(*  Title:      Pure/goal.ML

     Author:     Makarius

 Goals in tactical theorem proving, with support for forked proofs.

 *)

 signature BASIC_GOAL =

 sig

   val skip_proofs: bool Unsynchronized.ref

   val parallel_proofs: int Unsynchronized.ref

   val parallel_subproofs_saturation: int Unsynchronized.ref

   val parallel_subproofs_threshold: real 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 -> thm

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

   val norm_result: thm -> thm

   val fork_params: {name: string, pos: Position.T, pri: int} -> (unit -> 'a) -> 'a future

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

   val peek_futures: serial -> unit future list

   val reset_futures: unit -> Future.group list

   val shutdown_futures: unit -> unit

   val future_enabled_level: int -> bool

   val future_enabled: unit -> bool

   val future_enabled_nested: int -> bool

   val future_enabled_timing: Time.time -> bool

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

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

   val is_schematic: term -> bool

   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_future: theory -> 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 prove_sorry: Proof.context -> string list -> term list -> term ->

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

   val prove_sorry_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 =

   if Thm.no_prems th then th

   else

     raise THM ("Proof failed.\n" ^

       Pretty.string_of (Goal_Display.pretty_goal {main = true, limit = false} ctxt th), 0, [th]);

 fun finish ctxt = check_finished ctxt #> conclude;

 (** results **)

 (* normal form *)

 val norm_result =

   Drule.flexflex_unique

   #> Raw_Simplifier.norm_hhf_protect

   #> Thm.strip_shyps

   #> Drule.zero_var_indexes;

 (* forked proofs *)

 local

 val forked_proofs =

   Synchronized.var "forked_proofs"

     (0, []: Future.group list, Inttab.empty: unit future list Inttab.table);

 fun count_forked i =

   Synchronized.change forked_proofs (fn (m, groups, tab) =>

     let

       val n = m + i;

       val _ = Future.forked_proofs := n;

     in (n, groups, tab) end);

 fun register_forked id future =

   Synchronized.change forked_proofs (fn (m, groups, tab) =>

     let

       val groups' = Task_Queue.group_of_task (Future.task_of future) :: groups;

       val tab' = Inttab.cons_list (id, Future.map (K ()) future) tab;

     in (m, groups', tab') end);

 fun status task markups =

   let val props = Markup.properties [(Markup.taskN, Task_Queue.str_of_task task)]

   in Output.status (implode (map (Markup.markup_only o props) markups)) end;

 in

 fun fork_params {name, pos, pri} e =

   uninterruptible (fn _ => Position.setmp_thread_data pos (fn () =>

     let

       val id = the_default 0 (Position.parse_id pos);

       val _ = count_forked 1;

       val future =

         (singleton o Future.forks)

           {name = name, group = NONE, deps = [], pri = pri, interrupts = false}

           (fn () =>

             let

               val task = the (Future.worker_task ());

               val _ = status task [Markup.running];

               val result =

                 Exn.capture (Future.interruptible_task e) ()

                 |> Future.identify_result pos;

               val _ = status task [Markup.finished, Markup.joined];

               val _ =

                 (case result of

                   Exn.Res _ => ()

                 | Exn.Exn exn =>

                     if id = 0 orelse Exn.is_interrupt exn then ()

                     else

                       (status task [Markup.failed];

                        Output.report (Markup.markup_only Markup.bad);

                        List.app (Future.error_msg pos) (ML_Compiler.exn_messages_ids exn)));

               val _ = count_forked ~1;

             in Exn.release result end);

       val _ = status (Future.task_of future) [Markup.forked];

       val _ = register_forked id future;

     in future end)) ();

 fun fork pri e =

   fork_params {name = "Goal.fork", pos = Position.thread_data (), pri = pri} e;

 fun forked_count () = #1 (Synchronized.value forked_proofs);

 fun peek_futures id =

   Inttab.lookup_list (#3 (Synchronized.value forked_proofs)) id;

 fun reset_futures () =

   Synchronized.change_result forked_proofs (fn (_, groups, _) =>

     (Future.forked_proofs := 0; (groups, (0, [], Inttab.empty))));

 fun shutdown_futures () =

   (Future.shutdown ();

     (case map_filter Task_Queue.group_status (reset_futures ()) of

       [] => ()

     | exns => raise Par_Exn.make exns));

 end;

 (* scheduling parameters *)

 val skip_proofs = Unsynchronized.ref false;

 val parallel_proofs = Unsynchronized.ref 1;

 val parallel_subproofs_saturation = Unsynchronized.ref 100;

 val parallel_subproofs_threshold = Unsynchronized.ref 0.01;

 fun future_enabled_level n =

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

   is_some (Future.worker_task ());

 fun future_enabled () = future_enabled_level 1;

 fun future_enabled_nested n =

   future_enabled_level n andalso

   forked_count () < ! parallel_subproofs_saturation * Multithreading.max_threads_value ();

 fun future_enabled_timing t =

   future_enabled () andalso Time.toReal t >= ! parallel_subproofs_threshold;

 (* 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 (Logic.varify_types_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.close_derivation

       |> 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 variations *)

 fun is_schematic t =

   Term.exists_subterm Term.is_Var t orelse

   Term.exists_type (Term.exists_subtype Term.is_TVar) t;

 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 schematic = exists is_schematic props;

     val future = future_enabled ();

     val skip = not immediate andalso not schematic andalso future andalso ! skip_proofs;

     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.here 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 tac' args st =

       if skip then ALLGOALS Skip_Proof.cheat_tac st before Skip_Proof.report ctxt

       else tac args st;

     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 schematic orelse not future orelse skip

       then result ()

       else future_result ctxt' (fork ~1 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_future thy xs asms prop tac =

   Drule.export_without_context (prove_future (Proof_Context.init_global thy) 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);

 fun prove_sorry ctxt xs asms prop tac =

   if ! quick_and_dirty then

     prove ctxt xs asms prop (fn _ => ALLGOALS Skip_Proof.cheat_tac)

   else (if future_enabled () then prove_future else prove) ctxt xs asms prop tac;

 fun prove_sorry_global thy xs asms prop tac =

   Drule.export_without_context

     (prove_sorry (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_cterm 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 (Multithreading.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;