Bugs

• Type checking for build-in functions
• Type aliases in REPL
• Resolve union types to the smallest common base type before using it to typecheck expresion

Typesystem

The language is strict and strongly typed. There is support for all the well-know primitives, literals, arrays, records and lambdas.

Int

Ints contains a 32 bit integer value. There type is written als int. Ints also support literal typing. With literal typing we restrict the type to a specific value. A int literal is created by it's value (e.g 1 or 2).

let i :: int = 1
let i1 :: 1 = 1
let i2 :: 2 = 2

String

String contains a sequence of caracters. There type is written als string. They also support literal typing. You can get the length of a string with count("string"). A specific index is accesed with .[ID].

let s :: string = "hello"
let s1 :: "x" = "x"
let s2 :: "hello" = "hello"
let s3 :: string = s2.[1]
let size :: int = count(s2)

Bool

Bools contains true of false. They support literal typing.

let b :: bool = true
let b1 :: true = true

Unit

Unit is used as the no-data type. It's type is written als ().

let u :: () = ()

Arrays

Arrays contain multiple values of the same type. Their type is writting by post-fixing the inner type with []. When constructing an array you pre-fix the array with the type (e.g int [1]). You can get the length again with count(int[])

let a :: int[] = int []
let a1 :: int[] = int [1, 2, 3]
let a2 :: 1[] = int [1, 1, 1]
let l :: int = count(a2)

Records

Records contain key-value pairs. They are created with {}. You are allowed to have more properties in the actuval value then are requested by the type. However, the type system will in feature reference act like they aren't there.

let empty :: {} = {}
let o :: { x: 1 } = { x: 1 }
let o2 :: { x: 1, y: 3} = {x: 1, y: 3}
let o3 :: { y: 3 } = { x: 1, y: 3 }

You can acces properties with obj.ID.

let o2 :: { x: 1, y: 3} = {x: 1, y: 3}
let x :: 1 = o2.x

You can copy objects with an updated property like this:

let o2 :: { x: 1, y: int } = { x: 1, y: 3 }
let o3 :: { x: 1, y: int } = { o2 with y: 7 }

Lambda

Lambda's are created with the ->. When creating a lambda you always have to specify the type of the argument (([PARAM] :: [TYPE]) -> [EXPRESSION]). There type is written with [TYPE] -> [TYPE].

let f :: int -> int = (x :: int) -> x + 1

a lambda can return an other lambda. This means that multiple arguments and curring are supported.

let add :: int -> int -> int = (x :: int) -> (y :: int) -> x + y

You can also pass a lambda as an argument to another lambda.

let f :: (int -> int) -> int = (g :: int -> int) -> g(1)

Lambda's can have function body when using {}. The last expression is the return value. Lambda's get lexial scoping.

let f :: int -> int = (x :: int) -> {
  echo x
  x + 1
}

Lamdas also accept generic type arguments. When returning a value of a generic type the compiler will resolve the concrete provided type in de function call. Multiple typearguments are seperated with ','. Type constrains are indicated with :: TYPE.

let id = <a> (a :: a) -> a
let x = id<1>(1)

let addOne = <a :: int> = (i :: a) -> i + 1
let i = addOne<1>(1)

let readId = <a :: {Id: int}> (a :: a) -> a.Id
let id = readId<{Id: int, Name: string}>({Id: 1, Name: "Dave"})

let compose = <a,b,c> (f :: a -> b) -> (g :: b -> c) -> (a :: a) -> g(f(a))
let fst = <a> a :: a[] -> a.[0]

Unions

Type unions are created by listing the case, seperated by the |. Conditionals of where the branches produce incopatible types will also be of a union of the 2 types.

let x :: int | bool = true
let y = true ? 1 : true
let z :: 1 | true = y

Type aliases

Types can be given aliases to avoid repetition and extremely long expressions. They are created with type [ID] = [TYPE].

type String = string
type compose = (int -> int) -> (int -> int) -> int -> int
let compose :: compose = (f :: int -> int) -> (g :: int -> int) -> x -> g(f(x))

type user = {
  id: int,
  username: string
}

let user :: user = {
  id: 1,
  username: "Dave"
}

Types can also take type arguments. They are listed before the =. When using the type the arguments are listed within << and >>.

type data<a> = { value: a }
let d :: data<<string>> = { value: "hi" }
let f = <a> (d :: data<<a>>) -> d.value

Notes on literals

Literal types are directly assignable to their corresponding primitive:

let x :: 1 = 1
let x1 :: int = x

let xx :: { x: 1 } = { x: 1}
let xx1 :: { x: int } = xx

Conditionals can be used to narrow a primitive to a literal type:

let x :: int = 1
let x1 :: 1 = x == 1 ? x : 1

Because both of the branches return something that is assignable to the type 1 we can assign the variable x (of type int) to the literal of type 1.

Type inference

Variables can also be declared without an type. They will get the type the typechecker infers from the expression assigned to them. Type inference will not work on parameters for functions.

let x = 1
let xx :: int = x