src/Pure/goal.ML
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Fri, 04 Feb 2011 17:11:00 +0100
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(*  Title:      Pure/goal.ML
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    Author:     Makarius
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Goals in tactical theorem proving.
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*)
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signature BASIC_GOAL =
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sig
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  val parallel_proofs: int Unsynchronized.ref
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  val parallel_proofs_threshold: int Unsynchronized.ref
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  val SELECT_GOAL: tactic -> int -> tactic
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  val CONJUNCTS: tactic -> int -> tactic
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  val PRECISE_CONJUNCTS: int -> tactic -> int -> tactic
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  val PARALLEL_CHOICE: tactic list -> tactic
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  val PARALLEL_GOALS: tactic -> tactic
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end;
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signature GOAL =
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sig
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  include BASIC_GOAL
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  val init: cterm -> thm
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  val protect: thm -> thm
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  val conclude: thm -> thm
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  val check_finished: Proof.context -> thm -> unit
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  val finish: Proof.context -> thm -> thm
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  val norm_result: thm -> thm
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  val fork_name: string -> (unit -> 'a) -> 'a future
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  val fork: (unit -> 'a) -> 'a future
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  val future_enabled: unit -> bool
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  val local_future_enabled: unit -> bool
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  val future_result: Proof.context -> thm future -> term -> thm
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  val prove_internal: cterm list -> cterm -> (thm list -> tactic) -> thm
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  val prove_multi: Proof.context -> string list -> term list -> term list ->
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    ({prems: thm list, context: Proof.context} -> tactic) -> thm list
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  val prove_future: Proof.context -> string list -> term list -> term ->
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    ({prems: thm list, context: Proof.context} -> tactic) -> thm
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  val prove: Proof.context -> string list -> term list -> term ->
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    ({prems: thm list, context: Proof.context} -> tactic) -> thm
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  val prove_global: theory -> string list -> term list -> term ->
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    ({prems: thm list, context: Proof.context} -> tactic) -> thm
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  val extract: int -> int -> thm -> thm Seq.seq
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  val retrofit: int -> int -> thm -> thm -> thm Seq.seq
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  val conjunction_tac: int -> tactic
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  val precise_conjunction_tac: int -> int -> tactic
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  val recover_conjunction_tac: tactic
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  val norm_hhf_tac: int -> tactic
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  val compose_hhf_tac: thm -> int -> tactic
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  val assume_rule_tac: Proof.context -> int -> tactic
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end;
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structure Goal: GOAL =
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struct
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(** goals **)
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(*
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  -------- (init)
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  C ==> #C
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*)
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val init =
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  let val A = #1 (Thm.dest_implies (Thm.cprop_of Drule.protectI))
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  in fn C => Thm.instantiate ([], [(A, C)]) Drule.protectI end;
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(*
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   C
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  --- (protect)
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  #C
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*)
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fun protect th = Drule.comp_no_flatten (th, 0) 1 Drule.protectI;
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(*
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  A ==> ... ==> #C
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  ---------------- (conclude)
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  A ==> ... ==> C
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*)
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fun conclude th = Drule.comp_no_flatten (th, Thm.nprems_of th) 1 Drule.protectD;
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(*
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  #C
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  --- (finish)
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   C
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*)
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fun check_finished ctxt th =
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  (case Thm.nprems_of th of
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    0 => ()
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  | n => raise THM ("Proof failed.\n" ^
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      Pretty.string_of (Pretty.chunks
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        (Goal_Display.pretty_goals
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          (ctxt
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            |> Config.put Goal_Display.goals_limit n
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            |> Config.put Goal_Display.show_main_goal true) th)) ^
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      "\n" ^ string_of_int n ^ " unsolved goal(s)!", 0, [th]));
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fun finish ctxt th = (check_finished ctxt th; conclude th);
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(** results **)
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(* normal form *)
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val norm_result =
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  Drule.flexflex_unique
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  #> Raw_Simplifier.norm_hhf_protect
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  #> Thm.strip_shyps
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  #> Drule.zero_var_indexes;
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(* forked proofs *)
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val forked_proofs = Synchronized.var "forked_proofs" 0;
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fun forked i =
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  Synchronized.change forked_proofs (fn m =>
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    let
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      val n = m + i;
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      val _ =
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        Multithreading.tracing 1 (fn () =>
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          ("PROOFS " ^ Time.toString (Time.now ()) ^ ": " ^ string_of_int n));
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    in n end);
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fun fork_name name e =
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  uninterruptible (fn _ => fn () =>
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    let
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      val _ = forked 1;
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      val future =
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        singleton (Future.forks {name = name, group = NONE, deps = [], pri = ~1})
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          (fn () =>
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            (*interruptible*)
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            Exn.release
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              (Exn.capture Future.status e before forked ~1
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                handle exn => (forked ~1; reraise exn)));
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    in future end) ();
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fun fork e = fork_name "Goal.fork" e;
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(* scheduling parameters *)
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val parallel_proofs = Unsynchronized.ref 1;
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val parallel_proofs_threshold = Unsynchronized.ref 100;
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fun future_enabled () =
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  Multithreading.enabled () andalso ! parallel_proofs >= 1 andalso
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  is_some (Future.worker_task ());
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fun local_future_enabled () =
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  future_enabled () andalso ! parallel_proofs >= 2 andalso
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  Synchronized.value forked_proofs < ! parallel_proofs_threshold;
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(* future_result *)
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fun future_result ctxt result prop =
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  let
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    val thy = ProofContext.theory_of ctxt;
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    val _ = Context.reject_draft thy;
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    val cert = Thm.cterm_of thy;
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    val certT = Thm.ctyp_of thy;
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    val assms = Assumption.all_assms_of ctxt;
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    val As = map Thm.term_of assms;
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    val xs = map Free (fold Term.add_frees (prop :: As) []);
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    val fixes = map cert xs;
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    val tfrees = fold Term.add_tfrees (prop :: As) [];
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    val instT = map (fn (a, S) => (certT (TVar ((a, 0), S)), certT (TFree (a, S)))) tfrees;
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    val global_prop =
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      cert (Term.map_types Logic.varifyT_global
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        (fold_rev Logic.all xs (Logic.list_implies (As, prop))))
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      |> Thm.weaken_sorts (Variable.sorts_of ctxt);
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    val global_result = result |> Future.map
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      (Drule.flexflex_unique #>
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        Thm.adjust_maxidx_thm ~1 #>
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        Drule.implies_intr_list assms #>
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        Drule.forall_intr_list fixes #>
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        Thm.generalize (map #1 tfrees, []) 0 #>
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        Thm.strip_shyps);
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    val local_result =
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      Thm.future global_result global_prop
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      |> Thm.instantiate (instT, [])
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      |> Drule.forall_elim_list fixes
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      |> fold (Thm.elim_implies o Thm.assume) assms;
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  in local_result end;
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(** tactical theorem proving **)
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(* prove_internal -- minimal checks, no normalization of result! *)
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fun prove_internal casms cprop tac =
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  (case SINGLE (tac (map Assumption.assume casms)) (init cprop) of
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    SOME th => Drule.implies_intr_list casms
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      (finish (Syntax.init_pretty_global (Thm.theory_of_thm th)) th)
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  | NONE => error "Tactic failed");
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(* prove_common etc. *)
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fun prove_common immediate ctxt xs asms props tac =
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  let
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    val thy = ProofContext.theory_of ctxt;
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    val string_of_term = Syntax.string_of_term ctxt;
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    val pos = Position.thread_data ();
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    fun err msg = cat_error msg
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      ("The error(s) above occurred for the goal statement:\n" ^
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        string_of_term (Logic.list_implies (asms, Logic.mk_conjunction_list props)) ^
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        (case Position.str_of pos of "" => "" | s => "\n" ^ s));
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    fun cert_safe t = Thm.cterm_of thy (Envir.beta_norm (Term.no_dummy_patterns t))
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      handle TERM (msg, _) => err msg | TYPE (msg, _, _) => err msg;
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    val casms = map cert_safe asms;
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    val cprops = map cert_safe props;
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    val (prems, ctxt') = ctxt
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      |> Variable.add_fixes_direct xs
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      |> fold Variable.declare_term (asms @ props)
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      |> Assumption.add_assumes casms
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      ||> Variable.set_body true;
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    val sorts = Variable.sorts_of ctxt';
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    val stmt = Thm.weaken_sorts sorts (Conjunction.mk_conjunction_balanced cprops);
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    fun result () =
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      (case SINGLE (tac {prems = prems, context = ctxt'}) (init stmt) of
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        NONE => err "Tactic failed"
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      | SOME st =>
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          let val res = finish ctxt' st handle THM (msg, _, _) => err msg in
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            if Unify.matches_list thy [Thm.term_of stmt] [Thm.prop_of res]
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            then Thm.check_shyps sorts res
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            else err ("Proved a different theorem: " ^ string_of_term (Thm.prop_of res))
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          end);
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    val res =
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      if immediate orelse #maxidx (Thm.rep_cterm stmt) >= 0 orelse not (future_enabled ())
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      then result ()
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      else future_result ctxt' (fork result) (Thm.term_of stmt);
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  in
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    Conjunction.elim_balanced (length props) res
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    |> map (Assumption.export false ctxt' ctxt)
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    |> Variable.export ctxt' ctxt
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    |> map Drule.zero_var_indexes
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  end;
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val prove_multi = prove_common true;
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fun prove_future ctxt xs asms prop tac = hd (prove_common false ctxt xs asms [prop] tac);
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fun prove ctxt xs asms prop tac = hd (prove_common true ctxt xs asms [prop] tac);
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fun prove_global thy xs asms prop tac =
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  Drule.export_without_context (prove (ProofContext.init_global thy) xs asms prop tac);
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(** goal structure **)
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(* nested goals *)
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fun extract i n st =
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  (if i < 1 orelse n < 1 orelse i + n - 1 > Thm.nprems_of st then Seq.empty
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   else if n = 1 then Seq.single (Thm.cprem_of st i)
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   else
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     Seq.single (Conjunction.mk_conjunction_balanced (map (Thm.cprem_of st) (i upto i + n - 1))))
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  |> Seq.map (Thm.adjust_maxidx_cterm ~1 #> init);
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fun retrofit i n st' st =
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  (if n = 1 then st
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   else st |> Drule.with_subgoal i (Conjunction.uncurry_balanced n))
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  |> Thm.compose_no_flatten false (conclude st', Thm.nprems_of st') i;
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fun SELECT_GOAL tac i st =
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  if Thm.nprems_of st = 1 andalso i = 1 then tac st
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  else Seq.lifts (retrofit i 1) (Seq.maps tac (extract i 1 st)) st;
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(* multiple goals *)
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fun precise_conjunction_tac 0 i = eq_assume_tac i
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  | precise_conjunction_tac 1 i = SUBGOAL (K all_tac) i
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  | precise_conjunction_tac n i = PRIMITIVE (Drule.with_subgoal i (Conjunction.curry_balanced n));
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val adhoc_conjunction_tac = REPEAT_ALL_NEW
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  (SUBGOAL (fn (goal, i) =>
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    if can Logic.dest_conjunction goal then rtac Conjunction.conjunctionI i
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    else no_tac));
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val conjunction_tac = SUBGOAL (fn (goal, i) =>
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  precise_conjunction_tac (length (Logic.dest_conjunctions goal)) i ORELSE
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  TRY (adhoc_conjunction_tac i));
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val recover_conjunction_tac = PRIMITIVE (fn th =>
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  Conjunction.uncurry_balanced (Thm.nprems_of th) th);
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fun PRECISE_CONJUNCTS n tac =
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  SELECT_GOAL (precise_conjunction_tac n 1
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    THEN tac
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    THEN recover_conjunction_tac);
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fun CONJUNCTS tac =
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  SELECT_GOAL (conjunction_tac 1
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    THEN tac
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    THEN recover_conjunction_tac);
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(* hhf normal form *)
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val norm_hhf_tac =
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  rtac Drule.asm_rl  (*cheap approximation -- thanks to builtin Logic.flatten_params*)
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  THEN' SUBGOAL (fn (t, i) =>
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    if Drule.is_norm_hhf t then all_tac
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    else rewrite_goal_tac Drule.norm_hhf_eqs i);
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fun compose_hhf_tac th i st =
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  PRIMSEQ (Thm.bicompose false (false, Drule.lift_all (Thm.cprem_of st i) th, 0) i) st;
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(* non-atomic goal assumptions *)
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fun non_atomic (Const ("==>", _) $ _ $ _) = true
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  | non_atomic (Const ("all", _) $ _) = true
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  | non_atomic _ = false;
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fun assume_rule_tac ctxt = norm_hhf_tac THEN' CSUBGOAL (fn (goal, i) =>
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  let
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    val ((_, goal'), ctxt') = Variable.focus goal ctxt;
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    val goal'' = Drule.cterm_rule (singleton (Variable.export ctxt' ctxt)) goal';
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    val Rs = filter (non_atomic o Thm.term_of) (Drule.strip_imp_prems goal'');
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    val tacs = Rs |> map (fn R =>
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      Tactic.etac (Raw_Simplifier.norm_hhf (Thm.trivial R)) THEN_ALL_NEW assume_tac);
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  in fold_rev (curry op APPEND') tacs (K no_tac) i end);
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(* parallel tacticals *)
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(*parallel choice of single results*)
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fun PARALLEL_CHOICE tacs st =
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  (case Par_List.get_some (fn tac => SINGLE tac st) tacs of
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    NONE => Seq.empty
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  | SOME st' => Seq.single st');
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(*parallel refinement of non-schematic goal by single results*)
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exception FAILED of unit;
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fun PARALLEL_GOALS tac st =
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  let
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    val st0 = Thm.adjust_maxidx_thm ~1 st;
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    val _ = Thm.maxidx_of st0 >= 0 andalso
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      raise THM ("PARALLEL_GOALS: schematic goal state", 0, [st]);
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    fun try_tac g =
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      (case SINGLE tac g of
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        NONE => raise FAILED ()
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      | SOME g' => g');
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    val goals = Drule.strip_imp_prems (Thm.cprop_of st0);
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    val results = Par_List.map (try_tac o init) goals;
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  in ALLGOALS (fn i => retrofit i 1 (nth results (i - 1))) st0 end
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  handle FAILED () => Seq.empty;
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end;
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structure Basic_Goal: BASIC_GOAL = Goal;
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open Basic_Goal;