(********************************************************************)
(*                                                                  *)
(*  The Why3 Verification Platform   /   The Why3 Development Team  *)
(*  Copyright 2010-2023 --  Inria - CNRS - Paris-Saclay University  *)
(*                                                                  *)
(*  This software is distributed under the terms of the GNU Lesser  *)
(*  General Public License version 2.1, with the special exception  *)
(*  on linking described in file LICENSE.                           *)
(*                                                                  *)
(********************************************************************)

open Term

let debug_cont_size = Debug.register_info_flag "reduction_cont_size"
  ~desc:"check cont size invariant intensively"

(* {2 Values} *)

type value =
  | Term of term    (* invariant: is in normal form *)
  | Int of BigInt.t
  | Real of Number.real_value

let v_attr_copy orig v =
  match v with
  | Int _ -> v
  | Real _ -> v
  | Term t -> Term (t_attr_copy orig t)

let term_of_value v =
  let open Number in
  match v with
  | Term t -> t
  | Int n -> t_int_const n
  | Real { rv_sig = s; rv_pow2 = pow2; rv_pow5 = pow5 } -> t_real_const ~pow2 ~pow5 s

exception NotNum

let big_int_of_const c =
  match c with
  | Constant.ConstInt i -> i.Number.il_int
  | Constant.ConstReal _ -> assert false
  | Constant.ConstStr _ -> assert false

let big_int_of_value v =
  match v with
  | Int n -> n
  | Real _ -> assert false
  | Term { t_node = Tconst c } -> big_int_of_const c
  | Term _ -> raise NotNum

let real_of_const c =
  match c with
  | Constant.ConstReal r -> r.Number.rl_real
  | Constant.ConstInt _ -> assert false
  | Constant.ConstStr _ -> assert false

let real_of_value v =
  match v with
  | Real r -> r
  | Int _ -> assert false
  | Term { t_node = Tconst c } -> real_of_const c
  | Term _ -> raise NotNum

(* {2 Builtin symbols} *)

let builtins = Hls.create 17

(* all builtin functions *)

exception Undetermined

let to_bool b = if b then t_true else t_false

let _t_app_value ls l ty =
  Term (t_app ls (List.map term_of_value l) ty)

let is_zero v =
  try BigInt.eq (big_int_of_value v) BigInt.zero
  with NotNum -> false

let is_one v =
  try BigInt.eq (big_int_of_value v) BigInt.one
  with NotNum -> false

let eval_int_op op simpl ls l ty =
  match l with
  | [t1 ; t2] ->
    begin
      try
        let n1 = big_int_of_value t1 in
        let n2 = big_int_of_value t2 in
        Int (op n1 n2)
      with NotNum | Division_by_zero ->
        simpl ls t1 t2 ty
    end
  | _ -> assert false

let simpl_add _ls t1 t2 _ty =
  if is_zero t1 then t2 else
  if is_zero t2 then t1 else
  raise Undetermined

let simpl_sub _ls t1 t2 _ty =
  if is_zero t2 then t1 else
  raise Undetermined

let simpl_mul _ls t1 t2 _ty =
  if is_zero t1 then t1 else
  if is_zero t2 then t2 else
  if is_one t1 then t2 else
  if is_one t2 then t1 else
  raise Undetermined

let simpl_div _ls t1 t2 _ty =
  if is_zero t2 then raise Undetermined;
  if is_zero t1 then t1 else
  if is_one t2 then t1 else
  raise Undetermined

let simpl_mod _ls t1 t2 _ty =
  if is_zero t2 then raise Undetermined;
  if is_zero t1 then t1 else
  if is_one t2 then Int (BigInt.zero) else
  raise Undetermined

let simpl_minmax _ls v1 v2 _ty =
  match v1,v2 with
  | Term t1, Term t2 ->
    if t_equal t1 t2 then v1 else
      raise Undetermined
  | _ ->
    raise Undetermined

let eval_int_rel op _ls l _ty =
  match l with
  | [t1 ; t2] ->
    begin
      try
        let n1 = big_int_of_value t1 in
        let n2 = big_int_of_value t2 in
        Term (to_bool (op n1 n2))
      with NotNum | Division_by_zero ->
        raise Undetermined
    (*        t_app_value ls l ty *)
    end
  | _ -> assert false

let eval_int_uop op _ls l _ty =
  match l with
  | [t1] ->
    begin
      try
        let n1 = big_int_of_value t1 in Int (op n1)
      with NotNum | Division_by_zero ->
        raise Undetermined
    (*       t_app_value ls l ty *)
    end
  | _ -> assert false

let real_align ~pow2 ~pow5 r =
  let open Number in
  let { rv_sig = s; rv_pow2 = p2; rv_pow5 = p5 } = r in
  let s = BigInt.mul s (BigInt.pow_int_pos_bigint 2 (BigInt.sub p2 pow2)) in
  let s = BigInt.mul s (BigInt.pow_int_pos_bigint 5 (BigInt.sub p5 pow5)) in
  s

let eval_real_op op simpl ls l ty =
  match l with
  | [t1; t2] ->
    begin
      try
        let n1 = real_of_value t1 in
        let n2 = real_of_value t2 in
        Real (op n1 n2)
      with NotNum ->
        simpl ls t1 t2 ty
    end
  | _ -> assert false

let eval_real_uop op _ls l _ty =
  match l with
  | [t1] ->
    begin
      try
        let n1 = real_of_value t1 in
        Real (op n1)
      with NotNum ->
        raise Undetermined
    end
  | _ -> assert false

let eval_real_rel op _ls l _ty =
  let open Number in
  match l with
  | [t1 ; t2] ->
    begin
      try
        let n1 = real_of_value t1 in
        let n2 = real_of_value t2 in
        let s1, s2 =
          let { rv_sig = s1; rv_pow2 = p21; rv_pow5 = p51 } = n1 in
          let { rv_sig = s2; rv_pow2 = p22; rv_pow5 = p52 } = n2 in
          if BigInt.sign s1 <> BigInt.sign s2 then s1,s2
          else
            let pow2 = BigInt.min p21 p22 in
            let pow5 = BigInt.min p51 p52 in
            let s1 = real_align ~pow2 ~pow5 n1 in
            let s2 = real_align ~pow2 ~pow5 n2 in
            s1, s2 in
        Term (to_bool (op s1 s2))
      with NotNum ->
        raise Undetermined
    (*        t_app_value ls l ty *)
    end
  | _ -> assert false

let real_0 = Number.real_value BigInt.zero
let real_1 = Number.real_value BigInt.one

let is_real t r =
  try Number.compare_real (real_of_value t) r = 0
  with NotNum -> false

let real_opp r =
  let open Number in
  let { rv_sig = s; rv_pow2 = pow2; rv_pow5 = pow5 } = r in
  real_value ~pow2 ~pow5 (BigInt.minus s)

let real_add r1 r2 =
  let open Number in
  let { rv_sig = s1; rv_pow2 = p21; rv_pow5 = p51 } = r1 in
  let { rv_sig = s2; rv_pow2 = p22; rv_pow5 = p52 } = r2 in
  if BigInt.eq s1 BigInt.zero then r2 else
  if BigInt.eq s2 BigInt.zero then r1 else
  let pow2 = BigInt.min p21 p22 in
  let pow5 = BigInt.min p51 p52 in
  let s1 = real_align ~pow2 ~pow5 r1 in
  let s2 = real_align ~pow2 ~pow5 r2 in
  real_value ~pow2 ~pow5 (BigInt.add s1 s2)

let real_sub r1 r2 =
  let open Number in
  let { rv_sig = s1; rv_pow2 = p21; rv_pow5 = p51 } = r1 in
  let { rv_sig = s2; rv_pow2 = p22; rv_pow5 = p52 } = r2 in
  if BigInt.eq s2 BigInt.zero then r1 else
  if BigInt.eq s1 BigInt.zero then real_value ~pow2:p22 ~pow5:p52 (BigInt.minus s2) else
  let pow2 = BigInt.min p21 p22 in
  let pow5 = BigInt.min p51 p52 in
  let s1 = real_align ~pow2 ~pow5 r1 in
  let s2 = real_align ~pow2 ~pow5 r2 in
  real_value ~pow2 ~pow5 (BigInt.sub s1 s2)

let real_mul r1 r2 =
  let open Number in
  let { rv_sig = s1; rv_pow2 = p21; rv_pow5 = p51 } = r1 in
  let { rv_sig = s2; rv_pow2 = p22; rv_pow5 = p52 } = r2 in
  let s = BigInt.mul s1 s2 in
  let pow2 = BigInt.add p21 p22 in
  let pow5 = BigInt.add p51 p52 in
  real_value ~pow2 ~pow5 s

let simpl_real_add _ls t1 t2 _ty =
  if is_real t1 real_0 then t2 else
  if is_real t2 real_0 then t1 else
  raise Undetermined

let simpl_real_sub _ls t1 t2 _ty =
  if is_real t2 real_0 then t1 else
  raise Undetermined

let simpl_real_mul _ls t1 t2 _ty =
  if is_real t1 real_0 then t1 else
  if is_real t2 real_0 then t2 else
  if is_real t1 real_1 then t2 else
  if is_real t2 real_1 then t1 else
  raise Undetermined

let real_pow r1 r2 =
  let open Number in
  let { rv_sig = s1; rv_pow2 = p21; rv_pow5 = p51 } = r1 in
  let { rv_sig = s2; rv_pow2 = p22; rv_pow5 = p52 } = r2 in
  if BigInt.le s1 BigInt.zero then
    raise Undetermined
  else if BigInt.lt p22 BigInt.zero || BigInt.lt p52 BigInt.zero then
    raise NotNum
  else
    let s1 = try BigInt.to_int s1 with Failure _ -> raise NotNum in
    let s2 = BigInt.mul s2 (BigInt.pow_int_pos_bigint 2 p22) in
    let s2 = BigInt.mul s2 (BigInt.pow_int_pos_bigint 5 p52) in
    let s =
      if s1 = 1 then BigInt.one
      else if BigInt.lt s2 BigInt.zero then raise NotNum
      else BigInt.pow_int_pos_bigint s1 s2 in
    let pow2 = BigInt.mul p21 s2 in
    let pow5 = BigInt.mul p51 s2 in
    Number.real_value ~pow2 ~pow5 s

let simpl_real_pow _ls t1 _t2 _ty =
  if is_real t1 real_1 then t1 else
  raise Undetermined

let real_from_int _ls l _ty =
  match l with
  | [t] ->
    begin
      try
        let n = big_int_of_value t in
        Real (Number.real_value n)
      with NotNum ->
        raise Undetermined
    end
  | _ -> assert false

let built_in_theories =
  [
(*
 ["bool"],"Bool", [],
    [ "True", None, eval_true ;
      "False", None, eval_false ;
    ] ;
*)
    ["int"],"Int", [],
    [ Ident.op_infix "+", None, eval_int_op BigInt.add simpl_add;
      Ident.op_infix "-", None, eval_int_op BigInt.sub simpl_sub;
      Ident.op_infix "*", None, eval_int_op BigInt.mul simpl_mul;
      Ident.op_prefix "-", None, eval_int_uop BigInt.minus;
      Ident.op_infix "<", None, eval_int_rel BigInt.lt;
      Ident.op_infix "<=", None, eval_int_rel BigInt.le;
      Ident.op_infix ">", None, eval_int_rel BigInt.gt;
      Ident.op_infix ">=", None, eval_int_rel BigInt.ge;
    ] ;
    ["int"],"MinMax", [],
    [ "min", None, eval_int_op BigInt.min simpl_minmax;
      "max", None, eval_int_op BigInt.max simpl_minmax;
    ] ;
    ["int"],"ComputerDivision", [],
    [ "div", None, eval_int_op BigInt.computer_div simpl_div;
      "mod", None, eval_int_op BigInt.computer_mod simpl_mod;
    ] ;
    ["int"],"EuclideanDivision", [],
    [ "div", None, eval_int_op BigInt.euclidean_div simpl_div;
      "mod", None, eval_int_op BigInt.euclidean_mod simpl_mod;
    ] ;
    ["real"], "Real", [],
    [ Ident.op_prefix "-", None, eval_real_uop real_opp;
      Ident.op_infix "+", None, eval_real_op real_add simpl_real_add;
      Ident.op_infix "-", None, eval_real_op real_sub simpl_real_sub;
      Ident.op_infix "*", None, eval_real_op real_mul simpl_real_mul;
      Ident.op_infix "<", None, eval_real_rel BigInt.lt;
      Ident.op_infix "<=", None, eval_real_rel BigInt.le;
      Ident.op_infix ">", None, eval_real_rel BigInt.gt;
      Ident.op_infix ">=", None, eval_real_rel BigInt.ge ] ;
    ["real"], "FromInt", [],
    [ "from_int", None, real_from_int ] ;
    ["real"], "PowerReal", [],
    [ "pow", None, eval_real_op real_pow simpl_real_pow ] ;
(*
    ["map"],"Map", ["map", builtin_map_type],
    [ "const", Some ls_map_const, eval_map_const;
      "get", Some ls_map_get, eval_map_get;
      "set", Some ls_map_set, eval_map_set;
    ] ;
*)
  ]

let add_builtin_th env (l,n,t,d) =
  let th = Env.read_theory env l n in
  List.iter
    (fun (id,r) ->
      let ts = Theory.ns_find_ts th.Theory.th_export [id] in
      r ts)
    t;
  List.iter
    (fun (id,r,f) ->
      let ls = Theory.ns_find_ls th.Theory.th_export [id] in
      Hls.add builtins ls f;
      match r with
        | None -> ()
        | Some r -> r := ls)
    d

let get_builtins env =
  Hls.clear builtins;
  List.iter (add_builtin_th env) built_in_theories



(* {2 the reduction machine} *)


type rule = Svs.t * term list * term

type params =
  { compute_defs : bool;
    compute_builtin : bool;
    compute_def_set : Term.Sls.t;
    compute_max_quantifier_domain : int;
  }

type engine =
  { known_map : Decl.decl Ident.Mid.t;
    rules : rule list Mls.t;
    params : params;
    ls_lt : lsymbol; (* The lsymbol for [int.Int.(<)] *)
  }


(* OBSOLETE COMMENT

  A configuration is a pair (t,s) where t is a stack of terms and s is a
  stack of function symbols.

  A configuration ([t1;..;tn],[f1;..;fk]) represents a whole term, its
  model, as defined recursively by

    model([t],[]) = t

    model(t1::..::tn::t,f::s) = model(f(t1,..,tn)::t,s)
      where f is of arity n

  A given term can be "exploded" into a configuration by reversing the
  rules above

  During reduction, the terms in the first stack are kept in normal
  form (value). The normalization process can be defined as the repeated
  application of the following rules.

  ([t],[]) --> t  // t is in normal form

  if f(t1,..,tn) is not a redex then
  (t1::..::tn::t,f::s) --> (f(t1,..,tn)::t,s)

  if f(t1,..,tn) is a redex l sigma for a rule l -> r then
  (t1::..::tn::t,f::s) --> (subst(sigma) @ t,explode(r) @ s)




*)

type substitution = term Mvs.t

(* The size of an element of type [cont] is then defined by:
   1 (for the constructor) + the size of each term (this
   includes terms on [term_branch] list, and terms in substitutions).
*)
(*
   In the [config] type, we keep the following invariant
   for the continuation stack:
   the head (c,t,n) of the list is such that [n] is equal to
   the size of [c] + the size of the tail of the list.
   This is used in the [normalize] function, in order to stop
   the reduction if the term size is blowing up (i.e. the term
   is growing more than [max_growth]).
*)

type cont =
| Kapp of lsymbol * Ty.ty option
| Kif of term * term * substitution
| Klet of vsymbol * term * substitution
| Kcase of term_branch list * substitution
| Keps of vsymbol
| Kquant of quant * vsymbol list * trigger
| Kbinop of binop
| Knot
| Keval of term * substitution

type config = {
  config_value_stack : value list;
  config_cont_stack : (cont * term * int) list;
  (* second term is the original term, for attribute and loc copy *)
}

let cont_stack_size (c:(cont * term * int) list) : int =
  match c with
  | [] -> 0
  | (_, _, n)::_ -> n

let subst_size sigma =
  Mvs.fold (fun _ t acc -> acc + Term.term_size t) sigma 0

let cont_size (c:cont) : int =
  match c with
  | Kapp _ -> 1
  | Kif(t2,t3,s) ->
      let n2 = Term.term_size t2 in
      let n3 = Term.term_size t3 in
      let s = subst_size s in
      1+n2+n3+s
  | Klet(_,t,s) ->
      let n = Term.term_size t in
      let s = subst_size s in
      1+n+s
  | Kcase(tbl,s) ->
      let s = subst_size s in
      List.fold_left (fun acc tb ->
          let _,t = Term.t_open_branch tb in
          let n = Term.term_size t in acc+n)
        (1+s) tbl
  | Keps _ -> 1
  | Kquant _ -> 1
  | Kbinop _ -> 1
  | Knot -> 1
  | Keval(t,s) ->
      let n = Term.term_size t in
      let s = subst_size s in
      1+n+s

let rec cont_stack_size_invariant (c:(cont * term * int) list) : bool =
  match c with
  | [] -> true
  | (c,_t,n) :: rem ->
      cont_stack_size_invariant rem &&
      let srem = cont_stack_size rem in
      n = cont_size c + srem



let mk_config s c =
  if Debug.test_flag debug_cont_size then
    assert (cont_stack_size_invariant c);
  { config_value_stack = s; config_cont_stack = c }


(* This global variable is used to approximate a count of the elementary
   simplifications that are done during normalization. This is used for
   transformation step. *)
let rec_step_limit = ref 0

exception NoMatch of (term * term * term option) option
exception NoMatchpat of (pattern * pattern) option

let rec pattern_renaming (bound_vars, mt) p1 p2 =
  match p1.pat_node, p2.pat_node with
  | Pwild, Pwild ->
      (bound_vars, mt)
  | Pvar v1, Pvar v2 ->
      begin
        try
          let mt = Ty.ty_match mt v1.vs_ty v2.vs_ty in
          let bound_vars = Mvs.add v2 v1 bound_vars in
          (bound_vars, mt)
        with
        | Ty.TypeMismatch _ ->
          raise (NoMatchpat (Some (p1, p2)))
      end
  | Papp (ls1, tl1), Papp (ls2, tl2) when ls_equal ls1 ls2 ->
      List.fold_left2 pattern_renaming (bound_vars, mt) tl1 tl2
  | Por (p1a, p1b), Por (p2a, p2b) ->
      let (bound_vars, mt) =
        pattern_renaming (bound_vars, mt) p1a p2a in
      pattern_renaming (bound_vars, mt) p1b p2b
  | Pas (p1, v1), Pas (p2, v2) ->
      begin
        try
          let mt = Ty.ty_match mt v1.vs_ty v2.vs_ty in
          let bound_vars = Mvs.add v2 v1 bound_vars in
          pattern_renaming (bound_vars, mt) p1 p2
        with
        | Ty.TypeMismatch _ ->
          raise (NoMatchpat (Some (p1, p2)))
      end
  | _ -> raise (NoMatchpat (Some (p1, p2)))

let first_order_matching (vars : Svs.t) (largs : term list)
    (args : term list) : Ty.ty Ty.Mtv.t * substitution =
  let rec loop bound_vars ((mt,mv) as sigma) largs args =
    match largs,args with
      | [],[] -> sigma
      | t1::r1, t2::r2 ->
        begin
(*
          Format.eprintf "matching terms %a and %a...@."
            Pretty.print_term t1 Pretty.print_term t2;
*)
          match t1.t_node with
            | Tvar vs when Svs.mem vs vars ->
              begin
                try let t = Mvs.find vs mv in
                    if t_equal t t2 then
                      loop bound_vars sigma r1 r2
                    else
                      raise (NoMatch (Some (t1, t2, Some t)))
                with Not_found ->
                  try
                    let ts = Ty.ty_match mt vs.vs_ty (t_type t2) in
                    let fv2 = t_vars t2 in
                    if Mvs.is_empty (Mvs.set_inter bound_vars fv2) then
                      loop bound_vars (ts,Mvs.add vs t2 mv) r1 r2
                    else
                      raise (NoMatch (Some (t1, t2, None)))
                  with Ty.TypeMismatch _ ->
                    raise (NoMatch (Some (t1, t2, None)))
              end
            | Tapp(ls1,args1) ->
              begin
                match t2.t_node with
                  | Tapp(ls2,args2) when ls_equal ls1 ls2 ->
                    let mt, mv = loop bound_vars sigma
                        (List.rev_append args1 r1)
                        (List.rev_append args2 r2) in
                    begin
                      try Ty.oty_match mt t1.t_ty t2.t_ty, mv
                      with Ty.TypeMismatch _ ->
                        raise (NoMatch (Some (t1, t2, None)))
                    end
                  | _ -> raise (NoMatch (Some (t1, t2, None)))
              end
            | Tquant (q1, bv1) ->
              begin
                match t2.t_node with
                | Tquant (q2, bv2) when q1 = q2 ->
                  let (vl1, _tl1, term1) = t_open_quant bv1 in
                  let (vl2, _tl2, term2) = t_open_quant bv2 in
                  let (bound_vars, term1, mt) =
                    try List.fold_left2 (fun (bound_vars, term1, mt) e1 e2 ->
                      let mt = Ty.ty_match mt e1.vs_ty e2.vs_ty in
                      let bound_vars = Mvs.add e2 e1 bound_vars in
                      (bound_vars,term1, mt)) (bound_vars,term1, mt) vl1 vl2
                    with Invalid_argument _ | Ty.TypeMismatch _ ->
                      raise (NoMatch (Some (t1,t2,None)))
                  in
                  loop bound_vars (mt, mv) (term1 :: r1) (term2 :: r2)
                | _ -> raise (NoMatch (Some (t1, t2, None)))
              end
            | Tbinop (b1, t1_l, t1_r) ->
              begin
                match t2.t_node with
                | Tbinop (b2, t2_l, t2_r) when b1 = b2 ->
                  loop bound_vars (mt, mv) (t1_l :: t1_r :: r1) (t2_l :: t2_r :: r2)
                | _ -> raise (NoMatch (Some (t1, t2, None)))
              end
            | Tif (t11, t12, t13) ->
              begin
                match t2.t_node with
                | Tif (t21, t22, t23) ->
                  loop bound_vars (mt, mv) (t11 :: t12 :: t13 :: r1)
                      (t21 :: t22 :: t23 :: r2)
                | _ -> raise (NoMatch (Some (t1, t2, None)))
              end
            | Tlet (td1, tb1) ->
              begin
                match t2.t_node with
                | Tlet (td2, tb2) ->
                  let (v1, tl1) = t_open_bound tb1 in
                  let (v2, tl2) = t_open_bound tb2 in
                  let mt = try Ty.ty_match mt v1.vs_ty v2.vs_ty
                    with Ty.TypeMismatch _ ->
                      raise (NoMatch (Some (t1,t2, None))) in
                  let bound_vars = Mvs.add v2 v1 bound_vars in
                  loop bound_vars (mt, mv) (td1 :: tl1 :: r1) (td2 :: tl2 :: r2)
                | _ ->
                  raise (NoMatch (Some (t1, t2, None)))
              end
            | Tcase (ts1, tbl1) ->
              begin
                match t2.t_node with
                | Tcase (ts2, tbl2) ->
                    begin try
                      let (bound_vars, mt, l1, l2) =
                        List.fold_left2 (fun (bound_vars, mt, l1, l2) tb1 tb2 ->
                          let (p1, tb1) = t_open_branch tb1 in
                          let (p2, tb2) = t_open_branch tb2 in
                          let bound_vars, mt = pattern_renaming (bound_vars, mt) p1 p2 in
                          (bound_vars,mt, tb1 :: l1, tb2 :: l2)
                        ) (bound_vars,mt, ts1 :: r1, ts2 :: r2) tbl1 tbl2 in
                      loop bound_vars (mt,mv) l1 l2
                    with Invalid_argument _ ->
                      raise (NoMatch (Some (t1, t2, None)))
                    end
                | _ -> raise (NoMatch (Some (t1, t2, None)))
              end
            | Teps tb1 ->
              begin
                match t2.t_node with
                | Teps tb2 ->
                  let (v1, td1) = t_open_bound tb1 in
                  let (v2, td2) = t_open_bound tb2 in
                  let mt = try Ty.ty_match mt v1.vs_ty v2.vs_ty
                    with Ty.TypeMismatch _ ->
                      raise (NoMatch (Some (t1,t2,None))) in
                  let bound_vars = Mvs.add v2 v1 bound_vars in
                  loop bound_vars (mt, mv) (td1 :: r1) (td2 :: r2)
                | _ -> raise (NoMatch (Some (t1, t2, None)))
              end

            | Tnot t1 ->
              begin
                match t2.t_node with
                | Tnot t2 ->
                  loop bound_vars sigma (t1 :: r1) (t2 :: r2)
                | _ -> raise (NoMatch (Some (t1, t2, None)))
              end
            | Tvar v1 ->
                begin match t2.t_node with
                | Tvar v2 ->
                    begin try
                      if vs_equal v1 (Mvs.find v2 bound_vars) then
                        loop bound_vars sigma r1 r2
                      else
                        raise (NoMatch (Some (t1, t2, None)))
                    with
                      Not_found -> assert false
                    end
                | _ -> raise (NoMatch (Some (t1, t2, None)))
                end
            | (Tconst _ | Ttrue | Tfalse) when t_equal t1 t2 ->
                loop bound_vars sigma r1 r2
            | Tconst _ | Ttrue | Tfalse -> raise (NoMatch (Some (t1, t2, None)))
        end
      | _ -> raise (NoMatch None)
  in
  loop Mvs.empty (Ty.Mtv.empty, Mvs.empty) largs args

exception Irreducible

let one_step_reduce engine ls args =
  try
    let rules = Mls.find ls engine.rules in
    let rec loop rules =
      match rules with
        | [] -> raise Irreducible
        | (vars,largs,rhs)::rem ->
          begin
            try
              let sigma = first_order_matching vars largs args in
              sigma,rhs
            with NoMatch _ ->
              loop rem
          end
    in loop rules
  with Not_found ->
    raise Irreducible

let rec matching ((mt,mv) as sigma) t p =
  match p.pat_node with
  | Pwild -> sigma
  | Pvar v -> (mt,Mvs.add v t mv)
  | Por(p1,p2) ->
    begin
      try matching sigma t p1
      with NoMatch _ -> matching sigma t p2
    end
  | Pas(p,v) -> matching (mt,Mvs.add v t mv) t p
  | Papp(ls1,pl) ->
    match t.t_node with
      | Tapp(ls2,tl) ->
        if ls_equal ls1 ls2 then
          List.fold_left2 matching sigma tl pl
        else
          if ls2.ls_constr > 0 then raise (NoMatch None)
          else raise Undetermined
      | _ -> raise Undetermined


let rec extract_first n acc l =
  if n = 0 then acc,l else
    match l with
    | x :: r ->
      extract_first (n-1) (x::acc) r
    | [] -> assert false

(** If [t1] matches [i1 < vs] or [i1 <= vs] and [t2] matches [vs < i2] or
    [vs <= i2], then return the bounds [i1(+1), vs, i2(-1)]. The +1/-1 shift the
    bounds for strict unequalities operators to obtain inclusive bounds. *)
let bounds ls_lt t1 t2 =
  let lt order = function (* match [i < vs] or [vs < i], return [i, vs] *)
    | {t_node= Tapp (ls, [t1; t2])} when ls_equal ls ls_lt -> (
        assert Ty.(ty_equal (t_type t1) ty_int && ty_equal (t_type t2) ty_int);
        match order t1 t2 with
        | {t_node= Tconst (Constant.ConstInt {Number.il_int= i})},
          {t_node= Tvar vs} ->
            i, vs
        | _ -> raise Exit )
    | _ -> raise Exit in
  let eq order = function (* match [i = vs] or [vs = i], return [i, vs] *)
    | {t_node= Tapp (ls, [t1; t2])}
      when ls_equal ls Term.ps_equ
        && Ty.ty_equal (t_type t1) Ty.ty_int
        && Ty.ty_equal (t_type t2) Ty.ty_int -> (
        match order t1 t2 with
        | {t_node= Tconst (Constant.ConstInt {Number.il_int= i})},
          {t_node= Tvar vs} when Ty.ty_equal vs.vs_ty Ty.ty_int ->
            i, vs
        | _ -> raise Exit )
    | _ -> raise Exit in
  let le order = function (* match [i <= vs] or [vs <= i], return [i, vs] *)
    | {t_node= Tbinop (Tor, t1, t2)} ->
        let i, vs = lt order t1 in
        let i', vs' = eq order t2 in
        if not (BigInt.eq i i' && vs_equal vs vs') then raise Exit;
        i, vs
    | _ -> raise Exit in
  let bound order shift t = (* match [i op vs] or [vs op i], op is [<] or [<=] *)
    try le order t with Exit ->
      let i, vs = lt order t in
      shift i, vs in
  let i1, vs  = bound (fun t1 t2 -> t1, t2) BigInt.succ t1 in
  let i2, vs' = bound (fun t1 t2 -> t2, t1) BigInt.pred t2 in
  if not (vs_equal vs vs') then raise Exit;
  i1, vs, i2

(** [reduce_bounded_quant ls_lt limit t sigma st rem] detects a bounded
    quantification and reduces it to conjunction:

          forall v. a < v < b. t(v)
      --> f(a+1) /\ ... /\ f(b-1)

    @param ls_lt lsymbol for [int.Int.(<)]

    @param limit Reduce  if the difference between upper and lower bound is at
    most [limit].

    TODO:
    - expand to bounded quantifications on range values
    - compatiblity with reverse direction (forall i. b > i > a -> t)
    - detect SPARK-style [forall i. if a < i /\ i < b then t else true] *)
let reduce_bounded_quant ls_lt limit t nt sigma st rem =
  match st, rem with (* st = a < vs < b :: _; rem = -> :: forall vs :: _ *)
  | Term {t_node= Tbinop (Tand, t1, t2)} :: st,
    ((Kbinop Timplies, _, _) :: (Kquant (Tforall as quant, [vs], _), _orig, n) :: rem |
     (Kbinop Tand, _, _)     :: (Kquant (Texists as quant, [vs], _), _orig, n) :: rem)
    when Ty.ty_equal vs.vs_ty Ty.ty_int ->
      let t_empty, binop = match quant with
        | Tforall -> t_true, Tand
        | Texists -> t_false, Tor in
      let a, vs', b = bounds ls_lt t1 t2 in
      if not (vs_equal vs vs') then raise Exit;
      if BigInt.(gt (sub b a) (of_int limit)) then raise Exit;
      if BigInt.gt a b then (* empty range *)
        let c = mk_config (Term t_empty :: st) rem in c
      else
        let rec loop rem i =
          if BigInt.lt i a then
            rem
          else
            let t_i = t_const (Constant.int_const i) Ty.ty_int in
            let rem = (* conjunction for all i > a *)
              if BigInt.gt i a then
                let n1 = n + nt + 1 in
                let n2 = n1 + 1  in
                (Keval (t, Mvs.add vs t_i sigma), t_true, n2) ::
                  (Kbinop binop, t_true, n1) :: rem
              else
                let n' = n + nt + 1 in
                (Keval (t, Mvs.add vs t_i sigma), t_true, n') :: rem
            in
            loop rem (BigInt.pred i) in
        let r = loop rem b in
        let c = mk_config st r in c
  | _ -> raise Exit


let rec reduce engine c =
  match c.config_value_stack, c.config_cont_stack with
  | _, [] -> assert false
  | st, (Keval (t,sigma),orig,_) :: rem -> (
      let limit = engine.params.compute_max_quantifier_domain in
      let nt = Term.term_size t in
      try reduce_bounded_quant engine.ls_lt limit t nt sigma st rem with Exit ->
        reduce_eval engine st t ~orig sigma rem)
  | [], (Kif _, _, _) :: _ -> assert false
  | v :: st, (Kif(t2,t3,sigma), orig, n) :: rem ->
    begin
      match v with
      | Term { t_node = Ttrue } ->
        incr(rec_step_limit);
        let n' = n - Term.term_size t3 in
        let c = mk_config st ((Keval(t2,sigma),t_attr_copy orig t2, n')  :: rem) in
        c
      | Term { t_node = Tfalse } ->
        incr(rec_step_limit);
        let n' = n - Term.term_size t2 in
        let c = mk_config st ((Keval(t3,sigma),t_attr_copy orig t3, n') :: rem) in
        c
      | Term t1 -> begin
          match t1.t_node , t2.t_node , t3.t_node with
          | Tapp (ls,[b0;{ t_node = Tapp (ls1,_) }]) , Tapp(ls2,_) , Tapp(ls3,_)
            when ls_equal ls ps_equ && ls_equal ls1 fs_bool_true &&
              ls_equal ls2 fs_bool_true && ls_equal ls3 fs_bool_false ->
            incr(rec_step_limit);
            let c = mk_config (Term (t_attr_copy orig b0) :: st) rem in
            c
          | _ ->
              let c =
                mk_config
                  (Term
                     (t_attr_copy orig
                        (t_if t1 (t_subst sigma t2) (t_subst sigma t3))) :: st)
                  rem
              in c
        end
      | (Int _ | Real _) -> assert false (* would be ill-typed *)
    end
  | [], (Klet _, _, _) :: _ -> assert false
  | t1 :: st, (Klet(v,t2,sigma), orig, n) :: rem ->
      incr(rec_step_limit);
    let t1 = term_of_value t1 in
    (* we know that n = cont_size rem + 1 + term_size t2 + subst_size sigma
       we need to add the size of t1 in sigma
    *)
    let n = n + Term.term_size t1 in
    let c =
      mk_config st ((Keval(t2, Mvs.add v t1 sigma), t_attr_copy orig t2, n) :: rem)
    in c
  | [], (Kcase _, _, _) :: _ -> assert false
  | (Int _ | Real _) :: _, (Kcase _, _, _) :: _ -> assert false
  | (Term t1) :: st, (Kcase(tbl,sigma), orig, _) :: rem ->
    reduce_match st t1 ~orig tbl sigma rem
  | ([] | [_] | (Int _ | Real _) :: _ | Term _ :: (Int _ | Real _) :: _),
    (Kbinop _, _, _) :: _ -> assert false
  | (Term t1) :: (Term t2) :: st, (Kbinop op, orig, _) :: rem ->
    incr(rec_step_limit);
    let c=
      mk_config (Term (t_attr_copy orig (t_binary_simp op t2 t1)) :: st) rem
    in c
  | [], (Knot,_,_) :: _ -> assert false
  | (Int _ | Real _) :: _ , (Knot,_,_) :: _ -> assert false
  | (Term t) :: st, (Knot, orig, _) :: rem ->
    incr(rec_step_limit);
    let c=
      mk_config (Term (t_attr_copy orig (t_not_simp t)) :: st) rem
    in c
  | st, (Kapp(ls,ty), orig, _) :: rem ->
    reduce_app engine st ~orig ls ty rem
  | [], (Keps _, _, _) :: _ -> assert false
  | (Int _ | Real _) :: _ , (Keps _, _, _) :: _ -> assert false
  | Term t :: st, (Keps v, orig, _) :: rem ->
      let c=
        mk_config (Term (t_attr_copy orig (t_eps_close v t)) :: st) rem
      in c
  | [], (Kquant _, _, _) :: _ -> assert false
  | (Int _ | Real _) :: _, (Kquant _, _, _) :: _ -> assert false
  | Term t :: st, (Kquant(q,vl,tr), orig, _) :: rem ->
      let c=
        mk_config (Term (t_attr_copy orig (t_quant_close_simp q vl tr t)) :: st) rem
      in c

and reduce_match st u ~orig tbl sigma cont =
  let rec iter tbl =
    match tbl with
    | [] -> assert false (* pattern matching not exhaustive *)
    | b::rem ->
      let p,t = t_open_branch b in
      try
        let (mt',mv') = matching (Ty.Mtv.empty,sigma) u p in
(*
        Format.eprintf "Pattern-matching succeeded:@\nmt' = @[";
        Ty.Mtv.iter
          (fun tv ty -> Format.eprintf "%a -> %a,"
            Pretty.print_tv tv Pretty.print_ty ty)
          mt';
        Format.eprintf "@]@\n";
        Format.eprintf "mv' = @[";
        Mvs.iter
          (fun v t -> Format.eprintf "%a -> %a,"
            Pretty.print_vs v Pretty.print_term t)
          mv';
        Format.eprintf "@]@.";
        Format.eprintf "branch before inst: %a@." Pretty.print_term t;
*)
        let mv'',t = t_subst_types mt' mv' t in
(*
        Format.eprintf "branch after types inst: %a@." Pretty.print_term t;
        Format.eprintf "mv'' = @[";
        Mvs.iter
          (fun v t -> Format.eprintf "%a -> %a,"
            Pretty.print_vs v Pretty.print_term t)
          mv'';
        Format.eprintf "@]@.";
*)
        incr(rec_step_limit);
        let n_t = Term.term_size t in
        let n_mv = subst_size mv'' in
        let n' = cont_stack_size cont + n_t + 1 + n_mv in
        let c =
          mk_config st ((Keval(t,mv''), t_attr_copy orig t, n') :: cont)
        in c
      with NoMatch _ -> iter rem
  in
  try iter tbl with Undetermined ->
    let dmy = t_var (create_vsymbol (Ident.id_fresh "__dmy") (t_type u)) in
    let tbls =
      match t_subst sigma (t_case dmy tbl) with
      | { t_node = Tcase (_,tbls) } -> tbls
      | _ -> assert false
    in
    let c =
      mk_config (Term (t_attr_copy orig (t_case u tbls)) :: st) cont
    in c

and reduce_eval eng st t ~orig sigma rem =
  let orig = t_attr_copy orig t in
  let n_rem = cont_stack_size rem in
  match t.t_node with
  | Tvar v ->
    begin
      match Ident.Mid.find v.vs_name eng.known_map with
      | Decl.{d_node = Dlogic dl} ->
        incr rec_step_limit ;
        let _, ls_defn = List.find (fun (ls, _) -> String.equal ls.ls_name.Ident.id_string v.vs_name.Ident.id_string) dl in
        let vs, t = Decl.open_ls_defn ls_defn in
        let aux vs t =
          (* Create ε fc. λ vs. fc @ vs = t to make the value from
             known_map compatible to reduce_func_app *)
          let ty = Opt.get t.t_ty in
          let app_ty = Ty.ty_func vs.vs_ty ty in
          let fc = create_vsymbol (Ident.id_fresh "fc") app_ty in
          t_eps
            (t_close_bound fc
               (t_quant Tforall
                  (t_close_quant [vs] []
                     (t_app ps_equ
                        [t_app fs_func_app [t_var fc; t_var vs] (Some ty); t]
                        None)))) in
        let t = List.fold_right aux vs t in
        let c =
          mk_config (Term t :: st) rem
        in c
      | _ -> assert false
      | exception Not_found ->
        match Mvs.find v sigma with
        | t ->
          incr(rec_step_limit);
          let c =
            mk_config (Term (t_attr_copy orig t) :: st) rem
          in c
        | exception Not_found ->
          (* this may happen, e.g when computing below a quantified formula *)
          (* Format.eprintf "Tvar not found: %a@." Pretty.print_vs v;
              assert false *)
            let c =
              mk_config (Term orig :: st) rem
            in c
    end
  | Tif(t1,t2,t3) ->
    let n1 = Term.term_size t1 in
    let n2 = Term.term_size t2 in
    let n3 = Term.term_size t3 in
    let n_sigma = subst_size sigma in
    let n_if = n_rem + n2 + n3 + 1 + n_sigma in
    let n_eval = n_if + n1 + 1 + n_sigma in
    let c =
      mk_config st ((Keval(t1,sigma),t1,n_eval) ::
                    (Kif(t2,t3,sigma),orig,n_if) :: rem)
    in c
  | Tlet(t1,tb) ->
    let v,t2 = t_open_bound tb in
    let n1 = Term.term_size t1 in
    let n2 = Term.term_size t2 in
    let n_sigma = subst_size sigma in
    let n_let = n_rem + n2 + 1 + n_sigma in
    let n_eval = n_let + n1 + 1 + n_sigma in
    let c = mk_config st ((Keval(t1,sigma),t1,n_eval) ::
                          (Klet(v,t2,sigma),orig,n_let) :: rem)
    in c
  | Tcase(t1,tbl) ->
    let n1 = Term.term_size t1 in
    let ntbl =
      List.fold_left (fun acc tb -> acc + Term.term_branch_size tb) 0 tbl
    in
    let n_sigma = subst_size sigma in
    let n_case = n_rem + ntbl + 1 + n_sigma in
    let n_eval = n_case + n1 + 1 + n_sigma in
    let c =
      mk_config st ((Keval(t1,sigma),t1,n_eval) ::
                    (Kcase(tbl,sigma),orig,n_case) :: rem)
    in c
  | Tbinop(op,t1,t2) ->
    let n1 = Term.term_size t1 in
    let n2 = Term.term_size t2 in
    let n_sigma = subst_size sigma in
    let n_binop = n_rem + 1 in
    let n_eval2 = n_binop + n2 + 1 + n_sigma in
    let n_eval1 = n_eval2 + n1 + 1 + n_sigma in
    let c = mk_config st ((Keval(t1,sigma),t1,n_eval1) ::
                  (Keval(t2,sigma),t2,n_eval2) ::
                          (Kbinop op, orig, n_binop) :: rem)
    in c
  | Tnot t1 ->
    let n1 = Term.term_size t1 in
    let n_sigma = subst_size sigma in
    let n_not = n_rem + 1 in
    let n_eval = n_not + n1 + 1 + n_sigma in
    let c = mk_config st ((Keval(t1,sigma),t1,n_eval) ::
                          (Knot,orig,n_not) :: rem)
        in c
  | Teps tb ->
    let v,t1 = t_open_bound tb in
    let n1 = Term.term_size t1 in
    let n_sigma = subst_size sigma in
    let n_eps = n_rem + 1 in
    let n_eval = n_eps + n1 + 1 + n_sigma in
    let c = mk_config st ((Keval(t1,sigma),t1,n_eval) ::
                          (Keps v,orig,n_eps) :: rem)
    in c
  | Tquant(q,tq) ->
    let vl,tr,t1 = t_open_quant tq in
    let n1 = Term.term_size t1 in
    let n_quant = n_rem + 1 in
    let n_sigma = subst_size sigma in
    let n_eval = n_quant + n1 + 1 + n_sigma in
    let c =
      mk_config st ((Keval(t1,sigma),t1,n_eval) ::
                    (Kquant(q,vl,tr),orig,n_quant) :: rem)
    in c
  | Tapp(ls,tl) ->
    let n_app = cont_stack_size rem + 1 in
    let nsigma = subst_size sigma in
    let ct = (Kapp(ls,t.t_ty),orig,n_app) :: rem in
    let _,args =
      List.fold_left
        (fun (n,acc) t ->
           let nt = Term.term_size t in
           let n = n + nt + 1 + nsigma in
           (n,(Keval(t,sigma),t,n)::acc))
        (n_app,ct)
        (List.rev tl)
    in
    let c =
      mk_config st args
    in c
  | Ttrue | Tfalse | Tconst _ ->
      let c =
        mk_config (Term orig :: st) rem
      in c

and reduce_app engine st ls ~orig ty rem_cont =
  if ls_equal ls ps_equ then
    match st with
    | t2 :: t1 :: rem_st ->
      begin
        try
          if Debug.test_flag debug_cont_size then
            assert (cont_stack_size_invariant rem_cont);
          reduce_equ ~orig rem_st t1 t2 rem_cont
        with Undetermined ->
          reduce_app_no_equ engine st ls ~orig ty rem_cont
      end
    | _ -> assert false
  else
    if ls_equal ls fs_func_app then
      match st with
      | t2 :: t1 :: rem_st ->
        begin
          try
            reduce_func_app ~orig ty rem_st t1 t2 rem_cont
          with Undetermined ->
            reduce_app_no_equ engine st ls ~orig ty rem_cont
        end
      | _ ->  assert false
    else
      reduce_app_no_equ engine st ls ~orig ty rem_cont

and reduce_func_app ~orig _ty rem_st t1 t2 rem_cont =
    (* attempt to decompile t1 under the form
       (epsilon fc. forall x. fc @ x = body)
       that is equivalent to \x.body *)
    match t1 with
    | Term { t_node = Teps tb } ->
      let fc,t = Term.t_open_bound tb in
      begin match t.t_node with
      | Tquant(Tforall,tq) ->
        let vl,trig,t = t_open_quant tq in
        let process lhs body equ elim =
          let rvl = List.rev vl in
          let rec remove_var lhs rvh rvt = match lhs.t_node with
            | Tapp (ls2,[lhs1;{t_node = Tvar v1} as arg])
              when ls_equal ls2 fs_func_app && vs_equal v1 rvh ->
              begin
              match rvt , lhs1 with
              | rvh::rvt , _ ->
                let lhs1 , fc2 = remove_var lhs1 rvh rvt in
                let lhs2 = t_app ls2 [lhs1;arg] lhs.t_ty in
                t_attr_copy lhs lhs2 , fc2
              | [] , { t_node = Tvar fc1 } when vs_equal fc1 fc ->
                let fcn = fc.vs_name in
                let fc2 = Ident.id_derive fcn.Ident.id_string fcn in
                let fc2 = create_vsymbol fc2 (t_type lhs) in
                t_attr_copy lhs (t_var fc2) , fc2
              | _ -> raise Undetermined
              end
            | _ -> raise Undetermined
          in
          begin
          match rvl with
          | rvh :: rvt -> let lhs , fc2 = remove_var lhs rvh rvt in
            let (vh,vl) = match vl with
            | [] -> assert false
            | vh::vl -> (vh,vl)
            in
            let t2 = term_of_value t2 in
            begin
            match vl with
            | [] -> elim body vh t2
            | _ ->
              let eq = equ lhs body in
              let tq = t_quant Tforall (t_close_quant vl trig eq) in
              let body = t_attr_copy t (t_eps_close fc2 tq) in
              let n_body = Term.term_size body in
              let n2 = Term.term_size t2 in
              let n = n_body + 1 + n2 + cont_stack_size rem_cont in
              let c =
                mk_config rem_st ((Keval(body,Mvs.add vh t2 Mvs.empty),
                                   t_attr_copy orig body,n) :: rem_cont)
              in c
            end
          | _ -> raise Undetermined
          end
        in
        begin
        match t.t_node with
          | Tapp (ls1,[lhs;body]) when ls_equal ls1 ps_equ ->
            let equ lhs body = t_attr_copy t (t_app ps_equ [lhs;body] None) in
            let elim body vh t2 =
              let n_body = Term.term_size body in
              let n2 = Term.term_size t2 in
              let n = n_body + 1 + n2 + cont_stack_size rem_cont in
              let c =
                mk_config rem_st ((Keval(body,Mvs.add vh t2 Mvs.empty),
                                   t_attr_copy orig body,n) :: rem_cont)
              in c
            in
            process lhs body equ elim
          | Tbinop (Tiff,
            ({t_node=Tapp (ls1,[lhs;tr])} as teq),
            body)
            when ls_equal ls1 ps_equ && t_equal tr t_bool_true ->
            let equ lhs body =
              let lhs = t_attr_copy teq (t_app ps_equ [lhs;tr] None) in
              t_attr_copy t (t_binary Tiff lhs body) in
            let elim body vh t2 =
              let body = t_if body t_bool_true t_bool_false in
              let n_body = Term.term_size body in
              let n2 = Term.term_size t2 in
              let n = n_body + 1 + n2 + cont_stack_size rem_cont in
              let c =
                mk_config rem_st ((Keval(body,Mvs.add vh t2 Mvs.empty),
                                   t_attr_copy orig body,n) :: rem_cont)
              in c
            in
            process lhs body equ elim
          | _ -> raise Undetermined
        end
      | _ -> raise Undetermined
      end
    | _ -> raise Undetermined

and reduce_app_no_equ engine st ls ~orig ty rem_cont =
  let arity = List.length ls.ls_args in
  let args,rem_st = extract_first arity [] st in
  try
    let f = Hls.find builtins ls in
    let v = f ls args ty in
    let c=
      mk_config ((v_attr_copy orig v) :: rem_st) rem_cont
    in c
  with Not_found | Undetermined ->
    let args = List.map term_of_value args in
    match Ident.Mid.find ls.ls_name engine.known_map with
    | exception Not_found ->
      Format.eprintf "Reduction engine, ident not found: %s@."
        ls.ls_name.Ident.id_string ;
      let c=
        mk_config (Term (t_attr_copy orig (t_app ls args ty)) :: rem_st) rem_cont
      in c
    | d ->
      let rewrite () =
      (* try a rewrite rule *)
        try
(*
            Format.eprintf "try a rewrite rule on %a@." Pretty.print_ls ls;
*)
          let (mt,mv),rhs = one_step_reduce engine ls args in
(*
            Format.eprintf "rhs = %a@." Pretty.print_term rhs;
            Format.eprintf "sigma = ";
            Mvs.iter
              (fun v t -> Format.eprintf "%a -> %a,"
                Pretty.print_vs v Pretty.print_term t)
              (snd sigma);
            Format.eprintf "@.";
            Format.eprintf "try a type match: %a and %a@."
              (Pp.print_option Pretty.print_ty) ty
              (Pp.print_option Pretty.print_ty) rhs.t_ty;
*)
(*
            let type_subst = Ty.oty_match Ty.Mtv.empty rhs.t_ty ty in
            Format.eprintf "subst of rhs: ";
            Ty.Mtv.iter
              (fun tv ty -> Format.eprintf "%a -> %a,"
                Pretty.print_tv tv Pretty.print_ty ty)
              type_subst;
            Format.eprintf "@.";
            let rhs = t_ty_subst type_subst Mvs.empty rhs in
            let sigma =
              Mvs.map (t_ty_subst type_subst Mvs.empty) sigma
            in
            Format.eprintf "rhs = %a@." Pretty.print_term rhs;
            Format.eprintf "sigma = ";
            Mvs.iter
              (fun v t -> Format.eprintf "%a -> %a,"
                Pretty.print_vs v Pretty.print_term t)
              sigma;
            Format.eprintf "@.";
*)
          let mv,rhs = t_subst_types mt mv rhs in
          let n_rhs = Term.term_size rhs in
          let n_mv = subst_size mv in
          let n = Term.term_size orig + n_rhs + n_mv + 1 + cont_stack_size rem_cont in
          incr(rec_step_limit);
          let c=
            mk_config rem_st ((Keval(rhs,mv),orig,n) :: rem_cont)
          in c
        with Irreducible ->
          let c=
            mk_config (Term (t_attr_copy orig (t_app ls args ty)) :: rem_st) rem_cont
          in c
      in
      match d.Decl.d_node with
      | Decl.Dtype _ | Decl.Dprop _ -> assert false
      | Decl.Dlogic dl ->
        (* regular definition *)
        let d = List.assq ls dl in
        if engine.params.compute_defs ||
           Term.Sls.mem ls engine.params.compute_def_set
        then begin
          let vl,e = Decl.open_ls_defn d in
          let add (mt,mv) x y =
            Ty.ty_match mt x.vs_ty (t_type y), Mvs.add x y mv
          in
          let (mt,mv) = List.fold_left2 add (Ty.Mtv.empty, Mvs.empty) vl args in
          let mt = Ty.oty_match mt e.t_ty ty in
          let mv,e = t_subst_types mt mv e in
          let n_e = Term.term_size e in
          let n_mv = subst_size mv in
          let n = n_e + 1 + n_mv + cont_stack_size rem_cont in
          let c=
            mk_config rem_st ((Keval(e,mv),orig,n) :: rem_cont)
          in c
        end else rewrite ()
      | Decl.Dparam _ | Decl.Dind _ ->
        rewrite ()
      | Decl.Ddata dl ->
        (* constructor or projection *)
        begin try match args with
        | [ { t_node = Tapp(ls1,tl1) } ] ->
          (* if ls is a projection and ls1 is a constructor,
             we should compute that projection *)
          let rec iter dl =
            match dl with
            | [] -> raise Exit
            | (_,csl) :: rem ->
              let rec iter2 csl =
                match csl with
                | [] -> iter rem
                | (cs,prs) :: rem2 ->
                  if ls_equal cs ls1
                  then
                    (* we found the right constructor *)
                    let rec iter3 prs tl1 =
                      match prs,tl1 with
                      | (Some pr)::prs, t::tl1 ->
                        if ls_equal ls pr
                        then (* projection found! *)
                          let c=
                            mk_config ((Term (t_attr_copy orig t)) :: rem_st) rem_cont
                          in c
                        else
                          iter3 prs tl1
                      | None::prs, _::tl1 ->
                        iter3 prs tl1
                      | _ -> raise Exit
                    in iter3 prs tl1
                  else iter2 rem2
              in iter2 csl
          in iter dl
        | _ -> raise Exit
        with Exit -> rewrite () end


and reduce_equ (* engine *) ~orig st v1 v2 cont =
(*
  try
*)
    match v1,v2 with
    | Int n1, Int n2 ->
      let b = to_bool (BigInt.eq n1 n2) in
      incr(rec_step_limit);
      let c =
        mk_config (Term (t_attr_copy orig b) :: st) cont
      in c
    | Real r1, Real r2 ->
      let b = to_bool (Number.compare_real r1 r2 = 0) in
      incr rec_step_limit;
      let c =
        mk_config (Term (t_attr_copy orig b) :: st) cont
      in c
    | Int n, Term {t_node = Tconst c} | Term {t_node = Tconst c}, Int n ->
      begin
        try
          let n' = big_int_of_const c in
          let b = to_bool (BigInt.eq n n') in
          incr(rec_step_limit);
          let c =
            mk_config (Term (t_attr_copy orig b) :: st) cont
          in c
        with NotNum -> raise Undetermined
      end
    | Real r, Term {t_node = Tconst c} | Term {t_node = Tconst c}, Real r ->
      begin
        try
          let r' = real_of_const c in
          let b = to_bool (Number.compare_real r r' = 0) in
          incr rec_step_limit;
          let c =
            mk_config (Term (t_attr_copy orig b) :: st) cont
          in c
        with NotNum -> raise Undetermined
      end
    | Real _, Term _ | Term _, Real _ -> raise Undetermined
    | Int _,  Term _ | Term _,  Int _ -> raise Undetermined
    | Int _, Real _ | Real _, Int _ -> assert false
    | Term t1, Term t2 -> reduce_term_equ ~orig st t1 t2 cont
(*
  with Undetermined ->
    let c =
      mk_config (Term (t_equ (term_of_value v1) (term_of_value v2)) :: st)
                 cont
    in
    c
*)

and reduce_term_equ ~orig st t1 t2 cont =
  if t_equal t1 t2 then
    let () = incr(rec_step_limit) in
    let c =
      mk_config (Term (t_attr_copy orig t_true) :: st) cont
    in c
  else
  match (t1.t_node,t2.t_node) with
  | Tconst c1, Tconst c2 ->
    begin
      match c1,c2 with
      | Constant.ConstInt i1, Constant.ConstInt i2 ->
        let b =
          BigInt.eq i1.Number.il_int i2.Number.il_int
        in
        incr(rec_step_limit);
        let c=
          mk_config (Term (t_attr_copy orig (to_bool b)) :: st) cont
        in c
      | _ -> raise Undetermined
    end
  | Tapp(ls1,tl1), Tapp(ls2,tl2) when ls1.ls_constr > 0 && ls2.ls_constr > 0 ->
    if ls_equal ls1 ls2 then
      let rec aux sigma t tyl l1 l2 =
        match tyl,l1,l2 with
        | [],[],[] -> sigma,t
        | ty::tyl, t1::tl1, t2::tl2 ->
          let v1 = create_vsymbol (Ident.id_fresh "") ty in
          let v2 = create_vsymbol (Ident.id_fresh "") ty in
          aux
            (Mvs.add v1 t1 (Mvs.add v2 t2 sigma))
            (t_and_simp (t_equ (t_var v1) (t_var v2)) t)
            tyl tl1 tl2
        | _ ->  assert false
      in
      let sigma,t =
        aux Mvs.empty t_true ls1.ls_args tl1 tl2
      in
      let () = incr(rec_step_limit) in
      let n_sigma = subst_size sigma in
      let n_t = Term.term_size t in
      let n = n_t + 1 + n_sigma + cont_stack_size cont in
      let c =
        mk_config st ((Keval(t,sigma),orig,n) :: cont)
      in c
    else
      let c=
        mk_config (Term (t_attr_copy orig t_false) :: st) cont
      in c
  | Tif (b,{ t_node = Tapp(ls1,_) },{ t_node = Tapp(ls2,_) }) , Tapp(ls3,_)
    when ls_equal ls3 fs_bool_true && ls_equal ls1 fs_bool_true &&
         ls_equal ls2 fs_bool_false ->
    incr(rec_step_limit);
    let c=
      mk_config (Term (t_attr_copy orig b) :: st) cont
    in c
  | _ -> raise Undetermined



let rec reconstruct c =
  match c.config_value_stack, c.config_cont_stack with
  | [Term t], [] -> t
  | _, [] -> assert false
  | _, (k,orig,_) :: rem ->
    let t, st =
      match c.config_value_stack, k with
      | st, Keval (t,sigma) -> (t_subst sigma t), st
      | [], Kif _ -> assert false
      | v :: st, Kif(t2,t3,sigma) ->
        (t_if (term_of_value v) (t_subst sigma t2) (t_subst sigma t3)), st
      | [], Klet _ -> assert false
      | t1 :: st, Klet(v,t2,sigma) ->
        (t_let_close v (term_of_value t1) (t_subst sigma t2)), st
      | [], Kcase _ -> assert false
      | v :: st, Kcase(tbl,sigma) ->
        (t_subst sigma (t_case (term_of_value v) tbl)), st
      | ([] | [_]), Kbinop _ -> assert false
      | t1 :: t2 :: st, Kbinop op ->
        (t_binary_simp op (term_of_value t2) (term_of_value t1)), st
      | [], Knot -> assert false
      | t :: st, Knot -> (t_not (term_of_value t)), st
      | st, Kapp(ls,ty) ->
        let args,rem_st = extract_first (List.length ls.ls_args) [] st in
        let args = List.map term_of_value args in
        (t_app ls args ty), rem_st
      | [], Keps _ -> assert false
      | t :: st, Keps v -> (t_eps_close v (term_of_value t)), st
      | [], Kquant _ -> assert false
      | t :: st, Kquant(q,vl,tr) ->
        (t_quant_close_simp q vl tr (term_of_value t)), st
    in
    let c = mk_config ((Term (t_attr_copy orig t)) :: st) rem in
    reconstruct c


(** iterated reductions *)

let normalize ?(max_growth=1000) ?step_limit ~limit engine sigma t0 =
  let n0 = Term.term_size t0 in
  let cont_size_init = n0+1 in
  let c = mk_config [] [Keval(t0,sigma),t0,cont_size_init] in
  let cont_size_max = max_growth * cont_size_init in
  rec_step_limit := 0;
  let rec many_steps c n =
    match c.config_value_stack, c.config_cont_stack with
    | [Term t], [] -> t
    | _, [] -> assert false
    | _ ->
      if n = limit then
        begin
          let t1 = reconstruct c in
          Loc.warning "term reduction aborted (takes more than %d steps).@."
            limit;
          t1
        end
      else begin
        let reduce_until_size_max c n =
          let c' = reduce engine c in
          if cont_stack_size c'.config_cont_stack > cont_size_max then
            begin
              Loc.warning "term reduction aborted (term size blows up from %d to %d, after %d steps).@."
                cont_size_init (cont_stack_size c'.config_cont_stack) n;
              reconstruct c
            end
          else
            many_steps c' (n+1)
        in
        match step_limit with
        | None -> reduce_until_size_max c n
        | Some step_limit ->
            if !rec_step_limit >= step_limit then
              reconstruct c
            else reduce_until_size_max c n
      end
  in
  try
    many_steps c 0
  with exn ->
    Format.eprintf "%a@\n%s" Exn_printer.exn_printer exn
      (Printexc.get_backtrace ());
    exit 1

(* the rewrite engine *)

let create p env km =
  if p.compute_builtin
  then get_builtins env
  else Hls.clear builtins;
  let th = Env.read_theory env ["int"] "Int" in
  let ls_lt = Theory.ns_find_ls th.Theory.th_export [Ident.op_infix "<"] in
  { known_map = km ;
    rules = Mls.empty;
    params = p;
    ls_lt;
  }

exception NotARewriteRule of string

let extract_rule _km t =
(*
  let check_ls ls =
    try let _ = Hls.find builtins ls in
        raise (NotARewriteRule "root of lhs of rule must not be a built-in symbol")
    with Not_found ->
      let d = Ident.Mid.find ls.ls_name km in
      match d.Decl.d_node with
      | Decl.Dtype _ | Decl.Dprop _ -> assert false
      | Decl.Dlogic _ ->
        raise (NotARewriteRule "root of lhs of rule must not be defined symbol")
      | Decl.Ddata _ ->
        raise (NotARewriteRule "root of lhs of rule must not be a constructor nor a projection")
      | Decl.Dparam _ | Decl.Dind _ -> ()
  in
*)

  let check_vars acc t1 t2 =
    (* check that quantified variables all appear in the lefthand side
       (quantified variables not appearing could be removed and those appearing
       on right hand side cannot be guessed during rewriting). *)
    let vars_lhs = t_vars t1 in
    if Svs.exists (fun vs -> not (Mvs.mem vs vars_lhs)) acc
    then raise (NotARewriteRule "lhs should contain all variables");
    (* check the same with type variables *)
    if not
         (Ty.Stv.subset
            (t_ty_freevars Ty.Stv.empty t2) (t_ty_freevars Ty.Stv.empty t2))
    then raise (NotARewriteRule "lhs should contain all type variables")

  in
  let rec aux acc t =
    match t.t_node with
      | Tquant(Tforall,q) ->
        let vs,_,t = t_open_quant q in
        aux (List.fold_left (fun acc v -> Svs.add v acc) acc vs) t
      | Tbinop(Tiff,t1,t2) ->
        begin
          match t1.t_node with
            | Tapp(ls,args) ->
               (* check_ls ls; *)
               check_vars acc t1 t2;
               acc,ls,args,t2
            | _ -> raise
              (NotARewriteRule "lhs of <-> should be a predicate symbol")
        end
      | Tapp(ls,[t1;t2]) when ls == ps_equ ->
        begin
          match t1.t_node with
            | Tapp(ls,args) ->
               (* check_ls ls; *)
               check_vars acc t1 t2;
               acc,ls,args,t2
            | _ -> raise
              (NotARewriteRule "lhs of = should be a function symbol")
        end
      | _ -> raise
        (NotARewriteRule "rule should be of the form forall ... t1 = t2 or f1 <-> f2")
  in
  aux Svs.empty t


let add_rule t e =
  let vars,ls,args,r = extract_rule e.known_map t in
  let rules =
    try Mls.find ls e.rules
    with Not_found -> []
  in
  {e with rules =
      Mls.add ls ((vars,args,r)::rules) e.rules}
