Source file `TacNormalForm.ml`

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(**************************************************************************)
(*                                                                        *)
(*  SPDX-License-Identifier LGPL-2.1                                      *)
(*  Copyright (C)                                                         *)
(*  CEA (Commissariat à l'énergie atomique et aux énergies alternatives)  *)
(*                                                                        *)
(**************************************************************************)

open Lang
open Conditions
open Tactical

(** Useful **)

let str_case = "Case"
let sub_cases phi = function
  | []   -> List.map (fun t -> phi str_case (F.p_bool t))
  | [descr] -> List.map (fun t -> phi descr (F.p_bool t))
  | infos -> List.map2 (fun info t -> phi info (F.p_bool t)) infos

(* split into n sequents: [hyps] |- [subcases]_i *)
let f_replace_goal infos subcases (hyps,_) =
  let sub_case descr p  = descr, (hyps,p) in
  sub_cases sub_case infos subcases

(* split into n sequents: [subcases]_i, hyps/[hyp] |- goal
   in fact, [hyp] is replaced by [subcases]_i *)
let f_replace_hyp hyp infos subcases sequent =
  let sub_case descr p =
    descr, Conditions.(replace ~at:hyp.id (update_cond hyp ~descr (When p))
                         sequent)
  in sub_cases sub_case infos subcases

(* -------------------------------------------------------------------------- *)
(* --- FNC (goal) and FND (hyp) tacticals                                 --- *)
(* -------------------------------------------------------------------------- *)

let nf_conj_args e = match F.repr e with
  | Qed.Logic.And xs -> xs
  | _ -> [e]
let nf_disj_args e = match F.repr e with
  | Qed.Logic.Or xs -> xs
  | _ -> [e]

let f_nf_goal e   ~depth = f_replace_goal  ["CNF"] (nf_conj_args (WpTac.e_cnf ~depth e))
let f_nf_hyp  s e ~depth = f_replace_hyp s ["DNF"] (nf_disj_args (WpTac.e_dnf ~depth e))

let match_selection = function
  | Clause(Goal p) ->
    let e = Lang.F.e_prop p in
    if WpTac.is_cnf e then None
    else Some (true, e, f_nf_goal e)
  | Clause(Step s) ->
    begin
      match s.condition with
      | (Type p | Have p | When p | Core p | Init p) ->
        let e = Lang.F.e_prop p in
        if WpTac.is_dnf e then None
        else Some (false, e, f_nf_hyp s e)
      | _ -> None
    end
  | Inside(_,_) | Compose _ | Empty | Multi _ -> None

class normal_form =
  object
    inherit Tactical.make ~id:"Wp.normal_form"
        ~title:"Intuition"
        ~descr:"Decompose into conjunctive or disjunctive normal form."
        ~params:[]

    method select feedback (s : Tactical.selection) =
      match match_selection s with
      | Some (pol,_,continuation) ->
        feedback#set_title
          (if pol then "Intuition (CNF)" else "Intuition (DNF)") ;
        let depth = (-1) in
        Applicable (continuation ~depth)
      | _ -> Not_applicable

  end

let tactical = Tactical.export (new normal_form)
let strategy = Strategy.make tactical ~arguments:[]

(* -------------------------------------------------------------------------- *)