Objects in Caml

# Chapter 3 Objects in Caml

(Chapter written by Jérôme Vouillon, Didier Rémy and Jacques Garrigue)
This chapter gives an overview of the object-oriented features of Objective Caml. Note that the relation between object, class and type in Objective Caml is very different from that in main stream object-oriented languages like Java or C++, so that you should not assume that similar keywords mean the same thing.
3.1 Classes and objects
3.2 Immediate objects
3.3 Reference to self
3.4 Initializers
3.5 Virtual methods
3.6 Private methods
3.7 Class interfaces
3.8 Inheritance
3.9 Multiple inheritance
3.10 Parameterized classes
3.11 Polymorphic methods
3.12 Using coercions
3.13 Functional objects
3.14 Cloning objects
3.15 Recursive classes
3.16 Binary methods
3.17 Friends

## 3.1 Classes and objects

The class `point` below defines one instance variable `x` and two methods `get_x` and `move`. The initial value of the instance variable is `0`. The variable `x` is declared mutable, so the method `move` can change its value.

    #class point =
       object
         val mutable x = 0
         method get_x = x
         method move d = x <- x + d
       end;;
    class point :
      object val mutable x : int method get_x : int method move : int -> unit end

We now create a new point `p`, instance of the `point` class.

    #let p = new point;;
    val p : point = <obj>

Note that the type of `p` is `point`. This is an abbreviation automatically defined by the class definition above. It stands for the object type `<get_x : int; move : int -> unit>`, listing the methods of class `point` along with their types.
We now invoke some methods to `p`:

    #p#get_x;;
    - : int = 0

    #p#move 3;;
    - : unit = ()

    #p#get_x;;
    - : int = 3

The evaluation of the body of a class only takes place at object creation time. Therefore, in the following example, the instance variable `x` is initialized to different values for two different objects.

    #let x0 = ref 0;;
    val x0 : int ref = {contents = 0}

    #class point =
       object
         val mutable x = incr x0; !x0
         method get_x = x
         method move d = x <- x + d
       end;;
    class point :
      object val mutable x : int method get_x : int method move : int -> unit end

    #new point#get_x;;
    - : int = 1

    #new point#get_x;;
    - : int = 2

The class `point` can also be abstracted over the initial values of the `x` coordinate.

    #class point = fun x_init ->
       object
         val mutable x = x_init
         method get_x = x
         method move d = x <- x + d
       end;;
    class point :
      int ->
      object val mutable x : int method get_x : int method move : int -> unit end

Like in function definitions, the definition above can be abbreviated as:

    #class point x_init =
       object
         val mutable x = x_init
         method get_x = x
         method move d = x <- x + d
       end;;
    class point :
      int ->
      object val mutable x : int method get_x : int method move : int -> unit end

An instance of the class `point` is now a function that expects an initial parameter to create a point object:

    #new point;;
    - : int -> point = <fun>

    #let p = new point 7;;
    val p : point = <obj>

The parameter `x_init` is, of course, visible in the whole body of the definition, including methods. For instance, the method `get_offset` in the class below returns the position of the object relative to its initial position.

    #class point x_init =
       object
         val mutable x = x_init
         method get_x = x
         method get_offset = x - x_init
         method move d = x <- x + d
       end;;
    class point :
      int ->
      object
        val mutable x : int
        method get_offset : int
        method get_x : int
        method move : int -> unit
      end

Expressions can be evaluated and bound before defining the object body of the class. This is useful to enforce invariants. For instance, points can be automatically adjusted to the nearest point on a grid, as follows:

    #class adjusted_point x_init =
       let origin = (x_init / 10) * 10 in
       object
         val mutable x = origin
         method get_x = x
         method get_offset = x - origin
         method move d = x <- x + d
       end;;
    class adjusted_point :
      int ->
      object
        val mutable x : int
        method get_offset : int
        method get_x : int
        method move : int -> unit
      end

(One could also raise an exception if the `x_init` coordinate is not on the grid.) In fact, the same effect could here be obtained by calling the definition of class `point` with the value of the `origin`.

    #class adjusted_point x_init =  point ((x_init / 10) * 10);;
    class adjusted_point : int -> point

An alternative solution would have been to define the adjustment in a special allocation function:

    #let new_adjusted_point x_init = new point ((x_init / 10) * 10);;
    val new_adjusted_point : int -> point = <fun>

However, the former pattern is generally more appropriate, since the code for adjustment is part of the definition of the class and will be inherited.
This ability provides class constructors as can be found in other languages. Several constructors can be defined this way to build objects of the same class but with different initialization patterns; an alternative is to use initializers, as decribed below in section 3.4.

## 3.2 Immediate objects

There is another, more direct way to create an object: create it without going through a class.
The syntax is exactly the same as for class expressions, but the result is a single object rather than a class. All the constructs described in the rest of this section also apply to immediate objects.

    #let p =
       object
         val mutable x = 0
         method get_x = x
         method move d = x <- x + d
       end;;
    val p : < get_x : int; move : int -> unit > = <obj>

    #p#get_x;;
    - : int = 0

    #p#move 3;;
    - : unit = ()

    #p#get_x;;
    - : int = 3

Unlike classes, which cannot be defined inside an expression, immediate objects can appear anywhere, using variables from their environment.

    #let minmax x y =
       if x < y then object method min = x method max = y end
       else object method min = y method max = x end;;
    val minmax : 'a -> 'a -> < max : 'a; min : 'a > = <fun>

Immediate objects have two weaknesses compared to classes: their types are not abbreviated, and you cannot inherit from them. But these two weaknesses can be advantages in some situations, as we will see in sections 3.3 and 3.10.

## 3.3 Reference to self

A method or an initializer can send messages to self (that is, the current object). For that, self must be explicitly bound, here to the variable `s` (`s` could be any identifier, even though we will often choose the name `self`.)

    #class printable_point x_init =
       object (s)
         val mutable x = x_init
         method get_x = x
         method move d = x <- x + d
         method print = print_int s#get_x
       end;;
    class printable_point :
      int ->
      object
        val mutable x : int
        method get_x : int
        method move : int -> unit
        method print : unit
      end

    #let p = new printable_point 7;;
    val p : printable_point = <obj>

    #p#print;;
    7- : unit = ()

Dynamically, the variable `s` is bound at the invocation of a method. In particular, when the class `printable_point` is inherited, the variable `s` will be correctly bound to the object of the subclass.
A common problem with self is that, as its type may be extended in subclasses, you cannot fix it in advance. Here is a simple example.

    #let ints = ref [];;
    val ints : '_a list ref = {contents = []}

    #class my_int =
       object (self)
         method n = 1
         method register = ints := self :: !ints
       end;;
    This expression has type < n : int; register : 'a; .. >
    but is here used with type 'b
    Self type cannot escape its class

You can ignore the first two lines of the error message. What matters is the last one: putting self into an external reference would make it impossible to extend it afterwards. We will see in section 3.12 a workaround to this problem. Note however that, since immediate objects are not extensible, the problem does not occur with them.

    #let my_int =
       object (self)
         method n = 1
         method register = ints := self :: !ints
       end;;
    val my_int : < n : int; register : unit > = <obj>

## 3.4 Initializers

Let-bindings within class definitions are evaluated before the object is constructed. It is also possible to evaluate an expression immediately after the object has been built. Such code is written as an anonymous hidden method called an initializer. Therefore, is can access self and the instance variables.

    #class printable_point x_init =
       let origin = (x_init / 10) * 10 in
       object (self)
         val mutable x = origin
         method get_x = x
         method move d = x <- x + d
         method print = print_int self#get_x
         initializer print_string "new point at "; self#print; print_newline()
       end;;
    class printable_point :
      int ->
      object
        val mutable x : int
        method get_x : int
        method move : int -> unit
        method print : unit
      end

    #let p = new printable_point 17;;
    new point at 10
    val p : printable_point = <obj>

Initializers cannot be overridden. On the contrary, all initializers are evaluated sequentially. Initializers are particularly useful to enforce invariants. Another example can be seen in section 5.1.

## 3.5 Virtual methods

It is possible to declare a method without actually defining it, using the keyword `virtual`. This method will be provided later in subclasses. A class containing virtual methods must be flagged `virtual`, and cannot be instantiated (that is, no object of this class can be created). It still defines type abbreviations (treating virtual methods as other methods.)

    #class virtual abstract_point x_init =
       object (self)
         val mutable x = x_init
         method virtual get_x : int
         method get_offset = self#get_x - x_init
         method virtual move : int -> unit
       end;;
    class virtual abstract_point :
      int ->
      object
        val mutable x : int
        method get_offset : int
        method virtual get_x : int
        method virtual move : int -> unit
      end

    #class point x_init =
       object
         inherit abstract_point x_init
         method get_x = x
         method move d = x <- x + d
       end;;
    class point :
      int ->
      object
        val mutable x : int
        method get_offset : int
        method get_x : int
        method move : int -> unit
      end

## 3.6 Private methods

Private methods are methods that do not appear in object interfaces. They can only be invoked from other methods of the same object.

    #class restricted_point x_init =
       object (self)
         val mutable x = x_init
         method get_x = x
         method private move d = x <- x + d
         method bump = self#move 1
       end;;
    class restricted_point :
      int ->
      object
        val mutable x : int
        method bump : unit
        method get_x : int
        method private move : int -> unit
      end

    #let p = new restricted_point 0;;
    val p : restricted_point = <obj>

    #p#move 10;;
    This expression has type restricted_point
    It has no method move

    #p#bump;;
    - : unit = ()

Note that this is not the same thing as private and protected methods in Java or C++, which can be called from other objects of the same class. This is a direct consequence of the independence between types and classes in Objective Caml: two unrelated classes may produce objects of the same type, and there is no way at the type level to ensure that an object comes from a specific class. However a possible encoding of friend methods is given in section 3.17.
Private methods are inherited (they are by default visible in subclasses), unless they are hidden by signature matching, as described below.
Private methods can be made public in a subclass.

    #class point_again x =
       object (self)
         inherit restricted_point x
         method virtual move : _
       end;;
    class point_again :
      int ->
      object
        val mutable x : int
        method bump : unit
        method get_x : int
        method move : int -> unit
      end

The annotation `virtual` here is only used to mention a method without providing its definition. Since we didn't add the `private` annotation, this makes the method public, keeping the original definition.
An alternative definition is

    #class point_again x =
       object (self : < move : _; ..> )
         inherit restricted_point x
       end;;
    class point_again :
      int ->
      object
        val mutable x : int
        method bump : unit
        method get_x : int
        method move : int -> unit
      end

The constraint on self's type is requiring a public `move` method, and this is sufficient to override `private`.
One could think that a private method should remain private in a subclass. However, since the method is visible in a subclass, it is always possible to pick its code and define a method of the same name that runs that code, so yet another (heavier) solution would be:

    #class point_again x =
       object
         inherit restricted_point x as super
         method move = super#move
       end;;
    class point_again :
      int ->
      object
        val mutable x : int
        method bump : unit
        method get_x : int
        method move : int -> unit
      end

Of course, private methods can also be virtual. Then, the keywords must appear in this order `method private virtual`.

## 3.7 Class interfaces

Class interfaces are inferred from class definitions. They may also be defined directly and used to restrict the type of a class. Like class declarations, they also define a new type abbreviation.

    #class type restricted_point_type =
       object
         method get_x : int
         method bump : unit
     end;;
    class type restricted_point_type =
      object method bump : unit method get_x : int end

    #fun (x : restricted_point_type) -> x;;
    - : restricted_point_type -> restricted_point_type = <fun>

In addition to program documentation, class interfaces can be used to constrain the type of a class. Both instance variables and concrete private methods can be hidden by a class type constraint. Public and virtual methods, however, cannot.

    #class restricted_point' x = (restricted_point x : restricted_point_type);;
    class restricted_point' : int -> restricted_point_type

Or, equivalently:

    #class restricted_point' = (restricted_point : int -> restricted_point_type);;
    class restricted_point' : int -> restricted_point_type

The interface of a class can also be specified in a module signature, and used to restrict the inferred signature of a module.

    #module type POINT = sig
       class restricted_point' : int ->
         object
           method get_x : int
           method bump : unit
         end
     end;;
    module type POINT =
      sig
        class restricted_point' :
          int -> object method bump : unit method get_x : int end
      end

    #module Point : POINT = struct
       class restricted_point' = restricted_point
     end;;
    module Point : POINT

## 3.8 Inheritance

We illustrate inheritance by defining a class of colored points that inherits from the class of points. This class has all instance variables and all methods of class `point`, plus a new instance variable `c` and a new method `color`.

    #class colored_point x (c : string) =
       object
         inherit point x
         val c = c
         method color = c
       end;;
    class colored_point :
      int ->
      string ->
      object
        val c : string
        val mutable x : int
        method color : string
        method get_offset : int
        method get_x : int
        method move : int -> unit
      end

    #let p' = new colored_point 5 "red";;
    val p' : colored_point = <obj>

    #p'#get_x, p'#color;;
    - : int * string = (5, "red")

A point and a colored point have incompatible types, since a point has no method `color`. However, the function `get_x` below is a generic function applying method `get_x` to any object `p` that has this method (and possibly some others, which are represented by an ellipsis in the type). Thus, it applies to both points and colored points.

    #let get_succ_x p = p#get_x + 1;;
    val get_succ_x : < get_x : int; .. > -> int = <fun>

    #get_succ_x p + get_succ_x p';;
    - : int = 8

Methods need not be declared previously, as shown by the example:

    #let set_x p = p#set_x;;
    val set_x : < set_x : 'a; .. > -> 'a = <fun>

    #let incr p = set_x p (get_succ_x p);;
    val incr : < get_x : int; set_x : int -> 'a; .. > -> 'a = <fun>

## 3.9 Multiple inheritance

Multiple inheritance is allowed. Only the last definition of a method is kept: the redefinition in a subclass of a method that was visible in the parent class overrides the definition in the parent class. Previous definitions of a method can be reused by binding the related ancestor. Below, `super` is bound to the ancestor `printable_point`. The name `super` is a pseudo value identifier that can only be used to invoke a super-class method, as in `super#print`.

    #class printable_colored_point y c =
       object (self)
         val c = c
         method color = c
         inherit printable_point y as super
         method print =
           print_string "(";
           super#print;
           print_string ", ";
           print_string (self#color);
           print_string ")"
       end;;
    class printable_colored_point :
      int ->
      string ->
      object
        val c : string
        val mutable x : int
        method color : string
        method get_x : int
        method move : int -> unit
        method print : unit
      end

    #let p' = new printable_colored_point 17 "red";;
    new point at (10, red)
    val p' : printable_colored_point = <obj>

    #p'#print;;
    (10, red)- : unit = ()

A private method that has been hidden in the parent class is no longer visible, and is thus not overridden. Since initializers are treated as private methods, all initializers along the class hierarchy are evaluated, in the order they are introduced.

## 3.10 Parameterized classes

Reference cells can be implemented as objects. The naive definition fails to typecheck:

    #class ref x_init =
       object
         val mutable x = x_init
         method get = x
         method set y = x <- y
       end;;
    Some type variables are unbound in this type:
      class ref :
        'a ->
        object val mutable x : 'a method get : 'a method set : 'a -> unit end
    The method get has type 'a where 'a is unbound

The reason is that at least one of the methods has a polymorphic type (here, the type of the value stored in the reference cell), thus either the class should be parametric, or the method type should be constrained to a monomorphic type. A monomorphic instance of the class could be defined by:

    #class ref (x_init:int) =
       object
         val mutable x = x_init
         method get = x
         method set y = x <- y
       end;;
    class ref :
      int ->
      object val mutable x : int method get : int method set : int -> unit end

Note that since immediate objects do not define a class type, the have no such restriction.

    #let new_ref x_init =
       object
         val mutable x = x_init
         method get = x
         method set y = x <- y
       end;;
    val new_ref : 'a -> < get : 'a; set : 'a -> unit > = <fun>

On the other hand, a class for polymorphic references must explicitly list the type parameters in its declaration. Class type parameters are always listed between `[` and `]`. The type parameters must also be bound somewhere in the class body by a type constraint.

    #class ['a] ref x_init =
       object
         val mutable x = (x_init : 'a)
         method get = x
         method set y = x <- y
       end;;
    class ['a] ref :
      'a -> object val mutable x : 'a method get : 'a method set : 'a -> unit end

    #let r = new ref 1 in r#set 2; (r#get);;
    - : int = 2

The type parameter in the declaration may actually be constrained in the body of the class definition. In the class type, the actual value of the type parameter is displayed in the `constraint` clause.

    #class ['a] ref_succ (x_init:'a) =
       object
         val mutable x = x_init + 1
         method get = x
         method set y = x <- y
       end;;
    class ['a] ref_succ :
      'a ->
      object
        constraint 'a = int
        val mutable x : int
        method get : int
        method set : int -> unit
      end

Let us consider a more complex example: define a circle, whose center may be any kind of point. We put an additional type constraint in method `move`, since no free variables must remain unaccounted for by the class type parameters.

    #class ['a] circle (c : 'a) =
       object
         val mutable center = c
         method center = center
         method set_center c = center <- c
         method move = (center#move : int -> unit)
       end;;
    class ['a] circle :
      'a ->
      object
        constraint 'a = < move : int -> unit; .. >
        val mutable center : 'a
        method center : 'a
        method move : int -> unit
        method set_center : 'a -> unit
      end

An alternate definition of `circle`, using a `constraint` clause in the class definition, is shown below. The type `#point` used below in the `constraint` clause is an abbreviation produced by the definition of class `point`. This abbreviation unifies with the type of any object belonging to a subclass of class `point`. It actually expands to `< get_x : int; move : int -> unit; .. >`. This leads to the following alternate definition of `circle`, which has slightly stronger constraints on its argument, as we now expect `center` to have a method `get_x`.

    #class ['a] circle (c : 'a) =
       object
         constraint 'a = #point
         val mutable center = c
         method center = center
         method set_center c = center <- c
         method move = center#move
       end;;
    class ['a] circle :
      'a ->
      object
        constraint 'a = #point
        val mutable center : 'a
        method center : 'a
        method move : int -> unit
        method set_center : 'a -> unit
      end

The class `colored_circle` is a specialized version of class `circle` that requires the type of the center to unify with `#colored_point`, and adds a method `color`. Note that when specializing a parameterized class, the instance of type parameter must always be explicitly given. It is again written between `[` and `]`.

    #class ['a] colored_circle c =
       object
         constraint 'a = #colored_point
         inherit ['a] circle c
         method color = center#color
       end;;
    class ['a] colored_circle :
      'a ->
      object
        constraint 'a = #colored_point
        val mutable center : 'a
        method center : 'a
        method color : string
        method move : int -> unit
        method set_center : 'a -> unit
      end

## 3.11 Polymorphic methods

While parameterized classes may be polymorphic in their contents, they are not enough to allow polymorphism of method use.
A classical example is defining an iterator.

    #List.fold_left;;
    - : ('a -> 'b -> 'a) -> 'a -> 'b list -> 'a = <fun>

    #class ['a] intlist (l : int list) =
       object
         method empty = (l = [])
         method fold f (accu : 'a) = List.fold_left f accu l
       end;;
    class ['a] intlist :
      int list ->
      object method empty : bool method fold : ('a -> int -> 'a) -> 'a -> 'a end

At first look, we seem to have a polymorphic iterator, however this does not work in practice.

    #let l = new intlist [1; 2; 3];;
    val l : '_a intlist = <obj>

    #l#fold (fun x y -> x+y) 0;;
    - : int = 6

    #l;;
    - : int intlist = <obj>

    #l#fold (fun s x -> s ^ string_of_int x ^ " ") "";;
    This expression has type int but is here used with type string

Our iterator works, as shows its first use for summation. However, since objects themselves are not polymorphic (only their constructors are), using the `fold` method fixes its type for this individual object. Our next attempt to use it as a string iterator fails.
The problem here is that quantification was wrongly located: this is not the class we want to be polymorphic, but the `fold` method. This can be achieved by giving an explicitly polymorphic type in the method definition.

    #class intlist (l : int list) =
       object
         method empty = (l = [])
         method fold : 'a. ('a -> int -> 'a) -> 'a -> 'a =
           fun f accu -> List.fold_left f accu l
       end;;
    class intlist :
      int list ->
      object method empty : bool method fold : ('a -> int -> 'a) -> 'a -> 'a end

    #let l = new intlist [1; 2; 3];;
    val l : intlist = <obj>

    #l#fold (fun x y -> x+y) 0;;
    - : int = 6

    #l#fold (fun s x -> s ^ string_of_int x ^ " ") "";;
    - : string = "1 2 3 "

As you can see in the class type shown by the compiler, while polymorphic method types must be fully explicit in class definitions (appearing immediately after the method name), quantified type variables can be left implicit in class descriptions. Why require types to be explicit? The problem is that `(int -> int -> int) -> int -> int` would also be a valid type for `fold`, and it happens to be incompatible with the polymorphic type we gave (automatic instantiation only works for toplevel types variables, not for inner quantifiers, where it becomes an undecidable problem.) So the compiler cannot choose between those two types, and must be helped.
However, the type can be completely omitted in the class definition if it is already known, through inheritance or type constraints on self. Here is an example of method overriding.

    #class intlist_rev l =
       object
         inherit intlist l
         method fold f accu = List.fold_left f accu (List.rev l)
       end;;

The following idiom separates description and definition.

    #class type ['a] iterator =
       object method fold : ('b -> 'a -> 'b) -> 'b -> 'b end;;

     class intlist l =
       object (self : int #iterator)
         method empty = (l = [])
         method fold f accu = List.fold_left f accu l
       end;;

Note here the `(self : int #iterator)` idiom, which ensures that this object implements the interface `iterator`.
Polymorphic methods are called in exactly the same way as normal methods, but you should be aware of some limitations of type inference. Namely, a polymorphic method can only be called if its type is known at the call site. Otherwise, the method will be assumed to be monomorphic, and given an incompatible type.

    #let sum lst = lst#fold (fun x y -> x+y) 0;;
    val sum : < fold : (int -> int -> int) -> int -> 'a; .. > -> 'a = <fun>

    #sum l;;
    This expression has type intlist but is here used with type
      < fold : (int -> int -> int) -> int -> 'a; .. >
    Types for method fold are incompatible

The workaround is easy: you should put a type constraint on the parameter.

    #let sum (lst : _ #iterator) = lst#fold (fun x y -> x+y) 0;;
    val sum : int #iterator -> int = <fun>

Of course the constraint may also be an explicit method type. Only occurences of quantified variables are required.

    #let sum lst =
       (lst : < fold : 'a. ('a -> _ -> 'a) -> 'a -> 'a; .. >)#fold (+) 0;;
    val sum : < fold : 'a. ('a -> int -> 'a) -> 'a -> 'a; .. > -> int = <fun>

Another use of polymorphic methods is to allow some form of implicit subtyping in method arguments. We have already seen in section 3.8 how some functions may be polymorphic in the class of their argument. This can be extended to methods.

    #class type point0 = object method get_x : int end;;
    class type point0 = object method get_x : int end

    #class distance_point x =
       object
         inherit point x
         method distance : 'a. (#point0 as 'a) -> int =
           fun other -> abs (other#get_x - x)
       end;;
    class distance_point :
      int ->
      object
        val mutable x : int
        method distance : #point0 -> int
        method get_offset : int
        method get_x : int
        method move : int -> unit
      end

    #let p = new distance_point 3 in
     (p#distance (new point 8), p#distance (new colored_point 1 "blue"));;
    - : int * int = (5, 2)

Note here the special syntax `(#point0 as 'a)` we have to use to quantify the extensible part of `#point0`. As for the variable binder, it can be omitted in class specifications. If you want polymorphism inside object field it must be quantified independently.

    #class multi_poly =
       object
         method m1 : 'a. (< n1 : 'b. 'b -> 'b; .. > as 'a) -> _ =
           fun o -> o#n1 true, o#n1 "hello"
         method m2 : 'a 'b. (< n2 : 'b -> bool; .. > as 'a) -> 'b -> _ =
           fun o x -> o#n2 x
       end;;
    class multi_poly :
      object
        method m1 : < n1 : 'a. 'a -> 'a; .. > -> bool * string
        method m2 : < n2 : 'b -> bool; .. > -> 'b -> bool
      end

In method `m1`, `o` must be an object with at least a method `n1`, itself polymorphic. In method `m2`, the argument of `n2` and `x` must have the same type, which is quantified at the same level as `'a`.

## 3.12 Using coercions

Subtyping is never implicit. There are, however, two ways to perform subtyping. The most general construction is fully explicit: both the domain and the codomain of the type coercion must be given.
We have seen that points and colored points have incompatible types. For instance, they cannot be mixed in the same list. However, a colored point can be coerced to a point, hiding its `color` method:

    #let colored_point_to_point cp = (cp : colored_point :> point);;
    val colored_point_to_point : colored_point -> point = <fun>

    #let p = new point 3 and q = new colored_point 4 "blue";;
    val p : point = <obj>
    val q : colored_point = <obj>

    #let l = [p; (colored_point_to_point q)];;
    val l : point list = [<obj>; <obj>]

An object of type `t` can be seen as an object of type `t'` only if `t` is a subtype of `t'`. For instance, a point cannot be seen as a colored point.

    #(p : point :> colored_point);;
    Type point = < get_offset : int; get_x : int; move : int -> unit >
    is not a subtype of type
      colored_point =
        < color : string; get_offset : int; get_x : int; move : int -> unit >

Indeed, narrowing coercions would be unsafe, and could only be combined with a type case, possibly raising a runtime error. However, there is no such operation available in the language.
Be aware that subtyping and inheritance are not related. Inheritance is a syntactic relation between classes while subtyping is a semantic relation between types. For instance, the class of colored points could have been defined directly, without inheriting from the class of points; the type of colored points would remain unchanged and thus still be a subtype of points.
The domain of a coercion can usually be omitted. For instance, one can define:

    #let to_point cp = (cp :> point);;
    val to_point : #point -> point = <fun>

In this case, the function `colored_point_to_point` is an instance of the function `to_point`. This is not always true, however. The fully explicit coercion is more precise and is sometimes unavoidable. Consider, for example, the following class:

    #class c0 = object method m = {< >} method n = 0 end;;
    class c0 : object ('a) method m : 'a method n : int end

The object type `c0` is an abbreviation for `<m : 'a; n : int> as 'a`. Consider now the type declaration:

    #class type c1 =  object method m : c1 end;;
    class type c1 = object method m : c1 end

The object type `c1` is an abbreviation for the type `<m : 'a> as 'a`. The coercion from an object of type `c0` to an object of type `c1` is correct:

    #fun (x:c0) -> (x : c0 :> c1);;
    - : c0 -> c1 = <fun>

However, the domain of the coercion cannot be omitted here:

    #fun (x:c0) -> (x :> c1);;
    This expression cannot be coerced to type c1 = < m : c1 >; it has type
      c0 = < m : c0; n : int >
    but is here used with type < m : #c1 as 'a; .. >
    Type c0 = < m : c0; n : int > is not compatible with type 'a = < m : c1; .. >
    Type c0 = < m : c0; n : int > is not compatible with type c1 = < m : c1 >
    Only the first object type has a method n.
    This simple coercion was not fully general. Consider using a double coercion.

The solution is to use the explicit form. Sometimes, a change in the class-type definition can also solve the problem

    #class type c2 =  object ('a) method m : 'a end;;
    class type c2 = object ('a) method m : 'a end

    #fun (x:c0) -> (x :> c2);;
    - : c0 -> c2 = <fun>

While class types `c1` and `c2` are different, both object types `c1` and `c2` expand to the same object type (same method names and types). Yet, when the domain of a coercion is left implicit and its co-domain is an abbreviation of a known class type, then the class type, rather than the object type, is used to derive the coercion function. This allows to leave the domain implicit in most cases when coercing form a subclass to its superclass. The type of a coercion can always be seen as below:

    #let to_c1 x = (x :> c1);;
    val to_c1 : < m : #c1; .. > -> c1 = <fun>

    #let to_c2 x = (x :> c2);;
    val to_c2 : #c2 -> c2 = <fun>

Note the difference between the two coercions: in the second case, the type `#c2 = < m : 'a; .. > as 'a` is polymorphically recursive (according to the explicit recursion in the class type of `c2`); hence the success of applying this coercion to an object of class `c0`. On the other hand, in the first case, `c1` was only expanded and unrolled twice to obtain `< m : < m : c1; .. >; .. >` (remember `#c1 = < m : c1; .. >`), without introducing recursion. You may also note that the type of `to_c2` is `#c2 -> c2` while the type of `to_c1` is more general than `#c1 -> c1`. This is not always true, since there are class types for which some instances of `#c` are not subtypes of `c`, as explained in section 3.16. Yet, for parameterless classes the coercion `(_ :> c)` is always more general than `(_ : #c :> c)`.
A common problem may occur when one tries to define a coercion to a class `c` while defining class `c`. The problem is due to the type abbreviation not being completely defined yet, and so its subtypes are not clearly known. Then, a coercion `(_ :> c)` or `(_ : #c :> c)` is taken to be the identity function, as in

    #function x -> (x :> 'a);;
    - : 'a -> 'a = <fun>

As a consequence, if the coercion is applied to `self`, as in the following example, the type of `self` is unified with the closed type `c` (a closed object type is an object type without ellipsis). This would constrain the type of self be closed and is thus rejected. Indeed, the type of self cannot be closed: this would prevent any further extension of the class. Therefore, a type error is generated when the unification of this type with another type would result in a closed object type.

    #class c = object method m = 1 end
     and d = object (self)
       inherit c
       method n = 2
       method as_c = (self :> c)
     end;;
    This expression cannot be coerced to type c = < m : int >; it has type
      < as_c : c; m : int; n : int; .. >
    but is here used with type c
    Self type cannot be unified with a closed object type

However, the most common instance of this problem, coercing self to its current class, is detected as a special case by the type checker, and properly typed.

    #class c = object (self) method m = (self :> c) end;;
    class c : object method m : c end

This allows the following idiom, keeping a list of all objects belonging to a class or its subclasses:

    #let all_c = ref [];;
    val all_c : '_a list ref = {contents = []}

    #class c (m : int) =
       object (self)
         method m = m
         initializer all_c := (self :> c) :: !all_c
       end;;
    class c : int -> object method m : int end

This idiom can in turn be used to retrieve an object whose type has been weakened:

    #let rec lookup_obj obj = function [] -> raise Not_found
       | obj' :: l ->
          if (obj :> < >) = (obj' :> < >) then obj' else lookup_obj obj l ;;
    val lookup_obj : < .. > -> (< .. > as 'a) list -> 'a = <fun>

    #let lookup_c obj = lookup_obj obj !all_c;;
    val lookup_c : < .. > -> < m : int > = <fun>

The type `< m : int >` we see here is just the expansion of `c`, due to the use of a reference; we have succeeded in getting back an object of type `c`.
The previous coercion problem can often be avoided by first defining the abbreviation, using a class type:

    #class type c' = object method m : int end;;
    class type c' = object method m : int end

    #class c : c' = object method m = 1 end
     and d = object (self)
       inherit c
       method n = 2
       method as_c = (self :> c')
     end;;
    class c : c'
    and d : object method as_c : c' method m : int method n : int end

It is also possible to use a virtual class. Inheriting from this class simultaneously allows to enforce all methods of `c` to have the same type as the methods of `c'`.

    #class virtual c' = object method virtual m : int end;;
    class virtual c' : object method virtual m : int end

    #class c = object (self) inherit c' method m = 1 end;;
    class c : object method m : int end

One could think of defining the type abbreviation directly:

    #type c' = <m : int>;;

However, the abbreviation `#c'` cannot be defined directly in a similar way. It can only be defined by a class or a class-type definition. This is because `#` sharp abbreviations carry an implicit anonymous variable `..` that cannot be explicitly named. The closer you get to it is:

    #type 'a c'_class = 'a constraint 'a = < m : int; .. >;;

with an extra type variable capturing the open object type.

## 3.13 Functional objects

It is possible to write a version of class `point` without assignments on the instance variables. The construct `{< ... >}` returns a copy of “self” (that is, the current object), possibly changing the value of some instance variables.

    #class functional_point y =
       object
         val x = y
         method get_x = x
         method move d = {< x = x + d >}
       end;;
    class functional_point :
      int ->
      object ('a) val x : int method get_x : int method move : int -> 'a end

    #let p = new functional_point 7;;
    val p : functional_point = <obj>

    #p#get_x;;
    - : int = 7

    #(p#move 3)#get_x;;
    - : int = 10

    #p#get_x;;
    - : int = 7

Note that the type abbreviation `functional_point` is recursive, which can be seen in the class type of `functional_point`: the type of self is `'a` and `'a` appears inside the type of the method `move`.
The above definition of `functional_point` is not equivalent to the following:

    #class bad_functional_point y =
       object
         val x = y
         method get_x = x
         method move d = new bad_functional_point (x+d)
       end;;
    class bad_functional_point :
      int ->
      object
        val x : int
        method get_x : int
        method move : int -> bad_functional_point
      end

While objects of either class will behave the same, objects of their subclasses will be different. In a subclass of the latter, the method `move` will keep returning an object of the parent class. On the contrary, in a subclass of the former, the method `move` will return an object of the subclass.
Functional update is often used in conjunction with binary methods as illustrated in section 5.2.1.

## 3.14 Cloning objects

Objects can also be cloned, whether they are functional or imperative. The library function `Oo.copy` makes a shallow copy of an object. That is, it returns an object that is equal to the previous one. The instance variables have been copied but their contents are shared. Assigning a new value to an instance variable of the copy (using a method call) will not affect instance variables of the original, and conversely. A deeper assignment (for example if the instance variable if a reference cell) will of course affect both the original and the copy.
The type of `Oo.copy` is the following:

    #Oo.copy;;
    - : (< .. > as 'a) -> 'a = <fun>

The keyword `as` in that type binds the type variable `'a` to the object type `< .. >`. Therefore, `Oo.copy` takes an object with any methods (represented by the ellipsis), and returns an object of the same type. The type of `Oo.copy` is different from type `< .. > -> < .. >` as each ellipsis represents a different set of methods. Ellipsis actually behaves as a type variable.

    #let p = new point 5;;
    val p : point = <obj>

    #let q = Oo.copy p;;
    val q : < get_offset : int; get_x : int; move : int -> unit > = <obj>

    #q#move 7; (p#get_x, q#get_x);;
    - : int * int = (5, 12)

In fact, `Oo.copy p` will behave as `p#copy` assuming that a public method `copy` with body `{< >}` has been defined in the class of `p`.
Objects can be compared using the generic comparison functions `=` and `<>`. Two objects are equal if and only if they are physically equal. In particular, an object and its copy are not equal.

    #let q = Oo.copy p;;
    val q : < get_offset : int; get_x : int; move : int -> unit > = <obj>

    #p = q, p = p;;
    - : bool * bool = (false, true)

Other generic comparissons such as (`<`, `<=`,...) can also be used on objects. The relation `<` defines an unspecified but strict ordering on objets. The ordering relationship between two objects is fixed once for all after the two objects have been created and it is not affected by mutation of fields.
Cloning and override have a non empty intersection. They are interchangeable when used within an object and without overriding any field:

    #class copy =
       object
         method copy = {< >}
       end;;
    class copy : object ('a) method copy : 'a end

    #class copy =
       object (self)
         method copy = Oo.copy self
       end;;
    class copy : object ('a) method copy : 'a end

Only the override can be used to actually override fields, and only the `Oo.copy` primitive can be used externally.
Cloning can also be used to provide facilities for saving and restoring the state of objects.

    #class backup =
       object (self : 'mytype)
         val mutable copy = None
         method save = copy <- Some {< copy = None >}
         method restore = match copy with Some x -> x | None -> self
       end;;
    class backup :
      object ('a)
        val mutable copy : 'a option
        method restore : 'a
        method save : unit
      end

The above definition will only backup one level. The backup facility can be added to any class using multiple inheritance.

    #class ['a] backup_ref x = object inherit ['a] ref x inherit backup end;;
    class ['a] backup_ref :
      'a ->
      object ('b)
        val mutable copy : 'b option
        val mutable x : 'a
        method get : 'a
        method restore : 'b
        method save : unit
        method set : 'a -> unit
      end

    #let rec get p n = if n = 0 then p # get else get (p # restore) (n-1);;
    val get : (< get : 'b; restore : 'a; .. > as 'a) -> int -> 'b = <fun>

    #let p = new backup_ref 0  in
     p # save; p # set 1; p # save; p # set 2;
     [get p 0; get p 1; get p 2; get p 3; get p 4];;
    - : int list = [2; 1; 1; 1; 1]

A variant of backup could retain all copies. (We then add a method clear to manually erase all copies.)

    #class backup =
       object (self : 'mytype)
         val mutable copy = None
         method save = copy <- Some {< >}
         method restore = match copy with Some x -> x | None -> self
         method clear = copy <- None
       end;;
    class backup :
      object ('a)
        val mutable copy : 'a option
        method clear : unit
        method restore : 'a
        method save : unit
      end

    #class ['a] backup_ref x = object inherit ['a] ref x inherit backup end;;
    class ['a] backup_ref :
      'a ->
      object ('b)
        val mutable copy : 'b option
        val mutable x : 'a
        method clear : unit
        method get : 'a
        method restore : 'b
        method save : unit
        method set : 'a -> unit
      end

    #let p = new backup_ref 0  in
     p # save; p # set 1; p # save; p # set 2;
     [get p 0; get p 1; get p 2; get p 3; get p 4];;
    - : int list = [2; 1; 0; 0; 0]

## 3.15 Recursive classes

Recursive classes can be used to define objects whose types are mutually recursive.

    #class window =
       object
         val mutable top_widget = (None : widget option)
         method top_widget = top_widget
       end
     and widget (w : window) =
       object
         val window = w
         method window = window
       end;;
    class window :
      object
        val mutable top_widget : widget option
        method top_widget : widget option
      end
    and widget : window -> object val window : window method window : window end

Although their types are mutually recursive, the classes `widget` and `window` are themselves independent.

## 3.16 Binary methods

A binary method is a method which takes an argument of the same type as self. The class `comparable` below is a template for classes with a binary method `leq` of type `'a -> bool` where the type variable `'a` is bound to the type of self. Therefore, `#comparable` expands to `< leq : 'a -> bool; .. > as 'a`. We see here that the binder `as` also allows to write recursive types.

    #class virtual comparable =
       object (_ : 'a)
         method virtual leq : 'a -> bool
       end;;
    class virtual comparable : object ('a) method virtual leq : 'a -> bool end

We then define a subclass `money` of `comparable`. The class money simply wraps floats as comparable objects. We will extend it below with more operations. There is a type constraint on the class parameter `x` as the primitive `<=` is a polymorphic comparison function in Objective Caml. The `inherit` clause ensures that the type of objects of this class is an instance of `#comparable`.

    #class money (x : float) =
       object
         inherit comparable
         val repr = x
         method value = repr
         method leq p = repr <= p#value
       end;;
    class money :
      float ->
      object ('a)
        val repr : float
        method leq : 'a -> bool
        method value : float
      end

Note that the type `money1` is not a subtype of type `comparable`, as the self type appears in contravariant position in the type of method `leq`. Indeed, an object `m` of class `money` has a method `leq` that expects an argument of type `money` since it accesses its `value` method. Considering `m` of type `comparable` would allow to call method `leq` on `m` with an argument that does not have a method `value`, which would be an error.
Similarly, the type `money2` below is not a subtype of type `money`.

    #class money2 x =
       object
         inherit money x
         method times k = {< repr = k *. repr >}
       end;;
    class money2 :
      float ->
      object ('a)
        val repr : float
        method leq : 'a -> bool
        method times : float -> 'a
        method value : float
      end

It is however possible to define functions that manipulate objects of type either `money` or `money2`: the function `min` will return the minimum of any two objects whose type unifies with `#comparable`. The type of `min` is not the same as `#comparable -> #comparable -> #comparable`, as the abbreviation `#comparable` hides a type variable (an ellipsis). Each occurrence of this abbreviation generates a new variable.

    #let min (x : #comparable) y =
       if x#leq y then x else y;;
    val min : (#comparable as 'a) -> 'a -> 'a = <fun>

This function can be applied to objects of type `money` or `money2`.

    #(min (new money  1.3) (new money 3.1))#value;;
    - : float = 1.3

    #(min (new money2 5.0) (new money2 3.14))#value;;
    - : float = 3.14

More examples of binary methods can be found in sections 5.2.1 and 5.2.3.
Notice the use of functional update for method `times`. Writing `new money2 (k *. repr)` instead of `{< repr = k *. repr >}` would not behave well with inheritance: in a subclass `money3` of `money2` the `times` method would return an object of class `money2` but not of class `money3` as would be expected.
The class `money` could naturally carry another binary method. Here is a direct definition:

    #class money x =
       object (self : 'a)
         val repr = x
         method value = repr
         method print = print_float repr
         method times k = {< repr = k *. x >}
         method leq (p : 'a) = repr <= p#value
         method plus (p : 'a) = {< repr = x +. p#value >}
       end;;
    class money :
      float ->
      object ('a)
        val repr : float
        method leq : 'a -> bool
        method plus : 'a -> 'a
        method print : unit
        method times : float -> 'a
        method value : float
      end

## 3.17 Friends

The above class `money` reveals a problem that often occurs with binary methods. In order to interact with other objects of the same class, the representation of `money` objects must be revealed, using a method such as `value`. If we remove all binary methods (here `plus` and `leq`), the representation can easily be hidden inside objects by removing the method `value` as well. However, this is not possible as long as some binary requires access to the representation on object of the same class but different from self.

    #class safe_money x =
       object (self : 'a)
         val repr = x
         method print = print_float repr
         method times k = {< repr = k *. x >}
       end;;
    class safe_money :
      float ->
      object ('a)
        val repr : float
        method print : unit
        method times : float -> 'a
      end

Here, the representation of the object is known only to a particular object. To make it available to other objects of the same class, we are forced to make it available to the whole world. However we can easily restrict the visibility of the representation using the module system.

    #module type MONEY =
       sig
         type t
         class c : float ->
           object ('a)
             val repr : t
             method value : t
             method print : unit
             method times : float -> 'a
             method leq : 'a -> bool
             method plus : 'a -> 'a
           end
       end;;

     module Euro : MONEY =
       struct
         type t = float
         class c x =
           object (self : 'a)
             val repr = x
             method value = repr
             method print = print_float repr
             method times k = {< repr = k *. x >}
             method leq (p : 'a) = repr <= p#value
             method plus (p : 'a) = {< repr = x +. p#value >}
           end
       end;;

Another example of friend functions may be found in section 5.2.3. These examples occur when a group of objects (here objects of the same class) and functions should see each others internal representation, while their representation should be hidden from the outside. The solution is always to define all friends in the same module, give access to the representation and use a signature constraint to make the representation abstract outside of the module.