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Chapter 2  The module system

This chapter introduces the module system of Objective Caml.

2.1  Structures

A primary motivation for modules is to package together related definitions (such as the definitions of a data type and associated operations over that type) and enforce a consistent naming scheme for these definitions. This avoids running out of names or accidentally confusing names. Such a package is called a structure and is introduced by the structend construct, which contains an arbitrary sequence of definitions. The structure is usually given a name with the module binding. Here is for instance a structure packaging together a type of priority queues and their operations:

#module PrioQueue =
   struct
     type priority = int
     type 'a queue = Empty | Node of priority * 'a * 'a queue * 'a queue
     let empty = Empty
     let rec insert queue prio elt =
       match queue with
         Empty -> Node(prio, elt, Empty, Empty)
       | Node(p, e, left, right) ->
           if prio <= p
           then Node(prio, elt, insert right p e, left)
           else Node(p, e, insert right prio elt, left)
     exception Queue_is_empty
     let rec remove_top = function
         Empty -> raise Queue_is_empty
       | Node(prio, elt, left, Empty) -> left
       | Node(prio, elt, Empty, right) -> right
       | Node(prio, elt, (Node(lprio, lelt, _, _) as left),
                         (Node(rprio, relt, _, _) as right)) ->
           if lprio <= rprio
           then Node(lprio, lelt, remove_top left, right)
           else Node(rprio, relt, left, remove_top right)
     let extract = function
         Empty -> raise Queue_is_empty
       | Node(prio, elt, _, _) as queue -> (prio, elt, remove_top queue)
   end;;
module PrioQueue :
  sig
    type priority = int
    type 'a queue = Empty | Node of priority * 'a * 'a queue * 'a queue
    val empty : 'a queue
    val insert : 'a queue -> priority -> 'a -> 'a queue
    exception Queue_is_empty
    val remove_top : 'a queue -> 'a queue
    val extract : 'a queue -> priority * 'a * 'a queue
  end

Outside the structure, its components can be referred to using the “dot notation”, that is, identifiers qualified by a structure name. For instance, PrioQueue.insert in a value context is the function insert defined inside the structure PrioQueue. Similarly, PrioQueue.queue in a type context is the type queue defined in PrioQueue.

#PrioQueue.insert PrioQueue.empty 1 "hello";;
- : string PrioQueue.queue =
PrioQueue.Node (1, "hello", PrioQueue.Empty, PrioQueue.Empty)

2.2  Signatures

Signatures are interfaces for structures. A signature specifies which components of a structure are accessible from the outside, and with which type. It can be used to hide some components of a structure (e.g. local function definitions) or export some components with a restricted type. For instance, the signature below specifies the three priority queue operations empty, insert and extract, but not the auxiliary function remove_top. Similarly, it makes the queue type abstract (by not providing its actual representation as a concrete type).

#module type PRIOQUEUE =
   sig
     type priority = int         (* still concrete *)
     type 'a queue               (* now abstract *)
     val empty : 'a queue
     val insert : 'a queue -> int -> 'a -> 'a queue
     val extract : 'a queue -> int * 'a * 'a queue
     exception Queue_is_empty
   end;;
module type PRIOQUEUE =
  sig
    type priority = int
    type 'a queue
    val empty : 'a queue
    val insert : 'a queue -> int -> 'a -> 'a queue
    val extract : 'a queue -> int * 'a * 'a queue
    exception Queue_is_empty
  end

Restricting the PrioQueue structure by this signature results in another view of the PrioQueue structure where the remove_top function is not accessible and the actual representation of priority queues is hidden:

#module AbstractPrioQueue = (PrioQueue : PRIOQUEUE);;
module AbstractPrioQueue : PRIOQUEUE
 
#AbstractPrioQueue.remove_top;;
Unbound value AbstractPrioQueue.remove_top
 
#AbstractPrioQueue.insert AbstractPrioQueue.empty 1 "hello";;
- : string AbstractPrioQueue.queue = <abstr>

The restriction can also be performed during the definition of the structure, as in

module PrioQueue = (struct ... end : PRIOQUEUE);;

An alternate syntax is provided for the above:

module PrioQueue : PRIOQUEUE = struct ... end;;

2.3  Functors

Functors are “functions” from structures to structures. They are used to express parameterized structures: a structure A parameterized by a structure B is simply a functor F with a formal parameter B (along with the expected signature for B) which returns the actual structure A itself. The functor F can then be applied to one or several implementations B1Bn of B, yielding the corresponding structures A1An.

For instance, here is a structure implementing sets as sorted lists, parameterized by a structure providing the type of the set elements and an ordering function over this type (used to keep the sets sorted):

#type comparison = Less | Equal | Greater;;
type comparison = Less | Equal | Greater
 
#module type ORDERED_TYPE =
   sig
     type t
     val compare: t -> t -> comparison
   end;;
module type ORDERED_TYPE = sig type t val compare : t -> t -> comparison end
 
#module Set =
   functor (Elt: ORDERED_TYPE) ->
     struct
       type element = Elt.t
       type set = element list
       let empty = []
       let rec add x s =
         match s with
           [] -> [x]
         | hd::tl ->
            match Elt.compare x hd with
              Equal   -> s         (* x is already in s *)
            | Less    -> x :: s    (* x is smaller than all elements of s *)
            | Greater -> hd :: add x tl
       let rec member x s =
         match s with
           [] -> false
         | hd::tl ->
             match Elt.compare x hd with
               Equal   -> true     (* x belongs to s *)
             | Less    -> false    (* x is smaller than all elements of s *)
             | Greater -> member x tl
     end;;
module Set :
  functor (Elt : ORDERED_TYPE) ->
    sig
      type element = Elt.t
      type set = element list
      val empty : 'a list
      val add : Elt.t -> Elt.t list -> Elt.t list
      val member : Elt.t -> Elt.t list -> bool
    end

By applying the Set functor to a structure implementing an ordered type, we obtain set operations for this type:

#module OrderedString =
   struct
     type t = string
     let compare x y = if x = y then Equal else if x < y then Less else Greater
   end;;
module OrderedString :
  sig type t = string val compare : 'a -> 'a -> comparison end
 
#module StringSet = Set(OrderedString);;
module StringSet :
  sig
    type element = OrderedString.t
    type set = element list
    val empty : 'a list
    val add : OrderedString.t -> OrderedString.t list -> OrderedString.t list
    val member : OrderedString.t -> OrderedString.t list -> bool
  end
 
#StringSet.member "bar" (StringSet.add "foo" StringSet.empty);;
- : bool = false

2.4  Functors and type abstraction

As in the PrioQueue example, it would be good style to hide the actual implementation of the type set, so that users of the structure will not rely on sets being lists, and we can switch later to another, more efficient representation of sets without breaking their code. This can be achieved by restricting Set by a suitable functor signature:

#module type SETFUNCTOR =
   functor (Elt: ORDERED_TYPE) ->
     sig
       type element = Elt.t      (* concrete *)
       type set                  (* abstract *)
       val empty : set
       val add : element -> set -> set
       val member : element -> set -> bool
     end;;
module type SETFUNCTOR =
  functor (Elt : ORDERED_TYPE) ->
    sig
      type element = Elt.t
      type set
      val empty : set
      val add : element -> set -> set
      val member : element -> set -> bool
    end
 
#module AbstractSet = (Set : SETFUNCTOR);;
module AbstractSet : SETFUNCTOR
 
#module AbstractStringSet = AbstractSet(OrderedString);;
module AbstractStringSet :
  sig
    type element = OrderedString.t
    type set = AbstractSet(OrderedString).set
    val empty : set
    val add : element -> set -> set
    val member : element -> set -> bool
  end
 
#AbstractStringSet.add "gee" AbstractStringSet.empty;;
- : AbstractStringSet.set = <abstr>

In an attempt to write the type constraint above more elegantly, one may wish to name the signature of the structure returned by the functor, then use that signature in the constraint:

#module type SET =
   sig
     type element
     type set
     val empty : set
     val add : element -> set -> set
     val member : element -> set -> bool
   end;;
module type SET =
  sig
    type element
    type set
    val empty : set
    val add : element -> set -> set
    val member : element -> set -> bool
  end
 
#module WrongSet = (Set : functor(Elt: ORDERED_TYPE) -> SET);;
module WrongSet : functor (Elt : ORDERED_TYPE) -> SET
 
#module WrongStringSet = WrongSet(OrderedString);;
module WrongStringSet :
  sig
    type element = WrongSet(OrderedString).element
    type set = WrongSet(OrderedString).set
    val empty : set
    val add : element -> set -> set
    val member : element -> set -> bool
  end
 
#WrongStringSet.add "gee" WrongStringSet.empty;;
This expression has type string but is here used with type
  WrongStringSet.element = WrongSet(OrderedString).element

The problem here is that SET specifies the type element abstractly, so that the type equality between element in the result of the functor and t in its argument is forgotten. Consequently, WrongStringSet.element is not the same type as string, and the operations of WrongStringSet cannot be applied to strings. As demonstrated above, it is important that the type element in the signature SET be declared equal to Elt.t; unfortunately, this is impossible above since SET is defined in a context where Elt does not exist. To overcome this difficulty, Objective Caml provides a with type construct over signatures that allows to enrich a signature with extra type equalities:

#module AbstractSet = 
   (Set : functor(Elt: ORDERED_TYPE) -> (SET with type element = Elt.t));;
module AbstractSet :
  functor (Elt : ORDERED_TYPE) ->
    sig
      type element = Elt.t
      type set
      val empty : set
      val add : element -> set -> set
      val member : element -> set -> bool
    end

As in the case of simple structures, an alternate syntax is provided for defining functors and restricting their result:

module AbstractSet(Elt: ORDERED_TYPE) : (SET with type element = Elt.t) =
  struct ... end;;

Abstracting a type component in a functor result is a powerful technique that provides a high degree of type safety, as we now illustrate. Consider an ordering over character strings that is different from the standard ordering implemented in the OrderedString structure. For instance, we compare strings without distinguishing upper and lower case.

#module NoCaseString =
   struct
     type t = string
     let compare s1 s2 =
       OrderedString.compare (String.lowercase s1) (String.lowercase s2)
   end;;
module NoCaseString :
  sig type t = string val compare : string -> string -> comparison end
 
#module NoCaseStringSet = AbstractSet(NoCaseString);;
module NoCaseStringSet :
  sig
    type element = NoCaseString.t
    type set = AbstractSet(NoCaseString).set
    val empty : set
    val add : element -> set -> set
    val member : element -> set -> bool
  end
 
#NoCaseStringSet.add "FOO" AbstractStringSet.empty;;
This expression has type
  AbstractStringSet.set = AbstractSet(OrderedString).set
but is here used with type
  NoCaseStringSet.set = AbstractSet(NoCaseString).set

Notice that the two types AbstractStringSet.set and NoCaseStringSet.set are not compatible, and values of these two types do not match. This is the correct behavior: even though both set types contain elements of the same type (strings), both are built upon different orderings of that type, and different invariants need to be maintained by the operations (being strictly increasing for the standard ordering and for the case-insensitive ordering). Applying operations from AbstractStringSet to values of type NoCaseStringSet.set could give incorrect results, or build lists that violate the invariants of NoCaseStringSet.

2.5  Modules and separate compilation

All examples of modules so far have been given in the context of the interactive system. However, modules are most useful for large, batch-compiled programs. For these programs, it is a practical necessity to split the source into several files, called compilation units, that can be compiled separately, thus minimizing recompilation after changes.

In Objective Caml, compilation units are special cases of structures and signatures, and the relationship between the units can be explained easily in terms of the module system. A compilation unit A comprises two files:

Both files define a structure named A as if the following definition was entered at top-level:

module A: sig (* contents of file A.mli *) end
        = struct (* contents of file A.ml *) end;;

The files defining the compilation units can be compiled separately using the ocamlc -c command (the -c option means “compile only, do not try to link”); this produces compiled interface files (with extension .cmi) and compiled object code files (with extension .cmo). When all units have been compiled, their .cmo files are linked together using the ocaml command. For instance, the following commands compile and link a program composed of two compilation units Aux and Main:

$ ocamlc -c Aux.mli                     # produces aux.cmi
$ ocamlc -c Aux.ml                      # produces aux.cmo
$ ocamlc -c Main.mli                    # produces main.cmi
$ ocamlc -c Main.ml                     # produces main.cmo
$ ocamlc -o theprogram Aux.cmo Main.cmo

The program behaves exactly as if the following phrases were entered at top-level:

module Aux: sig (* contents of Aux.mli *) end
          = struct (* contents of Aux.ml *) end;;
module Main: sig (* contents of Main.mli *) end
           = struct (* contents of Main.ml *) end;;

In particular, Main can refer to Aux: the definitions and declarations contained in Main.ml and Main.mli can refer to definition in Aux.ml, using the Aux.ident notation, provided these definitions are exported in Aux.mli.

The order in which the .cmo files are given to ocaml during the linking phase determines the order in which the module definitions occur. Hence, in the example above, Aux appears first and Main can refer to it, but Aux cannot refer to Main.

Notice that only top-level structures can be mapped to separately-compiled files, but not functors nor module types. However, all module-class objects can appear as components of a structure, so the solution is to put the functor or module type inside a structure, which can then be mapped to a file.


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