Comparison of programming languages (algebraic data type)

This article compares the syntax for defining and instantiating an algebraic data type (ADT), sometimes also referred to as a tagged union, in various programming languages.

Examples of algebraic data types ATS

In ATS, an ADT may be defined with:

datatype tree = | Empty of () | Node of (int, tree, tree)

And instantiated as: val my_tree = Node(42, Node(0, Empty, Empty), Empty)

Additionally in ATS dataviewtypes are the linear type version of ADTs for the purpose of providing in the setting of manual memory management with the convenience of pattern matching. An example program might look like:

(* Alternatively one can use the datavtype keyword *) dataviewtype int_or_string_vt (bool) = | String_vt (true) of string | Int_vt (false) of int

(* Alternatively one can use the vtypedef keyword *) viewtypedef Int_or_String_vt = [b: bool] int_or_string_vt b

fn print_int_or_string (i_or_s: Int_or_String_vt): void = case+ i_or_s of (* ~ indicates i_or_s will be implicitly freed in this case *) | ~String_vt(s) => println!(s) (* @ indicates i_or_s must be explicitly freed in this case *) | @Int_vt(i) => begin $extfcall(void, "fprintf", stdout_ref, "%d\n", i); free@i_or_s; end

implement main0 (): void = let val string_hello_world = String_vt "Hello, world!" val int_0 = Int_vt 0 in print_int_or_string string_hello_world; print_int_or_string int_0; (* which prints: Hello, world! 0 *) end

Ceylon

In Ceylon, an ADT may be defined with:

abstract class Tree() of empty | Node {}

object empty extends Tree() {}

final class Node(shared Integer val, shared Tree left, shared Tree right) extends Tree() {}

And instantiated as:

value myTree = Node(42, Node(0, empty, empty), empty);

Clean

In Clean, an ADT may be defined with:

:: Tree = Empty | Node Int Tree Tree

And instantiated as:

myTree = Node 42 (Node 0 Empty Empty) Empty

C++

In C++, an ADT may be defined with:

struct Empty final {};

struct Node final { int value; std::unique_ptr<std::variant<Empty, Node>> left; std::unique_ptr<std::variant<Empty, Node>> right;

using Tree = std::variant<Empty, Node>;

And instantiated as:

Tree myTree { Node{ 42, std::make_unique<Tree>(Node{ 0, std::make_unique<Tree>(), std::make_unique<Tree>() }), std::make_unique<Tree>()

Dart

In Dart, an ADT may be defined with:

sealed class Tree {}

final class Empty extends Tree {}

final class Node extends Tree { final int value; final Tree left, right;

Node(this.value, this.left, this.right); }

And instantiated as:

final myTree = Node(42, Node(0, Empty(), Empty()), Empty());

Elm

In Elm, an ADT may be defined with:

type Tree = Empty | Node Int Tree Tree

And instantiated as:

myTree = Node 42 (Node 0 Empty Empty) Empty

F#

In F#, an ADT may be defined with:

type Tree = | Empty | Node of int * Tree * Tree

And instantiated as:

let myTree = Node(42, Node(0, Empty, Empty), Empty)

F*

In F*, an ADT may be defined with:

type tree = | Empty : tree | Node : value:nat -> left:tree -> right:tree -> tree

And instantiated as:

let my_tree = Node 42 (Node 0 Empty Empty) Empty

Free Pascal

In Free Pascal (in standard ISO Pascal mode), an ADT may be defined with variant records:

{$mode ISO} program MakeTree;

type TreeKind = (Empty, Node); PTree = ^Tree; Tree = record case Kind: TreeKind of Empty: (); Node: ( Value: Integer; Left, Right: PTree; ); end;

And instantiated as:

var MyTree: PTree;

begin new(MyTree, Node); with MyTree^ do begin Value := 42; new(Left, Node); with Left^ do begin Value := 0; new(Left, Empty); new(Right, Empty); end; new(Right, Empty); end; end.

Haskell

In Haskell, an ADT may be defined with:

data Tree = Empty | Node Int Tree Tree

And instantiated as:

myTree = Node 42 (Node 0 Empty Empty) Empty

Haxe

In Haxe, an ADT may be defined with:

enum Tree { Empty; Node(value:Int, left:Tree, right:Tree); }

And instantiated as:

var myTree = Node(42, Node(0, Empty, Empty), Empty);

Hope

In Hope, an ADT may be defined with:

data tree == empty ++ node (num # tree # tree);

And instantiated as:

dec mytree : tree; --- mytree <= node (42, node (0, empty, empty), empty);

Idris

In Idris, an ADT may be defined with:

data Tree = Empty | Node Nat Tree Tree

And instantiated as:

myTree : Tree myTree = Node 42 (Node 0 Empty Empty) Empty

Java

In Java, an ADT may be defined with:

sealed interface Tree { record Empty() implements Tree {} record Node(int value, Tree left, Tree right) implements Tree {} }

And instantiated as:

var myTree = new Tree.Node( 42, new Tree.Node(0, new Tree.Empty(), new Tree.Empty()), new Tree.Empty() );

Julia

In Julia, an ADT may be defined with:

struct Empty end

struct Node value::Int left::Union{Empty, Node} right::Union{Empty, Node} end

const Tree = Union{Empty, Node}

And instantiated as:

mytree = Node(42, Node(0, Empty(), Empty()), Empty())

Kotlin

In Kotlin, an ADT may be defined with:

sealed class Tree { object Empty : Tree() data class Node(val value: Int, val left: Tree, val right: Tree) : Tree() }

And instantiated as:

val myTree = Tree.Node( 42, Tree.Node(0, Tree.Empty, Tree.Empty), Tree.Empty, )

Limbo

In Limbo, an ADT may be defined with:

Tree: adt { pick { Empty => Node => value: int; left: ref Tree; right: ref Tree;

And instantiated as:

myTree := ref Tree.Node( 42, ref Tree.Node(0, ref Tree.Empty(), ref Tree.Empty()), ref Tree.Empty() );

Mercury

In Mercury, an ADT may be defined with:

:- type tree ---> empty ; node(int, tree, tree).

And instantiated as:

:- func my_tree = tree. my_tree = node(42, node(0, empty, empty), empty).

Miranda

In Miranda, an ADT may be defined with:

tree ::= Empty | Node num tree tree

And instantiated as:

my_tree = Node 42 (Node 0 Empty Empty) Empty

Nemerle

In Nemerle, an ADT may be defined with:

variant Tree { | Empty | Node { value: int; left: Tree; right: Tree;

And instantiated as:

def myTree = Tree.Node( 42, Tree.Node(0, Tree.Empty(), Tree.Empty()), Tree.Empty(), );

Nim

In Nim, an ADT may be defined with:

type TreeKind = enum tkEmpty tkNode

Tree = ref TreeObj

TreeObj = object case kind: TreeKind of tkEmpty: discard of tkNode: value: int left, right: Tree

And instantiated as:

let myTree = Tree(kind: tkNode, value: 42, left: Tree(kind: tkNode, value: 0, left: Tree(kind: tkEmpty), right: Tree(kind: tkEmpty)), right: Tree(kind: tkEmpty))

OCaml

In OCaml, an ADT may be defined with:

type tree = | Empty | Node of int * tree * tree

And instantiated as:

let my_tree = Node (42, Node (0, Empty, Empty), Empty)

Opa

In Opa, an ADT may be defined with:

type tree = { empty } or { node, int value, tree left, tree right }

And instantiated as:

my_tree = { node, value: 42, left: { node, value: 0, left: { empty }, right: { empty } }, right: { empty } }

OpenCog

In OpenCog's Atomese, an ADT is constructed inside the graph-based AtomSpace using explicit type constructors like SignatureLink and TypeChoice to represent sum and product types. A binary tree ADT may be defined with:; Define the "Tree" sum type choice (TypeChoice (DefinedTypeNode "Tree") (TypeSetLink (TypeNode "Empty") (SignatureLink (TypeNode "Node") (TypeSetLink (TypeNode "NumberNode") (DefinedTypeNode "Tree") (DefinedTypeNode "Tree")))))And instantiated as a graph structure:; Instantiate a tree structure equivalent to: Node(42, Node(0, Empty, Empty), Empty) (Node (NumberNode "42") (Node (NumberNode "0") (Empty) (Empty)) (Empty))

PureScript

In PureScript, an ADT may be defined with:

data Tree = Empty | Node Int Tree Tree

And instantiated as:

myTree = Node 42 (Node 0 Empty Empty) Empty

Python

In Python, an ADT may be defined with:

from __future__ import annotations from dataclasses import dataclass

@dataclass class Empty: pass

@dataclass class Node: value: int left: Tree right: Tree

Tree = Empty | Node

And instantiated as:

my_tree = Node(42, Node(0, Empty(), Empty()), Empty())

Racket

In Typed Racket, an ADT may be defined with:

(struct Empty ()) (struct Node ([value : Integer] [left : Tree] [right : Tree])) (define-type Tree (U Empty Node))

And instantiated as:

(define my-tree (Node 42 (Node 0 (Empty) (Empty)) (Empty)))

Reason

In Reason, an ADT may be defined with:

type Tree = | Empty | Node(int, Tree, Tree);

And instantiated as:

let myTree = Node(42, Node(0, Empty, Empty), Empty);

ReScript

In ReScript, an ADT may be defined with:

type rec Tree = | Empty | Node(int, Tree, Tree)

And instantiated as:

let myTree = Node(42, Node(0, Empty, Empty), Empty)

Rocq

In Rocq, an ADT may be defined with:

Inductive tree : Type := | empty : tree | node : nat -> tree -> tree -> tree.

And instantiated as:

Definition my_tree := node 42 (node 0 empty empty) empty.

Rust

In Rust, an ADT may be defined with:

enum Tree { Empty, Node(i32, Box<Tree>, Box<Tree>), }

And instantiated as:

let my_tree = Tree::Node( 42, Box::new(Tree::Node(0, Box::new(Tree::Empty), Box::new(Tree::Empty)), Box::new(Tree::Empty), );

Scala

Scala 2 In Scala 2, an ADT may be defined with:

sealed abstract class Tree extends Product with Serializable

object Tree { final case object Empty extends Tree final case class Node(value: Int, left: Tree, right: Tree) extends Tree }

And instantiated as:

val myTree = Tree.Node( 42, Tree.Node(0, Tree.Empty, Tree.Empty), Tree.Empty )

Scala 3 In Scala 3, an ADT may be defined with:

enum Tree: case Empty case Node(value: Int, left: Tree, right: Tree)

And instantiated as:

val myTree = Tree.Node( 42, Tree.Node(0, Tree.Empty, Tree.Empty), Tree.Empty )

Standard ML

In Standard ML, an ADT may be defined with:

datatype tree = EMPTY | NODE of int * tree * tree

And instantiated as:

val myTree = NODE (42, NODE (0, EMPTY, EMPTY), EMPTY)

Swift

In Swift, an ADT may be defined with:

enum Tree { case empty indirect case node(Int, Tree, Tree) }

And instantiated as:

let myTree: Tree = .node(42, .node(0, .empty, .empty), .empty)

TypeScript

In TypeScript, an ADT may be defined with:

type Tree = | { kind: "empty" } | { kind: "node"; value: number; left: Tree; right: Tree };

And instantiated as:

const myTree: Tree = { kind: "node", value: 42, left: { kind: "node", value: 0, left: { kind: "empty" }, right: { kind: "empty" }, }, right: { kind: "empty" },

Visual Prolog

In Visual Prolog, an ADT may be defined with:

domains tree = empty; node(integer, tree, tree).

And instantiated as:

constants my_tree : tree = node(42, node(0, empty, empty), empty).

Zig

In Zig, an ADT may be defined with:

const Tree = union(enum) { empty, node: struct { value: i32, left: *const Tree, right: *const Tree, },

And instantiated as:

const my_tree: Tree = .{ .node = .{ .value = 42, .left = &.{ .node = .{ .value = 0, .left = &.empty, .right = &.empty, } }, .right = &.empty,

References