diff --git a/src/proto_alpha/lib_benchmark/michelson_samplers.ml b/src/proto_alpha/lib_benchmark/michelson_samplers.ml
index 022b2b20a94a6892c0aa686d46f7043d1ccc0e49..0ced7ddd8a71ee272f37f15f625b2afcac46fc6f 100644
--- a/src/proto_alpha/lib_benchmark/michelson_samplers.ml
+++ b/src/proto_alpha/lib_benchmark/michelson_samplers.ml
@@ -318,20 +318,20 @@ end)
         (cmp_tn : 'a comparable_and_atomic) :
         Script_ir_translator.ex_comparable_ty =
       match cmp_tn with
-      | `TString -> Ex_comparable_ty string_key
-      | `TNat -> Ex_comparable_ty nat_key
-      | `TBytes -> Ex_comparable_ty bytes_key
-      | `TBool -> Ex_comparable_ty bool_key
-      | `TAddress -> Ex_comparable_ty address_key
-      | `TTx_rollup_l2_address -> Ex_comparable_ty tx_rollup_l2_address_key
-      | `TTimestamp -> Ex_comparable_ty timestamp_key
-      | `TKey_hash -> Ex_comparable_ty key_hash_key
-      | `TMutez -> Ex_comparable_ty mutez_key
-      | `TInt -> Ex_comparable_ty int_key
-      | `TUnit -> Ex_comparable_ty unit_key
-      | `TSignature -> Ex_comparable_ty signature_key
-      | `TKey -> Ex_comparable_ty key_key
-      | `TChain_id -> Ex_comparable_ty chain_id_key
+      | `TString -> Ex_comparable_ty string_t
+      | `TNat -> Ex_comparable_ty nat_t
+      | `TBytes -> Ex_comparable_ty bytes_t
+      | `TBool -> Ex_comparable_ty bool_t
+      | `TAddress -> Ex_comparable_ty address_t
+      | `TTx_rollup_l2_address -> Ex_comparable_ty tx_rollup_l2_address_t
+      | `TTimestamp -> Ex_comparable_ty timestamp_t
+      | `TKey_hash -> Ex_comparable_ty key_hash_t
+      | `TMutez -> Ex_comparable_ty mutez_t
+      | `TInt -> Ex_comparable_ty int_t
+      | `TUnit -> Ex_comparable_ty unit_t
+      | `TSignature -> Ex_comparable_ty signature_t
+      | `TKey -> Ex_comparable_ty key_t
+      | `TChain_id -> Ex_comparable_ty chain_id_t
 
     let rec m_type ~size : Script_ir_translator.ex_ty sampler =
       let open Script_ir_translator in
@@ -443,7 +443,7 @@ end)
       let option_case size =
         let size = size - 1 in
         let* (Ex_comparable_ty t) = m_comparable_type ~size in
-        match option_key (-1) t with
+        match comparable_option_t (-1) t with
         | Error _ -> (* what should be done here? *) assert false
         | Ok res_ty -> return @@ Ex_comparable_ty res_ty
       in
@@ -455,7 +455,7 @@ end)
         let size_right = size - size_left in
         let* (Ex_comparable_ty l) = m_comparable_type ~size:size_left in
         let* (Ex_comparable_ty r) = m_comparable_type ~size:size_right in
-        match pair_key (-1) l r with
+        match comparable_pair_t (-1) l r with
         | Error _ -> assert false
         | Ok res_ty -> return @@ Ex_comparable_ty res_ty
       in
@@ -467,7 +467,7 @@ end)
         let size_right = size - size_left in
         let* (Ex_comparable_ty l) = m_comparable_type ~size:size_left in
         let* (Ex_comparable_ty r) = m_comparable_type ~size:size_right in
-        match union_key (-1) l r with
+        match comparable_union_t (-1) l r with
         | Error _ -> assert false
         | Ok res_ty -> return @@ Ex_comparable_ty res_ty
       in
diff --git a/src/proto_alpha/lib_benchmarks_proto/interpreter_benchmarks.ml b/src/proto_alpha/lib_benchmarks_proto/interpreter_benchmarks.ml
index c036e023f030ed69a0c2cb7a4f5ee188bdf4c584..632fd4831facdd711cd8193394113fa8c112ec92 100644
--- a/src/proto_alpha/lib_benchmarks_proto/interpreter_benchmarks.ml
+++ b/src/proto_alpha/lib_benchmarks_proto/interpreter_benchmarks.ml
@@ -1118,13 +1118,12 @@ module Registration_section = struct
     let () =
       simple_benchmark
         ~name:Interpreter_workload.N_IEmpty_set
-        ~kinstr:
-          (IEmpty_set (kinfo_unit, unit_cmp, halt (set unit_cmp @$ unit @$ bot)))
+        ~kinstr:(IEmpty_set (kinfo_unit, unit, halt (set unit @$ unit @$ bot)))
         ()
 
     let set_iter_code =
       ISet_iter
-        ( kinfo (set int_cmp @$ unit @$ bot),
+        ( kinfo (set int @$ unit @$ bot),
           IDrop (kinfo (int @$ unit @$ bot), halt_unit),
           halt_unit )
 
@@ -1141,7 +1140,7 @@ module Registration_section = struct
        *)
       simple_benchmark
         ~name:Interpreter_workload.N_ISet_iter
-        ~intercept_stack:(Script_set.empty int_cmp, ((), eos))
+        ~intercept_stack:(Script_set.empty int, ((), eos))
         ~kinstr:set_iter_code
         ()
 
@@ -1150,9 +1149,8 @@ module Registration_section = struct
         ~name:Interpreter_workload.N_ISet_mem
         ~kinstr:
           (ISet_mem
-             ( kinfo (int @$ set int_cmp @$ unit @$ bot),
-               halt (bool @$ unit @$ bot) ))
-        ~intercept_stack:(Script_int.zero, (Script_set.empty int_cmp, ((), eos)))
+             (kinfo (int @$ set int @$ unit @$ bot), halt (bool @$ unit @$ bot)))
+        ~intercept_stack:(Script_int.zero, (Script_set.empty int, ((), eos)))
         ~stack_sampler:(fun cfg rng_state () ->
           assert (cfg.sampler.set_size.min >= 1) ;
           let n =
@@ -1164,7 +1162,7 @@ module Registration_section = struct
           let set =
             List.fold_left
               (fun set elt -> Script_set.update elt true set)
-              (Script_set.empty int_cmp)
+              (Script_set.empty int)
               elts
           in
           let elt =
@@ -1179,10 +1177,8 @@ module Registration_section = struct
         ~name:Interpreter_workload.N_ISet_update
         ~kinstr:
           (ISet_update
-             ( kinfo (int @$ bool @$ set int_cmp @$ bot),
-               halt (set int_cmp @$ bot) ))
-        ~intercept_stack:
-          (Script_int.zero, (false, (Script_set.empty int_cmp, eos)))
+             (kinfo (int @$ bool @$ set int @$ bot), halt (set int @$ bot)))
+        ~intercept_stack:(Script_int.zero, (false, (Script_set.empty int, eos)))
         ~stack_sampler:(fun cfg rng_state () ->
           assert (cfg.sampler.set_size.min >= 2) ;
           let n =
@@ -1197,7 +1193,7 @@ module Registration_section = struct
           let set =
             List.fold_left
               (fun set elt -> Script_set.update elt true set)
-              (Script_set.empty int_cmp)
+              (Script_set.empty int)
               in_set
           in
           let stack =
@@ -1217,7 +1213,7 @@ module Registration_section = struct
     let () =
       simple_benchmark
         ~name:Interpreter_workload.N_ISet_size
-        ~kinstr:(ISet_size (kinfo (set unit_cmp @$ bot), halt (nat @$ bot)))
+        ~kinstr:(ISet_size (kinfo (set unit @$ bot), halt (nat @$ bot)))
         ()
   end
 
@@ -1230,7 +1226,7 @@ module Registration_section = struct
       let map =
         List.fold_left
           (fun map i -> Script_map.update i (Some ()) map)
-          (Script_map.empty int_cmp)
+          (Script_map.empty int)
           keys
       in
       let (module M) = Script_map.get_module map in
@@ -1244,23 +1240,22 @@ module Registration_section = struct
       simple_benchmark
         ~name:Interpreter_workload.N_IEmpty_map
         ~kinstr:
-          (IEmpty_map
-             (kinfo_unit, unit_cmp, halt (map unit_cmp unit @$ unit @$ bot)))
+          (IEmpty_map (kinfo_unit, unit, halt (map unit unit @$ unit @$ bot)))
         ()
 
     (*
     let map_map_code =
       IMap_map
-        ( kinfo (map int_cmp unit @$ unit @$ bot),
+        ( kinfo (map int unit @$ unit @$ bot),
           ICdr (kinfo (cpair int unit @$ unit @$ bot), halt_unitunit),
-          halt (map int_cmp unit @$ unit @$ bot) )
+          halt (map int unit @$ unit @$ bot) )
      *)
 
     let map_map_code =
       IMap_map
-        ( kinfo (map int_cmp unit @$ unit @$ bot),
+        ( kinfo (map int unit @$ unit @$ bot),
           IFailwith (kinfo (cpair int unit @$ unit @$ bot), 0, cpair int unit),
-          halt (map int_cmp unit @$ unit @$ bot) )
+          halt (map int unit @$ unit @$ bot) )
 
     let () =
       (*
@@ -1272,14 +1267,14 @@ module Registration_section = struct
       simple_benchmark
         ~name:Interpreter_workload.N_IMap_map
         ~intercept_stack:
-          (let map = Script_map.empty int_cmp in
+          (let map = Script_map.empty int in
            (map, ((), eos)))
         ~kinstr:map_map_code
         ()
 
     let kmap_iter_code =
       IMap_iter
-        ( kinfo (map int_cmp unit @$ unit @$ bot),
+        ( kinfo (map int unit @$ unit @$ bot),
           IDrop (kinfo (cpair int unit @$ unit @$ bot), halt_unit),
           halt_unit )
 
@@ -1293,7 +1288,7 @@ module Registration_section = struct
       simple_benchmark
         ~name:Interpreter_workload.N_IMap_iter
         ~intercept_stack:
-          (let map = Script_map.empty int_cmp in
+          (let map = Script_map.empty int in
            (map, ((), eos)))
         ~kinstr:kmap_iter_code
         ()
@@ -1308,10 +1303,10 @@ module Registration_section = struct
         ~name:Interpreter_workload.N_IMap_mem
         ~kinstr:
           (IMap_mem
-             ( kinfo (int @$ map int_cmp unit @$ unit @$ bot),
+             ( kinfo (int @$ map int unit @$ unit @$ bot),
                halt (bool @$ unit @$ bot) ))
         ~intercept_stack:
-          (let map = Script_map.empty int_cmp in
+          (let map = Script_map.empty int in
            (Script_int.zero, (map, ((), eos))))
         ~stack_sampler:(fun cfg rng_state () ->
           let (key, map) = generate_map_and_key_in_map cfg rng_state in
@@ -1328,10 +1323,10 @@ module Registration_section = struct
         ~name:Interpreter_workload.N_IMap_get
         ~kinstr:
           (IMap_get
-             ( kinfo (int @$ map int_cmp unit @$ unit @$ bot),
+             ( kinfo (int @$ map int unit @$ unit @$ bot),
                halt (option unit @$ unit @$ bot) ))
         ~intercept_stack:
-          (let map = Script_map.empty int_cmp in
+          (let map = Script_map.empty int in
            (Script_int.zero, (map, ((), eos))))
         ~stack_sampler:(fun cfg rng_state () ->
           let (key, map) = generate_map_and_key_in_map cfg rng_state in
@@ -1348,10 +1343,10 @@ module Registration_section = struct
         ~name:Interpreter_workload.N_IMap_update
         ~kinstr:
           (IMap_update
-             ( kinfo (int @$ option unit @$ map int_cmp unit @$ bot),
-               halt (map int_cmp unit @$ bot) ))
+             ( kinfo (int @$ option unit @$ map int unit @$ bot),
+               halt (map int unit @$ bot) ))
         ~intercept_stack:
-          (let map = Script_map.empty int_cmp in
+          (let map = Script_map.empty int in
            (Script_int.zero, (None, (map, eos))))
         ~stack_sampler:(fun cfg rng_state () ->
           let (key, map) = generate_map_and_key_in_map cfg rng_state in
@@ -1369,10 +1364,10 @@ module Registration_section = struct
         ~name:Interpreter_workload.N_IMap_get_and_update
         ~kinstr:
           (IMap_get_and_update
-             ( kinfo (int @$ option unit @$ map int_cmp unit @$ bot),
-               halt (option unit @$ map int_cmp unit @$ bot) ))
+             ( kinfo (int @$ option unit @$ map int unit @$ bot),
+               halt (option unit @$ map int unit @$ bot) ))
         ~intercept_stack:
-          (let map = Script_map.empty int_cmp in
+          (let map = Script_map.empty int in
            (Script_int.zero, (None, (map, eos))))
         ~stack_sampler:(fun cfg rng_state () ->
           let (key, map) = generate_map_and_key_in_map cfg rng_state in
@@ -1388,9 +1383,9 @@ module Registration_section = struct
        *)
       simple_benchmark_with_stack_sampler
         ~name:Interpreter_workload.N_IMap_size
-        ~kinstr:(IMap_size (kinfo (map int_cmp unit @$ bot), halt (nat @$ bot)))
+        ~kinstr:(IMap_size (kinfo (map int unit @$ bot), halt (nat @$ bot)))
         ~stack_sampler:(fun _cfg _rng_state ->
-          let map = Script_map.empty int_cmp in
+          let map = Script_map.empty int in
           fun () -> (map, eos))
         ()
   end
@@ -1405,7 +1400,7 @@ module Registration_section = struct
       let map =
         List.fold_left
           (fun map i -> Script_map.update i (Some (Some ())) map)
-          (Script_map.empty int_cmp)
+          (Script_map.empty int)
           keys
       in
       let (module M) = Script_map.get_module map in
@@ -1417,9 +1412,7 @@ module Registration_section = struct
         raise_if_error
           (Lwt_main.run
              ( Execution_context.make ~rng_state >>=? fun (ctxt, _) ->
-               let big_map =
-                 Script_ir_translator.empty_big_map int_cmp unit_t
-               in
+               let big_map = Script_ir_translator.empty_big_map int unit_t in
                Script_map.fold
                  (fun k v acc ->
                    acc >>=? fun (bm, ctxt_acc) ->
@@ -1436,10 +1429,7 @@ module Registration_section = struct
         ~name:Interpreter_workload.N_IEmpty_big_map
         ~kinstr:
           (IEmpty_big_map
-             ( kinfo_unit,
-               unit_cmp,
-               unit,
-               halt (big_map unit_cmp unit @$ unit @$ bot) ))
+             (kinfo_unit, unit, unit, halt (big_map unit unit @$ unit @$ bot)))
         ()
 
     let () =
@@ -1453,7 +1443,7 @@ module Registration_section = struct
         ~name:Interpreter_workload.N_IBig_map_mem
         ~kinstr:
           (IBig_map_mem
-             ( kinfo (int @$ big_map int_cmp unit @$ unit @$ bot),
+             ( kinfo (int @$ big_map int unit @$ unit @$ bot),
                halt (bool @$ unit @$ bot) ))
         ~stack_sampler:(fun cfg rng_state () ->
           let (key, map) = generate_big_map_and_key_in_map cfg rng_state in
@@ -1470,10 +1460,10 @@ module Registration_section = struct
         ~name:Interpreter_workload.N_IBig_map_get
         ~kinstr:
           (IBig_map_get
-             ( kinfo (int @$ big_map int_cmp unit @$ unit @$ bot),
+             ( kinfo (int @$ big_map int unit @$ unit @$ bot),
                halt (option unit @$ unit @$ bot) ))
         ~intercept_stack:
-          (let map = Script_ir_translator.empty_big_map int_cmp unit in
+          (let map = Script_ir_translator.empty_big_map int unit in
            (Script_int.zero, (map, ((), eos))))
         ~stack_sampler:(fun cfg rng_state () ->
           let (key, map) = generate_big_map_and_key_in_map cfg rng_state in
@@ -1490,10 +1480,10 @@ module Registration_section = struct
         ~name:Interpreter_workload.N_IBig_map_update
         ~kinstr:
           (IBig_map_update
-             ( kinfo (int @$ option unit @$ big_map int_cmp unit @$ bot),
-               halt (big_map int_cmp unit @$ bot) ))
+             ( kinfo (int @$ option unit @$ big_map int unit @$ bot),
+               halt (big_map int unit @$ bot) ))
         ~intercept_stack:
-          (let map = Script_ir_translator.empty_big_map int_cmp unit in
+          (let map = Script_ir_translator.empty_big_map int unit in
            (Script_int.zero, (None, (map, eos))))
         ~stack_sampler:(fun cfg rng_state () ->
           let (key, map) = generate_big_map_and_key_in_map cfg rng_state in
@@ -1511,10 +1501,10 @@ module Registration_section = struct
         ~name:Interpreter_workload.N_IBig_map_get_and_update
         ~kinstr:
           (IBig_map_get_and_update
-             ( kinfo (int @$ option unit @$ big_map int_cmp unit @$ bot),
-               halt (option unit @$ big_map int_cmp unit @$ bot) ))
+             ( kinfo (int @$ option unit @$ big_map int unit @$ bot),
+               halt (option unit @$ big_map int unit @$ bot) ))
         ~intercept_stack:
-          (let map = Script_ir_translator.empty_big_map int_cmp unit in
+          (let map = Script_ir_translator.empty_big_map int unit in
            (Script_int.zero, (None, (map, eos))))
         ~stack_sampler:(fun cfg rng_state () ->
           let (key, map) = generate_big_map_and_key_in_map cfg rng_state in
@@ -2657,7 +2647,7 @@ module Registration_section = struct
       simple_benchmark
         ~name:Interpreter_workload.N_ITicket
         ~kinstr:
-          (ITicket (kinfo (unit @$ nat @$ bot), halt (ticket unit_cmp @$ bot)))
+          (ITicket (kinfo (unit @$ nat @$ bot), halt (ticket unit @$ bot)))
         ()
 
     let () =
@@ -2665,13 +2655,12 @@ module Registration_section = struct
         ~name:Interpreter_workload.N_IRead_ticket
         ~kinstr:
           (IRead_ticket
-             ( kinfo (ticket unit_cmp @$ bot),
-               halt (cpair address (cpair unit nat) @$ ticket unit_cmp @$ bot)
-             ))
+             ( kinfo (ticket unit @$ bot),
+               halt (cpair address (cpair unit nat) @$ ticket unit @$ bot) ))
         ()
 
     let split_ticket_instr =
-      let ticket_unit = ticket unit_cmp in
+      let ticket_unit = ticket unit in
       let (Ty_ex_c pair_ticket_unit_ticket_unit) =
         pair ticket_unit ticket_unit
       in
@@ -2707,9 +2696,7 @@ module Registration_section = struct
           fun () ->
             let half_amount = Samplers.Random_value.value nat rng_state in
             let amount = Script_int.add_n half_amount half_amount in
-            let ticket =
-              Samplers.Random_value.value (ticket unit_cmp) rng_state
-            in
+            let ticket = Samplers.Random_value.value (ticket unit) rng_state in
             let ticket = {ticket with amount} in
             Ex_stack_and_kinstr
               {
@@ -2719,11 +2706,11 @@ module Registration_section = struct
         ()
 
     let join_tickets_instr =
-      let ticket_str = ticket string_cmp in
+      let ticket_str = ticket string in
       let (Ty_ex_c pair_ticket_str_ticket_str) = pair ticket_str ticket_str in
       IJoin_tickets
         ( kinfo (pair_ticket_str_ticket_str @$ bot),
-          string_cmp,
+          string,
           halt (option ticket_str @$ bot) )
 
     let () =
@@ -2736,7 +2723,7 @@ module Registration_section = struct
           in
           fun () ->
             let ticket =
-              Samplers.Random_value.value (ticket string_cmp) rng_state
+              Samplers.Random_value.value (ticket string) rng_state
             in
             let ticket =
               {
@@ -2758,7 +2745,7 @@ module Registration_section = struct
           in
           fun () ->
             let ticket =
-              Samplers.Random_value.value (ticket string_cmp) rng_state
+              Samplers.Random_value.value (ticket string) rng_state
             in
             let alt_amount = Samplers.Random_value.value nat rng_state in
             let ticket' = {ticket with amount = alt_amount} in
@@ -3055,7 +3042,7 @@ module Registration_section = struct
 
     let map_enter_body_code =
       let kbody = ICdr (kinfo (cpair int unit @$ unit @$ bot), halt_unitunit) in
-      fun accu -> KMap_enter_body (kbody, accu, Script_map.empty int_cmp, KNil)
+      fun accu -> KMap_enter_body (kbody, accu, Script_map.empty int, KNil)
 
     let () =
       (*
diff --git a/src/proto_alpha/lib_benchmarks_proto/michelson_types.ml b/src/proto_alpha/lib_benchmarks_proto/michelson_types.ml
index 9887d7b003597953e77e9157d9d09c29dec4ab1d..95af373691cceef4e6ee0ed7162e7c715ab16b89 100644
--- a/src/proto_alpha/lib_benchmarks_proto/michelson_types.ml
+++ b/src/proto_alpha/lib_benchmarks_proto/michelson_types.ml
@@ -34,12 +34,6 @@ let bot = Bot_t
 
 let unit = unit_t
 
-let unit_cmp = unit_key
-
-let int_cmp = int_key
-
-let string_cmp = string_key
-
 (* the type of integers *)
 let int = int_t
 
@@ -98,7 +92,7 @@ let pair k1 k2 =
 
 (* comparable pair type constructor *)
 let cpair k1 k2 =
-  match pair_key (-1) k1 k2 with Error _ -> assert false | Ok t -> t
+  match comparable_pair_t (-1) k1 k2 with Error _ -> assert false | Ok t -> t
 
 (* union type constructor*)
 let union k1 k2 =
@@ -106,7 +100,7 @@ let union k1 k2 =
 
 (* comparable union type constructor *)
 let cunion k1 k2 =
-  match union_key (-1) k1 k2 with Error _ -> assert false | Ok t -> t
+  match comparable_union_t (-1) k1 k2 with Error _ -> assert false | Ok t -> t
 
 let lambda x y =
   match lambda_t (-1) x y with Error _ -> assert false | Ok t -> t
diff --git a/src/proto_alpha/lib_benchmarks_proto/ticket_benchmarks.ml b/src/proto_alpha/lib_benchmarks_proto/ticket_benchmarks.ml
index a298d2522e262d16d67bb20c907f3c73706dde0c..46df2541fd293a8f603d4da5746b4281372855eb 100644
--- a/src/proto_alpha/lib_benchmarks_proto/ticket_benchmarks.ml
+++ b/src/proto_alpha/lib_benchmarks_proto/ticket_benchmarks.ml
@@ -169,7 +169,7 @@ let () = Registration_helpers.register (module Compare_key_contract_benchmark)
 (* A simple ticket type for use in the benchmarks. *)
 let ticket_ty =
   let open Script_typed_ir in
-  WithExceptions.Result.get_ok ~loc:__LOC__ (ticket_t (-1) int_key)
+  WithExceptions.Result.get_ok ~loc:__LOC__ (ticket_t (-1) int_t)
 
 (* A dummy type generator, sampling linear terms of a given size.
    The generator always returns types of the shape:
diff --git a/src/proto_alpha/lib_benchmarks_proto/translator_benchmarks.ml b/src/proto_alpha/lib_benchmarks_proto/translator_benchmarks.ml
index 558a77503f00c80e28a8440ff1c42fc648a7cb3d..2fbb2f6c48dde48f77302856c6b810e23eb6feed 100644
--- a/src/proto_alpha/lib_benchmarks_proto/translator_benchmarks.ml
+++ b/src/proto_alpha/lib_benchmarks_proto/translator_benchmarks.ml
@@ -646,13 +646,15 @@ let rec dummy_type_generator size =
 let rec dummy_comparable_type_generator size =
   let open Script_ir_translator in
   let open Script_typed_ir in
-  if size <= 0 then Ex_comparable_ty unit_key
+  if size <= 0 then Ex_comparable_ty unit_t
   else
     match dummy_comparable_type_generator (size - 2) with
     | Ex_comparable_ty r ->
-        let l = unit_key in
+        let l = unit_t in
         Ex_comparable_ty
-          (match pair_key (-1) l r with Error _ -> assert false | Ok t -> t)
+          (match comparable_pair_t (-1) l r with
+          | Error _ -> assert false
+          | Ok t -> t)
 
 module Parse_type_shared = struct
   type config = {max_size : int}
diff --git a/src/proto_alpha/lib_protocol/script_ir_translator.ml b/src/proto_alpha/lib_protocol/script_ir_translator.ml
index 6fe18495b5081e27b2192f6d25b7ffb80e1101f4..7036bc9a6aac3ac2da9658a261db8dba9f4598d8 100644
--- a/src/proto_alpha/lib_protocol/script_ir_translator.ml
+++ b/src/proto_alpha/lib_protocol/script_ir_translator.ml
@@ -1039,48 +1039,43 @@ let[@coq_struct "ty"] rec parse_comparable_ty :
   else
     match ty with
     | Prim (loc, T_unit, [], annot) ->
-        check_type_annot loc annot >|? fun () ->
-        (Ex_comparable_ty unit_key, ctxt)
+        check_type_annot loc annot >|? fun () -> (Ex_comparable_ty unit_t, ctxt)
     | Prim (loc, T_never, [], annot) ->
-        check_type_annot loc annot >|? fun () ->
-        (Ex_comparable_ty never_key, ctxt)
+        check_type_annot loc annot >|? fun () -> (Ex_comparable_ty never_t, ctxt)
     | Prim (loc, T_int, [], annot) ->
-        check_type_annot loc annot >|? fun () -> (Ex_comparable_ty int_key, ctxt)
+        check_type_annot loc annot >|? fun () -> (Ex_comparable_ty int_t, ctxt)
     | Prim (loc, T_nat, [], annot) ->
-        check_type_annot loc annot >|? fun () -> (Ex_comparable_ty nat_key, ctxt)
+        check_type_annot loc annot >|? fun () -> (Ex_comparable_ty nat_t, ctxt)
     | Prim (loc, T_signature, [], annot) ->
         check_type_annot loc annot >|? fun () ->
-        (Ex_comparable_ty signature_key, ctxt)
+        (Ex_comparable_ty signature_t, ctxt)
     | Prim (loc, T_string, [], annot) ->
         check_type_annot loc annot >|? fun () ->
-        (Ex_comparable_ty string_key, ctxt)
+        (Ex_comparable_ty string_t, ctxt)
     | Prim (loc, T_bytes, [], annot) ->
-        check_type_annot loc annot >|? fun () ->
-        (Ex_comparable_ty bytes_key, ctxt)
+        check_type_annot loc annot >|? fun () -> (Ex_comparable_ty bytes_t, ctxt)
     | Prim (loc, T_mutez, [], annot) ->
-        check_type_annot loc annot >|? fun () ->
-        (Ex_comparable_ty mutez_key, ctxt)
+        check_type_annot loc annot >|? fun () -> (Ex_comparable_ty mutez_t, ctxt)
     | Prim (loc, T_bool, [], annot) ->
-        check_type_annot loc annot >|? fun () ->
-        (Ex_comparable_ty bool_key, ctxt)
+        check_type_annot loc annot >|? fun () -> (Ex_comparable_ty bool_t, ctxt)
     | Prim (loc, T_key_hash, [], annot) ->
         check_type_annot loc annot >|? fun () ->
-        (Ex_comparable_ty key_hash_key, ctxt)
+        (Ex_comparable_ty key_hash_t, ctxt)
     | Prim (loc, T_key, [], annot) ->
-        check_type_annot loc annot >|? fun () -> (Ex_comparable_ty key_key, ctxt)
+        check_type_annot loc annot >|? fun () -> (Ex_comparable_ty key_t, ctxt)
     | Prim (loc, T_timestamp, [], annot) ->
         check_type_annot loc annot >|? fun () ->
-        (Ex_comparable_ty timestamp_key, ctxt)
+        (Ex_comparable_ty timestamp_t, ctxt)
     | Prim (loc, T_chain_id, [], annot) ->
         check_type_annot loc annot >|? fun () ->
-        (Ex_comparable_ty chain_id_key, ctxt)
+        (Ex_comparable_ty chain_id_t, ctxt)
     | Prim (loc, T_address, [], annot) ->
         check_type_annot loc annot >|? fun () ->
-        (Ex_comparable_ty address_key, ctxt)
+        (Ex_comparable_ty address_t, ctxt)
     | Prim (loc, T_tx_rollup_l2_address, [], annot) ->
         if Constants.tx_rollup_enable ctxt then
           check_type_annot loc annot >|? fun () ->
-          (Ex_comparable_ty tx_rollup_l2_address_key, ctxt)
+          (Ex_comparable_ty tx_rollup_l2_address_t, ctxt)
         else error @@ Tx_rollup_addresses_disabled loc
     | Prim
         ( loc,
@@ -1103,7 +1098,8 @@ let[@coq_struct "ty"] rec parse_comparable_ty :
         >>? fun (Ex_comparable_ty right, ctxt) ->
         parse_comparable_ty ~stack_depth:(stack_depth + 1) ctxt left
         >>? fun (Ex_comparable_ty left, ctxt) ->
-        pair_key loc left right >|? fun ty -> (Ex_comparable_ty ty, ctxt)
+        comparable_pair_t loc left right >|? fun ty ->
+        (Ex_comparable_ty ty, ctxt)
     | Prim (loc, T_or, [left; right], annot) ->
         check_type_annot loc annot >>? fun () ->
         remove_field_annot left >>? fun left ->
@@ -1112,14 +1108,15 @@ let[@coq_struct "ty"] rec parse_comparable_ty :
         >>? fun (Ex_comparable_ty right, ctxt) ->
         parse_comparable_ty ~stack_depth:(stack_depth + 1) ctxt left
         >>? fun (Ex_comparable_ty left, ctxt) ->
-        union_key loc left right >|? fun ty -> (Ex_comparable_ty ty, ctxt)
+        comparable_union_t loc left right >|? fun ty ->
+        (Ex_comparable_ty ty, ctxt)
     | Prim (loc, ((T_pair | T_or) as prim), l, _) ->
         error (Invalid_arity (loc, prim, 2, List.length l))
     | Prim (loc, T_option, [t], annot) ->
         check_type_annot loc annot >>? fun () ->
         parse_comparable_ty ~stack_depth:(stack_depth + 1) ctxt t
         >>? fun (Ex_comparable_ty t, ctxt) ->
-        option_key loc t >|? fun ty -> (Ex_comparable_ty ty, ctxt)
+        comparable_option_t loc t >|? fun ty -> (Ex_comparable_ty ty, ctxt)
     | Prim (loc, T_option, l, _) ->
         error (Invalid_arity (loc, T_option, 1, List.length l))
     | Prim
@@ -2048,7 +2045,7 @@ let parse_uint11 = parse_uint ~nb_bits:11
 (* This type is used to:
    - serialize and deserialize tickets when they are stored or transferred,
    - type the READ_TICKET instruction. *)
-let opened_ticket_type loc ty = pair_3_key loc address_key ty nat_key
+let opened_ticket_type loc ty = comparable_pair_3_t loc address_t ty nat_t
 
 (* -- parse data of primitive types -- *)
 
@@ -5192,7 +5189,7 @@ and parse_toplevel :
             let allowed = [K_parameter; K_storage; K_code; K_view] in
             error (Invalid_primitive (loc, allowed, name))
       in
-      find_fields ctxt None None None (Script_map.empty string_key) fields
+      find_fields ctxt None None None (Script_map.empty string_t) fields
       >>? fun (ctxt, toplevel) ->
       match toplevel with
       | (None, _, _, _) -> error (Missing_field K_parameter)
diff --git a/src/proto_alpha/lib_protocol/script_typed_ir.ml b/src/proto_alpha/lib_protocol/script_typed_ir.ml
index e934766c2e328064457c5ad4f94098d1a288b6e8..ee7e39bc3e5b7e00127cf18be4eefecdc82e4998 100644
--- a/src/proto_alpha/lib_protocol/script_typed_ir.ml
+++ b/src/proto_alpha/lib_protocol/script_typed_ir.ml
@@ -1842,56 +1842,30 @@ type 'v ty_ex_c = Ty_ex_c : ('v, _) ty -> 'v ty_ex_c [@@ocaml.unboxed]
 
 let unit_t = Unit_t
 
-let unit_key = unit_t
-
 let int_t = Int_t
 
-let int_key = int_t
-
 let nat_t = Nat_t
 
-let nat_key = nat_t
-
 let signature_t = Signature_t
 
-let signature_key = signature_t
-
 let string_t = String_t
 
-let string_key = string_t
-
 let bytes_t = Bytes_t
 
-let bytes_key = bytes_t
-
 let mutez_t = Mutez_t
 
-let mutez_key = mutez_t
-
 let key_hash_t = Key_hash_t
 
-let key_hash_key = key_hash_t
-
 let key_t = Key_t
 
-let key_key = key_t
-
 let timestamp_t = Timestamp_t
 
-let timestamp_key = timestamp_t
-
 let address_t = Address_t
 
-let address_key = address_t
-
 let bool_t = Bool_t
 
-let bool_key = bool_t
-
 let tx_rollup_l2_address_t = Tx_rollup_l2_address_t
 
-let tx_rollup_l2_address_key = tx_rollup_l2_address_t
-
 let pair_t :
     type a ac b bc.
     Script.location -> (a, ac) ty -> (b, bc) ty -> (a, b) pair ty_ex_c tzresult
@@ -1901,11 +1875,12 @@ let pair_t :
   let (Ex_dand cmp) = dand (is_comparable l) (is_comparable r) in
   Ty_ex_c (Pair_t (l, r, {size}, cmp))
 
-let pair_key loc l r =
+let comparable_pair_t loc l r =
   Type_size.compound2 loc (ty_size l) (ty_size r) >|? fun size ->
   Pair_t (l, r, {size}, YesYes)
 
-let pair_3_key loc l m r = pair_key loc m r >>? fun r -> pair_key loc l r
+let comparable_pair_3_t loc l m r =
+  comparable_pair_t loc m r >>? fun r -> comparable_pair_t loc l r
 
 let union_t :
     type a ac b bc.
@@ -1919,7 +1894,7 @@ let union_t :
 let union_bytes_bool_t =
   Union_t (bytes_t, bool_t, {size = Type_size.three}, YesYes)
 
-let union_key loc l r =
+let comparable_union_t loc l r =
   Type_size.compound2 loc (ty_size l) (ty_size r) >|? fun size ->
   Union_t (l, r, {size}, YesYes)
 
@@ -1964,7 +1939,7 @@ let option_pair_int_nat_t =
       {size = Type_size.four},
       Yes )
 
-let option_key loc t =
+let comparable_option_t loc t =
   Type_size.compound1 loc (ty_size t) >|? fun size -> Option_t (t, {size}, Yes)
 
 let list_t loc t =
@@ -1999,12 +1974,8 @@ let sapling_state_t ~memo_size = Sapling_state_t memo_size
 
 let chain_id_t = Chain_id_t
 
-let chain_id_key = chain_id_t
-
 let never_t = Never_t
 
-let never_key = never_t
-
 let bls12_381_g1_t = Bls12_381_g1_t
 
 let bls12_381_g2_t = Bls12_381_g2_t
diff --git a/src/proto_alpha/lib_protocol/script_typed_ir.mli b/src/proto_alpha/lib_protocol/script_typed_ir.mli
index a1ea5b52702ae8c9ca422eabd60db18b5f86d21a..87f2c424bb26885ff02d2e53bf07da2d3a056db0 100644
--- a/src/proto_alpha/lib_protocol/script_typed_ir.mli
+++ b/src/proto_alpha/lib_protocol/script_typed_ir.mli
@@ -1554,58 +1554,6 @@ val is_comparable : ('v, 'c) ty -> 'c dbool
 
 type 'v ty_ex_c = Ty_ex_c : ('v, _) ty -> 'v ty_ex_c [@@ocaml.unboxed]
 
-val unit_key : unit comparable_ty
-
-val never_key : never comparable_ty
-
-val int_key : z num comparable_ty
-
-val nat_key : n num comparable_ty
-
-val signature_key : signature comparable_ty
-
-val string_key : Script_string.t comparable_ty
-
-val bytes_key : Bytes.t comparable_ty
-
-val mutez_key : Tez.t comparable_ty
-
-val bool_key : bool comparable_ty
-
-val key_hash_key : public_key_hash comparable_ty
-
-val key_key : public_key comparable_ty
-
-val timestamp_key : Script_timestamp.t comparable_ty
-
-val chain_id_key : Script_chain_id.t comparable_ty
-
-val address_key : address comparable_ty
-
-val tx_rollup_l2_address_key : tx_rollup_l2_address comparable_ty
-
-val pair_key :
-  Script.location ->
-  'a comparable_ty ->
-  'b comparable_ty ->
-  ('a, 'b) pair comparable_ty tzresult
-
-val pair_3_key :
-  Script.location ->
-  'a comparable_ty ->
-  'b comparable_ty ->
-  'c comparable_ty ->
-  ('a, ('b, 'c) pair) pair comparable_ty tzresult
-
-val union_key :
-  Script.location ->
-  'a comparable_ty ->
-  'b comparable_ty ->
-  ('a, 'b) union comparable_ty tzresult
-
-val option_key :
-  Script.location -> 'v comparable_ty -> 'v option comparable_ty tzresult
-
 val unit_t : unit comparable_ty
 
 val int_t : z num comparable_ty
@@ -1635,9 +1583,28 @@ val bool_t : bool comparable_ty
 val pair_t :
   Script.location -> ('a, _) ty -> ('b, _) ty -> ('a, 'b) pair ty_ex_c tzresult
 
+val comparable_pair_t :
+  Script.location ->
+  'a comparable_ty ->
+  'b comparable_ty ->
+  ('a, 'b) pair comparable_ty tzresult
+
+val comparable_pair_3_t :
+  Script.location ->
+  'a comparable_ty ->
+  'b comparable_ty ->
+  'c comparable_ty ->
+  ('a, ('b, 'c) pair) pair comparable_ty tzresult
+
 val union_t :
   Script.location -> ('a, _) ty -> ('b, _) ty -> ('a, 'b) union ty_ex_c tzresult
 
+val comparable_union_t :
+  Script.location ->
+  'a comparable_ty ->
+  'b comparable_ty ->
+  ('a, 'b) union comparable_ty tzresult
+
 val union_bytes_bool_t : (Bytes.t, bool) union comparable_ty
 
 val lambda_t :
@@ -1648,6 +1615,9 @@ val lambda_t :
 
 val option_t : Script.location -> ('v, 'c) ty -> ('v option, 'c) ty tzresult
 
+val comparable_option_t :
+  Script.location -> 'v comparable_ty -> 'v option comparable_ty tzresult
+
 val option_mutez_t : Tez.t option comparable_ty
 
 val option_string_t : Script_string.t option comparable_ty
diff --git a/src/proto_alpha/lib_protocol/test/integration/gas/test_gas_costs.ml b/src/proto_alpha/lib_protocol/test/integration/gas/test_gas_costs.ml
index 1f35489e470357a188533f73f66fa8048457ed30..ab5546d1fe6bc5e47677f8f98816d32000279f62 100644
--- a/src/proto_alpha/lib_protocol/test/integration/gas/test_gas_costs.ml
+++ b/src/proto_alpha/lib_protocol/test/integration/gas/test_gas_costs.ml
@@ -45,11 +45,11 @@ let forty_two_n = Script_int.abs forty_two
 
 let dummy_set =
   let open Script_set in
-  update forty_two true (empty Script_typed_ir.int_key)
+  update forty_two true (empty Script_typed_ir.int_t)
 
 let dummy_map =
   let open Script_map in
-  update forty_two (Some forty_two) (empty Script_typed_ir.int_key)
+  update forty_two (Some forty_two) (empty Script_typed_ir.int_t)
 
 let dummy_timestamp = Script_timestamp.of_zint (Z.of_int 42)
 
@@ -148,7 +148,7 @@ let all_interpreter_costs =
     ("dipn", dipn 42);
     ("dropn", dropn 42);
     ("neq", neq);
-    ("compare", compare Script_typed_ir.int_key forty_two forty_two);
+    ("compare", compare Script_typed_ir.int_t forty_two forty_two);
     ( "concat_string_precheck",
       concat_string_precheck Script_list.(cons "42" empty) );
     ("concat_string", concat_string (S.safe_int 42));
diff --git a/src/proto_alpha/lib_protocol/test/integration/michelson/test_interpretation.ml b/src/proto_alpha/lib_protocol/test/integration/michelson/test_interpretation.ml
index e0a111a7e440c9023c1ea9a9a9dfb7bb08e12a57..631f4901db68f16b818b02a12dcbc1cbeaeecfa9 100644
--- a/src/proto_alpha/lib_protocol/test/integration/michelson/test_interpretation.ml
+++ b/src/proto_alpha/lib_protocol/test/integration/michelson/test_interpretation.ml
@@ -160,17 +160,15 @@ let test_stack_overflow_in_lwt () =
   in
   let stack = Bot_t in
   let item ty s = Item_t (ty, s) in
-  let unit_t = unit_t in
-  let unit_k = unit_key in
   let bool_t = bool_t in
-  big_map_t (-1) unit_k unit_t >>??= fun big_map_t ->
+  big_map_t (-1) unit_t unit_t >>??= fun big_map_t ->
   let descr kinstr = {kloc = 0; kbef = stack; kaft = stack; kinstr} in
   let kinfo s = {iloc = -1; kstack_ty = s} in
   let stack1 = item big_map_t Bot_t in
   let stack2 = item big_map_t (item big_map_t Bot_t) in
   let stack3 = item unit_t stack2 in
   let stack4 = item bool_t stack1 in
-  let push_empty_big_map k = IEmpty_big_map (kinfo stack, unit_k, unit_t, k) in
+  let push_empty_big_map k = IEmpty_big_map (kinfo stack, unit_t, unit_t, k) in
   let large_mem_seq n =
     let rec aux n acc =
       if n = 0 then acc
diff --git a/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_accounting.ml b/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_accounting.ml
index 76d0586a66f527cadf7f151426e8cb058b4f0c79..b5927986155f7a8b952e05a618d5eae4a703bf72 100644
--- a/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_accounting.ml
+++ b/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_accounting.ml
@@ -413,7 +413,7 @@ let transfer_operation ctxt ~src ~destination ~arg_type ~arg =
 
 let ticket_string_type =
   WithExceptions.Result.get_ok ~loc:__LOC__
-  @@ Script_typed_ir.(ticket_t (-1) string_key)
+  @@ Script_typed_ir.(ticket_t (-1) string_t)
 
 let ticket_string_list_type =
   Result.value_f ~default:(fun _ -> assert false)
@@ -481,18 +481,18 @@ let string_ticket_token ticketer content =
   let*? ticketer = Environment.wrap_tzresult @@ Contract.of_b58check ticketer in
   return
     (Ticket_token.Ex_token
-       {ticketer; contents_type = Script_typed_ir.string_key; contents})
+       {ticketer; contents_type = Script_typed_ir.string_t; contents})
 
 let test_diffs_empty () =
   let open Lwt_tzresult_syntax in
   let open Script_typed_ir in
   let* (_contract, ctxt) = init () in
   let*? int_ticket_big_map_ty =
-    big_map_type ~key_type:int_key ~value_type:ticket_string_type
+    big_map_type ~key_type:int_t ~value_type:ticket_string_type
   in
   (* Start with an empty big-map *)
   let* (empty_big_map, ctxt) =
-    empty_big_map ctxt ~key_type:int_key ~value_type:ticket_string_type
+    empty_big_map ctxt ~key_type:int_t ~value_type:ticket_string_type
   in
   assert_ticket_diffs
     ctxt
@@ -623,17 +623,17 @@ let test_diffs_lazy_storage_alloc () =
   let open Script_typed_ir in
   let* (_contract, ctxt) = init () in
   let*? int_ticket_big_map_ty =
-    big_map_type ~key_type:int_key ~value_type:ticket_string_type
+    big_map_type ~key_type:int_t ~value_type:ticket_string_type
   in
   (* Start with an empty big-map *)
   let* (empty_big_map, ctxt) =
-    empty_big_map ctxt ~key_type:int_key ~value_type:ticket_string_type
+    empty_big_map ctxt ~key_type:int_t ~value_type:ticket_string_type
   in
   (* We add one ticket to the storage. *)
   let* (lazy_storage_diff, ctxt) =
     alloc_diff
       ctxt
-      ~key_type:int_key
+      ~key_type:int_t
       ~value_type:ticket_string_type
       [
         ( Script_int.of_int 1,
@@ -657,18 +657,18 @@ let test_diffs_remove_from_big_map () =
   let open Script_typed_ir in
   let* (contract, ctxt) = init () in
   let*? int_ticket_big_map_ty =
-    big_map_type ~key_type:int_key ~value_type:ticket_string_type
+    big_map_type ~key_type:int_t ~value_type:ticket_string_type
   in
   (* Start with an empty big-map *)
   let* (empty_big_map, ctxt) =
-    empty_big_map ctxt ~key_type:int_key ~value_type:ticket_string_type
+    empty_big_map ctxt ~key_type:int_t ~value_type:ticket_string_type
   in
   (* Remove one ticket from the lazy storage. *)
   let* (lazy_storage_diff, ctxt) =
     remove_diff
       ctxt
       contract
-      ~key_type:int_key
+      ~key_type:int_t
       ~value_type:ticket_string_type
       ~existing_entries:
         [
@@ -693,18 +693,18 @@ let test_diffs_copy_big_map () =
   let open Script_typed_ir in
   let* (contract, ctxt) = init () in
   let*? int_ticket_big_map_ty =
-    big_map_type ~key_type:int_key ~value_type:ticket_string_type
+    big_map_type ~key_type:int_t ~value_type:ticket_string_type
   in
   (* Start with an empty big-map *)
   let* (empty_big_map, ctxt) =
-    empty_big_map ctxt ~key_type:int_key ~value_type:ticket_string_type
+    empty_big_map ctxt ~key_type:int_t ~value_type:ticket_string_type
   in
   (* We add one ticket to the storage. *)
   let* (lazy_storage_diff, ctxt) =
     copy_diff
       ctxt
       contract
-      ~key_type:int_key
+      ~key_type:int_t
       ~value_type:ticket_string_type
       ~existing_entries:
         [
@@ -742,13 +742,13 @@ let test_diffs_add_to_existing_big_map () =
   let open Script_typed_ir in
   let* (contract, ctxt) = init () in
   let*? int_ticket_big_map_ty =
-    big_map_type ~key_type:int_key ~value_type:ticket_string_type
+    big_map_type ~key_type:int_t ~value_type:ticket_string_type
   in
   let* (old_storage, ctxt) =
     make_big_map
       ctxt
       contract
-      ~key_type:int_key
+      ~key_type:int_t
       ~value_type:ticket_string_type
       [
         (* It doesn't matter what the old entries are. They are never traversed *)
@@ -765,7 +765,7 @@ let test_diffs_add_to_existing_big_map () =
     existing_diff
       ctxt
       contract
-      ~key_type:int_key
+      ~key_type:int_t
       ~value_type:ticket_string_type
       ~existing_entries:
         [
@@ -806,14 +806,14 @@ let test_diffs_args_storage_and_lazy_diffs () =
   let open Script_typed_ir in
   let* (contract, ctxt) = init () in
   let*? int_ticket_big_map_ty =
-    big_map_type ~key_type:int_key ~value_type:ticket_string_type
+    big_map_type ~key_type:int_t ~value_type:ticket_string_type
   in
   let*? (Ty_ex_c list_big_map_pair_type) =
     Environment.wrap_tzresult
     @@ pair_t (-1) ticket_string_list_type int_ticket_big_map_ty
   in
   let* (empty_big_map, ctxt) =
-    empty_big_map ctxt ~key_type:int_key ~value_type:ticket_string_type
+    empty_big_map ctxt ~key_type:int_t ~value_type:ticket_string_type
   in
   (* We send two tickets in the args. *)
   let arg =
@@ -828,7 +828,7 @@ let test_diffs_args_storage_and_lazy_diffs () =
     existing_diff
       ctxt
       contract
-      ~key_type:int_key
+      ~key_type:int_t
       ~value_type:ticket_string_type
       ~existing_entries:[]
       ~updates:
diff --git a/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_balance.ml b/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_balance.ml
index ceed895495d9d7701a374eeb621c4737926047c5..ca33275908f7d2de61f3329141d0d666a5ddf75b 100644
--- a/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_balance.ml
+++ b/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_balance.ml
@@ -157,11 +157,11 @@ let string_token ~ticketer content =
     WithExceptions.Result.get_ok ~loc:__LOC__ @@ Script_string.of_string content
   in
   Ticket_token.Ex_token
-    {ticketer; contents_type = Script_typed_ir.string_key; contents}
+    {ticketer; contents_type = Script_typed_ir.string_t; contents}
 
 let unit_ticket ~ticketer =
   Ticket_token.Ex_token
-    {ticketer; contents_type = Script_typed_ir.unit_key; contents = ()}
+    {ticketer; contents_type = Script_typed_ir.unit_t; contents = ()}
 
 let new_contracts ~before ~after =
   let all_contracts current_block =
diff --git a/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_lazy_storage_diff.ml b/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_lazy_storage_diff.ml
index bbf5b4827362cd26bdf30b327771ca2c30d86f18..c9818c6eb9b2d16e8a44d7e2d64798b63b1cdec0 100644
--- a/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_lazy_storage_diff.ml
+++ b/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_lazy_storage_diff.ml
@@ -112,7 +112,7 @@ let updates_of_key_values ctxt key_values =
         wrap
           (Script_ir_translator.hash_comparable_data
              ctxt
-             Script_typed_ir.int_key
+             Script_typed_ir.int_t
              (Script_int.of_int key))
       in
       return
diff --git a/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_operations_diff.ml b/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_operations_diff.ml
index 668aefffca4fa9915e67074b0bc3d891345283e1..f9f07b9491bc6a5470168c221fbd0cd2d35f9f83 100644
--- a/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_operations_diff.ml
+++ b/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_operations_diff.ml
@@ -59,7 +59,7 @@ let big_map_updates_of_key_values ctxt key_values =
         wrap
           (Script_ir_translator.hash_comparable_data
              ctxt
-             Script_typed_ir.int_key
+             Script_typed_ir.int_t
              (Script_int.of_int key))
       in
       return
@@ -176,7 +176,7 @@ let string_token ~ticketer content =
     @@ Script_string.of_string content
   in
   Ticket_token.Ex_token
-    {ticketer; contents_type = Script_typed_ir.string_key; contents}
+    {ticketer; contents_type = Script_typed_ir.string_t; contents}
 
 (** Initializes one address for operations and one baker. *)
 let init ?tx_rollup_enable () =
@@ -381,7 +381,7 @@ let ticket_big_map_script =
   |}
 
 let list_ticket_string_ty =
-  ticket_t Micheline.dummy_location string_key >>? fun ticket_ty ->
+  ticket_t Micheline.dummy_location string_t >>? fun ticket_ty ->
   list_t Micheline.dummy_location ticket_ty
 
 let make_ticket (ticketer, contents, amount) =
@@ -1095,18 +1095,18 @@ let test_transfer_big_map_with_tickets () =
   in
   let open Lwt_tzresult_syntax in
   let*? value_type =
-    Environment.wrap_tzresult @@ ticket_t Micheline.dummy_location string_key
+    Environment.wrap_tzresult @@ ticket_t Micheline.dummy_location string_t
   in
   let*? parameters_ty =
     Environment.wrap_tzresult
-    @@ big_map_t Micheline.dummy_location int_key value_type
+    @@ big_map_t Micheline.dummy_location int_t value_type
   in
   let parameters =
     Big_map
       {
         id = Some big_map_id;
         diff = {map = Big_map_overlay.empty; size = 0};
-        key_type = int_key;
+        key_type = int_t;
         value_type;
       }
   in
@@ -1154,7 +1154,7 @@ let test_tx_rollup_deposit_one_ticket () =
   let* incr = Incremental.add_operation incr operation in
 
   let*? ticket_ty =
-    Script_typed_ir.(ticket_t Micheline.dummy_location string_key)
+    Script_typed_ir.(ticket_t Micheline.dummy_location string_t)
     |> Environment.wrap_tzresult
   in
   let*? (Ty_ex_c parameters_ty) =
diff --git a/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_scanner.ml b/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_scanner.ml
index 427c0bbd835a66ad7fd8c67d6564a9e06dcb22b0..a1601223180d6858a231ff13c978caa8b87d393f 100644
--- a/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_scanner.ml
+++ b/src/proto_alpha/lib_protocol/test/integration/michelson/test_ticket_scanner.ml
@@ -184,7 +184,7 @@ let tickets_from_big_map_ref ~pre_populated value_exp =
             wrap
             @@ Script_ir_translator.hash_comparable_data
                  ctxt
-                 Script_typed_ir.int_key
+                 Script_typed_ir.int_t
                  (Script_int.of_int key)
           in
           return
diff --git a/src/proto_alpha/lib_protocol/test/integration/michelson/test_typechecking.ml b/src/proto_alpha/lib_protocol/test/integration/michelson/test_typechecking.ml
index be2a0ae79b1513aeb51884c02656089571334a83..978e10fe7f4881660ebe595262a92e50c7526fa9 100644
--- a/src/proto_alpha/lib_protocol/test/integration/michelson/test_typechecking.ml
+++ b/src/proto_alpha/lib_protocol/test/integration/michelson/test_typechecking.ml
@@ -307,9 +307,9 @@ let test_unparse_comb_comparable_type () =
   let open Script in
   let open Script_typed_ir in
   let nat_prim = Prim ((), T_nat, [], []) in
-  let nat_ty = nat_key in
+  let nat_ty = nat_t in
   let pair_prim l = Prim ((), T_pair, l, []) in
-  let pair_ty ty1 ty2 = pair_key (-1) ty1 ty2 in
+  let pair_ty ty1 ty2 = comparable_pair_t (-1) ty1 ty2 in
   let pair_prim2 a b = pair_prim [a; b] in
   let pair_nat_nat_prim = pair_prim2 nat_prim nat_prim in
   pair_ty nat_ty nat_ty >>??= fun pair_nat_nat_ty ->
@@ -381,7 +381,7 @@ let test_parse_comb_data () =
   let pair_prim2 a b = pair_prim [a; b] in
   let pair_z_z_prim = pair_prim2 z_prim z_prim in
   list_t (-1) nat_ty >>??= fun list_nat_ty ->
-  big_map_t (-1) nat_key nat_ty >>??= fun big_map_nat_nat_ty ->
+  big_map_t (-1) nat_ty nat_ty >>??= fun big_map_nat_nat_ty ->
   test_context_with_nat_nat_big_map () >>=? fun (ctxt, big_map_id) ->
   (* Pair 0 0 *)
   test_parse_data __LOC__ ctxt pair_nat_nat_ty pair_z_z_prim (z, z)
@@ -452,9 +452,7 @@ let test_parse_comb_data () =
   let expected_big_map =
     let open Script_typed_ir in
     let diff = {map = Big_map_overlay.empty; size = 0} in
-    let nat_key_ty = nat_key in
-    Big_map
-      {id = Some big_map_id; diff; key_type = nat_key_ty; value_type = nat_ty}
+    Big_map {id = Some big_map_id; diff; key_type = nat_ty; value_type = nat_ty}
   in
   let ty_equal :
       type a ac1 ac2.
diff --git a/src/proto_alpha/lib_protocol/test/integration/operations/test_tx_rollup.ml b/src/proto_alpha/lib_protocol/test/integration/operations/test_tx_rollup.ml
index 06659ba0125495a23f1e5cc6fb54f4f1182095cc..7843633c3095854300761661305524d4616fd2e6 100644
--- a/src/proto_alpha/lib_protocol/test/integration/operations/test_tx_rollup.ml
+++ b/src/proto_alpha/lib_protocol/test/integration/operations/test_tx_rollup.ml
@@ -491,7 +491,7 @@ module Nat_ticket = struct
       @@ Script_int.(of_int contents_nat |> is_nat)
     in
     Ticket_token.Ex_token
-      {ticketer; contents_type = Script_typed_ir.nat_key; contents}
+      {ticketer; contents_type = Script_typed_ir.nat_t; contents}
 
   let contents = Expr.from_string (string_of_int contents_nat)
 
diff --git a/src/proto_alpha/lib_protocol/test/pbt/test_script_comparison.ml b/src/proto_alpha/lib_protocol/test/pbt/test_script_comparison.ml
index 3031db1659abb034ef5f3af5db7e25ed121d2b8a..dc0c058730dc43d0d76cefe66b6fb2fb2d55a1e4 100644
--- a/src/proto_alpha/lib_protocol/test/pbt/test_script_comparison.ml
+++ b/src/proto_alpha/lib_protocol/test/pbt/test_script_comparison.ml
@@ -342,7 +342,9 @@ let test_pack_unpack =
     comparable_data_arbitrary
     (fun (Ex_comparable_data (ty, x)) ->
       let oty =
-        match option_key (-1) ty with Ok ty -> ty | Error _ -> assert false
+        match comparable_option_t (-1) ty with
+        | Ok ty -> ty
+        | Error _ -> assert false
       in
       qcheck_eq
         ~cmp:(Script_comparable.compare_comparable oty)