Object-oriented programming in BQN

BQN's namespaces can be used to support a simple form of object-oriented programming (OOP) without type checking or inheritance. It's suitable for some program architectures but not others: making OOP work as a solution to every problem isn't a BQN design goal. In fact, BQN was never designed to support OOP at all! I added namespaces or modules as a way to structure programs. The techniques we're going to discuss are all just ways to use namespaces, and if it ever starts seeming like confusing magic it might help to go back to this model. However, thinking of namespaces as objects can be quite powerful in the right circumstances, and on this page I'm going to frame things in OOP terms. The following table shows which well-known aspects of OOP are supported in BQN:

Feature In BQN?
Objects Yes (namespaces)
Classes Yes (function returning namespace)
Fields Yes
Methods Yes
Class variables Yes (awkward syntax)
Access Public or instance-private
this No (well…)
Inheritance (is-a) No
Composition (has-a) Yes
Interfaces No
Abstract classes No
Mixins Not really (needs this)


An object in BQN is simply a namespace: its fields and methods are variables in the namespace, and a variable can be accessed outside of the namespace with dot syntax if it's exported with . Unexported variables are instance-private in OOP parlance, meaning that they're only visible to the object containing them. They could be utilities, or hold state for the object. As an example, the object below implements the Tower of Hanoi puzzle with five disks. You can view the state (a list of disks occupying each of the three rods) with towerOfHanoi.View, or move the top disk from one rod to another with towerOfHanoi.Move.

    towerOfHanoi  {
      l  ¨500
      View  {𝕤
      Move  {fromto:
        l  Transfer´(𝕩)(´𝕩) l
      # Move a disk from 𝕨 to 𝕩
      Transfer  {
        "No disk to move"!0<≠𝕨
        "Can't place larger disk on smaller one"!(0<≠)1,𝕨<⊑⊢𝕩
        1𝕨, 𝕨𝕩

Two variables l and Transfer aren't exported, for two different reasons. l encodes the state of the tower, but it's only exposed with the function View, which allows the internal representation to be changed freely. Transfer is just a utility function. While it's not dangerous to use outside of the object, there's no reason to expose it through towerOfHanoi's interface. If it's wanted in another place it should be moved to a common location.

Here are the results of a few applications of these functions.

    t  towerOfHanoi
⟨ ⟨ 0 1 2 3 4 ⟩ ⟨⟩ ⟨⟩ ⟩

    t.Move 02
⟨ ⟨ 1 2 3 4 ⟩ ⟨⟩ ⟨ 0 ⟩ ⟩

    t.Move 12
Error: No disk to move

    t.Move 01
⟨ ⟨ 2 3 4 ⟩ ⟨ 1 ⟩ ⟨ 0 ⟩ ⟩

    t.Move 21
⟨ ⟨ 2 3 4 ⟩ ⟨ 0 1 ⟩ ⟨⟩ ⟩


The object above is a singleton: there's just one of it, at least in the scope it occupies. It's often more useful to have a class that can be used to create objects. What we'll call a "class" is a namespace function, that is, a function that contains and so returns a namespace. It's very easy to convert a singleton object to a class: just add a no-op 𝕤 line to force it to be a function, and call it with @ when needed.

MakeStack  {𝕤
  Push{   st𝕩st}
  Pop {𝕤 rsst  sts  r}

But arguments don't have to be ignored: often it makes sense to use one or two arguments to initialize the object. For example, the stack class above can be modified to use 𝕩 as an initial list of values for the stack.

MakeStackInit  {
  Push{   st𝕩st}
  Pop {𝕤 rsst  sts  r}
  Push¨ 𝕩

A stack is a particularly simple class to make because its state can be represented efficiently as a BQN value. Other data structures don't allow this, and will often require an extra Node class in an implementation—see MakeQueue below.


An object is one way to transform variable mutation into mutable data. These are two different concepts: changes which value is attached to a name in a scope, while mutable data means that the behavior of a particular value can change. But if a value is linked to a scope (for an object, the scope that contains its fields), then variable mutation in that scope can change the value's behavior. In fact, in BQN this is the only way to create mutable data. Which doesn't mean it's rare: functions, modifiers, and namespaces are all potentially mutable. The difference between objects and the operations is just a matter of syntax. Mutability in operations can only be observed by calling them. For instance F 10 or -_m could return a different result even if the variables involved don't change value. Mutability in an object can only be observed by accessing a member, meaning that obj.field or fieldobj can yield different values over the course of a program even if obj is still the same object.

Let's look at how mutability plays out in an example class for a single-ended queue. This queue works by linking new nodes to the tail t of the queue, and detaching nodes from the head h when requested (a detached node will still point to h, but nothing in the queue points to it, so it's unreachable and will eventually be garbage collected). Each node has some data v and a single node reference n directed tailwards; in a double-ended queue or more complicated structure it would have more references. You can find every mutable variable in the queue by searching for , which shows that t and h in the queue, and n in a node, may be mutated. It's impossible for the other variables to change value once they're assigned.

MakeQueue  {𝕤
  Node{v𝕩ne  SetN{n𝕩}}
  Push{t.SetN nNode 𝕩  tn}
  Pop {𝕤vh.vhh.n{e=h?te;@}v}

Unlike a stack, a node's successor isn't known when it's created, and it has to be set. You might be inclined to make n settable directly, but we'll get more mileage out of a setter function SetN. This allows us to create a pseudo-node e (for "empty") indicating there are no values in the queue. Because it has no .v field, if h is e then Pop gives an error (but in a real implementation you'd want to test explicitly instead in order to give an appropriate error message). In fact it doesn't have an n field, and essentially uses the queue head h instead. With this empty "node", the queue definition is straightforward. The only tricky part to remember is that if Pop removes the last node, resulting in e=h, then the tail has to be set to e as well, or it will keep pointing to the removed node and cause bugs.


BQN classes don't support inheritance because there's no way to extend an existing class with new fields. But a lot of OOP enthusiasts these days are promoting composition over inheritance, and here BQN does pretty well. Forwarding methods from another class is as simple as a multiple assignment, like View below (in a real program undoableTowerOfHanoi should almost certainly be a class, but I introduced towerOfHanoi before classes, and I'm not about to write it again just to add an 𝕤).

undoableTowerOfHanoi  {
  PushPop  MakeStack@     # Copy methods as private
  View  ttowerOfHanoi   # Copy and export
  Move  t.Move  Push
  Undo  t.MovePop

This class composes a Tower of Hanoi with an undo stack that stores previous moves. To undo a move from a to b, it moves from b to a, although if you felt really fancy you might define Move in towerOfHanoi instead with an undo header 𝕊𝕩: 𝕊⌽𝕩.

It's also possible to copy several variables and only export some of them, with an export statement. For example, if I wasn't going to make another method called Move, I might have written ViewMove towerOfHanoi and then View. In fact, depending on your personal style and how complicated your classes are, you might prefer to avoid inline exports entirely, and declare all the exports at the top.


An object's class is given by 𝕊. Remember, a class is an ordinary BQN function! It might be useful for an object to produce another object of the same class (particularly if it's immutable), and an object might also expose a field class𝕤 to test whether an object o belongs to a class c with o.class = c.

It's not currently possible for an object to know its own value without some outside help, such as a special constructor:

IntrospectiveClass  {
  obj  {
    SetThis  { !this@  this𝕩 }
  obj.setThis obj

This is a pretty clunky solution, and exports a useless method SetThis (which gives an error if it's ever called). It would be possible for BQN to define a system value •this that just gets the namespace's value. It would work only at the top level, so it would have to be assigned (this•this) in order to use it in functions. This means it's always used before the namespace is done being defined, so a drawback is that it introduces the possibility that an object used in a program has undefined fields. Currently a namespace can only be created with all fields set: a block body doesn't have any sort of control flow other than the early exit ?, so it can only finish by executing every statement, including every field definition, in order.

Class members

As with this, creating variables that belong to a class and not its objects is a do-it-yourself sort of thing (or more positively, not at all magic (funny how programmer jargon goes the opposite way to ordinary English)). It's an easy one though, as this is exactly what lexical scoping does:

staticClass  {
  counter  0
    class  staticClass
    Count  {𝕤 counter+1 }

Now StaticClass is the inner function, because that function is the block's result, and it has some extra state that only it knows how to access. The differences in the definition are that staticClass ends up with a subject role and that each object's class has to be set to staticClass instead of the shortcut 𝕤, but these are purely syntactic issues: under it all, staticClass is the same as any other class, but has some extra state attached.