src/HOL/Tools/Sledgehammer/sledgehammer_preplay.ML

completely rewrote SH compress; added two parameters for experimentation/fine grained control

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

Preplaying of isar proofs.
*)

signature SLEDGEHAMMER_PREPLAY =
sig
  type isar_proof = Sledgehammer_Proof.isar_proof
  type isar_step = Sledgehammer_Proof.isar_step
  type label = Sledgehammer_Proof.label

  eqtype preplay_time
  val zero_preplay_time : preplay_time
  val some_preplay_time : preplay_time
  val add_preplay_time : preplay_time -> preplay_time -> preplay_time
  val string_of_preplay_time : preplay_time -> string
  val preplay : bool -> bool -> string -> string -> Proof.context ->
    Time.time -> isar_step -> preplay_time

  type preplay_interface =
  { get_time : label -> preplay_time,
    set_time : label -> preplay_time -> unit,
    preplay_quietly : Time.time -> isar_step -> preplay_time,
    preplay_fail : unit -> bool,
    overall_preplay_stats : unit -> preplay_time * bool }

  val proof_preplay_interface :
    bool -> Proof.context -> string -> string -> bool -> Time.time option
    -> bool -> isar_proof -> preplay_interface

end

structure Sledgehammer_Preplay : SLEDGEHAMMER_PREPLAY =
struct

open Sledgehammer_Util
open Sledgehammer_Proof

(* The boolean flag encodes whether the time is exact (false) or an lower bound
   (true):
      (t, false) = "t ms"
      (t, true)  = "> t ms" *)
type preplay_time = bool * Time.time

val zero_preplay_time = (false, Time.zeroTime) (* 0 ms *)
val some_preplay_time = (true, Time.zeroTime)  (* > 0 ms *)

fun add_preplay_time (b1, t1) (b2, t2) = (b1 orelse b2, Time.+(t1,t2))

val string_of_preplay_time = ATP_Util.string_of_ext_time

(* preplay tracing *)
fun preplay_trace ctxt assms concl time =
  let
    val ctxt = ctxt |> Config.put show_markup true
    val time = "[" ^ (string_of_preplay_time time) ^ "]" |> Pretty.str
    val nr_of_assms = length assms
    val assms = assms |> map (Display.pretty_thm ctxt)
                      |> (fn [] => Pretty.str ""
                           | [a] => a
                           | assms => Pretty.enum ";" "⟦" "⟧" assms)
    val concl = concl |> Syntax.pretty_term ctxt
    val trace_list = [] |> cons concl
                        |> nr_of_assms>0 ? cons (Pretty.str "⟹")
                        |> cons assms
                        |> cons time
    val pretty_trace = Pretty.blk(2, Pretty.breaks trace_list)
  in tracing (Pretty.string_of pretty_trace) end

(* timing *)
fun take_time timeout tac arg =
  let
    val timing = Timing.start ()
  in
    (TimeLimit.timeLimit timeout tac arg;
      Timing.result timing |> #cpu |> pair false)
    handle TimeLimit.TimeOut => (true, timeout)
  end

(* lookup facts in context *)
fun resolve_fact_names ctxt names =
  (names
    |>> map string_of_label
    |> op @
    |> maps (thms_of_name ctxt))
  handle ERROR msg => error ("preplay error: " ^ msg)

(* turn terms/proofs into theorems *)
fun thm_of_term ctxt = Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
fun thm_of_proof ctxt (Proof (Fix fixed_frees, Assume assms, steps)) =
  let
    val concl = (case try List.last steps of
                  SOME (Prove (_, Fix [], _, t, _, _)) => t
                | _ => raise Fail "preplay error: malformed subproof")
    val var_idx = maxidx_of_term concl + 1
    fun var_of_free (x, T) = Var((x, var_idx), T)
    val substitutions =
      map (`var_of_free #> swap #> apfst Free) fixed_frees
  in
    Logic.list_implies (assms |> map snd, concl)
      |> subst_free substitutions
      |> thm_of_term ctxt
  end


(* main function for preplaying isar_steps *)
fun preplay _ _ _ _ _ _ (Let _) = zero_preplay_time
  | preplay debug trace type_enc lam_trans ctxt timeout
      (Prove (_, Fix xs, _, t, subproofs, By_Metis fact_names)) =
  let
    val (prop, obtain) =
      (case xs of
        [] => (t, false)
      | _ =>
      (* proof obligation: !!thesis. (!!x. A x ==> thesis) ==> thesis
           (see ~~/src/Pure/Isar/obtain.ML) *)
        let
          val thesis = Term.Free ("thesis", HOLogic.boolT)
          val thesis_prop = thesis |> HOLogic.mk_Trueprop
          val frees = map Term.Free xs

          (* !!x1..xn. t ==> thesis (xs = [x1, .., xn]) *)
          val inner_prop =
            fold_rev Logic.all frees (Logic.mk_implies (t, thesis_prop))

          (* !!thesis. (!!x1..xn. t ==> thesis) ==> thesis *)
          val prop =
            Logic.all thesis (Logic.mk_implies (inner_prop, thesis_prop))
        in
          (prop, true)
        end)
    val facts =
      map (thm_of_proof ctxt) subproofs @ resolve_fact_names ctxt fact_names
    val ctxt = ctxt |> Config.put Metis_Tactic.verbose debug
                    |> obtain ? Config.put Metis_Tactic.new_skolem true
    val goal =
      Goal.prove (Config.put Metis_Tactic.verbose debug ctxt) [] [] prop
    fun tac {context = ctxt, prems = _} =
      Metis_Tactic.metis_tac [type_enc] lam_trans ctxt facts 1
    fun run_tac () = goal tac
      handle ERROR msg => error ("preplay error: " ^ msg)
    val preplay_time = take_time timeout run_tac ()
  in
    (* tracing *)
    (if trace then preplay_trace ctxt facts prop preplay_time else () ;
     preplay_time)
  end



(*** proof preplay interface ***)

type preplay_interface =
  { get_time : label -> preplay_time,
    set_time : label -> preplay_time -> unit,
    preplay_quietly : Time.time -> isar_step -> preplay_time,
    preplay_fail : unit -> bool,
    overall_preplay_stats : unit -> preplay_time * bool }


(* enriches context with local proof facts *)
fun enrich_context proof ctxt =
  let
    val thy = Proof_Context.theory_of ctxt

    fun enrich_with_fact l t =
      Proof_Context.put_thms false
        (string_of_label l, SOME [Skip_Proof.make_thm thy t])

    val enrich_with_assms = fold (uncurry enrich_with_fact)

    fun enrich_with_proof (Proof (_, Assume assms, isar_steps)) =
      enrich_with_assms assms #> fold enrich_with_step isar_steps

    and enrich_with_step (Let _) = I
      | enrich_with_step (Prove (_, _, l, t, subproofs, _)) =
          enrich_with_fact l t #> fold enrich_with_proof subproofs
  in
    enrich_with_proof proof ctxt
  end


(* Given a proof, produces an imperative preplay interface with a shared state.
   The preplay times are caluclated lazyly and cached to avoid repeated
   calculation.

   PRE CONDITION: the proof must be labeled canocially, see
   Slegehammer_Proof.relabel_proof_canonically
*)
fun proof_preplay_interface debug ctxt type_enc lam_trans do_preplay
      preplay_timeout preplay_trace proof : preplay_interface =
  if not do_preplay then
    (* the dont_preplay option pretends that everything works just fine *)
    { get_time = K zero_preplay_time,
      set_time = K (K ()),
      preplay_quietly = K (K zero_preplay_time),
      preplay_fail = K false,
      overall_preplay_stats = K (zero_preplay_time, false)}
  else
    let

      (* 60 seconds seems like a good interpreation of "no timeout" *)
      val preplay_timeout = preplay_timeout |> the_default (seconds 60.0)

      (* add local proof facts to context *)
      val ctxt = enrich_context proof ctxt

      val fail = Unsynchronized.ref false
      fun preplay_fail () = !fail

      fun preplay' timeout step =
        (* after preplay has failed once, exact preplay times are pointless *)
        if preplay_fail () then some_preplay_time
          else preplay debug preplay_trace type_enc lam_trans ctxt timeout step

      (* preplay steps without registering preplay_fails, treating exceptions
         like timeouts *)
      fun preplay_quietly timeout step =
        try (preplay' timeout) step
        |> the_default (true, timeout)

      val preplay_time_tab =
        let
          fun add_step_to_tab step tab =
            case label_of_step step of
              NONE => tab
            | SOME l =>
                Canonical_Lbl_Tab.update_new
                  (l, (fn () => preplay' preplay_timeout step) |> Lazy.lazy)
                  tab
            handle (exn as Canonical_Lbl_Tab.DUP _) =>
              raise Fail ("Sledgehammer_Preplay: preplay time table - "
                          ^ PolyML.makestring exn)
        in
          Canonical_Lbl_Tab.empty
          |> fold_isar_steps add_step_to_tab (steps_of_proof proof)
          |> Unsynchronized.ref
        end

      fun register_preplay_fail lazy_time = Lazy.force lazy_time
        handle exn =>
          if Exn.is_interrupt exn orelse debug then reraise exn
          else (fail := true; some_preplay_time)

      fun get_time lbl =
        register_preplay_fail
          (Canonical_Lbl_Tab.lookup (!preplay_time_tab) lbl |> the)
        handle
          Option.Option =>
            raise Fail "Sledgehammer_Preplay: preplay time table"

      fun set_time lbl time =
        preplay_time_tab :=
          Canonical_Lbl_Tab.update (lbl, Lazy.value time) (!preplay_time_tab)

      fun total_preplay_time () =
        Canonical_Lbl_Tab.fold
          (snd #> register_preplay_fail #> add_preplay_time)
          (!preplay_time_tab) zero_preplay_time

      fun overall_preplay_stats () = (total_preplay_time (), preplay_fail ())
    in
      { get_time = get_time,
        set_time = set_time,
        preplay_quietly = preplay_quietly,
        preplay_fail = preplay_fail,
        overall_preplay_stats = overall_preplay_stats}
    end

end