module Relational =
struct
  open GT
  (* open OCanren *)
  open OCanren.Std

  type data_ground = Nat.ground (* with show, gmap *)
  [@@deriving gt ~options:{ show; gmap }]
  type data_logic = Nat.logic
  [@@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 = AlwaysWr | MayWr | NeverWr
      [@@deriving gt ~options:{ show; gmap }]
      type nonrec ground = t
    ]
  end

  module CopyCap = struct
    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
    [%%ocanren_inject
      type nonrec t = Rf | Cp
      [@@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 Mode = struct
    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
    [%%ocanren_inject
      type nonrec ('i, 'o) t = Mode of 'i * 'o
      [@@deriving gt ~options:{ show; gmap }]
      type nonrec ground = (InCap.ground, OutCap.ground) t
    ]

    (* constructors *)
    let n_val = let open InCap in
                let open OutCap in
                ocanren { Mode (NIn, NOut) }
    let i_val = let open InCap in
                let open OutCap in
                ocanren { Mode (In, NOut) }
    let o_val = let open InCap in
                let open OutCap in
                ocanren { Mode (NIn, Out) }
    let io_val = let open InCap in
                 let open OutCap in
                 ocanren { Mode (In, Out) }

    (* accessors *)
    let is_ino m = let open InCap in ocanren {
                     fresh o_ in
                     m == Mode (In, o_) }
    let is_not_ino m = let open InCap in ocanren {
                         fresh o_ in
                         m == Mode (NIn, o_) }
    let is_outo m = let open OutCap in ocanren {
                      fresh i_ in
                      m == Mode (i_, Out) }
    let is_not_outo m = let open OutCap in ocanren {
                          fresh i_ in
                          m == Mode (i_, NOut) }

    (* module Test = struct *)
      (* @type answer = logic GT.list with show *)

      (* let test _ = show(answer) (Stream.take (run q (fun q -> let open InCap in *)
                                                              (* let open OutCap in *)
                                                              (* ocanren {q == Mode (In, NOut)}) *)
                                                    (* (fun q -> q#reify reify))) *)
    (* end *)
  end

  (* TODO: access: data or int ? *)
  module Path = struct
    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
    [%%ocanren_inject
      type nonrec ('d, 'p) t = VarP of 'd | DerefP of 'p | AccessP of 'p * 'd
      [@@deriving gt ~options:{ show; gmap }]
      type ground = (Nat.ground, ground) t
    ]
  end

  module Type = struct
    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
    [%%ocanren_inject
      type nonrec ('r, 'w, 'c, 't, 'tl, 'mtl) t = UnitT of 'r * 'w | RefT of 'c * 't | TupleT of 'tl | FunT of 'mtl
      [@@deriving gt ~options:{ show; gmap }]
      type ground = (ReadCap.ground, WriteCap.ground, CopyCap.ground, ground, ground List.ground, (Mode.ground * ground) List.ground) t
    ]
  end

  (* moded type - no separated type ? *)

  module Expr = struct
    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
    [%%ocanren_inject
      type nonrec ('d, 'p, 'el) t = UnitE | PathE of 'p | RefE of 'd | TupleE of 'el
      [@@deriving gt ~options:{ show; gmap }]
      type ground = (Nat.ground, Path.ground, ground List.ground) t
    ]
  end

  module Stmt = struct
    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
    [%%ocanren_inject
      type nonrec ('p, 'el, 's) t = SkipS | CallS of 'p * 'el | WriteS of 'p | ReadS of 'p | SeqS of 's * 's | ChoiceS of 's * 's
      [@@deriving gt ~options:{ show; gmap }]
      type ground = (Path.ground, Expr.ground List.ground, ground) t
    ]
  end

  (* TODO: list of 3 is not impelmented ?, replaced with two lists for now *)
  module Decl = struct
    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
    [%%ocanren_inject
      type nonrec ('d, 't, 'e, 'dl, 'mtl, 's) t = VarD of 'd * 't * 'e | FunD of 'd * 'dl * 'mtl * 's
      [@@deriving gt ~options:{ show; gmap }]
      type ground = (Nat.ground, Type.ground, Expr.ground, Nat.ground List.ground, (Mode.ground * Type.ground) List.ground, Stmt.ground) t
    ]
  end

  module Prog = struct
    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
    [%%ocanren_inject
      type nonrec ('dl, 's) t = Prog of 'dl * 's
      [@@deriving gt ~options:{ show; gmap }]
      type nonrec ground = (Decl.ground List.ground, Stmt.ground) t
    ]
  end

  (* NOTE: deepvalue - not used (?) *)

  module Value = struct
    [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"]
    [%%ocanren_inject
      type nonrec ('sl, 'd, 'vl) t = ZeroV | SmthV | BotV | FunV of 'sl | RefV of 'd | TupleV of 'vl
      [@@deriving gt ~options:{ show; gmap }]
      type ground = ((Nat.ground List.ground * Stmt.ground) List.ground, Nat.ground, ground List.ground) t
    ]
  end

  (* --- FIXME --- CURRENT REWRITE POINT --- FIXME --- *)

  (* 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, AlwaysWr, 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, NeverWr, 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, AlwaysWr, 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, NeverWr, 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, AlwaysWr, 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, NeverWr, 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, AlwaysWr, 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, NeverWr, Ref, In, NOut) } *)

    (* constraints *)
    (* let x_any tag = let open InCap in *)
                    (* let open OutCap in *)
                    (* ocanren { fresh r, w, c in *)
                              (* tag == Tag (r, w, c, NIn, NOut) } *)
    (* let i_any tag = let open InCap in *)
                    (* let open OutCap in *)
                    (* ocanren { fresh r, w, c in *)
                              (* tag == Tag (r, w, c, In, NOut) } *)
    (* let o_any tag = let open InCap in *)
                    (* let open OutCap in *)
                    (* ocanren { fresh r, w, c in *)
                              (* tag == Tag (r, w, c, NIn, Out) } *)
    (* let io_any tag = let open InCap in *)
                     (* let open OutCap in *)
                     (* ocanren { fresh r, w, c in *)
                               (* tag == Tag (r, w, c, In, Out) } *)

    (* 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_always_writeo tag = let open WriteCap in ocanren { *)
                                 (* fresh r_, c_, i_, o_ in *)
                                 (* tag == Tag (r_, AlwaysWr, c_, i_, o_) } *)
    (* let is_may_writeo tag = let open WriteCap in ocanren { *)
                              (* fresh r_, c_, i_, o_ in *)
                              (* { tag == Tag (r_, AlwaysWr, c_, i_, o_) | *)
                                (* tag == Tag (r_, MayWr, c_, i_, o_) } } *)
    (* let is_never_writeo tag = let open WriteCap in ocanren { *)
                                (* fresh r_, c_, i_, o_ in *)
                                (* tag == Tag (r_, NeverWr, 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) } *)

    (* let eq_copyo tag cp = let open CopyCap in ocanren { *)
                           (* fresh r_, w_, i_, o_ in *)
                           (* tag == Tag (r_, w_, cp, i_, o_) } *)

    (* 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, NeverWr, Ref, In, NOut)}) *)
                                                    (* (fun q -> q#reify reify))) *)
    (* end *)
  (* end *)

  (* module Stmt = struct *)
    (* [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"] *)
    (* [%%ocanren_inject *)
      (* type nonrec ('d, 'dl, 'sl) t = Call of 'd * 'dl | Read of 'd | Write of 'd | Choice of 'sl * 'sl *)
      (* [@@deriving gt ~options:{ show; gmap }] *)
      (* type ground = (Nat.ground, Nat.ground List.ground, ground List.ground) t *)
    (* ] *)

    (* module Test = struct *)
      (* @type answer = Nat.ground List.ground GT.list with show *)
      (* @type answer'  = ground GT.list with show *)

      (* let test1 _ = show(answer) (Stream.take (run q (fun q -> ocanren {Call (1, [2]) == Call (1, q)}) *)
                                                     (* (fun q -> q#reify (List.prj_exn Nat.prj_exn)))) *)

      (* let test2 _ = show(answer') (Stream.take (run q (fun q -> ocanren {Call (1, [2]) == q}) *)
                                                      (* (fun q -> q#reify (prj_exn)))) *)
    (* end *)
  (* end *)

  (* module FunDecl = struct *)
    (* [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"] *)
    (* [%%ocanren_inject *)
      (* type nonrec ('l, 'b) t = FunDecl of 'l * 'b *)
      (* [@@deriving gt ~options:{ show; gmap }] *)
      (* type nonrec ground = (Tag.ground List.ground, Stmt.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 Tag in *)
                                                              (* let open Stmt in *)
                                                              (* ocanren {FunDecl ([rwi_ref; rwi_val], [Call (1, [0]); Write 1]) == q}) *)
                                                    (* (fun q -> q#reify (prj_exn)))) *)
    (* end *)
  (* end *)

  (* module Prog = struct *)
    (* [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"] *)
    (* [%%ocanren_inject *)
      (* type nonrec ('l, 'f) t = Prog of 'l * 'f *)
      (* [@@deriving gt ~options:{ show; gmap }] *)
      (* type nonrec ground = (FunDecl.ground List.ground, FunDecl.ground) t *)
    (* ] *)

    (* module Test = struct *)
      (* @type answer  = ground GT.list with show *)
      (* 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 ([ri_val], [Write 0; Read 0])) == q}) *)
                                                    (* (fun q -> q#reify (prj_exn)))) *)
    (* end *)
  (* end *)

  (* module Arg = struct *)
    (* [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"] *)
    (* [%%ocanren_inject *)
      (* type nonrec 'd t = RValue | LValue of 'd *)
      (* [@@deriving gt ~options:{ show; gmap }] *)
      (* type nonrec ground = Nat.ground t *)
    (* ] *)

    (* module Test = struct *)
      (* @type answer = logic GT.list with show *)
      (* let test _ = show(answer) (Stream.take (run q (fun q -> ocanren {q == LValue 3}) *)
                                                    (* (fun q -> q#reify reify))) *)
    (* end *)
  (* end *)

  (* module Value = struct *)
    (* [@@@warning "-26-27-32-33-34-35-36-37-38-39-60-66-67"] *)
    (* [%%ocanren_inject *)
      (* type nonrec t = Unit | Undef | Bot *)
      (* [@@deriving gt ~options:{ show; gmap }] *)
      (* type nonrec ground = t *)
    (* ] *)

    (* module Test = struct *)
      (* @type answer = logic GT.list with show *)
      (* let test _ = show(answer) (Stream.take (run q (fun q -> ocanren {q == Bot | q == Unit}) *)
                                                    (* (fun q -> q#reify reify))) *)
    (* end *)
  (* end *)

  (* 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, 'visited) t = St of 'env * 'mem * 'last_mem * 'visited *)
      (* [@@deriving gt ~options:{ show; gmap }] *)
      (* 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 *)
                                                              (* 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 *)

  (* --- *)

  (* let rec list_zip_witho f xs ys zs = ocanren { *)
    (* { fresh x, xs', y, ys', z, zs' in *)
      (* xs == x :: xs' & *)
      (* ys == y :: ys' & *)
      (* zs == z :: zs' & *)
      (* f x y z & *)
      (* list_zip_witho f xs' ys' zs' } | *)
    (* { fresh x, xs' in *)
      (* xs == x :: xs' & *)
      (* ys == [] & *)
      (* zs == [] } | *)
    (* { fresh y, ys' in *)
      (* xs == [] & *)
      (* ys == y :: ys' & *)
      (* zs == [] } | *)
    (* { xs == [] & ys == [] & zs == [] } *)
  (* } *)

  (* --- *)

  (* let value_combineo left right res = let open Value in ocanren { *)
    (* { left == Unit & right == Unit & res == Unit } | *)
    (* { left == Bot & right == Bot & res == Bot } | *)
    (* { left == Unit & right == Bot & res == Undef } | *)
    (* { left == Bot & right == Unit & res == Undef } *)
  (* } *)

  (* let memory_combineo left right res = ocanren { *)
    (* list_zip_witho value_combineo left right res *)
  (* } *)

  (* let state_combineo left right res = let open St in ocanren { *)
    (* fresh lenv, lmem, lmem_len, lvisited, renv, rmem, rmem_len, rvisited, res_mem in *)
    (* left == St (lenv, lmem, lmem_len, lvisited) & *)
    (* right == St (renv, rmem, rmem_len, rvisited) & *)
    (* lenv == renv & lmem_len == rmem_len & *)
    (* memory_combineo lmem rmem res_mem  & *)
    (* res == St (lenv, rmem, lmem_len, List.appendo lvisited rvisited) *)
    (* TODO: union visited lists instead ? *)
  (* } *)

  (* --- *)

  (* let rec list_replaceo xs id value ys = ocanren { *)
    (* xs == [] & ys == [] | (* NOTE: error *) *)
    (* { fresh x, xs' in *)
        (* xs == x :: xs' & *)
        (* id == Nat.o & *)
        (* ys == value :: xs' } | *)
    (* { fresh x, xs', id', ys' in *)
        (* xs == x :: xs' & *)
        (* id == Nat.s id' & *)
        (* ys == x :: ys' & *)
        (* list_replaceo xs' id' value ys' } *)
  (* } *)

  (* let env_geto state id tag' mem_id' = *)
    (* let open St in *)
    (* ocanren { *)
    (* 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 tg mem_id state' = *)
    (* let open St in *)
    (* ocanren { *)
    (* 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 { *)
    (* fresh inv_id_inc in *)
      (* Nat.addo inv_id_inc id mem_len & *)
      (* Nat.addo id' 1 inv_id_inc *)
  (* } *)

  (* --- *)

  (* let rec list_ntho xs id x' = ocanren { *)
    (* xs == [] | (* NOTE: error *) *)
    (* { fresh y', xs' in *)
      (* id == Nat.o & *)
      (* y' :: xs' == xs & *)
      (* x' == y' } | *)
    (* { fresh id', y', xs' in *)
      (* Nat.s id' == id & *)
      (* y' :: xs' == xs & *)
      (* list_ntho xs' id' x' } *)
  (* } *)

  (* let mem_geto state id value' = *)
    (* let open St in *)
    (* ocanren { *)
    (* 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' *)
  (* } *)

  (* let mem_seto state id value state'= *)
    (* let open St in *)
    (* ocanren { *)
    (* 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' & *)
      (* 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', 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', visited) *)
  (* } *)

  (* let mem_checko state id = *)
    (* let open Value in *)
    (* ocanren { *)
      (* mem_geto state id Unit *)
    (* } *)

  (* --- *)

  (* let rec list_foldlo f acc xs acc' = ocanren { *)
    (* xs == [] & acc' == acc | *)
    (* { fresh x', xs', acc_upd in *)
      (* xs == x' :: xs' & *)
      (* list_foldlo f acc xs' acc_upd & *)
      (* f acc_upd x' acc' } *)
  (* } *)

  (* let rec list_foldro f acc xs acc' = ocanren { *)
    (* xs == [] & acc' == acc | *)
    (* { fresh x', xs', acc_upd in *)
      (* xs == x' :: xs' & *)
      (* f acc x' acc_upd & *)
      (* list_foldro f acc_upd xs' acc' } *)
    (* TODO: inf search on swap, investigate *)
  (* } *)


  (* let rec list_foldr2o f acc xs ys acc' = ocanren { *)
    (* xs == [] & ys == [] & acc' == acc | *)
    (* { fresh x', xs', y', ys', acc_upd in *)
      (* xs == x' :: xs' & *)
      (* ys == y' :: ys' & *)
      (* f acc x' y' acc_upd & *)
      (* list_foldr2o f acc_upd xs' ys' acc' } *)
  (* } *)

  (* let rec list_foldl2o f acc xs ys acc' = ocanren { *)
    (* xs == [] & ys == [] & acc' == acc | *)
    (* { fresh x', xs', y', ys', acc_upd in *)
      (* xs == x' :: xs' & *)
      (* ys == y' :: ys' & *)
      (* list_foldl2o f acc xs' ys' acc_upd & *)
      (* f acc_upd x' y' acc' } *)
  (* } *)

  (* let arg_to_valueo state arg value' = *)
    (* let open Arg in *)
    (* let open Value in *)
    (* ocanren { *)
    (* arg == RValue & value' == Unit | *)
    (* { fresh id in *)
      (* arg == LValue id & *)
      (* mem_geto state id value' } *)
  (* } *)

  (* let arg_to_rvalueo arg value' = *)
    (* let open Arg in *)
    (* 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, _visited in *)
      (* state == St (_env, _mem, mem_len', _visited) *)
  (* } *)

  (* let tag_correcto tg = *)
    (* let open Tag in *)
    (* ocanren { *)
      (* {is_not_outo tg | { is_outo tg & is_always_writeo tg } } & *)
      (* {is_not_reado tg | { is_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 { *)
        (* 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_never_writeo arg_tag | { is_may_writeo arg_tag & is_may_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_before state tg id state' = *)
    (* let open Value in *)
    (* let open Tag in *)
    (* let open St in *)
    (* ocanren { *)
      (* 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_reado tg | { is_reado tg & mem_checko state_before id } } & *)
      (* { { is_never_writeo tg & state == state'} | *)
        (* { is_always_writeo tg & *) 
          (* is_outo tg & is_may_writeo parent_tg & mem_seto state id Unit state' } | *)
        (* { is_may_writeo tg & { *)
          (* { is_not_outo tg & is_valueo tg & state == state' } | *)
          (* { is_not_outo tg & is_refo tg & is_may_writeo parent_tg & 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' *)
  (* } *)

  (* --- *)

  (* let arg_to_lvalueo arg arg' = *)
    (* let open Arg in *)
    (* ocanren { arg' == LValue arg } *)

  (* let rec list_dropo n xs xs' = ocanren { *)
    (* xs == [] & xs' == [] | *)
    (* n == Nat.o & xs == xs' & xs =/= [] | *)
    (* { fresh n', _y, ys in *)
        (* Nat.s n' == n & *)
        (* xs == _y :: ys & *)
        (* list_dropo n' ys xs' } *)
  (* } *)

  (* let rec list_not_membero xs x = ocanren { *)
    (* xs == [] | *)
    (* { fresh x', xs' in *)
        (* xs == x' :: xs' & *)
        (* x' =/= x & *)
        (* list_not_membero xs' x } *)
  (* } *)

  (* 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 *)
    (* } *)

  (* let not_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_not_membero visited 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) & *)
      (* 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 *)
    (* let open Tag in *)
    (* ocanren { *)
    (* { fresh f_id, args, f, args', state_after_call, 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' & *)
      (* TODO: FIXME: memoisation, do not do calls on check successfull *)
      
      (* NOTE: tmp simplification for less branching (TODO?) *)
      (* { { fresh state_with_visited in *)
          (* not_visited_checko state f_id & *)
          (* visited_addo state f_id state_with_visited & *)
          (* eval_funo state_with_visited prog f args' state_after_call } | *)
        (* { visited_checko state f_id & *)
          (* state_after_call == state } } & *)
      (* st_spoil_by_argso state_after_call 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 & *)
      (* is_may_writeo tag & *)
      (* mem_seto state id Unit state' } | *)
    (* { fresh xs, ys in *)
      (* stmt == Choice (xs, ys) } *)
    (* TODO: FIXME: choice actions *)
  (* } *)

  (* and eval_body_foldero prog state stmt state' = *)
    (* eval_stmto state prog stmt state' *)

  (* and eval_bodyo state prog body state' = *)
    (* list_foldro (eval_body_foldero prog) state body state' *) 

  (* and add_arg_foldero state_before state_c arg_tag arg state_c' = *)
    (* ocanren { *)
    (* fresh state, id, state', id' in *)
      (* state_c == Std.pair state id & *)
      (* st_add_argo state state_before id arg_tag arg state' & *)
      (* id' == Nat.s id & *)
      (* state_c' == Std.pair state' id' *)
  (* } *)

  (* and eval_funo state prog decl args state' = *)
    (* let open FunDecl in *)
    (* let open St in *)
    (* ocanren { *)
    (* fresh arg_tags, body, *)
          (* env_before, mem_before, len_before, visited_before, *)
          (* state_clean, *)
          (* state_with_vars, _counter, *)
          (* state_evaled, *)
          (* _env, _mem, _len, visited, *)
          (* nil_env, nil_visited in *)
      (* nil_env == [] & *)
      (* nil_visited == [] & *)
      (* decl == FunDecl (arg_tags, body) & *)
      (* 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 & *)
      (* 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' = *)
    (* let open FunDecl in *)
    (* ocanren { *)
    (* fresh arg_tags, args, _body in *)
      (* decl == FunDecl (arg_tags, _body) & *)
      (* List.mapo arg_to_rvalueo arg_tags args & *)
      (* eval_funo state prog decl args state' *)
  (* } *)

  (* --- *)

  (* let empty_stateo state = *)
    (* let open St in *)
    (* ocanren { *)
    (* fresh nil_env, nil_mem, nil_visited in *)
      (* nil_env == [] & *)
      (* nil_visited == [] & *)
      (* nil_mem == [] & *)
      (* state == St (nil_env, nil_mem, Nat.o, nil_visited) *)
  (* } *)

  (* let eval_progo all_prog state' = *)
    (* let open Prog in *)
    (* ocanren { *)
    (* fresh prog, main_decl, state in *)
      (* all_prog == Prog (prog, main_decl) & *)
      (* empty_stateo state & *)
      (* eval_fun_empty_argso state prog main_decl state' *)
  (* } *)
end