Question

module <name> =
   struct 
     .. 
   end;;


module type <name> =
    struct (* should have been sig *)
      .. 
end;;

Answer 1

The first declares a module and the second declares a module type (aka a signature). A module type contains type and val declarations, whereas a module can contain definitions (e.g., let bindings). You can use a signature to restrict the type of a module, much as you might for a function. For example,

module type T = sig
  val f : int -> int
end

module M : T = struct
  let f x = x + 1
  let g x = 2 * x
end

Now, we have

# M.f 0 ;;
- : int = 1
# M.g 0 ;;
Error: Unbound value M.g

M.g is unbound because it’s hidden by the signature T.

Another common way to use module types is as arguments to and return values of functors. For example, the Map.Make functor in the standard library takes a module with signature Map.OrderedType and creates a module with signature Map.S

P.S. Note that there’s a mistake in the question. A module type is declared using

module type <name> = sig
  ...
end