lift_epsilon.ml 3.11 KB
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(**************************************************************************)
(*                                                                        *)
(*  Copyright (C) 2010-                                                   *)
(*    Francois Bobot                                                      *)
(*    Jean-Christophe Filliatre                                           *)
(*    Johannes Kanig                                                      *)
(*    Andrei Paskevich                                                    *)
(*                                                                        *)
(*  This software is free software; you can redistribute it and/or        *)
(*  modify it under the terms of the GNU Library General Public           *)
(*  License version 2.1, with the special exception on linking            *)
(*  described in file LICENSE.                                            *)
(*                                                                        *)
(*  This software is distributed in the hope that it will be useful,      *)
(*  but WITHOUT ANY WARRANTY; without even the implied warranty of        *)
(*  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                  *)
(*                                                                        *)
(**************************************************************************)

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open Close_epsilon
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open Term
open Theory
open Task

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type lift_kind =
(*   | Goal (* prove the existence of a witness *) *)
  | Implied (* require the existence of a witness in an axiom *)
  | Implicit (* do not require a witness *)
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let lift kind =
  let rec term acc t =
    match t.t_node with
    | Teps fb ->
        let fv = Svs.elements (t_freevars Svs.empty t) in
        let x, f = f_open_bound fb in
        let acc, f = form acc f in
        let tys = List.map (fun x -> x.vs_ty) fv in
        let xs = Ident.id_derive "epsilon" x.vs_name in
        let xl = create_fsymbol xs tys x.vs_ty in
        let acc = add_decl acc (Decl.create_logic_decl [xl,None]) in
        let axs =
          Decl.create_prsymbol (Ident.id_derive ("epsilon_def") x.vs_name) in
        let xlapp = t_app xl (List.map (fun x -> t_var x) fv) t.t_ty in
        let f =
          match kind with
          (* assume that lambdas always exist *)
          | Implied when not (is_lambda t) ->
              f_forall_close_merge fv
                (f_implies (f_exists_close [x] [] f) (f_subst_single x xlapp f))
          | _ -> f_subst_single x xlapp f
        in
        let acc = add_decl acc (Decl.create_prop_decl Decl.Paxiom axs f) in
        acc, xlapp
    | _ -> t_map_fold term form acc t
  and form acc f = f_map_fold term form acc f in
  fun th acc ->
    let th = th.task_decl in
    match th.td_node with
    | Decl d ->
        let acc, d = Decl.decl_map_fold term form acc d in
        add_decl acc d
    | _ -> add_tdecl acc th
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let lift_epsilon = Trans.fold (lift Implicit) None
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let () = Trans.register_transform "lift_epsilon" lift_epsilon

(* TODO different variants for εx.P(x) :
  * logic x + axiom P(x)
  * goal ∃x.P(x) + logic x + axiom P(x)
  * logic x + axiom (∃x.P(x)) => P(x)
  *)