diff --git a/src/gen_rules.ml b/src/gen_rules.ml
index c692b2f1..bbcf4b18 100644
--- a/src/gen_rules.ml
+++ b/src/gen_rules.ml
@@ -24,19 +24,18 @@ module Gen(P : Install_rules.Params) = struct
      | Interpretation of [modules] fields                              |
      +-----------------------------------------------------------------+ *)
 
-  module Eval_modules = Ordered_set_lang.Make(struct
+  module Eval_modules = Ordered_set_lang.Make(Module.Name)(struct
       type t = (Module.t, Module.Name.t * Loc.t) result
-      let name r = (
-        (match r with
-         | Error (s, _) -> s
-         | Ok m -> Module.name m)
-        |> Module.Name.to_string
-      )
+
+      type key = Module.Name.t
+
+      let key = function
+        | Error (s, _) -> s
+        | Ok m -> Module.name m
     end)
 
-  let parse_modules ~(all_modules : Module.t Module.Name.Map.t) ~buildable =
-    let conf : Buildable.t = buildable in
-    let standard_modules = Module.Name.Map.map all_modules ~f:(fun m -> Ok m) in
+  let parse_modules ~(all_modules : Module.t Module.Name.Map.t)
+        ~buildable:(conf : Buildable.t) =
     let fake_modules = ref Module.Name.Map.empty in
     let parse ~loc s =
       let name = Module.Name.of_string s in
@@ -47,12 +46,10 @@ module Gen(P : Install_rules.Params) = struct
         Error (name, loc)
     in
     let modules =
-      let standard = Module.Name.Map.to_smap standard_modules in
       Eval_modules.eval_unordered
         conf.modules
         ~parse
-        ~standard
-      |> Module.Name.Map.of_smap
+        ~standard:(Module.Name.Map.map all_modules ~f:(fun m -> Ok m))
     in
     let only_present_modules modules =
       Module.Name.Map.filter_map ~f:(function
@@ -66,8 +63,7 @@ module Gen(P : Install_rules.Params) = struct
       Eval_modules.eval_unordered
         conf.modules_without_implementation
         ~parse
-        ~standard:String_map.empty
-      |> Module.Name.Map.of_smap
+        ~standard:Module.Name.Map.empty
     in
     let intf_only = only_present_modules intf_only in
     Module.Name.Map.iteri !fake_modules ~f:(fun m loc ->
@@ -124,9 +120,10 @@ module Gen(P : Install_rules.Params) = struct
         (* Re-evaluate conf.modules_without_implementation but this
            time keep locations *)
         let module Eval =
-          Ordered_set_lang.Make(struct
+          Ordered_set_lang.Make(Module.Name)(struct
             type t = Loc.t * Module.t
-            let name (_, m) = Module.Name.to_string (Module.name m)
+            type key = Module.Name.t
+            let key (_, m) = Module.name m
           end)
         in
         let parse ~loc s =
@@ -137,11 +134,10 @@ module Gen(P : Install_rules.Params) = struct
         in
         let parse ~loc s = (loc, parse ~loc s) in
         let shouldn't_be_listed =
-          let all_modules = Module.Name.Map.to_smap all_modules in
           Eval.eval_unordered conf.modules_without_implementation
             ~parse
-            ~standard:(String_map.map all_modules ~f:(fun m -> (Loc.none, m)))
-          |> String_map.values
+            ~standard:(Module.Name.Map.map all_modules ~f:(fun m -> (Loc.none, m)))
+          |> Module.Name.Map.values
           |> List.filter ~f:(fun (_, (m : Module.t)) ->
             Option.is_some m.impl)
         in
diff --git a/src/module.ml b/src/module.ml
index 7c6d6673..a612fda2 100644
--- a/src/module.ml
+++ b/src/module.ml
@@ -14,17 +14,8 @@ module Name = struct
   let pp = Format.pp_print_string
   let pp_quote fmt x = Format.fprintf fmt "%S" x
 
-  module Set = struct
-    include String_set
-    let of_sset x = x
-  end
-
-  module Map = struct
-    include String_map
-
-    let to_smap x = x
-    let of_smap x = x
-  end
+  module Set = String_set
+  module Map = String_map
 end
 
 module Syntax = struct
diff --git a/src/module.mli b/src/module.mli
index ffb22f42..bd07a8dc 100644
--- a/src/module.mli
+++ b/src/module.mli
@@ -13,17 +13,8 @@ module Name : sig
   val pp : Format.formatter -> t -> unit
   val pp_quote : Format.formatter -> t -> unit
 
-  module Set : sig
-    include Set.S with type elt = t
-
-    val of_sset : String_set.t -> t
-  end
-  module Map : sig
-    include Map.S with type key = t
-
-    val to_smap : 'a t -> 'a String_map.t
-    val of_smap : 'a String_map.t -> 'a t
-  end
+  module Set : Set.S with type elt = t
+  module Map : Map.S with type key = t
 end
 
 module Syntax : sig
diff --git a/src/ordered_set_lang.ml b/src/ordered_set_lang.ml
index b268ffd1..fe5a6dc7 100644
--- a/src/ordered_set_lang.ml
+++ b/src/ordered_set_lang.ml
@@ -58,10 +58,17 @@ let is_standard t =
 
 module type Value = sig
   type t
-  val name  : t -> string
+  type key
+  val key : t -> key
 end
 
-module Make(Value : Value) = struct
+module type Key = sig
+  type t
+  val compare : t -> t -> Ordering.t
+  module Map : Map.S with type key = t
+end
+
+module Make(Key : Key)(Value : Value with type key = Key.t) = struct
   module type Named_values = sig
     type t
 
@@ -99,23 +106,24 @@ module Make(Value : Value) = struct
       let union = List.flatten
       let diff a b =
         List.filter a ~f:(fun x ->
-          List.for_all b ~f:(fun y -> Value.name x <> Value.name y))
+          List.for_all b ~f:(fun y ->
+            Ordering.neq (Key.compare (Value.key x) (Value.key y))))
     end)
 
   module Unordered = Make(struct
-      type t = Value.t String_map.t
+      type t = Value.t Key.Map.t
 
-      let singleton x = String_map.singleton (Value.name x) x
+      let singleton x = Key.Map.singleton (Value.key x) x
 
       let union l =
-        List.fold_left l ~init:String_map.empty ~f:(fun acc t ->
-          String_map.merge acc t ~f:(fun _name x y ->
+        List.fold_left l ~init:Key.Map.empty ~f:(fun acc t ->
+          Key.Map.merge acc t ~f:(fun _name x y ->
             match x, y with
             | Some x, _ | _, Some x -> Some x
             | _ -> None))
 
       let diff a b =
-        String_map.merge a b ~f:(fun _name x y ->
+        Key.Map.merge a b ~f:(fun _name x y ->
           match x, y with
           | Some _, None -> x
           | _ -> None)
diff --git a/src/ordered_set_lang.mli b/src/ordered_set_lang.mli
index 483a1c08..cf975acb 100644
--- a/src/ordered_set_lang.mli
+++ b/src/ordered_set_lang.mli
@@ -12,10 +12,17 @@ val loc : t -> Loc.t option
 (** Value parsed from elements in the DSL *)
 module type Value = sig
   type t
-  val name : t -> string
+  type key
+  val key : t -> key
 end
 
-module Make(Value : Value) : sig
+module type Key = sig
+  type t
+  val compare : t -> t -> Ordering.t
+  module Map : Map.S with type key = t
+end
+
+module Make(Key : Key)(Value : Value with type key = Key.t) : sig
   (** Evaluate an ordered set. [standard] is the interpretation of [:standard] inside the
       DSL. *)
   val eval
@@ -28,8 +35,8 @@ module Make(Value : Value) : sig
   val eval_unordered
     :  t
     -> parse:(loc:Loc.t -> string -> Value.t)
-    -> standard:Value.t String_map.t
-    -> Value.t String_map.t
+    -> standard:Value.t Key.Map.t
+    -> Value.t Key.Map.t
 end
 
 val standard : t
diff --git a/src/stdune/ordering.ml b/src/stdune/ordering.ml
index 99d48e2a..27ee1fd3 100644
--- a/src/stdune/ordering.ml
+++ b/src/stdune/ordering.ml
@@ -15,3 +15,7 @@ let to_int = function
   | Lt -> -1
   | Eq ->  0
   | Gt ->  1
+
+let neq = function
+  | Eq -> false
+  | Lt | Gt -> true
diff --git a/src/stdune/ordering.mli b/src/stdune/ordering.mli
index 3c22f1f2..04bd168b 100644
--- a/src/stdune/ordering.mli
+++ b/src/stdune/ordering.mli
@@ -7,3 +7,5 @@ type t =
 
 val of_int : int -> t
 val to_int : t -> int
+
+val neq : t -> bool
diff --git a/src/super_context.ml b/src/super_context.ml
index 207badf1..9a83da73 100644
--- a/src/super_context.ml
+++ b/src/super_context.ml
@@ -649,7 +649,12 @@ end
 
 module Eval_strings = Ordered_set_lang.Make(struct
     type t = string
-    let name t = t
+    let compare = String.compare
+    module Map = String_map
+  end)(struct
+    type t = string
+    type key = string
+    let key x = x
   end)
 
 let expand_and_eval_set t ~scope ~dir ?extra_vars set ~standard =