<!DOCTYPE html> <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <meta name="generator" content="hevea 2.00"> <link rel="stylesheet" type="text/css" href="manual.css"> <title>The module system</title> </head> <body> <a href="coreexamples.html"><img src="previous_motif.gif" alt="Previous"></a> <a href="index.html"><img src="contents_motif.gif" alt="Up"></a> <a href="objectexamples.html"><img src="next_motif.gif" alt="Next"></a> <hr> <h1 class="chapter" id="sec17">Chapter 2  The module system</h1> <ul> <li><a href="moduleexamples.html#sec18">Structures</a> </li><li><a href="moduleexamples.html#sec19">Signatures</a> </li><li><a href="moduleexamples.html#sec20">Functors</a> </li><li><a href="moduleexamples.html#sec21">Functors and type abstraction</a> </li><li><a href="moduleexamples.html#sec22">Modules and separate compilation</a> </li></ul> <p> <a id="c:moduleexamples"></a> </p><p>This chapter introduces the module system of OCaml.</p> <h2 class="section" id="sec18">2.1  Structures</h2> <p>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</em> and is introduced by the <span class="c007">struct</span>…<span class="c007">end</span> construct, which contains an arbitrary sequence of definitions. The structure is usually given a name with the <span class="c007">module</span> binding. Here is for instance a structure packaging together a type of priority queues and their operations: </p><pre><span class="c004">#<span class="c003"> 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;; <span class="c006">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 </span></span></span></pre><p> Outside the structure, its components can be referred to using the “dot notation”, that is, identifiers qualified by a structure name. For instance, <span class="c007">PrioQueue.insert</span> is the function <span class="c007">insert</span> defined inside the structure <span class="c007">PrioQueue</span> and <span class="c007">PrioQueue.queue</span> is the type <span class="c007">queue</span> defined in <span class="c007">PrioQueue</span>. </p><pre><span class="c004">#<span class="c003"> PrioQueue.insert PrioQueue.empty 1 "hello";; <span class="c006">- : string PrioQueue.queue = PrioQueue.Node (1, "hello", PrioQueue.Empty, PrioQueue.Empty) </span></span></span></pre> <h2 class="section" id="sec19">2.2  Signatures</h2> <p>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 <span class="c007">empty</span>, <span class="c007">insert</span> and <span class="c007">extract</span>, but not the auxiliary function <span class="c007">remove_top</span>. Similarly, it makes the <span class="c007">queue</span> type abstract (by not providing its actual representation as a concrete type). </p><pre><span class="c004">#<span class="c003"> 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;; <span class="c006">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 </span></span></span></pre><p> Restricting the <span class="c007">PrioQueue</span> structure by this signature results in another view of the <span class="c007">PrioQueue</span> structure where the <span class="c007">remove_top</span> function is not accessible and the actual representation of priority queues is hidden: </p><pre><span class="c004">#</span><span class="c003"> module AbstractPrioQueue = (PrioQueue : PRIOQUEUE);; <span class="c006">module AbstractPrioQueue : PRIOQUEUE </span><span class="c004">#</span> <U>AbstractPrioQueue.remove_top</U>;; <span class="c006">Error: Unbound value AbstractPrioQueue.remove_top </span><span class="c004">#</span> AbstractPrioQueue.insert AbstractPrioQueue.empty 1 "hello";; </span><span class="c006">- : string AbstractPrioQueue.queue = <abstr> </span></pre><p> The restriction can also be performed during the definition of the structure, as in </p><pre>module PrioQueue = (struct ... end : PRIOQUEUE);; </pre><p>An alternate syntax is provided for the above: </p><pre>module PrioQueue : PRIOQUEUE = struct ... end;; </pre> <h2 class="section" id="sec20">2.3  Functors</h2> <p>Functors are “functions” from structures to structures. They are used to express parameterized structures: a structure <span class="c013">A</span> parameterized by a structure <span class="c013">B</span> is simply a functor <span class="c013">F</span> with a formal parameter <span class="c013">B</span> (along with the expected signature for <span class="c013">B</span>) which returns the actual structure <span class="c013">A</span> itself. The functor <span class="c013">F</span> can then be applied to one or several implementations <span class="c013">B</span><sub>1</sub> …<span class="c013">B</span><sub><span class="c013">n</span></sub> of <span class="c013">B</span>, yielding the corresponding structures <span class="c013">A</span><sub>1</sub> …<span class="c013">A</span><sub><span class="c013">n</span></sub>.</p><p>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): </p><pre><span class="c004">#</span><span class="c003"> type comparison = Less | Equal | Greater;; <span class="c006">type comparison = Less | Equal | Greater </span><span class="c004">#</span> module type ORDERED_TYPE = sig type t val compare: t -> t -> comparison end;; <span class="c006">module type ORDERED_TYPE = sig type t val compare : t -> t -> comparison end </span><span class="c004">#</span> 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;; </span><span class="c006">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 </span></pre><p> By applying the <span class="c007">Set</span> functor to a structure implementing an ordered type, we obtain set operations for this type: </p><pre><span class="c004">#</span><span class="c003"> module OrderedString = struct type t = string let compare x y = if x = y then Equal else if x < y then Less else Greater end;; <span class="c006">module OrderedString : sig type t = string val compare : 'a -> 'a -> comparison end </span><span class="c004">#</span> module StringSet = Set(OrderedString);; <span class="c006">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 </span><span class="c004">#</span> StringSet.member "bar" (StringSet.add "foo" StringSet.empty);; </span><span class="c006">- : bool = false </span></pre> <h2 class="section" id="sec21">2.4  Functors and type abstraction</h2> <p>As in the <span class="c007">PrioQueue</span> example, it would be good style to hide the actual implementation of the type <span class="c007">set</span>, 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 <span class="c007">Set</span> by a suitable functor signature: </p><pre><span class="c004">#</span><span class="c003"> 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;; <span class="c006">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 </span><span class="c004">#</span> module AbstractSet = (Set : SETFUNCTOR);; <span class="c006">module AbstractSet : SETFUNCTOR </span><span class="c004">#</span> module AbstractStringSet = AbstractSet(OrderedString);; <span class="c006">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 </span><span class="c004">#</span> AbstractStringSet.add "gee" AbstractStringSet.empty;; </span><span class="c006">- : AbstractStringSet.set = <abstr> </span></pre><p>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: </p><pre><span class="c004">#</span><span class="c003"> module type SET = sig type element type set val empty : set val add : element -> set -> set val member : element -> set -> bool end;; <span class="c006">module type SET = sig type element type set val empty : set val add : element -> set -> set val member : element -> set -> bool end </span><span class="c004">#</span> module WrongSet = (Set : functor(Elt: ORDERED_TYPE) -> SET);; <span class="c006">module WrongSet : functor (Elt : ORDERED_TYPE) -> SET </span><span class="c004">#</span> module WrongStringSet = WrongSet(OrderedString);; <span class="c006">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 </span><span class="c004">#</span> WrongStringSet.add <U>"gee"</U> WrongStringSet.empty;; </span><span class="c006">Error: This expression has type string but an expression was expected of type WrongStringSet.element = WrongSet(OrderedString).element </span></pre><p> The problem here is that <span class="c007">SET</span> specifies the type <span class="c007">element</span> abstractly, so that the type equality between <span class="c007">element</span> in the result of the functor and <span class="c007">t</span> in its argument is forgotten. Consequently, <span class="c007">WrongStringSet.element</span> is not the same type as <span class="c007">string</span>, and the operations of <span class="c007">WrongStringSet</span> cannot be applied to strings. As demonstrated above, it is important that the type <span class="c007">element</span> in the signature <span class="c007">SET</span> be declared equal to <span class="c007">Elt.t</span>; unfortunately, this is impossible above since <span class="c007">SET</span> is defined in a context where <span class="c007">Elt</span> does not exist. To overcome this difficulty, OCaml provides a <span class="c007">with type</span> construct over signatures that allows enriching a signature with extra type equalities: </p><pre><span class="c004">#<span class="c003"> module AbstractSet2 = (Set : functor(Elt: ORDERED_TYPE) -> (SET with type element = Elt.t));; <span class="c006">module AbstractSet2 : 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 </span></span></span></pre><p>As in the case of simple structures, an alternate syntax is provided for defining functors and restricting their result: </p><pre>module AbstractSet2(Elt: ORDERED_TYPE) : (SET with type element = Elt.t) = struct ... end;; </pre><p> 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 <span class="c007">OrderedString</span> structure. For instance, we compare strings without distinguishing upper and lower case. </p><pre><span class="c004">#</span><span class="c003"> module NoCaseString = struct type t = string let compare s1 s2 = OrderedString.compare (String.lowercase s1) (String.lowercase s2) end;; <span class="c006">module NoCaseString : sig type t = string val compare : string -> string -> comparison end </span><span class="c004">#</span> module NoCaseStringSet = AbstractSet(NoCaseString);; <span class="c006">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 </span><span class="c004">#</span> NoCaseStringSet.add "FOO" <U>AbstractStringSet.empty</U>;; </span><span class="c006">Error: This expression has type AbstractStringSet.set = AbstractSet(OrderedString).set but an expression was expected of type NoCaseStringSet.set = AbstractSet(NoCaseString).set </span></pre><p> Note that the two types <span class="c007">AbstractStringSet.set</span> and <span class="c007">NoCaseStringSet.set</span> 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 <span class="c007">AbstractStringSet</span> to values of type <span class="c007">NoCaseStringSet.set</span> could give incorrect results, or build lists that violate the invariants of <span class="c007">NoCaseStringSet</span>.</p> <h2 class="section" id="sec22">2.5  Modules and separate compilation</h2> <p>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.</p><p>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 <span class="c013">A</span> comprises two files: </p><ul class="itemize"><li class="li-itemize"> the implementation file <span class="c013">A</span><span class="c007">.ml</span>, which contains a sequence of definitions, analogous to the inside of a <span class="c007">struct</span>…<span class="c007">end</span> construct; </li><li class="li-itemize">the interface file <span class="c013">A</span><span class="c007">.mli</span>, which contains a sequence of specifications, analogous to the inside of a <span class="c007">sig</span>…<span class="c007">end</span> construct. </li></ul><p> These two files together define a structure named <span class="c013">A</span> as if the following definition was entered at top-level: </p><pre> module <span class="c013">A</span>: sig (* contents of file <span class="c013">A</span>.mli *) end = struct (* contents of file <span class="c013">A</span>.ml *) end;; </pre><p> The files that define the compilation units can be compiled separately using the <span class="c007">ocamlc -c</span> command (the <span class="c007">-c</span> option means “compile only, do not try to link”); this produces compiled interface files (with extension <span class="c007">.cmi</span>) and compiled object code files (with extension <span class="c007">.cmo</span>). When all units have been compiled, their <span class="c007">.cmo</span> files are linked together using the <span class="c007">ocamlc</span> command. For instance, the following commands compile and link a program composed of two compilation units <span class="c007">Aux</span> and <span class="c007">Main</span>: </p><pre>$ 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 </pre><p>The program behaves exactly as if the following phrases were entered at top-level: </p><pre> 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;; </pre><p> In particular, <span class="c007">Main</span> can refer to <span class="c007">Aux</span>: the definitions and declarations contained in <span class="c007">Main.ml</span> and <span class="c007">Main.mli</span> can refer to definition in <span class="c007">Aux.ml</span>, using the <span class="c007">Aux.</span><span class="c013">ident</span> notation, provided these definitions are exported in <span class="c007">Aux.mli</span>.</p><p>The order in which the <span class="c007">.cmo</span> files are given to <span class="c007">ocamlc</span> during the linking phase determines the order in which the module definitions occur. Hence, in the example above, <span class="c007">Aux</span> appears first and <span class="c007">Main</span> can refer to it, but <span class="c007">Aux</span> cannot refer to <span class="c007">Main</span>.</p><p>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. </p> <hr> <a href="coreexamples.html"><img src="previous_motif.gif" alt="Previous"></a> <a href="index.html"><img src="contents_motif.gif" alt="Up"></a> <a href="objectexamples.html"><img src="next_motif.gif" alt="Next"></a> </body> </html>