassing is because it both defines a function and passes that function back as an argument to whatever comes after the <- (which in this case is await Stdin.line).

Let's look at these two complete expressions side by side. They are both saying exactly the same thing, with different syntax!

Here's the original:

await Stdin.line \text ->
    Stdout.line "You just entered: \(text)"

And here's the equivalent expression with backpassing syntax:

text <- await Stdin.line

Stdout.line "You just entered: \(text)"

Here's the other function we're defining with backpassing:

_ <-
text <- await Stdin.line

Stdout.line "You just entered: \(text)"

We could also have written that function this way if we preferred:

_ <-

await Stdin.line \text ->
    Stdout.line "You just entered: \(text)"

This is using a mix of a backpassing function _ <- and a normal function \text ->, which is totally allowed! Since backpassing is nothing more than syntax sugar for defining a function and passing back as an argument to another function, there's no reason we can't mix and match if we like.

That said, the typical style in which this main would be written in Roc is using backpassing for all the await calls, like we had above:

main =
    _ <- await (Stdout.line "Type something press Enter:")
    text <- await Stdin.line

    Stdout.line "You just entered: \(text)"

This way, it reads like a series of instructions:

First, run the Stdout.line task and await its completion. Ignore its output (hence the underscore in _ <-)
Next, run the Stdin.line task and await its completion. Name its output text.
Finally, run the Stdout.line task again, using the text value we got from the Stdin.line effect.

Some important things to note about backpassing and await:

await is not a language keyword in Roc! It's referring to the Task.await function, which we imported unqualified by writing Task.{ await } in our module imports. (That said, it is playing a similar role here to the await keyword in languages that have async/await keywords, even though in this case it's a function instead of a special keyword.)
Backpassing syntax does not need to be used with await in particular. It can be used with any function.
Roc's compiler treats functions defined with backpassing exactly the same way as functions defined the other way. The only difference between \text -> and text <- is how they look, so feel free to use whichever looks nicer to you!

Appendix: Advanced Concepts

Here are some concepts you likely won't need as a beginner, but may want to know about eventually. This is listed as an appendix rather than the main tutorial, to emphasize that it's totally fine to stop reading here and go build things!

Open Records and Closed Records

Let's say I write a function which takes a record with a firstName and lastName field, and puts them together with a space in between:

fullName = \user ->
    "\(user.firstName) \(user.lastName)"

I can pass this function a record that has more fields than just firstName and lastName, as long as it has at least both of those fields (and both of them are strings). So any of these calls would work:

fullName { firstName: "Sam", lastName: "Sample" }
fullName { firstName: "Sam", lastName: "Sample", email: "blah@example.com" }
fullName { age: 5, firstName: "Sam", things: 3, lastName: "Sample", role: Admin }

This user argument is an open record - that is, a description of a minimum set of fields on a record, and their types. When a function takes an open record as an argument, it's okay if you pass it a record with more fields than just the ones specified.

In contrast, a closed record is one that requires an exact set of fields (and their types), with no additional fields accepted.

If we add a type annotation to this fullName function, we can choose to have it accept either an open record or a closed record:

# Closed record
fullName : { firstName : Str, lastName : Str } -> Str
fullName = \user ->
    "\(user.firstName) \(user.lastName)"

# Open record (because of the `*`)
fullName : { firstName : Str, lastName : Str }* -> Str
fullName = \user ->
    "\(user.firstName) \(user.lastName)"

The * in the type { firstName : Str, lastName : Str }* is what makes it an open record type. This * is the wildcard type we saw earlier with empty lists. (An empty list has the type List *, in contrast to something like List Str which is a list of strings.)

This is because record types can optionally end in a type variable. Just like how we can have List * or List a -> List a, we can also have { first : Str, last : Str }* or { first : Str, last : Str }a -> { first: Str, last : Str }a. The differences are that in List a, the type variable is required and appears with a space after List; in a record, the type variable is optional, and appears (with no space) immediately after }.

If the type variable in a record type is a * (such as in { first : Str, last : Str }*), then it's an open record. If the type variable is missing, then it's a closed record. You can also specify a closed record by putting a {} as the type variable (so for example, { email : Str }{} is another way to write { email : Str }). In practice, closed records are basically always written without the {} on the end, but later on we'll see a situation where putting types other than * in that spot can be useful.

Constrained Records

The type variable can also be a named type variable, like so:

addHttps : { url : Str }a -> { url : Str }a
addHttps = \record ->
    { record & url: "https://\(record.url)" }

This function uses constrained records in its type. The annotation is saying:

This function takes a record which has at least a url field, and possibly others
That url field has the type Str
It returns a record of exactly the same type as the one it was given

So if we give this function a record with five fields, it will return a record with those same five fields. The only requirement is that one of those fields must be url : Str.

In practice, constrained records appear in type annotations much less often than open or closed records do.

Here's when you can typically expect to encounter these three flavors of type variables in records:

Open records are what the compiler infers when you use a record as an argument, or when destructuring it (for example, { x, y } =).
Closed records are what the compiler infers when you create a new record (for example, { x: 5, y: 6 })
Constrained records are what the compiler infers when you do a record update (for example, { user & email: newEmail })

Of note, you can pass a closed record to a function that accepts a smaller open record, but not the reverse. So a function { a : Str, b : Bool }* -> Str can accept an { a : Str, b : Bool, c : Bool } record, but a function { a : Str, b : Bool, c : Bool } -> Str would not accept an { a : Str, b : Bool }* record.

This is because if a function accepts { a : Str, b : Bool, c : Bool }, that means it might access the c field of that record. So if you passed it a record that was not guaranteed to have all three of those fields present (such as an { a : Str, b : Bool }* record, which only guarantees that the fields a and b are present), the function might try to access a c field at runtime that did not exist!

Type Variables in Record Annotations

You can add type annotations to make record types less flexible than what the compiler infers, but not more flexible. For example, you can use an annotation to tell the compiler to treat a record as closed when it would be inferred as open (or constrained), but you can't use an annotation to make a record open when it would be inferred as closed.

If you like, you can always annotate your functions as accepting open records. However, in practice this may not always be the nicest choice. For example, let's say you have a User type alias, like so:

User : {
    email : Str,
    firstName : Str,
    lastName : Str,
}

This defines User to be a closed record, which in practice is the most common way records named User tend to be defined.

If you want to have a function take a User, you might write its type like so:

isValid : User -> Bool

If you want to have a function return a User, you might write its type like so:

userFromEmail : Str -> User

A function which takes a user and returns a user might look like this:

capitalizeNames : User -> User

This is a perfectly reasonable way to write all of these functions. However, I might decide that I really want the isValid function to take an open record - that is, a record with at least the fields of this User record, but possibly others as well.

Since open records have a type variable (like * in { email : Str }* or a in { email : Str }a -> { email : Str }a), in order to do this I'd need to add a type variable to the User type alias:

User a : {
    email : Str,
    firstName : Str,
    lastName : Str,
}a

Notice that the a type variable appears not only in User a but also in }a at the end of the record type!

Using User a type alias, I can still write the same three functions, but now their types need to look different. This is what the first one would look like:

isValid : User * -> Bool

Here, the User * type alias substitutes * for the type variable a in the type alias, which takes it from { email : Str, … }a to { email : Str, … }*. Now I can pass it any record that has at least the fields in User, and possibly others as well, which was my goal.

userFromEmail : Str -> User {}

Here, the User {} type alias substitutes {} for the type variable a in the type alias, which takes it from { email : Str, … }a to { email : Str, … }{}. As noted earlier, this is another way to specify a closed record: putting a {} after it, in the same place that you'd find a * in an open record.

Aside: This works because you can form new record types by replacing the type variable with other record types. For example, { a : Str, b : Str } can also be written { a : Str }{ b : Str }. You can chain these more than once, e.g. { a : Str }{ b : Str }{ c : Str, d : Str }. This is more useful when used with type annotations; for example, { a : Str, b : Str }User describes a closed record consisting of all the fields in the closed record User, plus a : Str and b : Str.

This function still returns the same record as it always did, it just needs to be annotated as User {} now instead of just User, because the User type alias has a variable in it that must be specified.

The third function might need to use a named type variable:

capitalizeNames : User a -> User a

If this function does a record update on the given user, and returns that - for example, if its definition were capitalizeNames = \user -> { user & email: "blah" } - then it needs to use the same named type variable for both the argument and return value.

However, if returns a new User that it created from scratch, then its type could instead be:

capitalizeNames : User * -> User {}

This says that it takes a record with at least the fields specified in the User type alias, and possibly others...and then returns a record with exactly the fields specified in the User type alias, and no others.

These three examples illustrate why it's relatively uncommon to use open records for type aliases: it makes a lot of types need to incorporate a type variable that otherwise they could omit, all so that isValid can be given something that has not only the fields User has, but some others as well. (In the case of a User record in particular, it may be that the extra fields were included due to a mistake rather than on purpose, and accepting an open record could prevent the compiler from raising an error that would have revealed the mistake.)

That said, this is a useful technique to know about if you want to (for example) make a record type that accumulates more and more fields as it progresses through a series of operations.

Open and Closed Tag Unions

Just like how Roc has open records and closed records, it also has open and closed tag unions.

The open tag union (or open union for short) [Foo Str, Bar Bool]* represents a tag that might be Foo Str and might be Bar Bool, but might also be some other tag whose type isn't known at compile time.

Because an open union represents possibilities that are impossible to know ahead of time, any when I use on a [Foo Str, Bar Bool]* value must include a catch-all _ -> branch. Otherwise, if one of those unknown tags were to come up, the when would not know what to do with it! For example:

example : [Foo Str, Bar Bool]* -> Bool
example = \tag ->
    when tag is
        Foo str -> Str.isEmpty str
        Bar bool -> bool
        _ -> False

In contrast, a closed tag union (or closed union) like [Foo Str, Bar Bool] (without the *) represents an exhaustive set of possible tags. If I use a when on one of these, I can match on Foo only and then on Bar only, with no need for a catch-all branch. For example:

example : [Foo Str, Bar Bool] -> Bool
example = \tag ->
    when tag is
        Foo str -> Str.isEmpty str
        Bar bool -> bool

If we were to remove the type annotations from the previous two code examples, Roc would infer the same types for them anyway.

It would infer tag : [Foo Str, Bar Bool] for the latter example because the when tag is expression only includes a Foo Str branch and a Bar Bool branch, and nothing else. Since the when doesn't handle any other possibilities, these two tags must be the only possible ones the tag argument could be.

It would infer tag : [Foo Str, Bar Bool]* for the former example because the when tag is expression includes a Foo Str branch and a Bar Bool branch - meaning we know about at least those two specific possibilities - but also a _ -> branch, indicating that there may be other tags we don't know about. Since the when is flexible enough to handle all possible tags, tag gets inferred as an open union.

Putting these together, whether a tag union is inferred to be open or closed depends on which possibilities the implementation actually handles.

Aside: As with open and closed records, we can use type annotations to make tag union types less flexible than what would be inferred. If we added a _ -> branch to the second example above, the compiler would still accept example : [Foo Str, Bar Bool] -> Bool as the type annotation, even though the catch-all branch would permit the more flexible example : [Foo Str, Bar Bool]* -> Bool annotation instead.

Combining Open Unions

When we make a new record, it's inferred to be a closed record. For example, in foo { a: "hi" }, the type of { a: "hi" } is inferred to be { a : Str }. In contrast, when we make a new tag, it's inferred to be an open union. So in foo (Bar "hi"), the type of Bar "hi" is inferred to be [Bar Str]*.

This is because open unions can accumulate additional tags based on how they're used in the program, whereas closed unions cannot. For example, let's look at this conditional:

if x > 5 then
    "foo"
else
    7

This will be a type mismatch because the two branches have incompatible types. Strings and numbers are not type-compatible! Now let's look at another example:

if x > 5 then
    Ok "foo"
else
    Err "bar"

This shouldn't be a type mismatch, because we can see that the two branches are compatible; they are both tags that could easily coexist in the same tag union. But if the compiler inferred the type of Ok "foo" to be the closed union [Ok Str], and likewise for Err "bar" and [Err Str], then this would have to be a type mismatch - because those two closed unions are incompatible.

Instead, the compiler infers Ok "foo" to be the open union [Ok Str]*, and Err "bar" to be the open union [Err Str]*. Then, when using them together in this conditional, the inferred type of the conditional becomes [Ok Str, Err Str]* - that is, the combination of the unions in each of its branches. (Branches in a when work the same way with open unions.)

Earlier we saw how a function which accepts an open union must account for more possibilities, by including catch-all _ -> patterns in its when expressions. So accepting an open union means you have more requirements. In contrast, when you already have a value which is an open union, you have fewer requirements. A value which is an open union (like Ok "foo", which has the type [Ok Str]*) can be provided to anything that's expecting a tag union (no matter whether it's open or closed), as long as the expected tag union includes at least the tags in the open union you're providing.

So if I have an [Ok Str]* value, I can pass it to functions with any of these types (among others):

[Ok Str]* -> Bool
[Ok Str] -> Bool
[Ok Str, Err Bool]* -> Bool
[Ok Str, Err Bool] -> Bool
[Ok Str, Err Bool, Whatever]* -> Bool
[Ok Str, Err Bool, Whatever] -> Bool
Result Str Bool -> Bool
[Err Bool, Whatever]* -> Bool

That last one works because a function accepting an open union can accept any unrecognized tag, including Ok Str - even though it is not mentioned as one of the tags in [Err Bool, Whatever]*! Remember, when a function accepts an open tag union, any when branches on that union must include a catch-all _ -> branch, which is the branch that will end up handling the Ok Str value we pass in.

However, I could not pass an [Ok Str]* to a function with a closed tag union argument that did not mention Ok Str as one of its tags. So if I tried to pass [Ok Str]* to a function with the type [Err Bool, Whatever] -> Str, I would get a type mismatch - because a when in that function could be handling the Err Bool possibility and the Whatever possibility, and since it would not necessarily have a catch-all _ -> branch, it might not know what to do with an Ok Str if it received one.

Note: It wouldn't be accurate to say that a function which accepts an open union handles "all possible tags." For example, if I have a function [Ok Str]* -> Bool and I pass it Ok 5, that will still be a type mismatch. If you think about it, a when in that function might have the branch Ok str -> which assumes there's a string inside that Ok, and if Ok 5 type-checked, then that assumption would be false and things would break!

So [Ok Str]* is more restrictive than []*. It's basically saying "this may or may not be an Ok tag, but if it is an Ok tag, then it's guaranteed to have a payload of exactly Str."

In summary, here's a way to think about the difference between open unions in a value you have, compared to a value you're accepting:

If you have a closed union, that means it has all the tags it ever will, and can't accumulate more.
If you have an open union, that means it can accumulate more tags through conditional branches.
If you accept a closed union, that means you only have to handle the possibilities listed in the union.
If you accept an open union, that means you have to handle the possibility that it has a tag you can't know about.

Type Variables in Tag Unions

Earlier we saw these two examples, one with an open tag union and the other with a closed one:

example : [Foo Str, Bar Bool]* -> Bool
example = \tag ->
    when tag is
        Foo str -> Str.isEmpty str
        Bar bool -> bool
        _ -> False

example : [Foo Str, Bar Bool] -> Bool
example = \tag ->
    when tag is
        Foo str -> Str.isEmpty str
        Bar bool -> bool

Similarly to how there are open records with a *, closed records with nothing, and constrained records with a named type variable, we can also have constrained tag unions with a named type variable. Here's an example:

example : [Foo Str, Bar Bool]a -> [Foo Str, Bar Bool]a
example = \tag ->
    when tag is
        Foo str -> Bar (Str.isEmpty str)
        Bar _ -> Bar False
        other -> other

This type says that the example function will take either a Foo Str tag, or a Bar Bool tag, or possibly another tag we don't know about at compile time - and it also says that the function's return type is the same as the type of its argument.

So if we give this function a [Foo Str, Bar Bool, Baz (List Str)] argument, then it will be guaranteed to return a [Foo Str, Bar Bool, Baz (List Str)] value. This is more constrained than a function that returned [Foo Str, Bar Bool]* because that would say it could return any other tag (in addition to the Foo Str and Bar Bool we already know about).

If we removed the type annotation from example above, Roc's compiler would infer the same type anyway. This may be surprising if you look closely at the body of the function, because:

The return type includes Foo Str, but no branch explicitly returns Foo. Couldn't the return type be [Bar Bool]a instead?
The argument type includes Bar Bool even though we never look at Bar's payload. Couldn't the argument type be inferred to be Bar * instead of Bar Bool, since we never look at it?

The reason it has this type is the other -> other branch. Take a look at that branch, and ask this question: "What is the type of other?" There has to be exactly one answer! It can't be the case that other has one type before the -> and another type after it; whenever you see a named value in Roc, it is guaranteed to have the same type everywhere it appears in that scope.

For this reason, any time you see a function that only runs a when on its only argument, and that when includes a branch like x -> x or other -> other, the function's argument type and return type must necessarily be equivalent.

Note: Just like with records, you can also replace the type variable in tag union types with a concrete type. For example, [Foo Str][Bar Bool][Baz (List Str)] is equivalent to [Foo Str, Bar Bool, Baz (List Str)].

Also just like with records, you can use this to compose tag union type aliases. For example, you can write NetworkError : [Timeout, Disconnected] and then Problem : [InvalidInput, UnknownFormat]NetworkError

Phantom Types