diff --git a/simplest_model_with_mods/dune b/simplest_model_with_mods/dune
index 85a5b6b..35cc40d 100644
--- a/simplest_model_with_mods/dune
+++ b/simplest_model_with_mods/dune
@@ -23,34 +23,36 @@
  (preprocess
   (pps GT.ppx GT.ppx_all ppx_expect ppx_inline_test)))
 
-(library
- (name tests_modt)
- (modules tests)
- (flags (-rectypes))
- (libraries synthesizer_mods tests_f_mods)
- (inline_tests)
- (wrapped false)
- (preprocess
-  (pps ppx_expect ppx_inline_test)))
+; TODO: tmp, during change
+; (library
+;  (name tests_mods)
+;  (modules tests)
+;  (flags (-rectypes))
+;  (libraries synthesizer_mods tests_f_mods)
+;  (inline_tests)
+;  (wrapped false)
+;  (preprocess
+;   (pps ppx_expect ppx_inline_test)))
 
-(library
- (name tests_f_mods)
- (modules tests_f)
- (flags (-rectypes))
- (libraries OCanren OCanren.tester synthesizer_mods)
- (preprocessor_deps ../camlp5/pp5+gt+plugins+ocanren+dump.exe)
- (wrapped false)
- (preprocess
-  (pps
-   OCanren-ppx.ppx_repr
-   OCanren-ppx.ppx_deriving_reify
-   OCanren-ppx.ppx_fresh
-   GT.ppx
-   GT.ppx_all
-   OCanren-ppx.ppx_distrib
-   --
-   -pp
-   camlp5/pp5+gt+plugins+ocanren+dump.exe)))
+; TODO: tmp, during change
+; (library
+;  (name tests_f_mods)
+;  (modules tests_f)
+;  (flags (-rectypes))
+;  (libraries OCanren OCanren.tester synthesizer_mods)
+;  (preprocessor_deps ../camlp5/pp5+gt+plugins+ocanren+dump.exe)
+;  (wrapped false)
+;  (preprocess
+;   (pps
+;    OCanren-ppx.ppx_repr
+;    OCanren-ppx.ppx_deriving_reify
+;    OCanren-ppx.ppx_fresh
+;    GT.ppx
+;    GT.ppx_all
+;    OCanren-ppx.ppx_distrib
+;    --
+;    -pp
+;    camlp5/pp5+gt+plugins+ocanren+dump.exe)))
 
 (library
  (name synthesizer_mods)
diff --git a/simplest_model_with_mods/synthesizer.ml b/simplest_model_with_mods/synthesizer.ml
index aa2e4da..328d947 100644
--- a/simplest_model_with_mods/synthesizer.ml
+++ b/simplest_model_with_mods/synthesizer.ml
@@ -10,7 +10,159 @@ struct
   [@@deriving gt ~options:{ show; gmap }]
   type data_injected = Nat.injected
 
+  module ReadCap = struct
+    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
+    [%%ocanren_inject
+      type nonrec t = Rd | NRd
+      [@@deriving gt ~options:{ show; gmap }]
+      type nonrec ground = t
+    ]
+  end
+
+  module WriteCap = struct
+    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
+    [%%ocanren_inject
+      type nonrec t = Wr | NWr
+      [@@deriving gt ~options:{ show; gmap }]
+      type nonrec ground = t
+    ]
+  end
+
+  (* NOTE: rename names ?? *)
+  module CopyCap = struct
+    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
+    [%%ocanren_inject
+      type nonrec t = Ref | Val
+      [@@deriving gt ~options:{ show; gmap }]
+      type nonrec ground = t
+    ]
+
+  end
+
+  module InCap = struct
+    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
+    [%%ocanren_inject
+      type nonrec t = In | NIn
+      [@@deriving gt ~options:{ show; gmap }]
+      type nonrec ground = t
+    ]
+  end
+
+  module OutCap = struct
+    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
+    [%%ocanren_inject
+      type nonrec t = Out | NOut
+      [@@deriving gt ~options:{ show; gmap }]
+      type nonrec ground = t
+    ]
+  end
+
   module Tag = struct
+    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
+    [%%ocanren_inject
+      type nonrec ('r, 'w, 'c, 'i, 'o) t = Tag of 'r * 'w * 'c * 'i * 'o
+      [@@deriving gt ~options:{ show; gmap }]
+      type nonrec ground = (ReadCap.ground, WriteCap.ground, CopyCap.ground, InCap.ground, OutCap.ground) t
+    ]
+
+    (* TODO: less repeats *)
+    (* common constructors *)
+    let rwi_val = let open ReadCap in
+                  let open WriteCap in
+                  let open CopyCap in
+                  let open InCap in
+                  let open OutCap in
+                  ocanren { Tag (Rd, Wr, Val, In, NOut) }
+    let ri_val = let open ReadCap in
+                 let open WriteCap in
+                 let open CopyCap in
+                 let open InCap in
+                 let open OutCap in
+                 ocanren { Tag (Rd, NWr, Val, In, NOut) }
+    let wi_val = let open ReadCap in
+                 let open WriteCap in
+                 let open CopyCap in
+                 let open InCap in
+                 let open OutCap in
+                 ocanren { Tag (NRd, Wr, Val, In, NOut) }
+    let i_val = let open ReadCap in
+                let open WriteCap in
+                let open CopyCap in
+                let open InCap in
+                let open OutCap in
+                ocanren { Tag (NRd, NWr, Val, In, NOut) }
+    let rwi_ref = let open ReadCap in
+                  let open WriteCap in
+                  let open CopyCap in
+                  let open InCap in
+                  let open OutCap in
+                  ocanren { Tag (Rd, Wr, Ref, In, NOut) }
+    let ri_ref = let open ReadCap in
+                 let open WriteCap in
+                 let open CopyCap in
+                 let open InCap in
+                 let open OutCap in
+                 ocanren { Tag (Rd, NWr, Ref, In, NOut) }
+    let wi_ref = let open ReadCap in
+                 let open WriteCap in
+                 let open CopyCap in
+                 let open InCap in
+                 let open OutCap in
+                 ocanren { Tag (NRd, Wr, Ref, In, NOut) }
+    let i_ref = let open ReadCap in
+                let open WriteCap in
+                let open CopyCap in
+                let open InCap in
+                let open OutCap in
+                ocanren { Tag (NRd, NWr, Ref, In, NOut) }
+
+    (* accessors *)
+    let is_reado tag = let open ReadCap in ocanren {
+                      fresh w_, c_, i_, o_ in
+                        tag == Tag (Rd, w_, c_, i_, o_) }
+    let is_not_reado tag = let open ReadCap in ocanren {
+                      fresh w_, c_, i_, o_ in
+                        tag == Tag (NRd, w_, c_, i_, o_) }
+    let is_writeo tag = let open WriteCap in ocanren {
+                      fresh r_, c_, i_, o_ in
+                        tag == Tag (r_, Wr, c_, i_, o_) }
+    let is_not_writeo tag = let open WriteCap in ocanren {
+                      fresh r_, c_, i_, o_ in
+                        tag == Tag (r_, NWr, c_, i_, o_) }
+    let is_refo tag = let open CopyCap in ocanren {
+                      fresh r_, w_, i_, o_ in
+                        tag == Tag (r_, w_, Ref, i_, o_) }
+    let is_valueo tag = let open CopyCap in ocanren {
+                      fresh r_, w_, i_, o_ in
+                        tag == Tag (r_, w_, Val, i_, o_) }
+    let is_ino tag = let open InCap in ocanren {
+                      fresh r_, w_, c_, o_ in
+                        tag == Tag (r_, w_, c_, In, o_) }
+    let is_not_ino tag = let open InCap in ocanren {
+                      fresh r_, w_, c_, o_ in
+                        tag == Tag (r_, w_, c_, NIn, o_) }
+    let is_outo tag = let open OutCap in ocanren {
+                      fresh r_, w_, c_, i_ in
+                        tag == Tag (r_, w_, c_, i_, Out) }
+    let is_not_outo tag = let open OutCap in ocanren {
+                      fresh r_, w_, c_, i_ in
+                        tag == Tag (r_, w_, c_, i_, NOut) }
+
+    module Test = struct
+      @type answer = logic GT.list with show
+
+      let test _ = show(answer) (Stream.take (run q (fun q -> let open ReadCap in
+                                                              let open WriteCap in
+                                                              let open CopyCap in
+                                                              let open InCap in
+                                                              let open OutCap in
+                                                              ocanren {q == Tag (Rd, NWr, Ref, In, NOut)})
+                                                    (fun q -> q#reify reify)))
+    end
+  end
+
+  (* TODO: tmp *)
+  module Tag' = struct
     [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
     [%%ocanren_inject
       type nonrec t = Ref | Val
@@ -58,7 +210,7 @@ struct
       @type answer  = ground GT.list with show
       let test _ = show(answer) (Stream.take (run q (fun q -> let open Tag in
                                                               let open Stmt in
-                                                              ocanren {FunDecl ([Ref; Val], [Call (1, [0]); Write 1]) == q})
+                                                              ocanren {FunDecl ([rwi_ref; rwi_val], [Call (1, [0]); Write 1]) == q})
                                                     (fun q -> q#reify (prj_exn))))
     end
   end
@@ -76,7 +228,7 @@ struct
       let test _ = show(answer) (Stream.take (run q (fun q -> let open FunDecl in
                                                               let open Tag in
                                                               let open Stmt in
-                                                              ocanren {Prog ([], FunDecl ([Val], [Write 0; Read 0])) == q})
+                                                              ocanren {Prog ([], FunDecl ([ri_val], [Write 0; Read 0])) == q})
                                                     (fun q -> q#reify (prj_exn))))
     end
   end
@@ -114,16 +266,17 @@ struct
   module St = struct
     [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
     [%%ocanren_inject
-      type nonrec ('env, 'mem, 'last_mem, 'assignments) t = St of 'env * 'mem * 'last_mem * 'assignments
+      type nonrec ('env, 'mem, 'last_mem, 'visited) t = St of 'env * 'mem * 'last_mem * 'visited
       [@@deriving gt ~options:{ show; gmap }]
-      type nonrec ground = (((Nat.ground, Nat.ground) Pair.ground) List.ground,
+      type nonrec ground = (((Nat.ground, ((Tag.ground, Nat.ground) Pair.ground)) Pair.ground) List.ground,
                             Value.ground List.ground, Nat.ground, Nat.ground List.ground) t
     ]
 
     module Test = struct
       @type answer  = ground GT.list with show
       let test _ = show(answer) (Stream.take (run q (fun q -> let open Value in
-                                                              ocanren {St ([Std.pair 0 0], [Bot], 1, [0]) == q})
+                                                              let open Tag in
+                                                              ocanren {St ([Std.pair 0 (Std.pair rwi_val 0)], [Bot], 1, [0]) == q})
                                                     (fun q -> q#reify (prj_exn))))
     end
   end
@@ -141,30 +294,23 @@ struct
         list_replaceo xs' id' value ys' }
     }
 
-  (* let rec list_assoco a xs v' = *)
-    (* ocanren { *)
-    (* fresh a', b', xs' in *)
-      (* (Std.pair a' b') :: xs' == xs & *)
-      (* { a =/= a' & list_assoco a xs' v' | *)
-        (* a == a' & v' == b' } *)
-  (* } *)
-  (* TODO: difference from List.assoco ?? *)
-
-  let env_geto state id mem_id' =
+  let env_geto state id tag' mem_id' =
     let open St in
     ocanren {
-    fresh env, mem, mem_len, assignments in
-      state == St (env, mem, mem_len, assignments) &
-      List.assoco id env mem_id'
+    fresh env, _mem, _mem_len, _visited, elem in
+      state == St (env, _mem, _mem_len, _visited) &
+      List.assoco id env elem &
+      Std.pair tag' mem_id' == elem
   }
 
-  let env_addo state id mem_id state' =
+  let env_addo state id tg mem_id state' =
     let open St in
     ocanren {
-    fresh env, env', mem, mem_len, assignments in
-      state == St (env, mem, mem_len, assignments) &
-      state' == St (env', mem, mem_len, assignments) &
-      (Std.pair id mem_id) :: env == env'
+    fresh env, env', mem, mem_len, visited, elem in
+      state == St (env, mem, mem_len, visited) &
+      Std.pair tg mem_id == elem & 
+      (Std.pair id elem) :: env == env' &
+      state' == St (env', mem, mem_len, visited)
   }
 
   let inv_ido mem_len id id' = ocanren {
@@ -190,9 +336,9 @@ struct
   let mem_geto state id value' =
     let open St in
     ocanren {
-    fresh mem, mem_len, mem_id, mem_id_inv, _env, _assignments in
-    state == St (_env, mem, mem_len, _assignments) &
-    env_geto state id mem_id &
+    fresh mem, mem_len, mem_id, mem_id_inv, _env, _visited, _tag in
+    state == St (_env, mem, mem_len, _visited) &
+    env_geto state id _tag mem_id &
     inv_ido mem_len mem_id mem_id_inv &
     list_ntho mem mem_id_inv value'
   }
@@ -200,30 +346,29 @@ struct
   let mem_seto state id value state'=
     let open St in
     ocanren {
-    fresh env, mem, mem_len, assignments, mem_id, inv_mem_id, mem', assignments' in
-      state == St (env, mem, mem_len, assignments) &
-      env_geto state id mem_id &
+    fresh env, mem, mem_len, visited, mem_id, inv_mem_id, mem', _tag in
+      state == St (env, mem, mem_len, visited) &
+      env_geto state id _tag mem_id &
       inv_ido mem_len mem_id inv_mem_id &
       list_replaceo mem inv_mem_id value mem' &
-      assignments' == id :: assignments &
-      state' == St (env, mem', mem_len, assignments')
+      state' == St (env, mem', mem_len, visited)
   }
 
   let mem_addo state value state' =
     let open St in
     ocanren {
-    fresh env, mem, mem_len, mem_len', assignments, mem' in
-      state == St (env, mem, mem_len, assignments) &
+      fresh env, mem, mem_len, mem_len', visited, mem' in
+      state == St (env, mem, mem_len, visited) &
       mem' == value :: mem &
       mem_len' == Nat.s mem_len &
-      state' == St (env, mem', mem_len', assignments)
+      state' == St (env, mem', mem_len', visited)
   }
 
-  let mem_checko state id state' =
+  let mem_checko state id =
     let open Value in
     ocanren {
-    mem_geto state id Unit & state' == state
-  }
+      mem_geto state id Unit
+    }
 
   (* --- *)
 
@@ -273,50 +418,85 @@ struct
       mem_geto state id value' }
   }
 
-  let arg_to_rvalueo _arg value' =
+  let arg_to_rvalueo arg value' =
     let open Arg in
-    ocanren { value' == RValue }
+    let open Tag in
+    ocanren { is_valueo arg & value' == RValue }
 
   let st_mem_leno state mem_len' =
     let open St in
     ocanren {
-    fresh _env, _mem, _assignments in
-      state == St (_env, _mem, mem_len', _assignments)
+    fresh _env, _mem, _visited in
+      state == St (_env, _mem, mem_len', _visited)
   }
 
+  let tag_correcto tg =
+    let open Tag in
+    ocanren {
+      {is_not_outo tg | is_writeo tg} &
+      {is_not_reado tg | is_ino tg}
+    }
+
   let st_add_argo state state_before id arg_tag arg state'' =
     (* let open Nat in *)
+    let open Value in
     let open Arg in
     let open Tag in
     ocanren {
-    (* arg_tag == Tag.ref & arg == Arg.rvalue & state'' == state | *)
-      (* NOTE: error, TODO: allow later ?? *)
-    { fresh arg', value' in
-      arg_tag == Ref &
-      arg == LValue arg' &
-      env_geto state_before arg' value' &
-      env_addo state id value' state'' } |
-    { fresh value', state', mem_len_prev' in
-      arg_tag == Val &
-      arg_to_valueo state_before arg value' &
-      mem_addo state value' state' &
-      st_mem_leno state mem_len_prev' &
-      env_addo state' id mem_len_prev' state'' }
-  }
+        tag_correcto arg_tag & {
+        { fresh value', state', mem_len_prev' in
+          is_valueo arg_tag &
+          arg_to_valueo state_before arg value' &
+          mem_addo state value' state' &
+          st_mem_leno state mem_len_prev' &
+          env_addo state' id arg_tag mem_len_prev' state'' } |
+        { fresh arg', parent_tag, mem_id, state' in
+          is_refo arg_tag &
+            (* { arg == RValue } *) (* NOTE: not allowed for now *)
+          arg == LValue arg' &
+          env_geto state_before id parent_tag mem_id &
+          env_addo state id arg_tag mem_id state' &
+          { is_not_writeo arg_tag | is_writeo parent_tag } &
+          {
+            { is_reado arg_tag & state' == state'' } |
+            { is_not_reado arg_tag & mem_seto state' id Bot state'' }
+          }
+        }
+      }
+    }
 
-  let st_spoil_foldero state id state' =
+  let st_spoil_foldero state_before state tg id state' =
     let open Value in
-    ocanren {
-    mem_seto state id Bot state'
-  }
-
-  let st_spoil_assignmentso state state' =
+    let open Tag in
     let open St in
     ocanren {
-    fresh _env, _mem, _mem_len, assignments in
-      state == St (_env, _mem, _mem_len, assignments) &
-      list_foldlo st_spoil_foldero state assignments state'
-  }
+      fresh env, mem, mem_len, _visited, parent_tg, _mem_id in
+      state == St (env, mem, mem_len, _visited) &
+      env_geto state id parent_tg _mem_id &
+      { is_not_writeo tg | is_writeo parent_tg } &
+      { is_not_reado tg | mem_checko state_before id } &
+      { { is_not_writeo tg & state == state'} |
+        { is_outo tg & mem_seto state id Unit state' } |
+        { is_not_outo tg & is_valueo tg & state == state' } |
+        { is_not_outo tg & is_refo tg & mem_seto state id Bot state' }
+      } &
+      mem_seto state id Bot state'
+    }
+
+  let st_spoil_by_argso state arg_tags args state' =
+    ocanren {
+      fresh state_before in
+      state == state_before & (* TODO: required ? *)
+      list_foldl2o (st_spoil_foldero state_before) state arg_tags args state'
+    }
+
+  (* let st_spoil_assignmentso state state' = *)
+    (* let open St in *)
+    (* ocanren { *)
+    (* fresh _env, _mem, _mem_len, visited in *)
+      (* state == St (_env, _mem, _mem_len, visited) & *)
+      (* list_foldlo st_spoil_foldero state visited state' *)
+  (* } *)
 
   (* --- *)
 
@@ -333,17 +513,47 @@ struct
         list_dropo n' ys xs' }
   }
 
+  let visited_checko state f_id =
+    let open St in
+    ocanren {
+      fresh _env, _mem, _mem_len, visited in
+      state == St (_env, _mem, _mem_len, visited) &
+      List.membero visited f_id
+    }
+
+  (* TODO *)
+  (* let visited_not_checko state f_id = ??? *)
+
+  let visited_addo state f_id state' =
+    let open St in
+    ocanren {
+      fresh env, mem, mem_len, visited, visited' in
+      state == St (env, mem, mem_len, visited) &
+      List.membero visited f_id &
+      visited' == f_id :: visited &
+      state' == St (env,mem, mem_len, visited')
+    }
+
   let rec eval_stmto state prog stmt state' =
     let open Stmt in
     let open Value in
+    let open FunDecl in
     ocanren {
-    { fresh f_id, args, f, args' in
+    { fresh f_id, args, f, args', state_after_call, state_with_visited, arg_tags, _body in
       stmt == Call (f_id, args) &
       list_ntho prog f_id f &
+      FunDecl (arg_tags, _body) == f &
       List.mapo arg_to_lvalueo args args' &
-      eval_funo state prog f args' state' } |
-    { fresh id in stmt == Read id & mem_checko state id state' } |
-    { fresh id in stmt === Write id & mem_seto state id Unit state' }
+      (* TODO: FIXME: memoisation, do not do calls on check successfull *)
+      eval_funo state prog f args' state_after_call &
+      (* NOTE: tmp simplification for less branching (TODO?) *)
+      visited_addo state_after_call f_id state_with_visited &
+      st_spoil_by_argso state_with_visited arg_tags args state'} |
+    { fresh id in stmt == Read id & mem_checko state id & state == state' } |
+    { fresh id, tag, _mem_id in
+      stmt === Write id &
+      env_geto state id tag _mem_id &
+      mem_seto state id Unit state' }
   }
 
   and eval_body_foldero prog state stmt state' =
@@ -366,27 +576,23 @@ struct
     let open St in
     ocanren {
     fresh arg_tags, body,
-          env_before, mem_before, len_before, assignments_before,
+          env_before, mem_before, len_before, visited_before,
           state_clean,
           state_with_vars, _counter,
           state_evaled,
-          state_spoiled,
-          _env, mem_spoiled, len, _assignments,
-          mem_updated,
-          len_to_drop,
-          nil_env, nil_assignments in
+          _env, _mem, _len, visited,
+          nil_env, nil_visited in
       nil_env == [] &
-      nil_assignments == [] &
+      nil_visited == [] &
       decl == FunDecl (arg_tags, body) &
-      state == St (env_before, mem_before, len_before, assignments_before) &
-      state_clean == St (nil_env, mem_before, len_before, nil_assignments) &
-      list_foldr2o (add_arg_foldero state) (Std.pair state Nat.o) arg_tags args (Std.pair state_with_vars _counter) & (* TODO: or foldr2o ?? *)
+      state == St (env_before, mem_before, len_before, visited_before) &
+      state_clean == St (nil_env, mem_before, len_before, nil_visited) &
+      list_foldr2o (add_arg_foldero state)
+                   (Std.pair state Nat.o) arg_tags args
+                   (Std.pair state_with_vars _counter) & (* TODO: or foldr2o ?? *)
       eval_bodyo state_with_vars prog body state_evaled &
-      st_spoil_assignmentso state_evaled state_spoiled &
-      state_spoiled == St (_env, mem_spoiled, len, _assignments) &
-      Nat.addo len_to_drop len_before len &
-      list_dropo len_to_drop mem_spoiled mem_updated &
-      state' == St (env_before, mem_updated, len_before, assignments_before)
+      state_evaled == St (_env,_mem, _len, visited) &
+      state' == St (env_before, mem_before, len_before, visited)
   }
 
   and eval_fun_empty_argso state prog decl state' =
@@ -403,11 +609,11 @@ struct
   let empty_stateo state =
     let open St in
     ocanren {
-    fresh nil_env, nil_mem, nil_assignments in
+    fresh nil_env, nil_mem, nil_visited in
       nil_env == [] &
-      nil_assignments == [] &
+      nil_visited == [] &
       nil_mem == [] &
-      state == St (nil_env, nil_mem, Nat.o, nil_assignments)
+      state == St (nil_env, nil_mem, Nat.o, nil_visited)
   }
 
   let eval_progo all_prog state' =