Question

I am having a bit of a problem with a functor (and it’s resultant type). Below, I have a Set functor that uses an Ordered type. I actually used the set.ml that comes with OCaml for some guidance, but I seem to be doing everything ahem right. I created an Ordered module with integers and applied it to the Set functor to get the last module on this code sample, IntSet.

The next line fails, when I try to insert an integer. I get the following type error:

Error: This expression has type int but is here used with type          SetInt.elt = Set(OrdInt).elt 

Don’t get me wrong, the type system is correct here. The top level reports that the type of the SetInt.elt is Set(OrdInt).elt, but when I do the same operations to set up a Set using the one provided by OCaml the ‘same’ line is, SetInt.elt = OrderedInt.t. Seems like I should be getting SetInt.elt = Ordered.t.

This is so simple, I’m probably just missing some stupid detail! argh!

Please Note: I have simplified the member/insert functions here since this issue has to do with types.

module type Ordered =   sig     type t      val lt : t -> t -> bool     val eq : t -> t -> bool     val leq : t -> t -> bool   end  module type S =   sig     type elt     type t     exception Already_Exists     val empty  : t     val insert : elt -> t -> t     val member : elt -> t -> bool   end  module Set (Elt:Ordered) : S =    struct     type elt = Elt.t     type t = Leaf | Node of t * elt * t     exception Already_Exists     let empty = Leaf     let insert e t = t     let member e t = false   end  module OrdInt : Ordered =   struct     type t = int     let lt a b = a < b     let eq a b = a = b     let leq a b = a <= b   end  module IntSet = Set (OrdInt)  (* line that fails *) let one_elm = IntSet.insert 1 IntSet.empty 

Answer 1

You need to change these two lines

module Set (Elt:Ordered) : S =  module OrdInt : Ordered = 

to

module Set (Elt:Ordered) : S with type elt = Elt.t =  module OrdInt : Ordered with type t = int = 

Without these, the modules will not have signatures that expose the types elt and t as int.

[Edit]: The set.ml doesn’t have the ‘with’ bit, because there’s a sml.mli, which declares the signature for the functor and it does have the ‘with’. Also, OrdInt doesn’t need ‘with’ if you don’t explicitly specify a signature for it, like this:

module OrdInt = 

You can also construct the set by defining the module in place:

module IntSet = Set (struct  type t = int  let lt a b = a < b  let eq a b = a = b  let leq a b = a <= b end)