Type checking

Luau supports a gradual type system through the use of type annotations and type inference.

Type inference modes

There are three modes currently available. They must be annotated on the top few lines among the comments.

--!nocheck,
--!nonstrict (default), and
--!strict

nocheck mode will simply not start the type inference engine whatsoever.

As for the other two, they are largely similar but with one important difference: in nonstrict mode, we infer any for most of the types if we couldn’t figure it out early enough. This means that given this snippet:

local foo = 1

We can infer foo to be of type number, whereas the foo in the snippet below is inferred any:

local foo
foo = 1

However, given the second snippet in strict mode, the type checker would be able to infer number for foo.

Structural type system

Luau’s type system is structural by default, which is to say that we inspect the shape of two tables to see if they are similar enough. This was the obvious choice because Lua 5.1 is inherently structural.

type A = {x: number, y: number, z: number?}
type B = {x: number, y: number, z: number}

local a1: A = {x = 1, y = 2}        -- ok
local b1: B = {x = 1, y = 2, z = 3} -- ok

local a2: A = b1 -- ok
local b2: B = a1 -- not ok

Builtin types

The Luau VM supports 10 primitive types: nil, string, number, boolean, table, function, thread, userdata, vector, and buffer. Of these, table and function are not represented by name, but have their dedicated syntax as covered in this syntax document, userdata is represented by concrete types, while vector is not representable by name at all; other types can be specified by their name.

The type checker also provides the builtin types unknown, never, and any.

local s = "foo"
local n = 1
local b = true
local t = coroutine.running()

local a: any = 1
print(a.x) -- Type checker believes this to be ok, but crashes at runtime.

There’s a special case where we intentionally avoid inferring nil. It’s a good thing because it’s never useful for a local variable to always be nil, thereby permitting you to assign things to it for Luau to infer that instead.

local a
local b = nil

`unknown` type

unknown is also said to be the top type, that is it’s a union of all types.

local a: unknown = "hello world!"
local b: unknown = 5
local c: unknown = function() return 5 end

Unlike any, unknown will not allow itself to be used as a different type!

local function unknown(): unknown
    return if math.random() > 0.5 then "hello world!" else 5
end

local a: string = unknown() -- not ok
local b: number = unknown() -- not ok
local c: string | number = unknown() -- not ok

In order to turn a variable of type unknown into a different type, you must apply type refinements on that variable.

local x = unknown()
if typeof(x) == "number" then
    -- x : number
end

`never` type

never is also said to be the bottom type, meaning there doesn’t exist a value that inhabits the type never. In fact, it is the dual of unknown. never is useful in many scenarios, and one such use case is when type refinements proves it impossible:

local x = unknown()
if typeof(x) == "number" and typeof(x) == "string" then
    -- x : never
end

`any` type

any is just like unknown, except that it allows itself to be used as an arbitrary type without further checks or annotations. Essentially, it’s an opt-out from the type system entirely.

local x: any = 5
local y: string = x -- no type errors here!

Function types

Let’s start with something simple.

local function f(x) return x end

local a: number = f(1)     -- ok
local b: string = f("foo") -- ok
local c: string = f(true)  -- not ok

In strict mode, the inferred type of this function f is <A>(A) -> A (take a look at generics), whereas in nonstrict we infer (any) -> any. We know this is true because f can take anything and then return that. If we used x with another concrete type, then we would end up inferring that.

Similarly, we can infer the types of the parameters with ease. By passing a parameter into anything that also has a type, we are saying “this and that has the same type.”

local function greetingsHelper(name: string)
    return "Hello, " .. name
end

local function greetings(name)
    return greetingsHelper(name)
end

print(greetings("Alexander"))          -- ok
print(greetings({name = "Alexander"})) -- not ok

Table types

From the type checker perspective, each table can be in one of three states. They are: unsealed table, sealed table, and generic table. This is intended to represent how the table’s type is allowed to change.

Unsealed tables

An unsealed table is a table which supports adding new properties, which updates the tables type. Unsealed tables are created using table literals. This is one way to accumulate knowledge of the shape of this table.

local t = {x = 1} -- {x: number}
t.y = 2           -- {x: number, y: number}
t.z = 3           -- {x: number, y: number, z: number}

However, if this local were written as local t: { x: number } = { x = 1 }, it ends up sealing the table, so the two assignments henceforth will not be ok.

Furthermore, once we exit the scope where this unsealed table was created in, we seal it.

local function vec2(x, y)
    local t = {}
    t.x = x
    t.y = y
    return t
end

local v2 = vec2(1, 2)
v2.z = 3 -- not ok

Unsealed tables are exact in that any property of the table must be named by the type. Since Luau treats missing properties as having value nil, this means that we can treat an unsealed table which does not mention a property as if it mentioned the property, as long as that property is optional.

local t = {x = 1}
local u : { x : number, y : number? } = t -- ok because y is optional
local v : { x : number, z : number } = t  -- not ok because z is not optional

Sealed tables

A sealed table is a table that is now locked down. This occurs when the table type is spelled out explicitly via a type annotation, or if it is returned from a function.

local t : { x: number } = {x = 1}
t.y = 2 -- not ok

Sealed tables are inexact in that the table may have properties which are not mentioned in the type. As a result, sealed tables support width subtyping, which allows a table with more properties to be used as a table with fewer properties.

type Point1D = { x : number }
type Point2D = { x : number, y : number }
local p : Point2D = { x = 5, y = 37 }
local q : Point1D = p -- ok because Point2D has more properties than Point1D

Generic tables

This typically occurs when the symbol does not have any annotated types or were not inferred anything concrete. In this case, when you index on a parameter, you’re requesting that there is a table with a matching interface.

local function f(t)
    return t.x + t.y
           --^   --^ {x: _, y: _}
end

f({x = 1, y = 2})        -- ok
f({x = 1, y = 2, z = 3}) -- ok
f({x = 1})               -- not ok

Table indexers

These are particularly useful for when your table is used similarly to an array.

local t = {"Hello", "world!"} -- {[number]: string}
print(table.concat(t, ", "))

Luau supports a concise declaration for array-like tables, {T} (for example, {string} is equivalent to {[number]: string}); the more explicit definition of an indexer is still useful when the key isn’t a number, or when the table has other fields like { [number]: string, n: number }.

Generics

The type inference engine was built from the ground up to recognize generics. A generic is simply a type parameter in which another type could be slotted in. It’s extremely useful because it allows the type inference engine to remember what the type actually is, unlike any.

type Pair<T> = {first: T, second: T}

local strings: Pair<string> = {first="Hello", second="World"}
local numbers: Pair<number> = {first=1, second=2}

Generic functions

As well as generic type aliases like Pair<T>, Luau supports generic functions. These are functions that, as well as their regular data parameters, take type parameters. For example, a function which reverses an array is:

function reverse(a)
  local result = {}
  for i = #a, 1, -1 do
    table.insert(result, a[i])
  end
  return result
end

The type of this function is that it can reverse an array, and return an array of the same type. Luau can infer this type, but if you want to be explicit, you can declare the type parameter T, for example:

function reverse<T>(a: {T}): {T}
  local result: {T} = {}
  for i = #a, 1, -1 do
    table.insert(result, a[i])
  end
  return result
end

When a generic function is called, Luau infers type arguments, for example

local x: {number} = reverse({1, 2, 3})
local y: {string} = reverse({"a", "b", "c"})

Generic types are used for built-in functions as well as user functions, for example the type of two-argument table.insert is:

<T>({T}, T) -> ()

Union types

A union type represents one of the types in this set. If you try to pass a union onto another thing that expects a more specific type, it will fail.

For example, what if this string | number was passed into something that expects number, but the passed in value was actually a string?

local stringOrNumber: string | number = "foo"

local onlyString: string = stringOrNumber -- not ok
local onlyNumber: number = stringOrNumber -- not ok

Note: it’s impossible to be able to call a function if there are two or more function types in this union.

Intersection types

An intersection type represents all of the types in this set. It’s useful for two main things: to join multiple tables together, or to specify overloadable functions.

type XCoord = {x: number}
type YCoord = {y: number}
type ZCoord = {z: number}

type Vector2 = XCoord & YCoord
type Vector3 = XCoord & YCoord & ZCoord

local vec2: Vector2 = {x = 1, y = 2}        -- ok
local vec3: Vector3 = {x = 1, y = 2, z = 3} -- ok

type SimpleOverloadedFunction = ((string) -> number) & ((number) -> string)

local f: SimpleOverloadedFunction

local r1: number = f("foo") -- ok
local r2: number = f(12345) -- not ok
local r3: string = f("foo") -- not ok
local r4: string = f(12345) -- ok

Note: it’s impossible to create an intersection type of some primitive types, e.g. string & number, or string & boolean, or other variations thereof.

Note: Luau still does not support user-defined overloaded functions. Some of Roblox and Lua 5.1 functions have different function signature, so inherently requires overloaded functions.

Singleton types (aka literal types)

Luau’s type system also supports singleton types, which means it’s a type that represents one single value at runtime. At this time, both string and booleans are representable in types.

We do not currently support numbers as types. For now, this is intentional.

local foo: "Foo" = "Foo" -- ok
local bar: "Bar" = foo   -- not ok
local baz: string = foo  -- ok

local t: true = true -- ok
local f: false = false -- ok

This happens all the time, especially through type refinements and is also incredibly useful when you want to enforce program invariants in the type system! See tagged unions for more information.

Variadic types

Luau permits assigning a type to the ... variadic symbol like any other parameter:

local function f(...: number)
end

f(1, 2, 3)     -- ok
f(1, "string") -- not ok

f accepts any number of number values.

In type annotations, this is written as ...T:

type F = (...number) -> ...string

Type packs

Multiple function return values as well as the function variadic parameter use a type pack to represent a list of types.

When a type alias is defined, generic type pack parameters can be used after the type parameters:

type Signal<T, U...> = { f: (T, U...) -> (), data: T }

Keep in mind that ...T is a variadic type pack (many elements of the same type T), while U... is a generic type pack that can contain zero or more types and they don’t have to be the same.

It is also possible for a generic function to reference a generic type pack from the generics list:

local function call<T, U...>(s: Signal<T, U...>, ...: U...)
    s.f(s.data, ...)
end

Generic types with type packs can be instantiated by providing a type pack:

local signal: Signal<string, (number, number, boolean)> = --

call(signal, 1, 2, false)

There are also other ways to instantiate types with generic type pack parameters:

type A<T, U...> = (T) -> U...

type B = A<number, ...string> -- with a variadic type pack
type C<S...> = A<number, S...> -- with a generic type pack
type D = A<number, ()> -- with an empty type pack

Trailing type pack argument can also be provided without parentheses by specifying variadic type arguments:

type List<Head, Rest...> = (Head, Rest...) -> ()

type B = List<number> -- Rest... is ()
type C = List<number, string, boolean> -- Rest is (string, boolean)

type Returns<T...> = () -> T...

-- When there are no type parameters, the list can be left empty
type D = Returns<> -- T... is ()

Type pack parameters are not limited to a single one, as many as required can be specified:

type Callback<Args..., Rets...> = { f: (Args...) -> Rets... }

type A = Callback<(number, string), ...number>

Adding types for faux object oriented programs

One common pattern we see with existing Lua/Luau code is the following OO code. While Luau is capable of inferring a decent chunk of this code, it cannot pin down on the types of self when it spans multiple methods.

local Account = {}
Account.__index = Account

function Account.new(name, balance)
    local self = {}
    self.name = name
    self.balance = balance

    return setmetatable(self, Account)
end

-- The `self` type is different from the type returned by `Account.new`
function Account:deposit(credit)
    self.balance += credit
end

-- The `self` type is different from the type returned by `Account.new`
function Account:withdraw(debit)
    self.balance -= debit
end

local account = Account.new("Alexander", 500)

For example, the type of Account.new is <a, b>(name: a, balance: b) -> { ..., name: a, balance: b, ... } (snipping out the metatable). For better or worse, this means you are allowed to call Account.new(5, "hello") as well as Account.new({}, {}). In this case, this is quite unfortunate, so your first attempt may be to add type annotations to the parameters name and balance.

There’s the next problem: the type of self is not shared across methods of Account, this is because you are allowed to explicitly opt for a different value to pass as self by writing account.deposit(another_account, 50). As a result, the type of Account:deposit is <a, b>(self: { balance: a }, credit: b) -> (). Consequently, Luau cannot infer the result of the + operation from a and b, so a type error is reported.

We can see there’s a lot of problems happening here. This is a case where you will have to guide Luau, but using the power of top-down type inference you only need to do this in exactly one place!

type AccountImpl = {
    __index: AccountImpl,
    new: (name: string, balance: number) -> Account,
    deposit: (self: Account, credit: number) -> (),
    withdraw: (self: Account, debit: number) -> (),
}

type Account = typeof(setmetatable({} :: { name: string, balance: number }, {} :: AccountImpl))

-- Only these two annotations are necessary
local Account: AccountImpl = {} :: AccountImpl
Account.__index = Account

-- Using the knowledge of `Account`, we can take in information of the `new` type from `AccountImpl`, so:
-- Account.new :: (name: string, balance: number) -> Account
function Account.new(name, balance)
    local self = {}
    self.name = name
    self.balance = balance

    return setmetatable(self, Account)
end

-- Ditto:
-- Account:deposit :: (self: Account, credit: number) -> ()
function Account:deposit(credit)
    self.balance += credit
end

-- Ditto:
-- Account:withdraw :: (self: Account, debit: number) -> ()
function Account:withdraw(debit)
    self.balance -= debit
end

local account = Account.new("Alexander", 500)

Tagged unions

Tagged unions are just union types! In particular, they’re union types of tables where they have at least some common properties but the structure of the tables are different enough. Here’s one example:

type Ok<T> = { type: "ok", value: T }
type Err<E> = { type: "err", error: E }
type Result<T, E> = Ok<T> | Err<E>

This Result<T, E> type can be discriminated by using type refinements on the property type, like so:

if result.type == "ok" then
    -- result is known to be Ok<T>
    -- and attempting to index for error here will fail
    print(result.value)
elseif result.type == "err" then
    -- result is known to be Err<E>
    -- and attempting to index for value here will fail
    print(result.error)
end

Which works out because value: T exists only when type is in actual fact "ok", and error: E exists only when type is in actual fact "err".

When we check the type of any lvalue (a global, a local, or a property), what we’re doing is we’re refining the type, hence “type refinement.” The support for this is arbitrarily complex, so go at it!

Here are all the ways you can refine:

Truthy test: if x then will refine x to be truthy.
Type guards: if type(x) == "number" then will refine x to be number.
Equality: if x == "hello" then will refine x to be a singleton type "hello".

And they can be composed with many of and/or/not. not, just like ~=, will flip the resulting refinements, that is not x will refine x to be falsy.

The assert(..) function may also be used to refine types instead of if/then.

Using truthy test:

local maybeString: string? = nil

if maybeString then
    local onlyString: string = maybeString -- ok
    local onlyNil: nil = maybeString       -- not ok
end

if not maybeString then
    local onlyString: string = maybeString -- not ok
    local onlyNil: nil = maybeString       -- ok
end

Using type test:

local stringOrNumber: string | number = "foo"

if type(stringOrNumber) == "string" then
    local onlyString: string = stringOrNumber -- ok
    local onlyNumber: number = stringOrNumber -- not ok
end

if type(stringOrNumber) ~= "string" then
    local onlyString: string = stringOrNumber -- not ok
    local onlyNumber: number = stringOrNumber -- ok
end

Using equality test:

local myString: string = f()

if myString == "hello" then
    local hello: "hello" = myString -- ok because it is absolutely "hello"!
    local copy: string = myString   -- ok
end

And as said earlier, we can compose as many of and/or/not as we wish with these refinements:

local function f(x: any, y: any)
    if (x == "hello" or x == "bye") and type(y) == "string" then
        -- x is of type "hello" | "bye"
        -- y is of type string
    end

    if not (x ~= "hi") then
        -- x is of type "hi"
    end
end

assert can also be used to refine in all the same ways:

local stringOrNumber: string | number = "foo"

assert(type(stringOrNumber) == "string")

local onlyString: string = stringOrNumber -- ok
local onlyNumber: number = stringOrNumber -- not ok

Type casts

Expressions may be typecast using ::. Typecasting is useful for specifying the type of an expression when the automatically inferred type is too generic.

For example, consider the following table constructor where the intent is to store a table of names:

local myTable = {names = {}}
table.insert(myTable.names, 42)         -- Inserting a number ought to cause a type error, but doesn't

In order to specify the type of the names table a typecast may be used:

local myTable = {names = {} :: {string}}
table.insert(myTable.names, 42)         -- not ok, invalid 'number' to 'string' conversion

A typecast itself is also type checked to ensure the conversion is made to a subtype of the expression’s type or any:

local numericValue = 1
local value = numericValue :: any             -- ok, all expressions may be cast to 'any'
local flag = numericValue :: boolean          -- not ok, invalid 'number' to 'boolean' conversion

Roblox types

Roblox supports a rich set of classes and data types, documented here. All of them are readily available for the type checker to use by their name (e.g. Part or RaycastResult).

When one type inherits from another type, the type checker models this relationship and allows to cast a subclass to the parent class implicitly, so you can pass a Part to a function that expects an Instance.

All enums are also available to use by their name as part of the Enum type library, e.g. local m: Enum.Material = part.Material.

We can automatically deduce what calls like Instance.new and game:GetService are supposed to return:

local part = Instance.new("Part")
local basePart: BasePart = part

Finally, Roblox types can be refined using IsA:

local function getText(x : Instance) : string
    if x:IsA("TextLabel") or x:IsA("TextButton") or x:IsA("TextBox") then
        return child.Text
    end
    return ""
end

Note that many of these types provide some properties and methods in both lowerCase and UpperCase; the lowerCase variants are deprecated, and the type system will ask you to use the UpperCase variants instead.

Module interactions

Let’s say that we have two modules, Foo and Bar. Luau will try to resolve the paths if it can find any require in any scripts. In this case, when you say script.Parent.Bar, Luau will resolve it as: relative to this script, go to my parent and get that script named Bar.

-- Module Foo
local Bar = require(script.Parent.Bar)

local baz1: Bar.Baz = 1     -- not ok
local baz2: Bar.Baz = "foo" -- ok

print(Bar.Quux)         -- ok
print(Bar.FakeProperty) -- not ok

Bar.NewProperty = true -- not ok

-- Module Bar
export type Baz = string

local module = {}

module.Quux = "Hello, world!"

return module

There are some caveats here though. For instance, the require path must be resolvable statically, otherwise Luau cannot accurately type check it.

Cyclic module dependencies

Cyclic module dependencies can cause problems for the type checker. In order to break a module dependency cycle a typecast of the module to any may be used:

local myModule = require(MyModule) :: any