# Chapter 8 Advanced examples with classes and modules

- 8.1 Extended example: bank accounts
- 8.2 Simple modules as classes
- 8.3 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 known as virtual types through the example of window managers.

## ﻿8.1 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 track 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;;
- : 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 method virtual deposit: m -> unit 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 to provide the client’s view as a functor Client so that client accounts can still be built 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;;

## ﻿8.2 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.

### ﻿8.2.1 Strings

A naive definition of strings as objects could be:

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

However, the method escaped returns an object of the class ostring, and not an object of the current class. Hence, if the class is further extended, the method escaped 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 escaped : ostring method get : int -> char method print : 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 print = print_string repr method escaped = {< repr = String.escaped repr >} method sub start len = {< repr = String.sub s start len >} end;;
class better_string : string -> object ('a) val repr : string method escaped : 'a method get : int -> char method print : unit method sub : int -> int -> 'a end

As shown in the inferred type, the methods escaped 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 print = print_string repr method escaped = {< repr = String.escaped 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 escaped : 'a method get : int -> char method print : unit method repr : string method sub : int -> int -> 'a end

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

# class cstring n = ostring (String.make 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 : ('_weak1, '_weak2) 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

### ﻿8.2.2 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 hash tables 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 value = table <- (key, value) :: 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 table… 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

### ﻿8.2.3 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;;

## ﻿8.3 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 ['subject, 'event] observer : object method virtual notify : 'subject -> 'event -> 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, 'event] subject : object ('b) constraint 'a = < notify : 'b -> 'event -> unit; .. > val mutable observers : 'a list method add_observer : 'a -> unit method notify_observers : 'event -> unit end

The difficulty usually lies 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

As can be expected, the type of window is recursive.

# let window = new window_subject;;
val window : (< notify : 'a -> event -> unit; .. > as '_weak3) 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; .. > as '_weak4) 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 refine 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 attach several observers to the same object:

# let window = new richer_window_subject;;
val window : (< notify : 'a -> event -> unit; .. > as '_weak5) 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 = ()