diff --git a/src/Action.ml b/src/Action.ml
index f3e34573..54ee5d1c 100644
--- a/src/Action.ml
+++ b/src/Action.ml
@@ -34,7 +34,7 @@ let rec run_ ~union ~hooks ~rev_prefix pat t =
     List.fold_left ~f ~init:(ret t) pats
   | P_union pats ->
     let+ ts = ResultMonad.map (fun pat -> run_ ~union ~hooks ~rev_prefix pat t) pats in
-    List.fold_left ~f:(Trie.union union) ~init:Trie.empty ts
+    List.fold_left ~f:(Trie.union union ~rev_prefix) ~init:Trie.empty ts
   | P_hook h -> hooks h ~rev_prefix t
 
 let run_with_hooks ?(rev_prefix=[]) ~union ~hooks = run_ ~union ~hooks ~rev_prefix
diff --git a/test/TestAction.ml b/test/TestAction.ml
index 17685046..9dc7b436 100644
--- a/test/TestAction.ml
+++ b/test/TestAction.ml
@@ -9,7 +9,20 @@ let trie (type a) (elem : a Alcotest.testable) : a Trie.t Alcotest.testable =
   end in
   (module M)
 
-let cantor ~rev_path:_ x y = if x == y then x else (x + y) * (x + y + 1) / 2 + y
+type data = N of int | U of string list * data * data
+
+let data : data Alcotest.testable =
+  let module M = struct
+    type t = data
+    let rec pp fmt =
+      function
+      | N i -> Format.pp_print_int fmt i
+      | U (rp, d1, d2) -> Format.fprintf fmt "U(%a,%a,%a)" Alcotest.(pp @@ list string) rp pp d1 pp d2
+    let equal = (=)
+  end in
+  (module M)
+
+let myunion ~rev_path x y = U (rev_path, x, y)
 
 let of_list l =
   Trie.of_seq
@@ -27,187 +40,173 @@ let error : [`BindingNotFound of Pattern.path] Alcotest.testable =
 let run_result elem = Alcotest.result (trie elem) error
 
 let test_none_1 () =
-  Alcotest.(check @@ run_result int) "ok"
+  Alcotest.(check @@ run_result data) "ok"
     (Ok (of_list []))
-    (Action.run ~union:cantor none (of_list [["x"], 10]))
+    (Action.run ~union:myunion none (of_list [["x"], N 10]))
 
 let test_none_2 () =
-  Alcotest.(check @@ run_result int) "ok"
+  Alcotest.(check @@ run_result data) "ok"
     (Ok (of_list []))
-    (Action.run ~union:cantor none (of_list [[], 10]))
+    (Action.run ~union:myunion none (of_list [[], N 10]))
 
 let test_none_3 () =
-  Alcotest.(check @@ run_result int) "error"
+  Alcotest.(check @@ run_result data) "error"
     (Error (`BindingNotFound []))
-    (Action.run ~union:cantor none Trie.empty)
+    (Action.run ~union:myunion none Trie.empty)
 
 let test_any_1 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [["x"], 10]))
-    (Action.run ~union:cantor any (of_list [["x"], 10]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [["x"], N 10]))
+    (Action.run ~union:myunion any (of_list [["x"], N 10]))
 
 let test_any_2 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [[], 10]))
-    (Action.run ~union:cantor any (of_list [[], 10]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [[], N 10]))
+    (Action.run ~union:myunion any (of_list [[], N 10]))
 
 let test_any_3 () =
-  Alcotest.(check @@ run_result int) "error"
+  Alcotest.(check @@ run_result data) "error"
     (Error (`BindingNotFound []))
-    (Action.run ~union:cantor any Trie.empty)
+    (Action.run ~union:myunion any Trie.empty)
 
 let test_any_4 () =
-  let t = of_list [[], 10] in
-  Alcotest.(check bool) "true"
-    true
-    (Trie.equal Int.equal t @@ Result.get_ok (Action.run ~union:cantor any t))
+  let t = of_list [[], N 10] in
+  Alcotest.(check @@ run_result data) "true"
+    (Ok t)
+    (Action.run ~union:myunion any t)
 
 let test_only_1 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [["x"], 10]))
-    (Action.run ~union:cantor (only ["x"]) (of_list [["x"], 10; ["y"], 20]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [["x"], N 10]))
+    (Action.run ~union:myunion (only ["x"]) (of_list [["x"], N 10; ["y"], N 20]))
 
 let test_only_2 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [["x"; "y"], 10; ["x"; "x"], 20]))
-    (Action.run ~union:cantor (only ["x"]) (of_list [["x"; "y"], 10; ["x"; "x"], 20; ["y"], 30]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [["x"; "y"], N 10; ["x"; "x"], N 20]))
+    (Action.run ~union:myunion (only ["x"]) (of_list [["x"; "y"], N 10; ["x"; "x"], N 20; ["y"], N 30]))
 
 let test_only_3 () =
-  Alcotest.(check @@ run_result int) "error"
+  Alcotest.(check @@ run_result data) "error"
     (Error (`BindingNotFound ["x"]))
-    (Action.run ~union:cantor (only ["x"]) Trie.empty)
+    (Action.run ~union:myunion (only ["x"]) Trie.empty)
 
 let test_only_4 () =
-  let t = of_list [["x"], 10] in
-  Alcotest.(check @@ run_result int) "ok"
+  let t = of_list [["x"], N 10] in
+  Alcotest.(check @@ run_result data) "ok"
     (Ok t)
-    (Action.run ~union:cantor (only ["x"]) t)
+    (Action.run ~union:myunion (only ["x"]) t)
 
 let test_except_1 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [["y"], 20]))
-    (Action.run ~union:cantor (except ["x"]) (of_list [["x"], 10; ["y"], 20]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [["y"], N 20]))
+    (Action.run ~union:myunion (except ["x"]) (of_list [["x"], N 10; ["y"], N 20]))
 
 let test_except_2 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [["y"], 30]))
-    (Action.run ~union:cantor (except ["x"]) (of_list [["x"; "y"], 10; ["x"; "x"], 20; ["y"], 30]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [["y"], N 30]))
+    (Action.run ~union:myunion (except ["x"]) (of_list [["x"; "y"], N 10; ["x"; "x"], N 20; ["y"], N 30]))
 
 let test_except_3 () =
-  Alcotest.(check @@ run_result int) "error"
+  Alcotest.(check @@ run_result data) "error"
     (Error (`BindingNotFound ["x"]))
-    (Action.run ~union:cantor (except ["x"]) Trie.empty)
+    (Action.run ~union:myunion (except ["x"]) Trie.empty)
 
 let test_in_1 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [["x"; "z"], 10; ["y"], 20]))
-    (Action.run ~union:cantor (in_ ["x"] (renaming [] ["z"])) (of_list [["x"], 10; ["y"], 20]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [["x"; "z"], N 10; ["y"], N 20]))
+    (Action.run ~union:myunion (in_ ["x"] (renaming [] ["z"])) (of_list [["x"], N 10; ["y"], N 20]))
 
 let test_in_2 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [["x"; "y"], 10; ["x"; "w"], 20; ["y"], 30]))
-    (Action.run ~union:cantor (in_ ["x"] (renaming ["x"] ["w"])) (of_list [["x"; "y"], 10; ["x"; "x"], 20; ["y"], 30]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [["x"; "y"], N 10; ["x"; "w"], N 20; ["y"], N 30]))
+    (Action.run ~union:myunion (in_ ["x"] (renaming ["x"] ["w"])) (of_list [["x"; "y"], N 10; ["x"; "x"], N 20; ["y"], N 30]))
 
 let test_in_3 () =
-  Alcotest.(check @@ run_result int) "error"
+  Alcotest.(check @@ run_result data) "error"
     (Error (`BindingNotFound ["x"]))
-    (Action.run ~union:cantor (in_ ["x"] any) Trie.empty)
+    (Action.run ~union:myunion (in_ ["x"] any) Trie.empty)
 
 let test_in_4 () =
-  let t = of_list [["x"; "y"], 10; ["x"; "x"], 20; ["y"], 30] in
-  Alcotest.(check @@ run_result int) "ok"
+  let t = of_list [["x"; "y"], N 10; ["x"; "x"], N 20; ["y"], N 30] in
+  Alcotest.(check @@ run_result data) "ok"
     (Ok t)
-    (Action.run ~union:cantor (in_ ["x"] (renaming ["x"] ["x"])) t)
+    (Action.run ~union:myunion (in_ ["x"] (renaming ["x"] ["x"])) t)
 
 let test_renaming_1 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [["z"], 10; ["y"], 20]))
-    (Action.run ~union:cantor (renaming ["x"] ["z"]) (of_list [["x"], 10; ["y"], 20]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [["z"], N 10; ["y"], N 20]))
+    (Action.run ~union:myunion (renaming ["x"] ["z"]) (of_list [["x"], N 10; ["y"], N 20]))
 
 let test_renaming_2 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [["z"; "y"], 10; ["z"; "x"], 20; ["y"], 30]))
-    (Action.run ~union:cantor (renaming ["x"] ["z"]) (of_list [["x"; "y"], 10; ["x"; "x"], 20; ["y"], 30]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [["z"; "y"], N 10; ["z"; "x"], N 20; ["y"], N 30]))
+    (Action.run ~union:myunion (renaming ["x"] ["z"]) (of_list [["x"; "y"], N 10; ["x"; "x"], N 20; ["y"], N 30]))
 
 let test_renaming_3 () =
-  Alcotest.(check @@ run_result int) "error"
+  Alcotest.(check @@ run_result data) "error"
     (Error (`BindingNotFound ["x"]))
-    (Action.run ~union:cantor (renaming ["x"] ["z"]) Trie.empty)
+    (Action.run ~union:myunion (renaming ["x"] ["z"]) Trie.empty)
 
 let test_renaming_4 () =
-  let t = of_list [["x"; "y"], 10; ["x"; "w"], 20; ["y"], 30] in
-  Alcotest.(check @@ run_result int) "ok"
+  let t = of_list [["x"; "y"], N 10; ["x"; "w"], N 20; ["y"], N 30] in
+  Alcotest.(check @@ run_result data) "ok"
     (Ok t)
-    (Action.run ~union:cantor (renaming ["x"] ["x"]) t)
+    (Action.run ~union:myunion (renaming ["x"] ["x"]) t)
 
 let test_renaming_5 () =
-  let t = of_list [["x"; "y"], 10; ["x"; "w"], 20; ["y"], 30] in
-  Alcotest.(check @@ run_result int) "ok"
+  let t = of_list [["x"; "y"], N 10; ["x"; "w"], N 20; ["y"], N 30] in
+  Alcotest.(check @@ run_result data) "ok"
     (Ok t)
-    (Action.run ~union:cantor (renaming ["x"; "y"] ["x"; "y"]) t)
+    (Action.run ~union:myunion (renaming ["x"; "y"] ["x"; "y"]) t)
 
 let test_seq_1 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [["w"], 10; ["y"], 20]))
-    (Action.run ~union:cantor (seq [renaming ["x"] ["z"]; renaming ["z"] ["w"]]) (of_list [["x"], 10; ["y"], 20]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [["w"], N 10; ["y"], N 20]))
+    (Action.run ~union:myunion (seq [renaming ["x"] ["z"]; renaming ["z"] ["w"]]) (of_list [["x"], N 10; ["y"], N 20]))
 
 let test_seq_2 () =
-  Alcotest.(check @@ run_result int) "error"
+  Alcotest.(check @@ run_result data) "error"
     (Error (`BindingNotFound []))
-    (Action.run ~union:cantor (seq [none; any]) (of_list [["x"; "y"], 10; ["x"; "x"], 20; ["y"], 30]))
+    (Action.run ~union:myunion (seq [none; any]) (of_list [["x"; "y"], N 10; ["x"; "x"], N 20; ["y"], N 30]))
 
 let test_seq_3 () =
-  Alcotest.(check @@ run_result int) "error"
+  Alcotest.(check @@ run_result data) "error"
     (Error (`BindingNotFound []))
-    (Action.run ~union:cantor (seq [none; none]) Trie.empty)
+    (Action.run ~union:myunion (seq [none; none]) Trie.empty)
 
 let test_seq_4 () =
-  Alcotest.(check @@ run_result int) "error"
+  Alcotest.(check @@ run_result data) "error"
     (Error (`BindingNotFound ["x"]))
-    (Action.run ~union:cantor (seq [renaming ["x"] ["z"]; only ["x"]]) (of_list [["x"], 10; ["y"], 20]))
+    (Action.run ~union:myunion (seq [renaming ["x"] ["z"]; only ["x"]]) (of_list [["x"], N 10; ["y"], N 20]))
 
 let test_seq_5 () =
-  let t = of_list [["x"; "y"], 10; ["x"; "w"], 20; ["y"], 30] in
-  Alcotest.(check @@ run_result int) "ok"
+  let t = of_list [["x"; "y"], N 10; ["x"; "w"], N 20; ["y"], N 30] in
+  Alcotest.(check @@ run_result data) "ok"
     (Ok t)
-    (Action.run ~union:cantor (seq [seq []; seq []]) t)
+    (Action.run ~union:myunion (seq [seq []; seq []]) t)
 
 let test_union_1 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [["x"], 10; ["y"], 20]))
-    (Action.run ~union:cantor (union [only ["x"]; except ["x"]]) (of_list [["x"], 10; ["y"], 20]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [["x"], U (["x"], N 10, N 10); ["y"], N 20]))
+    (Action.run ~union:myunion (union [only ["x"]; except ["x"]; only ["x"]]) (of_list [["x"], N 10; ["y"], N 20]))
 
 let test_union_2 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list []))
-    (Action.run ~union:cantor (union []) (of_list [["x"], 10; ["y"], 20]))
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list [["x"], U (["x"], N 10, N 10); ["y"], N 20]))
+    (Action.run ~union:myunion (in_ ["x"] (union [only []; only []])) (of_list [["x"], N 10; ["y"], N 20]))
 
 let test_union_3 () =
-  let t = of_list [["x"; "y"], 10; ["x"; "w"], 20; ["y"], 30] in
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok t)
-    (Action.run ~union:cantor (union [seq []]) t)
-
-let test_filter_map_1 () =
-  Alcotest.(check @@ run_result int) "ok"
-    (Ok (of_list [["y"], 110]))
-    (Action.run_with_hooks
-       ~hooks:(fun () ~rev_prefix t ->
-           Result.ok @@ Trie.filter_mapi ~rev_prefix
-             (fun ~rev_path:_ d -> if d > 20 then Some (d + 80) else None) t)
-       ~union:cantor
-       (hook ()) (of_list [["x"; "y"], 10; ["x"; "x"], 20; ["y"], 30]))
-
-let test_filter_map_2 () =
-  let t = of_list [["x"; "y"], 10; ["x"; "w"], 20; ["y"], 30] in
-  Alcotest.(check @@ run_result int) "ok"
+  Alcotest.(check @@ run_result data) "ok"
+    (Ok (of_list []))
+    (Action.run ~union:myunion (union []) (of_list [["x"], N 10; ["y"], N 20]))
+
+let test_union_4 () =
+  let t = of_list [["x"; "y"], N 10; ["x"; "w"], N 20; ["y"], N 30] in
+  Alcotest.(check @@ run_result data) "ok"
     (Ok t)
-    (Action.run_with_hooks
-       ~hooks:(fun () ~rev_prefix t ->
-           Result.ok @@ Trie.filter_mapi ~rev_prefix
-             (fun ~rev_path:_ x -> Some x) t)
-       ~union:cantor
-       (hook ()) t)
+    (Action.run ~union:myunion (union [seq []]) t)
+
+(* FIXME: design new test cases for hooks *)
 
 let () =
   let open Alcotest in
@@ -258,9 +257,6 @@ let () =
       test_case "union" `Quick test_union_1;
       test_case "union" `Quick test_union_2;
       test_case "union" `Quick test_union_3;
-    ];
-    "filter_map", [
-      test_case "filter_map" `Quick test_filter_map_1;
-      test_case "filter_map" `Quick test_filter_map_2;
+      test_case "union" `Quick test_union_4;
     ];
   ]