# Chapter 5 Advanced examples with classes and modules

- Extended example: bank accounts
- Simple modules as classes
- The subject/observer pattern

(Chapter written by Didier Rémy)

In this chapter, we show some larger examples using objects, classes and modules. We review many of the object features simultaneously on the example of a bank account. We show how modules taken from the standard library can be expressed as classes. Lastly, we describe a programming pattern know of as virtual types through the example of window managers.

## 5.1 Extended example: bank accounts

In this section, we illustrate most aspects of Object and inheritance by refining, debugging, and specializing the following initial naive definition of a simple bank account. (We reuse the module `Euro` defined at the end of chapter 3.)

    #let euro = new Euro.c;;
    val euro : float -> Euro.c = <fun>

    #let zero = euro 0.;;
    val zero : Euro.c = <obj>

    #let neg x = x#times (-1.);;
    val neg : < times : float -> ’a; .. > -> ’a = <fun>

    #class account =
       object
         val mutable balance = zero
         method balance = balance
         method deposit x = balance <- balance # plus x
         method withdraw x =
           if x#leq balance then (balance <- balance # plus (neg x); x) else zero
       end;;
    class account :
      object
        val mutable balance : Euro.c
        method balance : Euro.c
        method deposit : Euro.c -> unit
        method withdraw : Euro.c -> Euro.c
      end

    #let c = new account in c # deposit (euro 100.); c # withdraw (euro 50.);;
    - : Euro.c = <obj>

We now refine this definition with a method to compute interest.

    #class account_with_interests =
       object (self)
         inherit account
         method private interest = self # deposit (self # balance # times 0.03)
       end;;
    class account_with_interests :
      object
        val mutable balance : Euro.c
        method balance : Euro.c
        method deposit : Euro.c -> unit
        method private interest : unit
        method withdraw : Euro.c -> Euro.c
      end

We make the method `interest` private, since clearly it should not be called freely from the outside. Here, it is only made accessible to subclasses that will manage monthly or yearly updates of the account.

We should soon fix a bug in the current definition: the deposit method can be used for withdrawing money by depositing negative amounts. We can fix this directly:

    #class safe_account =
       object
         inherit account
         method deposit x = if zero#leq x then balance <- balance#plus x
       end;;
    class safe_account :
      object
        val mutable balance : Euro.c
        method balance : Euro.c
        method deposit : Euro.c -> unit
        method withdraw : Euro.c -> Euro.c
      end

However, the bug might be fixed more safely by the following definition:

    #class safe_account =
       object
         inherit account as unsafe
         method deposit x =
           if zero#leq x then unsafe # deposit x
           else raise (Invalid_argument "deposit")
       end;;
    class safe_account :
      object
        val mutable balance : Euro.c
        method balance : Euro.c
        method deposit : Euro.c -> unit
        method withdraw : Euro.c -> Euro.c
      end

In particular, this does not require the knowledge of the implementation of the method `deposit`.

To keep trace of operations, we extend the class with a mutable field `history` and a private method `trace` to add an operation in the log. Then each method to be traced is redefined.

    #type ’a operation = Deposit of ’a | Retrieval of ’a;;
    type ’a operation = Deposit of ’a | Retrieval of ’a

    #class account_with_history =
       object (self)
         inherit safe_account as super
         val mutable history = []
         method private trace x = history <- x :: history
         method deposit x = self#trace (Deposit x);  super#deposit x
         method withdraw x = self#trace (Retrieval x); super#withdraw x
         method history = List.rev history
       end;;
    class account_with_history :
      object
        val mutable balance : Euro.c
        val mutable history : Euro.c operation list
        method balance : Euro.c
        method deposit : Euro.c -> unit
        method history : Euro.c operation list
        method private trace : Euro.c operation -> unit
        method withdraw : Euro.c -> Euro.c
      end

One may wish to open an account and simultaneously deposit some initial amount. Although the initial implementation did not address this requirement, it can be achieved by using an initializer.

    #class account_with_deposit x =
       object
         inherit account_with_history
         initializer balance <- x
       end;;
    class account_with_deposit :
      Euro.c ->
      object
        val mutable balance : Euro.c
        val mutable history : Euro.c operation list
        method balance : Euro.c
        method deposit : Euro.c -> unit
        method history : Euro.c operation list
        method private trace : Euro.c operation -> unit
        method withdraw : Euro.c -> Euro.c
      end

A better alternative is:

    #class account_with_deposit x =
       object (self)
         inherit account_with_history
         initializer self#deposit x
       end;;
    class account_with_deposit :
      Euro.c ->
      object
        val mutable balance : Euro.c
        val mutable history : Euro.c operation list
        method balance : Euro.c
        method deposit : Euro.c -> unit
        method history : Euro.c operation list
        method private trace : Euro.c operation -> unit
        method withdraw : Euro.c -> Euro.c
      end

Indeed, the latter is safer since the call to `deposit` will automatically benefit from safety checks and from the trace. Let’s test it:

    #let ccp = new account_with_deposit (euro 100.) in
     let balance = ccp#withdraw (euro 50.) in
     ccp#history;;
    Warning 26: unused variable balance.
    - : Euro.c operation list = [Deposit <obj>; Retrieval <obj>]

Closing an account can be done with the following polymorphic function:

    #let close c = c#withdraw (c#balance);;
    val close : < balance : ’a; withdraw : ’a -> ’b; .. > -> ’b = <fun>

Of course, this applies to all sorts of accounts.

Finally, we gather several versions of the account into a module `Account` abstracted over some currency.

    #let today () = (01,01,2000) (* an approximation *)
     module Account (M:MONEY) =
       struct
         type m = M.c
         let m = new M.c
         let zero = m 0.

         class bank =
           object (self)
             val mutable balance = zero
             method balance = balance
             val mutable history = []
             method private trace x = history <- x::history
             method deposit x =
               self#trace (Deposit x);
               if zero#leq x then balance <- balance # plus x
               else raise (Invalid_argument "deposit")
             method withdraw x =
               if x#leq balance then
                 (balance <- balance # plus (neg x); self#trace (Retrieval x); x)
               else zero
             method history = List.rev history
           end

         class type client_view =
           object
             method deposit : m -> unit
             method history : m operation list
             method withdraw : m -> m
             method balance : m
           end

         class virtual check_client x =
           let y = if (m 100.)#leq x then x
           else raise (Failure "Insufficient initial deposit") in
           object (self) initializer self#deposit y end

         module Client (B : sig class bank : client_view end) =
           struct
             class account x : client_view =
               object
                 inherit B.bank
                 inherit check_client x
               end

             let discount x =
               let c = new account x in
               if today() < (1998,10,30) then c # deposit (m 100.); c
           end
       end;;

This shows the use of modules to group several class definitions that can in fact be thought of as a single unit. This unit would be provided by a bank for both internal and external uses. This is implemented as a functor that abstracts over the currency so that the same code can be used to provide accounts in different currencies.

The class `bank` is the real implementation of the bank account (it could have been inlined). This is the one that will be used for further extensions, refinements, etc. Conversely, the client will only be given the client view.

    #module Euro_account = Account(Euro);;

     module Client = Euro_account.Client (Euro_account);;

     new Client.account (new Euro.c 100.);;

Hence, the clients do not have direct access to the `balance`, nor the `history` of their own accounts. Their only way to change their balance is to deposit or withdraw money. It is important to give the clients a class and not just the ability to create accounts (such as the promotional `discount` account), so that they can personalize their account. For instance, a client may refine the `deposit` and `withdraw` methods so as to do his own financial bookkeeping, automatically. On the other hand, the function `discount` is given as such, with no possibility for further personalization.

It is important that to provide the client’s view as a functor `Client` so that client accounts can still be build after a possible specialization of the `bank`. The functor `Client` may remain unchanged and be passed the new definition to initialize a client’s view of the extended account.

    #module Investment_account (M : MONEY) =
       struct
         type m = M.c
         module A = Account(M)

         class bank =
           object
             inherit A.bank as super
             method deposit x =
               if (new M.c 1000.)#leq x then
                 print_string "Would you like to invest?";
               super#deposit x
           end

         module Client = A.Client
       end;;

The functor `Client` may also be redefined when some new features of the account can be given to the client.

    #module Internet_account (M : MONEY) =
       struct
         type m = M.c
         module A = Account(M)

         class bank =
           object
             inherit A.bank
             method mail s = print_string s
           end

         class type client_view =
           object
             method deposit : m -> unit
             method history : m operation list
             method withdraw : m -> m
             method balance : m
             method mail : string -> unit
           end

         module Client (B : sig class bank : client_view end) =
           struct
             class account x : client_view =
               object
                 inherit B.bank
                 inherit A.check_client x
               end
           end
       end;;

## 5.2 Simple modules as classes

One may wonder whether it is possible to treat primitive types such as integers and strings as objects. Although this is usually uninteresting for integers or strings, there may be some situations where this is desirable. The class `money` above is such an example. We show here how to do it for strings.

### 5.2.1 Strings

A naive definition of strings as objects could be:

    #class ostring s =
       object
          method get n = String.get s n
          method set n c = String.set s n c
          method print = print_string s
          method copy = new ostring (String.copy s)
       end;;
    class ostring :
      string ->
      object
        method copy : ostring
        method get : int -> char
        method print : unit
        method set : int -> char -> unit
      end

However, the method `copy` returns an object of the class `ostring`, and not an objet of the current class. Hence, if the class is further extended, the method `copy` will only return an object of the parent class.

    #class sub_string s =
       object
          inherit ostring s
          method sub start len = new sub_string (String.sub s  start len)
       end;;
    class sub_string :
      string ->
      object
        method copy : ostring
        method get : int -> char
        method print : unit
        method set : int -> char -> unit
        method sub : int -> int -> sub_string
      end

As seen in section 3.16, the solution is to use functional update instead. We need to create an instance variable containing the representation `s` of the string.

    #class better_string s =
       object
          val repr = s
          method get n = String.get repr n
          method set n c = String.set repr n c
          method print = print_string repr
          method copy = {< repr = String.copy repr >}
          method sub start len = {< repr = String.sub s  start len >}
       end;;
    class better_string :
      string ->
      object (’a)
        val repr : string
        method copy : ’a
        method get : int -> char
        method print : unit
        method set : int -> char -> unit
        method sub : int -> int -> ’a
      end

As shown in the inferred type, the methods `copy` and `sub` now return objects of the same type as the one of the class.

Another difficulty is the implementation of the method `concat`. In order to concatenate a string with another string of the same class, one must be able to access the instance variable externally. Thus, a method `repr` returning s must be defined. Here is the correct definition of strings:

    #class ostring s =
       object (self : ’mytype)
          val repr = s
          method repr = repr
          method get n = String.get repr n
          method set n c = String.set repr n c
          method print = print_string repr
          method copy = {< repr = String.copy repr >}
          method sub start len = {< repr = String.sub s start len >}
          method concat (t : ’mytype) = {< repr = repr ^ t#repr >}
       end;;
    class ostring :
      string ->
      object (’a)
        val repr : string
        method concat : ’a -> ’a
        method copy : ’a
        method get : int -> char
        method print : unit
        method repr : string
        method set : int -> char -> unit
        method sub : int -> int -> ’a
      end

Another constructor of the class string can be defined to return an uninitialized string of a given length:

    #class cstring n = ostring (String.create n);;
    class cstring : int -> ostring

Here, exposing the representation of strings is probably harmless. We do could also hide the representation of strings as we hid the currency in the class `money` of section 3.17.

#### Stacks

There is sometimes an alternative between using modules or classes for parametric data types. Indeed, there are situations when the two approaches are quite similar. For instance, a stack can be straightforwardly implemented as a class:

    #exception Empty;;
    exception Empty

    #class [’a] stack =
       object
         val mutable l = ([] : ’a list)
         method push x = l <- x::l
         method pop = match l with [] -> raise Empty | a::l’ -> l <- l’; a
         method clear = l <- []
         method length = List.length l
       end;;
    class [’a] stack :
      object
        val mutable l : ’a list
        method clear : unit
        method length : int
        method pop : ’a
        method push : ’a -> unit
      end

However, writing a method for iterating over a stack is more problematic. A method `fold` would have type `(’b -> ’a -> ’b) -> ’b -> ’b`. Here `’a` is the parameter of the stack. The parameter `’b` is not related to the class `’a stack` but to the argument that will be passed to the method `fold`. A naive approach is to make `’b` an extra parameter of class `stack`:

    #class [’a, ’b] stack2 =
       object
         inherit [’a] stack
         method fold f (x : ’b) = List.fold_left f x l
       end;;
    class [’a, ’b] stack2 :
      object
        val mutable l : ’a list
        method clear : unit
        method fold : (’b -> ’a -> ’b) -> ’b -> ’b
        method length : int
        method pop : ’a
        method push : ’a -> unit
      end

However, the method `fold` of a given object can only be applied to functions that all have the same type:

    #let s = new stack2;;
    val s : (’_a, ’_b) stack2 = <obj>

    #s#fold (+) 0;;
    - : int = 0

    #s;;
    - : (int, int) stack2 = <obj>

A better solution is to use polymorphic methods, which were introduced in OCaml version 3.05. Polymorphic methods makes it possible to treat the type variable `’b` in the type of `fold` as universally quantified, giving `fold` the polymorphic type `Forall ’b. (’b -> ’a -> ’b) -> ’b -> ’b`. An explicit type declaration on the method `fold` is required, since the type checker cannot infer the polymorphic type by itself.

    #class [’a] stack3 =
       object
         inherit [’a] stack
         method fold : ’b. (’b -> ’a -> ’b) -> ’b -> ’b
                     = fun f x -> List.fold_left f x l
       end;;
    class [’a] stack3 :
      object
        val mutable l : ’a list
        method clear : unit
        method fold : (’b -> ’a -> ’b) -> ’b -> ’b
        method length : int
        method pop : ’a
        method push : ’a -> unit
      end

### 5.2.2 Hashtbl

A simplified version of object-oriented hash tables should have the following class type.

    #class type [’a, ’b] hash_table =
       object
         method find : ’a -> ’b
         method add : ’a -> ’b -> unit
       end;;
    class type [’a, ’b] hash_table =
      object method add : ’a -> ’b -> unit method find : ’a -> ’b end

A simple implementation, which is quite reasonable for small hastables is to use an association list:

    #class [’a, ’b] small_hashtbl : [’a, ’b] hash_table =
       object
         val mutable table = []
         method find key = List.assoc key table
         method add key valeur = table <- (key, valeur) :: table
       end;;
    class [’a, ’b] small_hashtbl : [’a, ’b] hash_table

A better implementation, and one that scales up better, is to use a true hash tables… whose elements are small hash tables!

    #class [’a, ’b] hashtbl size : [’a, ’b] hash_table =
       object (self)
         val table = Array.init size (fun i -> new small_hashtbl)
         method private hash key =
           (Hashtbl.hash key) mod (Array.length table)
         method find key = table.(self#hash key) # find key
         method add key = table.(self#hash key) # add key
       end;;
    class [’a, ’b] hashtbl : int -> [’a, ’b] hash_table

### 5.2.3 Sets

Implementing sets leads to another difficulty. Indeed, the method `union` needs to be able to access the internal representation of another object of the same class.

This is another instance of friend functions as seen in section 3.17. Indeed, this is the same mechanism used in the module `Set` in the absence of objects.

In the object-oriented version of sets, we only need to add an additional method `tag` to return the representation of a set. Since sets are parametric in the type of elements, the method `tag` has a parametric type `’a tag`, concrete within the module definition but abstract in its signature. From outside, it will then be guaranteed that two objects with a method `tag` of the same type will share the same representation.

    #module type SET =
       sig
         type ’a tag
         class [’a] c :
           object (’b)
             method is_empty : bool
             method mem : ’a -> bool
             method add : ’a -> ’b
             method union : ’b -> ’b
             method iter : (’a -> unit) -> unit
             method tag : ’a tag
           end
       end;;

     module Set : SET =
       struct
         let rec merge l1 l2 =
           match l1 with
             [] -> l2
           | h1 :: t1 ->
               match l2 with
                 [] -> l1
               | h2 :: t2 ->
                   if h1 < h2 then h1 :: merge t1 l2
                   else if h1 > h2 then h2 :: merge l1 t2
                   else merge t1 l2
         type ’a tag = ’a list
         class [’a] c =
           object (_ : ’b)
             val repr = ([] : ’a list)
             method is_empty = (repr = [])
             method mem x = List.exists ((=) x) repr
             method add x = {< repr = merge [x] repr >}
             method union (s : ’b) = {< repr = merge repr s#tag >}
             method iter (f : ’a -> unit) = List.iter f repr
             method tag = repr
           end
       end;;

## 5.3 The subject/observer pattern

The following example, known as the subject/observer pattern, is often presented in the literature as a difficult inheritance problem with inter-connected classes. The general pattern amounts to the definition a pair of two classes that recursively interact with one another.

The class `observer` has a distinguished method `notify` that requires two arguments, a subject and an event to execute an action.

    #class virtual [’subject, ’event] observer =
       object
         method virtual notify : ’subject ->  ’event -> unit
       end;;
    class virtual [’a, ’b] observer :
      object method virtual notify : ’a -> ’b -> unit end

The class `subject` remembers a list of observers in an instance variable, and has a distinguished method `notify_observers` to broadcast the message `notify` to all observers with a particular event `e`.

    #class [’observer, ’event] subject =
       object (self)
         val mutable observers = ([]:’observer list)
         method add_observer obs = observers <- (obs :: observers)
         method notify_observers (e : ’event) =
             List.iter (fun x -> x#notify self e) observers
       end;;
    class [’a, ’b] subject :
      object (’c)
        constraint ’a = < notify : ’c -> ’b -> unit; .. >
        val mutable observers : ’a list
        method add_observer : ’a -> unit
        method notify_observers : ’b -> unit
      end

The difficulty usually relies in defining instances of the pattern above by inheritance. This can be done in a natural and obvious manner in Ocaml, as shown on the following example manipulating windows.

    #type event = Raise | Resize | Move;;
    type event = Raise | Resize | Move

    #let string_of_event = function
         Raise -> "Raise" | Resize -> "Resize" | Move -> "Move";;
    val string_of_event : event -> string = <fun>

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

    #class [’observer] window_subject =
       let id = count := succ !count; !count in
       object (self)
         inherit [’observer, event] subject
         val mutable position = 0
         method identity = id
         method move x = position <- position + x; self#notify_observers Move
         method draw = Printf.printf "{Position = %d}\n"  position;
       end;;
    class [’a] window_subject :
      object (’b)
        constraint ’a = < notify : ’b -> event -> unit; .. >
        val mutable observers : ’a list
        val mutable position : int
        method add_observer : ’a -> unit
        method draw : unit
        method identity : int
        method move : int -> unit
        method notify_observers : event -> unit
      end

    #class [’subject] window_observer =
       object
         inherit [’subject, event] observer
         method notify s e = s#draw
       end;;
    class [’a] window_observer :
      object
        constraint ’a = < draw : unit; .. >
        method notify : ’a -> event -> unit
      end

Unsurprisingly the type of `window` is recursive.

    #let window = new window_subject;;
    val window : < notify : ’a -> event -> unit; _.. > window_subject as ’a =
      <obj>

However, the two classes of `window_subject` and `window_observer` are not mutually recursive.

    #let window_observer = new window_observer;;
    val window_observer : < draw : unit; _.. > window_observer = <obj>

    #window#add_observer window_observer;;
    - : unit = ()

    #window#move 1;;
    {Position = 1}
    - : unit = ()

Classes `window_observer` and `window_subject` can still be extended by inheritance. For instance, one may enrich the `subject` with new behaviors and refined the behavior of the observer.

    #class [’observer] richer_window_subject =
       object (self)
         inherit [’observer] window_subject
         val mutable size = 1
         method resize x = size <- size + x; self#notify_observers Resize
         val mutable top = false
         method raise = top <- true; self#notify_observers Raise
         method draw = Printf.printf "{Position = %d; Size = %d}\n"  position size;
       end;;
    class [’a] richer_window_subject :
      object (’b)
        constraint ’a = < notify : ’b -> event -> unit; .. >
        val mutable observers : ’a list
        val mutable position : int
        val mutable size : int
        val mutable top : bool
        method add_observer : ’a -> unit
        method draw : unit
        method identity : int
        method move : int -> unit
        method notify_observers : event -> unit
        method raise : unit
        method resize : int -> unit
      end

    #class [’subject] richer_window_observer =
       object
         inherit [’subject] window_observer as super
         method notify s e = if e <> Raise then s#raise; super#notify s e
       end;;
    class [’a] richer_window_observer :
      object
        constraint ’a = < draw : unit; raise : unit; .. >
        method notify : ’a -> event -> unit
      end

We can also create a different kind of observer:

    #class [’subject] trace_observer =
       object
         inherit [’subject, event] observer
         method notify s e =
           Printf.printf
             "<Window %d <== %s>\n" s#identity (string_of_event e)
       end;;
    class [’a] trace_observer :
      object
        constraint ’a = < identity : int; .. >
        method notify : ’a -> event -> unit
      end

and attached several observers to the same object:

    #let window = new richer_window_subject;;
    val window :
      < notify : ’a -> event -> unit; _.. > richer_window_subject as ’a = <obj>

    #window#add_observer (new richer_window_observer);;
    - : unit = ()

    #window#add_observer (new trace_observer);;
    - : unit = ()

    #window#move 1; window#resize 2;;
    <Window 1 <== Move>
    <Window 1 <== Raise>
    {Position = 1; Size = 1}
    {Position = 1; Size = 1}
    <Window 1 <== Resize>
    <Window 1 <== Raise>
    {Position = 1; Size = 3}
    {Position = 1; Size = 3}
    - : unit = ()