Ante has an algebraic type system with refinement types. In other words, Ante supports sum types (tagged unions), product types, as well as types with an added boolean condition.

Types in Ante are lexically distinct from identifiers. All user-defined types are in the form [A-Z][A-Za-z]*, and all other types are in the forms described below.

Primitive Types

Most primitive types are in the form of [a-z]\d+. Where the letter specifies its general type (signed integer, unsigned integer, floating-point, or char), and the number afterwards specifies its size in bits. The size may also be sz which indicates that the type is the size of a pointer on the current platform.

Signed integer types: i8 i16 i32 i64 isz

Unsigned integer types: u8 u16 u32 u64 usz

Floating-point types: f16 f32 f64

Character types: c8 c16 c32 c64

Other: bool void

Despite its name, Ante’s void type is more analogous to a unit type in other languages rather than the conventional void type. This is due to it having () as its single value rather than most void types which have no values.

Pointer Types

Pointer types are in the form of <type>\* and represent a C-style pointer to the given type.

typeof (new 3)      //=> i32*
typeof (new new 3)  //=> i32**

Pointer types are unmanaged by default. It is strongly reccomended to choose a memory management strategy early on by importing either the standard GC module or the Ownership module.

Array Types

Array types are in the form \[<size> <type>\] where the size is optional. If the size is included then the array is a constant array without a length field. If it is excluded it is a possibly dynamic array with a separate length field.

typeof [1, 2]  //=> [2 i32]
typeof []      //=> [0 't]

typeof <| [1..10]#(2..4)        //=> [3 i32]
typeof <| [1..10].slice (2..4)  //=> [i32]

Tuple Types

A tuple type is an aggregate type that is contiguous and heterogenous. Its type is a combination of each of its element types separated with a comma.

typeof (2, 3)    //=> i32, i32
typeof ("hi", 5) //=> Str, i32

typeof (["three"], new 3)  //=> [1 Str], i32*
typeof (1u8, 2u16, 3u32)   //=> u8, u16, u32

A single element tuple is expressed with a trailing comma:

typeof (5,)   //=> i32,

Function Types

The type of a function is the tuple of its parameters followed by -> and its return type.

fun add: i32 a, i32 b -> i32
    a + b

typeof add    //=> (i32, i32) -> i32
typeof puts   //=> (c8*,) -> i32
typeof printf //=> (c8*, ...) -> i32

Record Types and Sum Types

Record types and sum types currently must be given a name after declaration as they have no inline equivalent. See the type declarations section for info on how to declare these types.

//record type
type Person = Str name, u8 age

typeof Person("George", 3)  //=> Person

//Sum type
type Day = Mon | Tue | Wed | Thurs | Fri | Sat | Sun

typeof Tue  //=> Day

Type Variables

Type variables can stand in for any type and are the building block for generic types. Their syntax is an apostrophe followed by an identifier.

//x is any type
fun print: 't x = ...

//p is any pointer type
fun print_ptr: 't* p = ...

Functions that accept a type variable anywhere in their parameters are generic functions and are recompiled for every valid type variant of arguments that are used. For a given variable x of type 't the expression x + 1 is invalid because a type variable must be able to be substituted with any type and not every type defines the + operator. Resultingly, generic functions in Ante can be type checked sooner and type checked only once for faster compilation. If one wishes to have a function generic over any function that implements addition, traits should be used instead.

//invalid: + not defined for any type 't
fun inc: 't x =
    x + 1

//valid, + is defined for all Addable types
fun inc: Addable x =
    x + 1

fun extract_index: Arr 't a, usz idx -> Maybe 't
    if idx in indices a then
        Some (a#idx)

let int_arr = [1, 2, 3, 4]
let str_arr = ["one", "two", "three"]

//compile a variant just for 't = i32
extract_index int_arr 2

//compile a variant just for 't = Str
extract_index str_arr 1

Generic Types

Generic types are types that themselves take other types of parameters. For example, the Maybe type is generic over the type of value it holds. The arguments of a generic type are specified after the type and are separated with spaces. The generic type with no type arguments is referred to as the parent type (Maybe in this case), and each version with type arguments, eg. Maybe i32 is a variant of the parent type. Two generic variants are equal if their parent types are equal and their generic arguments are equal.

typeof (Some 3)  //=> Maybe i32
typeof [2, 3]    //=> Vec i32
typeof (Err 0)   //=> Result 't i32

If a function omits the generic arguments of a parameter then the resulting type is the parent type, and is generic for any variant of the parent type.

//print will accept any variant of Maybe
fun print: Maybe m
    match m with
    | Some val -> print val
    | None -> print "None"

let mi = Some 3
let ms = Some "string"

//both Maybe i32 and Maybe Str are valid inputs
print mi
print ms

Trait Types

The type of a trait is also its name. The type of a type satisfying multiple traits can be expressed as each trait’s type joined by +.

trait T1
trait T2

T1     //The type of the trait T1
T1+T2  //The type of the composition of T1 and T2

A function accepting a trait type as an argument is generic over any type that satisfies that trait.

fun echo: Printable p
    print p

//compiles a function echo:i32 for integers
echo 3

//compiles a function echo:c8* for c8 pointers
echo (new 'h')

Functions with trait parameters are normally statically dispatched however if desired they can be used with dynamic dispatch by using trait objects. Trait objects can be created by wrapping the desired trait in the Trait type.

//EqList is a heterogenous list of any type that implements Eq
type EqList is List (Trait Eq)

let l = EqList(2, "three", (5usz, -2i8), 'h')

//take two parameters using dynamic dispatch for the = function.
fun f: Trait Eq a b =
    not(a = b)

f 2 3  //compile f:(Trait Eq, Trait Eq)

f "a" "a"  //f is not recompiled

Trait object types hide the actual value behind a pointer which contains both the value itself and a vtable.

Refinement Types

Refinement types consist of a normal type, and a boolean condition after delimited by curly brackets. This condition is called a refinement. Refinement types “depend” on values and are thus a limited form of dependent types, intentionally limited to a subset that is automatically solvable by a SMT solver so that no proofs need to be made by the programmer.

In practice, refinement types are useful for changing many runtime errors into compile-time errors. The classic example is preventing array/memory indexing errors by refining an index to be less than the length of the array:

fun get: Array 't arr, usz idx {idx < len arr} -> 't

let a = Arr(2, 4, 6)

get a 0  //=> 2
get a 3  //=> compile-time error: 3 >= len a

Preventing division by 0:

fun (/): Num a, Num b {b != 0} -> Num

Refinement expressions are limited to use only the following operators, in addition to uninterpreted functions. In this context, an uninterpreted function is not evaluated. Instead, it is type checked and the type of its result must satisfy the boolean expression.

Operators allowed:

*                // Multiplication by constants only
.                // Member access
#                // Tuple member access only
f arg1 ... argN  // Uninterpreted function call