src/HOL/Tools/Sledgehammer/sledgehammer_proof_methods.ML

Importation of basic group theory results, due to Jakob von Raumer from his AFP entry Jordan-Hölder Theorem

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

Reconstructors.
*)

signature SLEDGEHAMMER_PROOF_METHODS =
sig
  type stature = ATP_Problem_Generate.stature

  datatype SMT_backend =
    SMT_Z3 |
    SMT_Verit of string

  datatype proof_method =
    Metis_Method of string option * string option |
    Meson_Method |
    SMT_Method of SMT_backend |
    SATx_Method |
    Blast_Method |
    Simp_Method |
    Auto_Method |
    Fastforce_Method |
    Force_Method |
    Moura_Method |
    Linarith_Method |
    Presburger_Method |
    Algebra_Method

  datatype play_outcome =
    Played of Time.time |
    Play_Timed_Out of Time.time |
    Play_Failed

  type one_line_params =
    ((string * stature) list * (proof_method * play_outcome)) * string * int * int

  val is_proof_method_direct : proof_method -> bool
  val string_of_proof_method : string list -> proof_method -> string
  val tac_of_proof_method : Proof.context -> thm list * thm list -> proof_method -> int -> tactic
  val string_of_play_outcome : play_outcome -> string
  val play_outcome_ord : play_outcome ord
  val one_line_proof_text : Proof.context -> int -> one_line_params -> string
end;

structure Sledgehammer_Proof_Methods : SLEDGEHAMMER_PROOF_METHODS =
struct

open ATP_Util
open ATP_Problem_Generate
open ATP_Proof_Reconstruct

datatype SMT_backend =
  SMT_Z3 |
  SMT_Verit of string

datatype proof_method =
  Metis_Method of string option * string option |
  Meson_Method |
  SMT_Method of SMT_backend |
  SATx_Method |
  Blast_Method |
  Simp_Method |
  Auto_Method |
  Fastforce_Method |
  Force_Method |
  Moura_Method |
  Linarith_Method |
  Presburger_Method |
  Algebra_Method

datatype play_outcome =
  Played of Time.time |
  Play_Timed_Out of Time.time |
  Play_Failed

type one_line_params =
  ((string * stature) list * (proof_method * play_outcome)) * string * int * int

fun is_proof_method_direct (Metis_Method _) = true
  | is_proof_method_direct Meson_Method = true
  | is_proof_method_direct (SMT_Method _) = true
  | is_proof_method_direct Simp_Method = true
  | is_proof_method_direct _ = false

fun is_proof_method_multi_goal Auto_Method = true
  | is_proof_method_multi_goal _ = false

fun maybe_paren s = s |> not (Symbol_Pos.is_identifier s) ? enclose "(" ")"

fun string_of_proof_method ss meth =
  let
    val meth_s =
      (case meth of
        Metis_Method (NONE, NONE) => "metis"
      | Metis_Method (type_enc_opt, lam_trans_opt) =>
        "metis (" ^ commas (map_filter I [type_enc_opt, lam_trans_opt]) ^ ")"
      | Meson_Method => "meson"
      | SMT_Method SMT_Z3 => "smt (z3)"
      | SMT_Method (SMT_Verit strategy) =>
        "smt (" ^ commas ("verit" :: (if strategy = "default" then [] else [strategy])) ^ ")"
      | SATx_Method => "satx"
      | Blast_Method => "blast"
      | Simp_Method => if null ss then "simp" else "simp add:"
      | Auto_Method => "auto"
      | Fastforce_Method => "fastforce"
      | Force_Method => "force"
      | Moura_Method => "moura"
      | Linarith_Method => "linarith"
      | Presburger_Method => "presburger"
      | Algebra_Method => "algebra")
  in
    maybe_paren (space_implode " " (meth_s :: ss))
  end

fun tac_of_proof_method ctxt (local_facts, global_facts) meth =
  let
    fun tac_of_metis (type_enc_opt, lam_trans_opt) =
      let
        val ctxt = ctxt
          |> Config.put Metis_Tactic.verbose false
          |> Config.put Metis_Tactic.trace false
      in
        SELECT_GOAL (Metis_Tactic.metis_method ((Option.map single type_enc_opt, lam_trans_opt),
          global_facts) ctxt local_facts)
      end

    fun tac_of_smt SMT_Z3 = SMT_Solver.smt_tac
      | tac_of_smt (SMT_Verit strategy) = Verit_Strategies.verit_tac_stgy strategy
  in
    (case meth of
      Metis_Method options => tac_of_metis options
    | SMT_Method backend => tac_of_smt backend ctxt (local_facts @ global_facts)
    | _ =>
      Method.insert_tac ctxt local_facts THEN'
      (case meth of
        Meson_Method => Meson_Tactic.meson_general_tac ctxt global_facts
      | Simp_Method => Simplifier.asm_full_simp_tac (ctxt addsimps global_facts)
      | _ =>
        Method.insert_tac ctxt global_facts THEN'
        (case meth of
          SATx_Method => SAT.satx_tac ctxt
        | Blast_Method => blast_tac ctxt
        | Auto_Method => SELECT_GOAL (Clasimp.auto_tac ctxt)
        | Fastforce_Method => Clasimp.fast_force_tac ctxt
        | Force_Method => Clasimp.force_tac ctxt
        | Moura_Method => moura_tac ctxt
        | Linarith_Method => Lin_Arith.tac ctxt
        | Presburger_Method => Cooper.tac true [] [] ctxt
        | Algebra_Method => Groebner.algebra_tac [] [] ctxt)))
  end

fun string_of_play_outcome (Played time) = string_of_ext_time (false, time)
  | string_of_play_outcome (Play_Timed_Out time) =
    if time = Time.zeroTime then "" else string_of_ext_time (true, time) ^ ", timed out"
  | string_of_play_outcome Play_Failed = "failed"

fun play_outcome_ord (Played time1, Played time2) =
    int_ord (apply2 Time.toMilliseconds (time1, time2))
  | play_outcome_ord (Played _, _) = LESS
  | play_outcome_ord (_, Played _) = GREATER
  | play_outcome_ord (Play_Timed_Out time1, Play_Timed_Out time2) =
    int_ord (apply2 Time.toMilliseconds (time1, time2))
  | play_outcome_ord (Play_Timed_Out _, _) = LESS
  | play_outcome_ord (_, Play_Timed_Out _) = GREATER
  | play_outcome_ord (Play_Failed, Play_Failed) = EQUAL

fun apply_on_subgoal _ 1 = "by "
  | apply_on_subgoal 1 _ = "apply "
  | apply_on_subgoal i n = "prefer " ^ string_of_int i ^ " " ^ apply_on_subgoal 1 n

(* FIXME *)
fun proof_method_command meth i n used_chaineds _(*num_chained*) extras =
  let
    val (indirect_ss, direct_ss) =
      if is_proof_method_direct meth then ([], extras) else (extras, [])
  in
    (if null indirect_ss then "" else "using " ^ space_implode " " indirect_ss ^ " ") ^
    apply_on_subgoal i n ^ string_of_proof_method direct_ss meth ^
    (if is_proof_method_multi_goal meth andalso n <> 1 then "[1]" else "")
  end

fun try_command_line banner play command =
  let val s = string_of_play_outcome play in
    banner ^ Active.sendback_markup_command command ^ (s |> s <> "" ? enclose " (" ")")
  end

fun one_line_proof_text _ num_chained
    ((used_facts, (meth, play)), banner, subgoal, subgoal_count) =
  let val (chained, extra) = List.partition (fn (_, (sc, _)) => sc = Chained) used_facts in
    map fst extra
    |> proof_method_command meth subgoal subgoal_count (map fst chained) num_chained
    |> (if play = Play_Failed then prefix "One-line proof reconstruction failed: "
        else try_command_line banner play)
  end

end;