For the past few classes we have been considering abstraction and
modular design, primarily through the use of the module
mechanism in OCaml. We have seen that good design principles include
writing clear specifications of interfaces, independent of the actual
implementation. We have also seen that writing good documentation of
the implementation is important. Today we will consider another means
of abstraction called functors, a construct that enables modules to be
combined by parameterizing a module in terms of other modules.
Consider the SET data abstraction that we have looked at during the
past few classes:
module type SET = sig type 'a set val empty : 'a set val mem : 'a -> 'a set -> bool val add : 'a -> 'a set -> 'a set val rem : 'a -> 'a set -> 'a set val size: 'a set -> int val union: 'a set -> 'a set -> 'a set val inter: 'a set -> 'a set -> 'a set end
While this interface uses polymorphism to enable sets with
different types of elements to be created, any implementation of this
signature needs to use the built-in = function in testing
whether an element is a member of such a set. Thus we cannot for
example have a set of strings where comparison of the elements is done
in a case-insensitive manner, or a set of integers where elements are
considered equal when their magnitudes (absolute values) are equal.
We could write two separate signatures, one for sets with
string elements and one for sets with integer elements, and then in
the implementation of each signature use an appropriate comparison
function. However this would yield a lot of nearly duplicated code,
both in the signatures and in the implementation. Such nearly
duplicated code is more work to write and maintain and more
importantly is often a source of bugs when things are changed in one
place and not another.
A functor is a mapping from modules to modules. It allows the construction of a module parameterized by one or more other modules. Functors allow us to create a set module that is parameterized by another module that does the equality testing, thereby allowing the same code to be used for different equality tests. To make this concrete, we will consider an example using the following signatures:
module type EQUAL = sig type t val equal : t -> t -> bool end
module type SETFUNCTOR =
functor (Equal : EQUAL) ->
sig
type elt = Equal.t
type set
val empty : set
val mem : elt -> set -> bool
val add: elt -> set -> set
val size: set -> int
end
The signature EQUAL describes the input type for the functor.
To implement EQUAL, a module need only specify a type t and a
comparison function equal : t -> t -> bool, but these can be
anything.
The signature SETFUNCTOR describes the type of the functor. This differs
from the SET interface in several respects. First,
the keyword functor indicates that it is a functor accepting a
parameter, which in this case is any module of type EQUAL. Note how
the syntax is reminiscent of the notation for functions.
The parameter is referenced by the name Equal in the body of SETFUNCTOR,
but that does not have to be its actual name.
The body of SETFUNCTOR describes the type of the module that will
be produced. In the body, instead of the polymorphic 'a of SET,
the type of the elements is named elt and is defined to be the same as
the type t of the module Equal, whatever that is.
There is also a fixed but unspecified type set, along with some set
operations of the appropriate types, specified in terms of elt
and set. (We have omitted a few of the operations
for simplicity of the presentation, although they could easily be added back in.)
Now we are ready to define a functor implementing
the SETFUNCTOR signature.
module MakeSet : SETFUNCTOR =
functor (Equal : EQUAL) ->
struct
open Equal
type elt = t
type set = elt list
let empty = []
let mem x = List.exists (equal x)
let add x s = if mem x s then s else x :: s
let size = List.length
end
First, the header
module MakeSet : SETFUNCTOR =
indicates that we are defining an implementation named MakeSet of the functor type SETFUNCTOR. The second line
functor (Equal : EQUAL) ->
indicates that we are defining a functor with parameter Equal of type EQUAL.
Again, the module implementing EQUAL is referenced by
the name Equal in the body of MakeSet,
but that does not have to be its actual name.
In general there can be any number of parameter modules,
each of which must be specified with a name and signature.
Note that these parameters can only be modules, including other
parameterized modules—they cannot be
first-class objects of the language such as functions or other types.
Finally, the body of MakeSet between struct and end
describes the implementation of the output module. This module must satisfy the signature
described in the body of SETFUNCTOR.