Exactly, and we can say this is the only book of reference. The answers for this thread are given here:
By the way, I’ll try to explain how modules and functors work with a simple example.
Modules.
Imagine that you want to define the notion of set of int
with one value and two functions on it:
 the
empty
set

is_element
to test if an int
belongs to a given set

add
to add an int in a set (but only if it is not already present).
We can represent a set of int as a list of int, so we define this module:
module Int_Set = struct
type elt = int (* an alias to `int` for the elements of the set *)
type t = elt list (* an alias for the type of sets *)
let (empty : t) = []
let rec is_element i (set : t) =
match set with
 [] > false
 x :: xs > (x = i)  is_element i xs
let add i set = if is_element i set then set else i :: set
end
We can play around a bit with it:
let s = Int_Set.(add 1 (add 2 empty));;
val s : Int_Set.t = [1; 2]
Int_Set.is_element 2 s;;
 : bool = true
Int_Set.is_element 3 s;;
 : bool = false
We can also add
elements and verify that it satisfies the invariant that an element already present isn’t added again:
Int_Set.add 3 s;;
 : Int_Set.t = [3; 1; 2]
Int_Set.add 2 s;; (* the invariant is satisfied *)
 : Int_Set.t = [1; 2]
But there is a problem: since the concrete representation for the type of sets is known (they are just lists), we can break the invariant.
Int_Set.add 3 (2 :: s);;
 : Int_Set.t = [3; 2; 1; 2]
The solution is to use what is called abstract type.
Signatures.
When you define a module, the compiler infer automatically its type or its signature. For the module defined above, the toplevel returns:
module Int_Set :
sig
type elt = int
type t = elt list
val empty : t
val is_element : elt > t > bool
val add : elt > t > t
end
What we can do is to define a less precise signature to hide the fact that sets are implemented using lists:
module type S = sig
type elt = int
type t
val empty : t
val is_element : elt > t > bool
val add : elt > t > t
end
Here, since we want to add int
s in our sets, we don’t hide the fact that elements are int
.
We can now restrict the interface of our module and the invariant can’t be broken anymore:
module Abstract_Int_Set = (Int_Set : S)
let s1 = Abstract_Int_Set.(add 1 (add 2 empty));;
val s1 : Abstract_Int_Set.t = <abstr>
1 :: s1;;
Error: This expression has type Abstract_Int_Set.t
but an expression was expected of type int list
Ok, that’s fine: we have a simple notion of sets of int and we can preserve some invariant, but what to do if we want to generalize this notion to have sets over other types without repeat ourself? That’s where functors come into play.
Functors.
In the same way that functions are used to construct new values from given one, functors are used to construct modules from given one.
First, as in our int
case, to define sets for a given type we need to know when two values are equal. So we define this signature:
module type EQ = sig
type t
val eq : t > t > bool
end
Then we define the general signature for a set module:
module type SET = sig
type elt
type t
val empty : t
val is_element : elt > t > bool
val add : elt > t > t
end
Finally we write code to explain how to construct a module of set over a type when we have a function to test equality between its values:
module Make_Set (Elt : EQ) : SET with type elt = Elt.t = struct
type elt = Elt.t
type t = elt list
let empty = []
let rec is_element i set =
match set with
 [] > false
 x :: xs > (Elt.eq x i)  is_element i xs
let add i set = if is_element i set then set else i :: set
end
The code is mostly the same as before, except in the function is_element
where to test for equality we use the function Elt.eq
given by the parameter of the functor.
Now, with this generic way to construct module of sets, we can easily redifine our previous one:
module Abstract_Int_Set = Make_Set (struct type t = int let eq = (=) end)
let s2 = Abstract_Int_Set.(add 1 (add 2 empty));;
val s2 : Abstract_Int_Set.t = <abstr>
Abstract_Int_Set.is_element 2 s2;;
 : bool = true
Abstract_Int_Set.is_element 3 s2;;
 : bool = false
But we can also use it to have sets of string
:
module String_Set = Make_Set (struct type t = string let eq = (=) end)
let s = String_Set.(add "hello" (add "world" empty));;
val s : String_Set.t = <abstr>
String_Set.is_element "hello" s;;
 : bool = true
String_Set.is_element "foo" s;;
 : bool = false
I hope that you can now see what are functors, how to define them and how to use them.