\chapter{The module system} \label{c:moduleexamples}
\pdfchapterfold{-5}{Tutorial: The module system}
%HEVEA\cutname{moduleexamples.html}

This chapter introduces the module system of OCaml.

\section{Structures}
\pdfsection{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 {\em structure} and
is introduced by the "struct"\ldots"end" 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:
\begin{caml_example}{toplevel}
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;;
\end{caml_example}
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" is the function "insert" defined
inside the structure "PrioQueue" and "PrioQueue.queue" is the type
"queue" defined in "PrioQueue".
\begin{caml_example}{toplevel}
PrioQueue.insert PrioQueue.empty 1 "hello";;
\end{caml_example}

Another possibility is to open the module, which brings all
identifiers defined inside the module in the scope of the current
structure.

\begin{caml_example}{toplevel}
  open PrioQueue;;
  insert empty 1 "hello";;
\end{caml_example}

Opening a module enables lighter access to its components, at the
cost of making it harder to identify in which module a identifier
has been defined. In particular, opened modules can shadow
identifiers present in the current scope, potentially leading
to confusing errors:

\begin{caml_example}{toplevel}
  let empty = []
  open PrioQueue;;
  let x = 1 :: empty [@@expect error];;
\end{caml_example}


A partial solution to this conundrum is to open modules locally,
making the components of the module available only in the
concerned expression. This can also make the code easier to read
-- the open statement is closer to where it is used-- and to refactor
-- the code fragment is more self-contained.
Two constructions are available for this purpose:
\begin{caml_example}{toplevel}
  let open PrioQueue in
  insert empty 1 "hello";;
\end{caml_example}
and
\begin{caml_example}{toplevel}
  PrioQueue.(insert empty 1 "hello");;
\end{caml_example}
In the second form, when the body of a local open is itself delimited
by parentheses, braces or bracket, the parentheses of the local open
can be omitted. For instance,
\begin{caml_example}{toplevel}
  PrioQueue.[empty] = PrioQueue.([empty]);;
  PrioQueue.[|empty|] = PrioQueue.([|empty|]);;
   PrioQueue.{ contents = empty } = PrioQueue.({ contents = empty });;
\end{caml_example}
becomes
\begin{caml_example}{toplevel}
  PrioQueue.[insert empty 1 "hello"];;
\end{caml_example}

It is also possible to copy the components of a module inside
another module by using an "include" statement. This can be
particularly useful to extend existing modules. As an illustration,
we could add functions that returns an optional value rather than
an exception when the priority queue is empty.
\begin{caml_example}{toplevel}
  module PrioQueueOpt =
  struct
    include PrioQueue

    let remove_top_opt x =
      try Some(remove_top x) with Queue_is_empty -> None

    let extract_opt x =
      try Some(extract x) with Queue_is_empty -> None
  end;;
\end{caml_example}

\section{Signatures}
\pdfsection{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).
\begin{caml_example}{toplevel}
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;;
\end{caml_example}
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:
\begin{caml_example}{toplevel}
module AbstractPrioQueue = (PrioQueue : PRIOQUEUE);;
AbstractPrioQueue.remove_top [@@expect error];;
AbstractPrioQueue.insert AbstractPrioQueue.empty 1 "hello";;
\end{caml_example}
The restriction can also be performed during the definition of the
structure, as in
\begin{verbatim}
module PrioQueue = (struct ... end : PRIOQUEUE);;
\end{verbatim}
An alternate syntax is provided for the above:
\begin{verbatim}
module PrioQueue : PRIOQUEUE = struct ... end;;
\end{verbatim}

Like for modules, it is possible to include a signature to copy
its components inside the current signature. For instance, we
can extend the PRIOQUEUE signature with the "extract_opt"
function:

\begin{caml_example}{toplevel}
module type PRIOQUEUE_WITH_OPT =
  sig
    include PRIOQUEUE
    val extract_opt : 'a queue -> (int * 'a * 'a queue) option
  end;;
\end{caml_example}


\section{Functors}
\pdfsection{Functors}

Functors are ``functions'' from structures to structures. They are used to
express parameterized structures: a structure \var{A} parameterized by a
structure \var{B} is simply a functor \var{F} with a formal parameter
\var{B} (along with the expected signature for \var{B}) which returns
the actual structure \var{A} itself. The functor \var{F} can then be
applied to one or several implementations \nth{B}{1} \ldots \nth{B}{n}
of \var{B}, yielding the corresponding structures
\nth{A}{1} \ldots \nth{A}{n}.

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):
\begin{caml_example}{toplevel}
type comparison = Less | Equal | Greater;;
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;;
\end{caml_example}
By applying the "Set" functor to a structure implementing an ordered
type, we obtain set operations for this type:
\begin{caml_example}{toplevel}
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 StringSet = Set(OrderedString);;
StringSet.member "bar" (StringSet.add "foo" StringSet.empty);;
\end{caml_example}

\section{Functors and type abstraction}
\pdfsection{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:
\begin{caml_example}{toplevel}
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 AbstractSet = (Set : SETFUNCTOR);;
module AbstractStringSet = AbstractSet(OrderedString);;
AbstractStringSet.add "gee" AbstractStringSet.empty;;
\end{caml_example}

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:
\begin{caml_example}{toplevel}
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 WrongStringSet = WrongSet(OrderedString);;
WrongStringSet.add "gee" WrongStringSet.empty [@@expect error];;
\end{caml_example}
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, OCaml provides a
"with type" construct over signatures that allows enriching a signature
with extra type equalities:
\begin{caml_example}{toplevel}
module AbstractSet2 =
  (Set : functor(Elt: ORDERED_TYPE) -> (SET with type element = Elt.t));;
\end{caml_example}

As in the case of simple structures, an alternate syntax is provided
for defining functors and restricting their result:
\begin{verbatim}
module AbstractSet2(Elt: ORDERED_TYPE) : (SET with type element = Elt.t) =
  struct ... end;;
\end{verbatim}

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.
\begin{caml_example}{toplevel}
module NoCaseString =
  struct
    type t = string
    let compare s1 s2 =
      OrderedString.compare (String.lowercase_ascii s1) (String.lowercase_ascii s2)
  end;;
module NoCaseStringSet = AbstractSet(NoCaseString);;
NoCaseStringSet.add "FOO" AbstractStringSet.empty [@@expect error];;
\end{caml_example}
Note 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), they 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".

\section{Modules and separate compilation}
\pdfsection{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 OCaml, 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 \var{A}
comprises two files:
\begin{itemize}
\item the implementation file \var{A}".ml", which contains a sequence
of definitions, analogous to the inside of a "struct"\ldots"end"
construct;
\item the interface file \var{A}".mli", which contains a sequence of
specifications, analogous to the inside of a "sig"\ldots"end"
construct.
\end{itemize}
These two files together define a structure named \var{A} as if
the following definition was entered at top-level:
\begin{alltt}
module \var{A}: sig (* \hbox{contents of file} \var{A}.mli *) end
        = struct (* \hbox{contents of file} \var{A}.ml *) end;;
\end{alltt}
The files that define 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 "ocamlc" command. For instance, the following
commands compile and link a program composed of two compilation units
"Aux" and "Main":
\begin{verbatim}
$ 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
\end{verbatim}
The program behaves exactly as if the following phrases were entered
at top-level:
\begin{alltt}
module Aux: sig (* \rminalltt{contents of} Aux.mli *) end
          = struct (* \rminalltt{contents of} Aux.ml *) end;;
module Main: sig (* \rminalltt{contents of} Main.mli *) end
           = struct (* \rminalltt{contents of} Main.ml *) end;;
\end{alltt}
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."\var{ident} notation, provided
these definitions are exported in "Aux.mli".

The order in which the ".cmo" files are given to "ocamlc" 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".

Note that only top-level structures can be mapped to
separately-compiled files, but neither 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.
