open Util
open Util.Vars
open Pure
open Num

type problem =
 { freshno: int
 ; ps: i_n_var list (* the n-th inert must become n *)
 ; sigma: (int * nf) list (* the computed substitution *)
 ; deltas: (int * nf) list ref list (* collection of all branches *)
 }

let print_problem {freshno; ps; deltas} =
 let deltas = String.concat "\n" (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
 let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
 deltas ^ (if deltas = "" then "" else "\n") ^
 String.concat "\n" (List.mapi (fun i t -> string_of_int i ^ ": " ^ print ~l (t :> nf)) ps)
;;

let make_fresh_var freshno =
 freshno+1, freshno+1

let make_fresh_vars p m =
 let rec aux =
  function
     0 -> p.freshno,[]
   | n when n > 0 ->
      let freshno,vars = aux (n-1) in
      let freshno,v = make_fresh_var freshno in
      freshno,`Var (0,v)::vars
   | _ -> assert false in
 let freshno,vars = aux m in
 {p with freshno}, vars

let simple_expand_match ps =
  let rec aux level = function
  | #i_num_var as t -> aux_i_num_var level t
  | `Lam(b,t) -> `Lam(b, aux (level+1) t)
  and aux_i_num_var level = function
  | `Match(ar,u,bs_lift,bs,args) as torig ->
    let u = aux_i_num_var level u in
    bs := List.map (fun (n, x) -> n, aux 0 x) !bs;
    (try
       (match u with
         | #i_n_var as u ->
            let i = index_of (lift (-level) u) (ps :> nf list) (* can raise Not_found *)
            in let t = mk_match ar (`N i) bs_lift bs args in
            if t <> torig then
            aux level (t :> nf)
           else raise Not_found
         | _ -> raise Not_found)
      with Not_found ->
       `Match(ar,cast_to_i_num_var u,bs_lift,bs,List.map (aux level) args))
  | `I(ar,k,args) -> `I(ar,k,Listx.map (aux level) args)
  | `N _ | `Var _ as t -> t
in aux_i_num_var 0;;

let rec super_simplify_ps ps it =
  let it' = List.map (fun t -> cast_to_i_num_var (simple_expand_match ps t)) (it :> i_num_var list) in
  if it <> it' then super_simplify_ps ps it' else it'

let super_simplify ({ps} as p) =
  let ps = super_simplify_ps p.ps (p.ps :> i_num_var list) in
  {p with ps=List.map cast_to_i_n_var ps}

let subst_in_problem x inst ({freshno; ps; sigma} as p) =
 let len_ps = List.length ps in
(*(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
  let rec aux ((freshno,acc_ps,acc_new_ps) as acc) =
   function
      [] -> acc
    | t::todo_ps ->
(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
       let t = subst false x inst (t :> nf) in
(*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
       let freshno,new_t,acc_new_ps =
        expand_match (freshno,acc_ps@`Var(-1,max_int/3)::todo_ps,acc_new_ps) t
       in
        aux (freshno,acc_ps@[new_t],acc_new_ps) todo_ps

  and expand_match ((freshno,acc_ps, acc_new_ps) as acc) t =
   match t with
    | `Match(ar,u',bs_lift,bs,args) ->
        let freshno,u,acc_new_ps = expand_match acc (u' :> nf) in
        let acc_new_ps,i =
         match u with
            `N i -> acc_new_ps,i
          | _ ->
            let ps = List.map (fun t -> cast_to_i_num_var (subst false x inst (t:> nf))) (acc_ps@acc_new_ps) in
            let super_simplified_ps = super_simplify_ps ps ps in
(*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplified_ps;*)
            match index_of_opt ~eq:eta_eq super_simplified_ps u with
               Some i -> acc_new_ps, i
             | None -> acc_new_ps@[u], len_ps + List.length acc_new_ps
        in
         let freshno=
          if List.exists (fun (j,_) -> i=j) !bs then
           freshno
          else
           let freshno,v = make_fresh_var freshno in
           bs := !bs @ [i, `Var (ar - 1,v)] ;
           freshno in
(*prerr_endlie ("t DA RIDURRE:" ^ print (`Match(`N i,arity,bs_lift,bs,args) :> nf) ^ " more_args=" ^ string_of_int more_args);*)
         let t = mk_match ar (`N i) bs_lift bs args in
(*prerr_endline ("NUOVO t:" ^ print (fst t :> nf) ^ " more_args=" ^ string_of_int (snd t));*)
          expand_match (freshno,acc_ps,acc_new_ps) t
    | `Lam _ ->
         (* the cast will fail *)
         (* freshno,(cast_to_i_n_var t),acc_new_ps *)
         assert false
    | #i_n_var as x ->
       let x = simple_expand_match (acc_ps@acc_new_ps) x in
       freshno,cast_to_i_num_var x,acc_new_ps in
  let freshno,old_ps,new_ps = aux (freshno,[],[]) (ps :> i_num_var list) in
  let ps = List.map cast_to_i_n_var (old_ps @ new_ps) in
(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
  let p = {p with freshno; ps; sigma = sigma@[x,inst]} in
  let p = super_simplify p in
prerr_endline (print_problem p); p

exception Dangerous

let rec dangerous arities showstoppers =
 function
    `N _
  | `Var _
  | `Lam _ -> ()
  | `Match(_,t,liftno,bs,args) ->
      (* CSC: XXX partial dependency on the encoding *)
      (match t with
          `N _ -> List.iter (dangerous arities showstoppers) args
        | `Match _ as t -> dangerous arities showstoppers t ; List.iter (dangerous arities showstoppers) args
        | `Var (_,x) -> dangerous_inert arities showstoppers x args 2 (* 2 coming from Scott's encoding *)
        | `I(_,x,args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
      )
  | `I(_,k,args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0

and dangerous_inert arities showstoppers k args more_args =
 List.iter (dangerous arities showstoppers) args ;
 if List.mem k showstoppers then raise Dangerous else
 try
  let _,_,y = List.find (fun (v,_,_) -> v=k) arities in
  let arity = match y with `Var _ -> 0 | `I(_,_,args) -> Listx.length args | _ -> assert false in
  if List.length args + more_args > arity then raise Dangerous else ()
 with
  Not_found -> ()

(* inefficient algorithm *)
let edible arities showstoppers ps =
 let rec aux showstoppers =
  function
     [] -> showstoppers
   | x::xs when List.exists (fun y -> hd_of x = Some y) showstoppers ->
      (* se la testa di x e' uno show-stopper *)
      let new_showstoppers = sort_uniq (showstoppers @ free_vars (x :> nf)) in
      (* aggiungi tutte le variabili libere di x *)
      if List.length showstoppers <> List.length new_showstoppers then
       aux new_showstoppers ps
      else
       aux showstoppers xs
   | x::xs ->
      match hd_of x with
         None -> aux showstoppers xs
       | Some h ->
          try
           dangerous arities showstoppers (x : i_n_var :> nf) ;
           aux showstoppers xs
          with
           Dangerous ->
            aux (sort_uniq (h::showstoppers)) ps
 in
  aux showstoppers ps

let precompute_edible_data {ps} xs =
 List.map (fun x ->
  let y = List.find (fun y -> hd_of y = Some x) ps in
  x, index_of ~eq:eta_eq y ps, y) xs
;;

let critical_showstoppers p =
  let p = super_simplify p in
  let showstoppers_step =
  List.concat (List.map (fun bs ->
    let heads = List.map (fun (i,_) -> List.nth p.ps i) !bs in
    let heads = List.sort compare (filter_map hd_of heads) in
    snd (split_duplicates heads)
    ) p.deltas) in
  let showstoppers_step = sort_uniq showstoppers_step in
  let showstoppers_eat =
   let heads_and_arities =
    List.sort (fun (k,_) (h,_) -> compare k h)
     (filter_map (function `Var (_,k) -> Some (k,0) | `I(_,k,args) -> Some (k,Listx.length args) | _ -> None ) p.ps) in
   let rec multiple_arities =
    function
       []
     | [_] -> []
     | (x,i)::(y,j)::tl when x = y && i <> j ->
         x::multiple_arities tl
     | _::tl -> multiple_arities tl in
   multiple_arities heads_and_arities in

  let showstoppers_eat = sort_uniq showstoppers_eat in
  let showstoppers_eat = List.filter
    (fun x -> not (List.mem x showstoppers_step))
    showstoppers_eat in
  List.iter (fun v -> prerr_endline ("DANGEROUS STEP: " ^ string_of_var v)) showstoppers_step;
  List.iter (fun v -> prerr_endline ("DANGEROUS EAT: " ^ string_of_var v)) showstoppers_eat;
  p, showstoppers_step, showstoppers_eat
  ;;

let eat p =
  let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p in
  let showstoppers = showstoppers_step @ showstoppers_eat in
  let heads = List.sort compare (filter_map hd_of ps) in
  let arities = precompute_edible_data p (uniq heads) in
  let showstoppers = edible arities showstoppers ps in
  let l = List.filter (fun (x,_,_) -> not (List.mem x showstoppers)) arities in
  let p =
  List.fold_left (fun p (x,pos,(xx : i_n_var)) ->
   let n = match xx with `I(_,_,args) -> Listx.length args | _ -> 0 in
   let v = `N(pos) in
   let inst = make_lams v n in
(let l = Array.to_list (Array.init (p.freshno + 1) string_of_var) in
 prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
   (* CSC: XXX to avoid applied numbers in safe positions that
      trigger assert failures subst_in_problem x inst p*)
   { p with sigma = p.sigma @ [x,inst] }
  ) p l in
 let ps =
  List.map (fun t ->
   try
    let _,j,_ = List.find (fun (h,_,_) -> hd_of t = Some h) l in
    `N j
   with Not_found -> t
  ) ps in
 List.iter
  (fun bs ->
    bs :=
     List.map
      (fun (n,t as res) ->
        match List.nth ps n with
           `N m -> m,t
         | _ -> res
      ) !bs
  ) p.deltas ;
 let p = { p with ps } in
 if l <> [] then prerr_endline (print_problem p);
 if List.for_all (function `N _ -> true | _ -> false) ps then
  `Finished p
 else
  `Continue p

let instantiate p x n =
  let p,vars = make_fresh_vars p n in
  let freshno,zero = make_fresh_var p.freshno in
  let p = {p with freshno} in
  let zero = Listx.Nil (`Var (0,zero)) in
  let args = if n = 0 then zero else Listx.append zero (Listx.from_list vars) in
  let bs = ref [] in
  let inst = `Lam(false,`Match(-1,`I(-1,0,Listx.map (lift 1) args),1,bs,[])) in
  let p = {p with deltas=bs::p.deltas} in
  subst_in_problem x inst p
;;

let compute_special_k tms =
  let rec aux k (t: nf) = Pervasives.max k (match t with
    | `Lam(b,t) -> aux (k + if b then 1 else 0) t
    | `I(_, n, tms) -> Listx.max (Listx.map (aux 0) tms)
    | `Match(_, t, liftno, bs, args) ->
        List.fold_left max 0 (List.map (aux 0) ((t :> nf)::args@List.map snd !bs))
    | `N _ -> 0
    | `Var _ -> 0
  ) in Listx.max (Listx.map (aux 0) tms)
;;

let auto_instantiate (n,p) =
  let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p in
 let x =
  match showstoppers_step, showstoppers_eat with
    | [], y::_ ->
      prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
    | [], [] ->
     let heads = List.sort compare (filter_map (fun t -> match t with `Var _ -> None | x -> hd_of x) ps) in
     (match heads with
         [] -> assert false
       | x::_ ->
          prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
          x)
  | x::_, _ ->
      prerr_endline ("INSTANTIATING " ^ string_of_var x);
      x in
(* Strategy that decreases the special_k to 0 first (round robin)
1:11m42 2:14m5 3:11m16s 4:14m46s 5:12m7s 6:6m31s *)
let x =
 try
  (match hd_of (List.find (fun t -> compute_special_k (Listx.Nil (t :> nf)) > 0) ps) with
      None -> assert false
    | Some x ->
       prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
       x)
 with
  Not_found -> x
in
(* Instantiate in decreasing order of compute_special_k
1:15m14s 2:13m14s 3:4m55s 4:4m43s 5:4m34s 6:6m28s 7:3m31s
let x =
 try
  (match hd_of (snd (List.hd (List.sort (fun c1 c2 -> - compare (fst c1) (fst c2)) (filter_map (function `I _ as t -> Some (compute_special_k (Listx.Nil (t :> nf)),t) | _ -> None) ps)))) with
      None -> assert false
    | Some x ->
       prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
       x)
 with
  Not_found -> x
in*)
 let special_k =
     compute_special_k (Listx.from_list (p.ps :> nf list) )in
 if special_k < n then
  prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@");
 let p = instantiate p x special_k in
 special_k,p

let problem_measure {ps} =
  (* let rec term_size_i_n_var =
    function
    | `I(v,nfs) ->
      (Listx.length nfs) *
      (List.fold_right (fun (a,b) c -> 10 + ((a+1) * term_size b) + c) (List.mapi (fun x y -> (x,y)) (Listx.to_list nfs)) 0)
    | `Var _ -> 1
    | `N _ -> 0
  and term_size =
    function
    | #i_n_var as t -> term_size_i_n_var t
    | `Match(t,lift,bs,args) -> 1 + (term_size (t :> nf)) + 1 + (List.fold_right ((+) ++ term_size) args 0)
    | `Lam(b,t) -> (if b then 0 else 1) + term_size t
  (* in List.fold_right ((+) ++ term_size_i_n_var) ps 0;; *)
  in ... *)
  0

let rec auto_eat (n,({ps} as p)) =
 match eat p with
    `Finished p -> p
  | `Continue p ->
    let p' = auto_instantiate (n,p) in
    let m' = problem_measure (snd p') in
    let delta = m' - problem_measure p in
    (if delta >= 0
    then print_endline ("$$$$ MEASURE DID NOT DECREASE (after inst) delta=" ^ string_of_int delta));
    let p'' = auto_eat p' in
    (if m' <= problem_measure p''
    then print_endline ("$$$$ MEASURE DID NOT DECREASE (after eat) $$$"));
    p''
;;

let auto p n =
 prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
 auto_eat (n,p)
;;

(*
0 = snd

      x y = y 0    a y = k  k z = z 0  c y = k   y u = u h1 h2 0          h2 a = h3
1 x a c    1 a 0 c  1 k c    1 c 0      1 k        1 k                     1 k
2 x a y    2 a 0 y  2 k y    2 y 0      2 y 0      2 h2 0                  2 h3
3 x b y    3 b 0 y  3 b 0 y  3 b 0 y    3 b 0 y    3 b 0 (\u. u h1 h2 0)   3 b 0 (\u. u h1 (\w.h3) 0)
4 x b c    4 b 0 c  4 b 0 c  4 b 0 c    4 b 0 c    4 b 0 c                 4 b 0 c
5 x (b e)  5 b e 0  5 b e 0  5 b e 0    5 b e 0    5 b e 0                 5 b e 0
6 y y      6 y y    6 y y    6 y y      6 y y      6 h1 h1 h2 0 h2 0       6 h1 h1 (\w. h3) 0 (\w. h3) 0

                                l2 _ = l3
b u = u l1 l2 0                 e _ _ _ _ = f                         l3 n = n j 0
1 k                             1 k                                  1 k
2 h3                            2 h3                                 2 h3
3 l2 0 (\u. u h1 (\w. h3) 0)    3 l3 (\u. u h1 (\w. h3) 0)           3 j h1 (\w. h3) 0 0
4 l2 0 c                        4 l3 c                               4 c j 0
5 e l1 l2 0 0                   5 f                                  5 f
6 h1 h1 (\w. h3) 0 (\w. h3) 0   6 h1 h1 (\w. h3) 0 (\w. h3) 0        6 h1 h1 (\w. h3) 0 (\w. h3) 0
*)

(*
                x n = n 0 ?
x a (b (a c))   a 0 = 1 ? (b (a c))   8
x a (b d')      a 0 = 1 ? (b d')      7
x b (a c)       b 0 = 1 ? (a c)       4
x b (a c')      b 0 = 1 ? (a c')      5

c = 2
c' = 3
a 2 = 4  (* a c *)
a 3 = 5  (* a c' *)
d' = 6
b 6 = 7  (* b d' *)
b 4 = 8  (* b (a c) *)
b 0 = 1
a 0 = 1
*)

(************** Tests ************************)

let optimize_numerals p =
  let replace_in_sigma perm =
    let rec aux = function
    | `N n -> `N (List.nth perm n)
    | `I _ | `Var _ -> assert false
    | `Lam(v,t) -> `Lam(v, aux t)
    | `Match(_,_,_,bs,_) as t -> (bs := List.map (fun (n,t) -> (List.nth perm n, t)) !bs); t
    in List.map (fun (n,t) -> (n,aux t))
  in
  let deltas' = List.mapi (fun n d -> (n, List.map fst !d)) p.deltas in
  let maxs = Array.to_list (Array.init (List.length deltas') (fun _ -> 0)) in
  let max = Listx.max (Listx.from_list (
    List.concat (List.map snd deltas')
  )) in
  let perm,_ = List.fold_left (fun (perm, maxs) (curr_n:int) ->
      let containing = filter_map (fun (i, bs) -> if List.mem curr_n bs then Some i else None) deltas' in
      (* (prerr_endline (string_of_int curr_n ^ " occurs in: " ^ (String.concat " " (List.map string_of_int containing)))); *)
      let neww = Listx.max (Listx.from_list (List.mapi (fun n max -> if List.mem n containing then max else 0) maxs)) in
      let maxs = List.mapi (fun i m -> if List.mem i containing then neww+1 else m) maxs in
      (neww::perm, maxs)
    ) ([],maxs) (Array.to_list (Array.init (max+1) (fun x -> x))) in
  replace_in_sigma (List.rev perm) p.sigma
;;

prerr_endline "########## main ##########";;

(* Commands:
    v ==> v := \a. a k1 .. kn \^m.0
    + ==> v := \^k. numero  for every v such that ...
    * ==> tries v as long as possible and then +v as long as possible
*)
let main problems =
 let rec aux ({ps} as p) n l =
  if List.for_all (function `N _ -> true | _ -> false) ps then begin
   assert (l = []);
   p
  end else
   let _ = prerr_endline (print_problem p) in
   let x,l =
    match l with
     | cmd::l -> cmd,l
     | [] -> read_line (),[] in
   let cmd =
    if x = "+" then
     `DoneWith
    else if x = "*" then
     `Auto
    else
     `Step x in
   match cmd with
    | `DoneWith -> assert false (*aux (eat p) n l*) (* CSC: TODO *)
    | `Step x ->
        let x = var_of_string x in
        aux (instantiate p x n) n l
    | `Auto -> aux (auto p n) n l
 in
  List.iter
   (fun (p,n,cmds) ->
     let p_finale = aux p n cmds in
     let freshno,sigma = p_finale.freshno, p_finale.sigma in
     prerr_endline "------- <DONE> ------";
     prerr_endline (print_problem p);
     prerr_endline "---------------------";
     let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
     List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
(*
     prerr_endline "----------------------";
     let ps =
      List.fold_left (fun ps (x,inst) ->
       (* CSC: XXXX Is the subst always sorted correctly? Otherwise, implement a recursive subst *)
       (* In this non-recursive version, the intermediate states may containt Matchs *)
       List.map (fun t -> let t = subst false x inst (t :> nf) in cast_to_i_num_var t) ps)
       (p.ps :> i_num_var list) sigma in
     prerr_endline (print_problem {p with ps= List.map (function t -> cast_to_i_n_var t) ps; freshno});
     List.iteri (fun i (n,more_args) -> assert (more_args = 0 && n = `N i)) ps ;
*)
     prerr_endline "---------<OPT>----------";
     let sigma = optimize_numerals p_finale in (* optimize numerals *)
     let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
     List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
     prerr_endline "---------<PURE>---------";
     let ps = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.ps in
     let sigma = List.map (fun (x,inst) -> x, ToScott.t_of_nf inst) sigma in
     (*let ps_ok = List.fold_left (fun ps (x,inst) ->
       List.map (Pure.subst false x inst) ps) ps sigma in*)
     let e =
      let rec aux n =
       if n > freshno then
        []
       else
        let e = aux (n+1) in
        (try
         e,Pure.lift (-n-1) (let t = (snd (List.find (fun (i,_) -> i = n) sigma)) in prerr_endline (string_of_var n ^ " := " ^ Pure.print t); t),[]
        with
         Not_found -> [],Pure.V n,[])::e
      in
       aux 0 in
(*
     prerr_endline "---------<PPP>---------";
let rec print_e e =
 "[" ^ String.concat ";" (List.map (fun (e,t,[]) -> print_e e ^ ":" ^ Pure.print t) e) ^ "]"
in
     prerr_endline (print_e e);
     List.iter (fun (t,t_ok) ->
      prerr_endline ("T0= " ^ Pure.print t ^ "\nTM= " ^ Pure.print (Pure.unwind (e,t,[])) ^ "\nOM= " ^ Pure.print t_ok);
      (*assert (Pure.unwind (e,t,[]) = t_ok)*)
     ) (List.combine ps ps_ok);
*)
     prerr_endline "--------<REDUCE>---------";
     List.iteri (fun i n ->
       (*prerr_endline ((string_of_int i) ^ "::: " ^ (Pure.print n));*)
       let t = Pure.mwhd (e,n,[]) in
       prerr_endline ((string_of_int i) ^ ":: " ^ (Pure.print t));
       assert (t = Scott.mk_n i)
     ) ps ;
     prerr_endline "-------- </DONE> --------"
   ) problems

(********************** problems *******************)

let zero = `Var (0,0);;

let append_zero =
 function
  | `I _
  | `Var _ as i ->  cast_to_i_n_var (mk_app i zero)
  | _ -> assert false
;;

type t = problem * int * string list;;

let magic strings cmds =
  let tms, _ = parse' strings in (*  *)
  let tms = sort_uniq ~compare:eta_compare tms in
  let special_k = compute_special_k (Listx.from_list tms) in (* compute special K *)
  let fv = sort_uniq (List.concat (List.map free_vars tms)) in (* free variables *)
  let tms = List.map cast_to_i_n_var tms in (* cast nf list -> i_n_var list *)
  let ps = List.map append_zero tms in (* crea lista applicando zeri o dummies *)
  (*let _ =  prerr_endline ("Free vars: " ^ String.concat ", " (List.map string_of_var fv)) in*)
  let freshno = Listx.max (Listx.from_list fv) in
  let dummy = `Var (-1,max_int / 2) in
  let deltas = [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
  {freshno; ps; sigma=[] ; deltas}, special_k, cmds
;;

let magic_conv ~div:_ ~conv:_ ~nums:_ _ = assert false;;