src/HOL/Tools/Sledgehammer/sledgehammer_isar_minimize.ML

eliminated "xname" and variants;

(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_isar_minimize.ML
    Author:     Steffen Juilf Smolka, TU Muenchen
    Author:     Jasmin Blanchette, TU Muenchen

Minimize dependencies (used facts) of Isar proof steps.
*)

signature SLEDGEHAMMER_ISAR_MINIMIZE =
sig
  type isar_step = Sledgehammer_Isar_Proof.isar_step
  type isar_proof = Sledgehammer_Isar_Proof.isar_proof
  type isar_preplay_data = Sledgehammer_Isar_Preplay.isar_preplay_data

  val keep_fastest_method_of_isar_step : isar_preplay_data -> isar_step -> isar_step
  val minimized_isar_step : Proof.context -> Time.time -> isar_step -> Time.time * isar_step
  val minimize_isar_step_dependencies : Proof.context -> isar_preplay_data Unsynchronized.ref ->
    isar_step -> isar_step
  val postprocess_isar_proof_remove_show_stuttering : isar_proof -> isar_proof
  val postprocess_isar_proof_remove_unreferenced_steps : (isar_step -> isar_step) -> isar_proof ->
    isar_proof
end;

structure Sledgehammer_Isar_Minimize : SLEDGEHAMMER_ISAR_MINIMIZE =
struct

open Sledgehammer_Util
open Sledgehammer_Proof_Methods
open Sledgehammer_Isar_Proof
open Sledgehammer_Isar_Preplay

fun keep_fastest_method_of_isar_step preplay_data
      (Prove (qs, xs, l, t, subproofs, facts, meths, comment)) =
    Prove (qs, xs, l, t, subproofs, facts,
      meths |> List.partition (curry (op =) (fastest_method_of_isar_step preplay_data l)) |> op @,
      comment)
  | keep_fastest_method_of_isar_step _ step = step

val slack = seconds 0.025

fun minimized_isar_step ctxt time
    (Prove (qs, xs, l, t, subproofs, (lfs0, gfs0), meths as meth :: _, comment)) =
  let
    fun mk_step_lfs_gfs lfs gfs =
      Prove (qs, xs, l, t, subproofs, sort_facts (lfs, gfs), meths, comment)

    fun minimize_half _ min_facts [] time = (min_facts, time)
      | minimize_half mk_step min_facts (fact :: facts) time =
        (case preplay_isar_step_for_method ctxt [] (time + slack) meth
            (mk_step (min_facts @ facts)) of
          Played time' => minimize_half mk_step min_facts facts time'
        | _ => minimize_half mk_step (fact :: min_facts) facts time)

    val (min_lfs, time') = minimize_half (fn lfs => mk_step_lfs_gfs lfs gfs0) [] lfs0 time
    val (min_gfs, time'') = minimize_half (mk_step_lfs_gfs min_lfs) [] gfs0 time'
  in
    (time'', mk_step_lfs_gfs min_lfs min_gfs)
  end

fun minimize_isar_step_dependencies ctxt preplay_data
      (step as Prove (_, _, l, _, _, _, meth :: meths, _)) =
    (case Lazy.force (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth) of
      Played time =>
      let
        fun old_data_for_method meth' =
          (meth', peek_at_outcome (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth'))

        val (time', step') = minimized_isar_step ctxt time step
      in
        set_preplay_outcomes_of_isar_step ctxt time' preplay_data step'
          ((meth, Played time') :: (if step' = step then map old_data_for_method meths else []));
        step'
      end
    | _ => step (* don't touch steps that time out or fail *))
  | minimize_isar_step_dependencies _ _ step = step

fun postprocess_isar_proof_remove_show_stuttering (Proof (fix, assms, steps)) =
  let
    fun process_steps [] = []
      | process_steps (steps as [Prove ([], [], _, t1, subs1, facts1, meths1, comment1),
          Prove ([Show], [], l2, t2, _, _, _, comment2)]) =
        if t1 aconv t2 then [Prove ([Show], [], l2, t2, subs1, facts1, meths1, comment1 ^ comment2)]
        else steps
      | process_steps (step :: steps) = step :: process_steps steps
  in
    Proof (fix, assms, process_steps steps)
  end

fun postprocess_isar_proof_remove_unreferenced_steps postproc_step =
  let
    fun process_proof (Proof (fix, assms, steps)) =
      process_steps steps ||> (fn steps => Proof (fix, assms, steps))
    and process_steps [] = ([], [])
      | process_steps steps =
        (* the last step is always implicitly referenced *)
        let val (steps, (used, concl)) = split_last steps ||> process_used_step in
          fold_rev process_step steps (used, [concl])
        end
    and process_step step (used, accu) =
      (case label_of_isar_step step of
        NONE => (used, step :: accu)
      | SOME l =>
        if Ord_List.member label_ord used l then
          process_used_step step |>> Ord_List.union label_ord used ||> (fn step => step :: accu)
        else
          (used, accu))
    and process_used_step step = process_used_step_subproofs (postproc_step step)
    and process_used_step_subproofs (Prove (qs, xs, l, t, subproofs, (lfs, gfs), meths, comment)) =
      let
        val (used, subproofs) =
          map process_proof subproofs
          |> split_list
          |>> Ord_List.unions label_ord
          |>> fold (Ord_List.insert label_ord) lfs
      in
        (used, Prove (qs, xs, l, t, subproofs, (lfs, gfs), meths, comment))
      end
  in
    snd o process_proof
  end

end;