(*  Title:      Pure/goal.ML

     Author:     Makarius

 Goals in tactical theorem proving.

 *)

 signature BASIC_GOAL =

 sig

   val parallel_proofs: int Unsynchronized.ref

   val parallel_proofs_threshold: int Unsynchronized.ref

   val SELECT_GOAL: tactic -> int -> tactic

   val CONJUNCTS: tactic -> int -> tactic

   val PRECISE_CONJUNCTS: int -> tactic -> int -> tactic

   val PARALLEL_CHOICE: tactic list -> tactic

   val PARALLEL_GOALS: tactic -> tactic

 end;

 signature GOAL =

 sig

   include BASIC_GOAL

   val init: cterm -> thm

   val protect: thm -> thm

   val conclude: thm -> thm

   val check_finished: Proof.context -> thm -> unit

   val finish: Proof.context -> thm -> thm

   val norm_result: thm -> thm

   val fork_name: string -> (unit -> 'a) -> 'a future

   val fork: (unit -> 'a) -> 'a future

   val future_enabled: unit -> bool

   val local_future_enabled: unit -> bool

   val future_result: Proof.context -> thm future -> term -> thm

   val prove_internal: cterm list -> cterm -> (thm list -> tactic) -> thm

   val prove_multi: Proof.context -> string list -> term list -> term list ->

     ({prems: thm list, context: Proof.context} -> tactic) -> thm list

   val prove_future: Proof.context -> string list -> term list -> term ->

     ({prems: thm list, context: Proof.context} -> tactic) -> thm

   val prove: Proof.context -> string list -> term list -> term ->

     ({prems: thm list, context: Proof.context} -> tactic) -> thm

   val prove_global: theory -> string list -> term list -> term ->

     ({prems: thm list, context: Proof.context} -> tactic) -> thm

   val extract: int -> int -> thm -> thm Seq.seq

   val retrofit: int -> int -> thm -> thm -> thm Seq.seq

   val conjunction_tac: int -> tactic

   val precise_conjunction_tac: int -> int -> tactic

   val recover_conjunction_tac: tactic

   val norm_hhf_tac: int -> tactic

   val compose_hhf_tac: thm -> int -> tactic

   val assume_rule_tac: Proof.context -> int -> tactic

 end;

 structure Goal: GOAL =

 struct

 (** goals **)

 (*

   -------- (init)

   C ==> #C

 *)

 val init =

   let val A = #1 (Thm.dest_implies (Thm.cprop_of Drule.protectI))

   in fn C => Thm.instantiate ([], [(A, C)]) Drule.protectI end;

 (*

    C

   --- (protect)

   #C

 *)

 fun protect th = Drule.comp_no_flatten (th, 0) 1 Drule.protectI;

 (*

   A ==> ... ==> #C

   ---------------- (conclude)

   A ==> ... ==> C

 *)

 fun conclude th = Drule.comp_no_flatten (th, Thm.nprems_of th) 1 Drule.protectD;

 (*

   #C

   --- (finish)

    C

 *)

 fun check_finished ctxt th =

   (case Thm.nprems_of th of

     0 => ()

   | n => raise THM ("Proof failed.\n" ^

       Pretty.string_of (Pretty.chunks

         (Goal_Display.pretty_goals

           (ctxt

             |> Config.put Goal_Display.goals_limit n

             |> Config.put Goal_Display.show_main_goal true) th)) ^

       "\n" ^ string_of_int n ^ " unsolved goal(s)!", 0, [th]));

 fun finish ctxt th = (check_finished ctxt th; conclude th);

 (** results **)

 (* normal form *)

 val norm_result =

   Drule.flexflex_unique

   #> Raw_Simplifier.norm_hhf_protect

   #> Thm.strip_shyps

   #> Drule.zero_var_indexes;

 (* forked proofs *)

 val forked_proofs = Synchronized.var "forked_proofs" 0;

 fun forked i =

   Synchronized.change forked_proofs (fn m =>

     let

       val n = m + i;

       val _ =

         Multithreading.tracing 2 (fn () =>

           ("PROOFS " ^ Time.toString (Time.now ()) ^ ": " ^ string_of_int n));

     in n end);

 fun fork_name name e =

   uninterruptible (fn _ => fn () =>

     let

       val _ = forked 1;

       val future =

         singleton (Future.forks {name = name, group = NONE, deps = [], pri = ~1})

           (fn () =>

             (*interruptible*)

             Exn.release

               (Exn.capture Future.status e before forked ~1

                 handle exn => (forked ~1; reraise exn)));

     in future end) ();

 fun fork e = fork_name "Goal.fork" e;

 (* scheduling parameters *)

 val parallel_proofs = Unsynchronized.ref 1;

 val parallel_proofs_threshold = Unsynchronized.ref 50;

 fun future_enabled () =

   Multithreading.enabled () andalso ! parallel_proofs >= 1 andalso

   is_some (Future.worker_task ());

 fun local_future_enabled () =

   future_enabled () andalso ! parallel_proofs >= 2 andalso

   Synchronized.value forked_proofs <

     ! parallel_proofs_threshold * Multithreading.max_threads_value ();

 (* future_result *)

 fun future_result ctxt result prop =

   let

     val thy = Proof_Context.theory_of ctxt;

     val _ = Context.reject_draft thy;

     val cert = Thm.cterm_of thy;

     val certT = Thm.ctyp_of thy;

     val assms = Assumption.all_assms_of ctxt;

     val As = map Thm.term_of assms;

     val xs = map Free (fold Term.add_frees (prop :: As) []);

     val fixes = map cert xs;

     val tfrees = fold Term.add_tfrees (prop :: As) [];

     val instT = map (fn (a, S) => (certT (TVar ((a, 0), S)), certT (TFree (a, S)))) tfrees;

     val global_prop =

       cert (Term.map_types Logic.varifyT_global

         (fold_rev Logic.all xs (Logic.list_implies (As, prop))))

       |> Thm.weaken_sorts (Variable.sorts_of ctxt);

     val global_result = result |> Future.map

       (Drule.flexflex_unique #>

         Thm.adjust_maxidx_thm ~1 #>

         Drule.implies_intr_list assms #>

         Drule.forall_intr_list fixes #>

         Thm.generalize (map #1 tfrees, []) 0 #>

         Thm.strip_shyps);

     val local_result =

       Thm.future global_result global_prop

       |> Thm.instantiate (instT, [])

       |> Drule.forall_elim_list fixes

       |> fold (Thm.elim_implies o Thm.assume) assms;

   in local_result end;

 (** tactical theorem proving **)

 (* prove_internal -- minimal checks, no normalization of result! *)

 fun prove_internal casms cprop tac =

   (case SINGLE (tac (map Assumption.assume casms)) (init cprop) of

     SOME th => Drule.implies_intr_list casms

       (finish (Syntax.init_pretty_global (Thm.theory_of_thm th)) th)

   | NONE => error "Tactic failed");

 (* prove_common etc. *)

 fun prove_common immediate ctxt xs asms props tac =

   let

     val thy = Proof_Context.theory_of ctxt;

     val string_of_term = Syntax.string_of_term ctxt;

     val pos = Position.thread_data ();

     fun err msg = cat_error msg

       ("The error(s) above occurred for the goal statement:\n" ^

         string_of_term (Logic.list_implies (asms, Logic.mk_conjunction_list props)) ^

         (case Position.str_of pos of "" => "" | s => "\n" ^ s));

     fun cert_safe t = Thm.cterm_of thy (Envir.beta_norm (Term.no_dummy_patterns t))

       handle TERM (msg, _) => err msg | TYPE (msg, _, _) => err msg;

     val casms = map cert_safe asms;

     val cprops = map cert_safe props;

     val (prems, ctxt') = ctxt

       |> Variable.add_fixes_direct xs

       |> fold Variable.declare_term (asms @ props)

       |> Assumption.add_assumes casms

       ||> Variable.set_body true;

     val sorts = Variable.sorts_of ctxt';

     val stmt = Thm.weaken_sorts sorts (Conjunction.mk_conjunction_balanced cprops);

     fun result () =

       (case SINGLE (tac {prems = prems, context = ctxt'}) (init stmt) of

         NONE => err "Tactic failed"

       | SOME st =>

           let val res = finish ctxt' st handle THM (msg, _, _) => err msg in

             if Unify.matches_list thy [Thm.term_of stmt] [Thm.prop_of res]

             then Thm.check_shyps sorts res

             else err ("Proved a different theorem: " ^ string_of_term (Thm.prop_of res))

           end);

     val res =

       if immediate orelse #maxidx (Thm.rep_cterm stmt) >= 0 orelse not (future_enabled ())

       then result ()

       else future_result ctxt' (fork result) (Thm.term_of stmt);

   in

     Conjunction.elim_balanced (length props) res

     |> map (Assumption.export false ctxt' ctxt)

     |> Variable.export ctxt' ctxt

     |> map Drule.zero_var_indexes

   end;

 val prove_multi = prove_common true;

 fun prove_future ctxt xs asms prop tac = hd (prove_common false ctxt xs asms [prop] tac);

 fun prove ctxt xs asms prop tac = hd (prove_common true ctxt xs asms [prop] tac);

 fun prove_global thy xs asms prop tac =

   Drule.export_without_context (prove (Proof_Context.init_global thy) xs asms prop tac);

 (** goal structure **)

 (* nested goals *)

 fun extract i n st =

   (if i < 1 orelse n < 1 orelse i + n - 1 > Thm.nprems_of st then Seq.empty

    else if n = 1 then Seq.single (Thm.cprem_of st i)

    else

      Seq.single (Conjunction.mk_conjunction_balanced (map (Thm.cprem_of st) (i upto i + n - 1))))

   |> Seq.map (Thm.adjust_maxidx_cterm ~1 #> init);

 fun retrofit i n st' st =

   (if n = 1 then st

    else st |> Drule.with_subgoal i (Conjunction.uncurry_balanced n))

   |> Thm.compose_no_flatten false (conclude st', Thm.nprems_of st') i;

 fun SELECT_GOAL tac i st =

   if Thm.nprems_of st = 1 andalso i = 1 then tac st

   else Seq.lifts (retrofit i 1) (Seq.maps tac (extract i 1 st)) st;

 (* multiple goals *)

 fun precise_conjunction_tac 0 i = eq_assume_tac i

   | precise_conjunction_tac 1 i = SUBGOAL (K all_tac) i

   | precise_conjunction_tac n i = PRIMITIVE (Drule.with_subgoal i (Conjunction.curry_balanced n));

 val adhoc_conjunction_tac = REPEAT_ALL_NEW

   (SUBGOAL (fn (goal, i) =>

     if can Logic.dest_conjunction goal then rtac Conjunction.conjunctionI i

     else no_tac));

 val conjunction_tac = SUBGOAL (fn (goal, i) =>

   precise_conjunction_tac (length (Logic.dest_conjunctions goal)) i ORELSE

   TRY (adhoc_conjunction_tac i));

 val recover_conjunction_tac = PRIMITIVE (fn th =>

   Conjunction.uncurry_balanced (Thm.nprems_of th) th);

 fun PRECISE_CONJUNCTS n tac =

   SELECT_GOAL (precise_conjunction_tac n 1

     THEN tac

     THEN recover_conjunction_tac);

 fun CONJUNCTS tac =

   SELECT_GOAL (conjunction_tac 1

     THEN tac

     THEN recover_conjunction_tac);

 (* hhf normal form *)

 val norm_hhf_tac =

   rtac Drule.asm_rl  (*cheap approximation -- thanks to builtin Logic.flatten_params*)

   THEN' SUBGOAL (fn (t, i) =>

     if Drule.is_norm_hhf t then all_tac

     else rewrite_goal_tac Drule.norm_hhf_eqs i);

 fun compose_hhf_tac th i st =

   PRIMSEQ (Thm.bicompose false (false, Drule.lift_all (Thm.cprem_of st i) th, 0) i) st;

 (* non-atomic goal assumptions *)

 fun non_atomic (Const ("==>", _) $ _ $ _) = true

   | non_atomic (Const ("all", _) $ _) = true

   | non_atomic _ = false;

 fun assume_rule_tac ctxt = norm_hhf_tac THEN' CSUBGOAL (fn (goal, i) =>

   let

     val ((_, goal'), ctxt') = Variable.focus goal ctxt;

     val goal'' = Drule.cterm_rule (singleton (Variable.export ctxt' ctxt)) goal';

     val Rs = filter (non_atomic o Thm.term_of) (Drule.strip_imp_prems goal'');

     val tacs = Rs |> map (fn R =>

       Tactic.etac (Raw_Simplifier.norm_hhf (Thm.trivial R)) THEN_ALL_NEW assume_tac);

   in fold_rev (curry op APPEND') tacs (K no_tac) i end);

 (* parallel tacticals *)

 (*parallel choice of single results*)

 fun PARALLEL_CHOICE tacs st =

   (case Par_List.get_some (fn tac => SINGLE tac st) tacs of

     NONE => Seq.empty

   | SOME st' => Seq.single st');

 (*parallel refinement of non-schematic goal by single results*)

 exception FAILED of unit;

 fun PARALLEL_GOALS tac =

   Thm.adjust_maxidx_thm ~1 #>

   (fn st =>

     if not (future_enabled ()) orelse Thm.maxidx_of st >= 0 orelse Thm.nprems_of st <= 1

     then DETERM tac st

     else

       let

         fun try_tac g =

           (case SINGLE tac g of

             NONE => raise FAILED ()

           | SOME g' => g');

         val goals = Drule.strip_imp_prems (Thm.cprop_of st);

         val results = Par_List.map (try_tac o init) goals;

       in ALLGOALS (fn i => retrofit i 1 (nth results (i - 1))) st end

       handle FAILED () => Seq.empty);

 end;

 structure Basic_Goal: BASIC_GOAL = Goal;

 open Basic_Goal;