This chapter introduces the module system of OCaml.
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 struct…end construct, which contains an arbitrary sequence of definitions. The structure is usually given a name with the module binding. For instance, here is a structure packaging together a type of FIFO queues and their operations:
Outside the structure, its components can be referred to using the “dot notation”, that is, identifiers qualified by a structure name. For instance, Fifo.add is the function add defined inside the structure Fifo and Fifo.queue is the type queue defined in Fifo.
Another possibility is to open the module, which brings all identifiers defined inside the module into the scope of the current structure.
Opening a module enables lighter access to its components, at the cost of making it harder to identify in which module an identifier has been defined. In particular, opened modules can shadow identifiers present in the current scope, potentially leading to confusing errors:
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 both easier to read (since the open statement is closer to where it is used) and easier to refactor (since the code fragment is more self-contained). Two constructions are available for this purpose:
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,
This second form also works for patterns:
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 return an optional value rather than an exception when the queue is empty.
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 queue operations empty, add, top and pop, but not the auxiliary function make. Similarly, it makes the queue type abstract (by not providing its actual representation as a concrete type). This ensures that users of the Fifo module cannot violate data structure invariants that operations rely on, such as “if the front list is empty, the rear list must also be empty”.
Restricting the Fifo structure to this signature results in another view of the Fifo structure where the make function is not accessible and the actual representation of queues is hidden:
The restriction can also be performed during the definition of the structure, as in
module Fifo = (struct ... end : FIFO);;
An alternate syntax is provided for the above:
module Fifo : FIFO = struct ... end;;
Like for modules, it is possible to include a signature to copy its components inside the current signature. For instance, we can extend the FIFO signature with the top_opt and pop_opt functions:
Functors are “functions” from modules to modules. Functors let you create parameterized modules and then provide other modules as parameter(s) to get a specific implementation. For instance, a Set module implementing sets as sorted lists could be parameterized to work with any module that provides an element type and a comparison function compare (such as OrderedString):
By applying the Set functor to a structure implementing an ordered type, we obtain set operations for this type:
As in the Fifo 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:
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:
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:
As in the case of simple structures, an alternate syntax is provided for defining functors and restricting their result:
module AbstractSet2(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.
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.
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 A comprises two files:
These two files together 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 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:
$ 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 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.