src/HOL/Tools/atp_minimal.ML

added Philipp Meyer's implementation of AtpMinimal
together with related changes in the sledgehammer-interface:
adapted type of prover, optional relevance filtering,
public get_prover for registered atps in AtpManager,
included atp_minimize in s/h response;

(*  Title:      HOL/Tools/atp_minimal.ML
    Author:     Philipp Meyer, TU Muenchen

Minimalization of theorem list for metis by using an external automated theorem prover
*)

structure AtpMinimal =
struct

  (* output control *)
  fun debug str = Output.debug (fn () => str)
  fun debug_fn f = if !Output.debugging then f() else ()
  fun answer str = Output.writeln str
  fun println str = Output.priority str

  fun order_unique name_list = OrdList.make (String.collate Char.compare) name_list
  fun length_string namelist = Int.toString (length namelist)

  fun print_names name_thms_pairs =
    let
      val names = (map fst name_thms_pairs)
      val ordered = order_unique names
    in
      app (fn name => (debug ("  " ^ name))) ordered
    end

  (* minimalization algorithm *)
  local
    fun isplit (l,r) [] = (l,r)
      | isplit (l,r) (h::[]) = (h::l, r)
      | isplit (l,r) (h1::h2::t) = isplit (h1::l, h2::r) t
  in
    fun split lst = isplit ([],[]) lst
  end

  local
    fun min p sup [] = raise Empty
      | min p sup [s0] = [s0]
      | min p sup s =
        let
          val (l0, r0) = split s
        in
          if p(sup @ l0)
          then min p sup l0
          else
            if p(sup @ r0)
            then min p sup r0
            else
              let
                val l = min p (sup @ r0) l0
                val r = min p (sup @ l) r0
              in
                l @ r
              end
        end
  in
    (* return a minimal subset v of s that satisfies p
     @pre p(s) & ~p([]) & monotone(p)
     @post v subset s & p(v) &
           forall e in v. ~p(v \ e)
     *)
    fun minimal p s = min p [] s
  end

 (* failure check and producing answer*)
  datatype 'a prove_result = Success of 'a | Failure | Timeout | Error

  val string_of_result = fn
    Success _ => "Success"
  | Failure => "Failure"
  | Timeout => "Timeout"
  | Error => "Error"

  val failure_strings =
     [("SPASS beiseite: Ran out of time.", Timeout),
     ("Timeout", Timeout),
     ("time limit exceeded", Timeout),
     ("# Cannot determine problem status within resource limit", Timeout),
     ("Error", Error)]

  fun produce_answer (success, message, result_string, thm_name_vec) =
    if success then
      (Success (Vector.foldr op:: [] thm_name_vec), result_string)
    else
      let
        val failure = get_first (fn (s, t) => if String.isSubstring s result_string then SOME (t, result_string) else NONE) failure_strings
      in
        if is_some failure then
          the failure
        else
          (Failure, result_string)
      end

  (* wrapper for calling external prover *)
  fun sh_test_thms prover prover_name time_limit subgoalno state name_thms_pairs =
    let
      val _ = println ("Testing " ^ (length_string name_thms_pairs) ^ " theorems... ")
      val name_thm_pairs = flat (map (fn (n, ths) => map_index (fn (i, th) => (n, th)) ths) name_thms_pairs)
      val _ = debug_fn (fn () => print_names name_thm_pairs)
      val axclauses = ResAxioms.cnf_rules_pairs (Proof.theory_of state) name_thm_pairs
      val (result, proof) =
        (produce_answer (prover time_limit (SOME axclauses) prover_name subgoalno (Proof.get_goal state)))
      val _ = println (string_of_result result)
      val _ = debug proof
    in
      (result, proof)
    end

  (* minimalization of thms *)
  fun minimalize prover prover_name time_limit state name_thms_pairs =
    let
      val _ = println ("Minimize called with " ^ (length_string name_thms_pairs) ^ " theorems, prover: "
                       ^ prover_name ^ ", time limit: " ^ (Int.toString time_limit) ^ " seconds")
      val _ = debug_fn (fn () => app (fn (n, tl) => (debug n; app (fn t => debug ("  " ^ Display.string_of_thm t)) tl)) name_thms_pairs)
      val test_thms_fun = sh_test_thms prover prover_name time_limit 1 state
      fun test_thms thms = case test_thms_fun thms of (Success _, _) => true | _ => false
    in
      (* try proove first to check result and get used theorems *)
      (case test_thms_fun name_thms_pairs of
        (Success used, _) =>
          let
            val ordered_used = order_unique used
            val to_use =
              if length ordered_used < length name_thms_pairs then
                filter (fn (name1, _) => List.exists (equal name1) ordered_used) name_thms_pairs
              else
                name_thms_pairs
            val min_thms = (minimal test_thms to_use)
            val min_names = order_unique (map fst min_thms)
            val _ = println ("Minimal " ^ (length_string min_thms) ^ " theorems")
            val _ = debug_fn (fn () => print_names min_thms)
          in
            answer ("Try this command: " ^ Markup.markup Markup.sendback ("apply (metis " ^ (space_implode " " min_names) ^ ")"))
          end
      | (Timeout, _) =>
          answer ("Timeout: You may need to increase the time limit of " ^ (Int.toString time_limit) ^ " seconds. Call atp_minimize [time=...] ")
      | (Error, msg) =>
          answer ("Error in prover: " ^ msg)
      | (Failure, _) =>
          answer "Failure: No proof with the theorems supplied")
      handle ResHolClause.TOO_TRIVIAL =>
          answer ("Trivial: Try this command: " ^ Markup.markup Markup.sendback "apply metis")
      | ERROR msg =>
          answer ("Error: " ^ msg)
    end

  (* isar command and parsing input *)

  local structure K = OuterKeyword and P = OuterParse and T = OuterLex in

  fun get_thms context =
    map (fn (name, interval) =>
      let
        val thmref = Facts.Named ((name, Position.none), interval)
        val ths = ProofContext.get_fact context thmref
        val name' = Facts.string_of_ref thmref
      in
        (name', ths)
      end)

  val default_prover = "remote_vampire"
  val default_time_limit = 5

  fun get_time_limit_arg time_string =
    (case Int.fromString time_string of
      SOME t => t
    | NONE => error ("Invalid time limit: " ^ quote time_string))

  val get_options =
    let
      val def = (default_prover, default_time_limit)
    in
      foldl (fn ((name, a), (p, t)) => (case name of
        "time" => (p, (get_time_limit_arg a))
      | "atp" => (a, t)
      | n => error ("Invalid argument: " ^ n))) def
    end

  fun sh_min_command args thm_names state =
    let
      val (prover_name, time_limit) = get_options args
      val prover =
        case AtpManager.get_prover prover_name (Proof.theory_of state) of
          SOME prover => prover
        | NONE => error ("Unknown prover: " ^ quote prover_name)
      val name_thms_pairs = get_thms (Proof.context_of state) thm_names
    in
      minimalize prover prover_name time_limit state name_thms_pairs
    end

  val parse_args = Scan.optional (Args.bracks (P.list (P.xname --| P.$$$ "=" -- P.xname) )) []
  val parse_thm_names = Scan.repeat (P.xname -- Scan.option Attrib.thm_sel)

  val _ =
    OuterSyntax.command "atp_minimize" "minimize theorem list with external prover" K.diag
      (parse_args -- parse_thm_names >> (fn (args, thm_names) =>
        Toplevel.no_timing o Toplevel.unknown_proof o Toplevel.keep ((sh_min_command args thm_names) o Toplevel.proof_of)))

  end
end