src/Pure/Isar/proof.ML
author wenzelm
Wed Dec 14 16:59:41 2016 +0100 (2016-12-14)
changeset 64567 7141a3a4dc83
parent 64420 2efc128370fa
child 65458 cf504b7a7aa7
permissions -rw-r--r--
always close derivation, for significantly improved performance without parallel proofs;
     1 (*  Title:      Pure/Isar/proof.ML
     2     Author:     Markus Wenzel, TU Muenchen
     3 
     4 The Isar/VM proof language interpreter: maintains a structured flow of
     5 context elements, goals, refinements, and facts.
     6 *)
     7 
     8 signature PROOF =
     9 sig
    10   type context = Proof.context
    11   type method = Method.method
    12   type state
    13   val init: context -> state
    14   val level: state -> int
    15   val assert_bottom: bool -> state -> state
    16   val context_of: state -> context
    17   val theory_of: state -> theory
    18   val map_context: (context -> context) -> state -> state
    19   val map_context_result : (context -> 'a * context) -> state -> 'a * state
    20   val map_contexts: (context -> context) -> state -> state
    21   val propagate_ml_env: state -> state
    22   val report_improper: state -> unit
    23   val the_facts: state -> thm list
    24   val the_fact: state -> thm
    25   val set_facts: thm list -> state -> state
    26   val reset_facts: state -> state
    27   val improper_reset_facts: state -> state
    28   val assert_forward: state -> state
    29   val assert_chain: state -> state
    30   val assert_forward_or_chain: state -> state
    31   val assert_backward: state -> state
    32   val assert_no_chain: state -> state
    33   val enter_forward: state -> state
    34   val enter_chain: state -> state
    35   val enter_backward: state -> state
    36   val has_bottom_goal: state -> bool
    37   val using_facts: thm list -> state -> state
    38   val pretty_state: state -> Pretty.T list
    39   val refine: Method.text -> state -> state Seq.result Seq.seq
    40   val refine_end: Method.text -> state -> state Seq.result Seq.seq
    41   val refine_singleton: Method.text -> state -> state
    42   val refine_insert: thm list -> state -> state
    43   val refine_primitive: (Proof.context -> thm -> thm) -> state -> state
    44   val raw_goal: state -> {context: context, facts: thm list, goal: thm}
    45   val goal: state -> {context: context, facts: thm list, goal: thm}
    46   val simple_goal: state -> {context: context, goal: thm}
    47   val let_bind: (term list * term) list -> state -> state
    48   val let_bind_cmd: (string list * string) list -> state -> state
    49   val write: Syntax.mode -> (term * mixfix) list -> state -> state
    50   val write_cmd: Syntax.mode -> (string * mixfix) list -> state -> state
    51   val fix: (binding * typ option * mixfix) list -> state -> state
    52   val fix_cmd: (binding * string option * mixfix) list -> state -> state
    53   val assm: Assumption.export -> (binding * typ option * mixfix) list ->
    54     (term * term list) list list -> (Thm.binding * (term * term list) list) list ->
    55     state -> state
    56   val assm_cmd: Assumption.export -> (binding * string option * mixfix) list ->
    57     (string * string list) list list -> (Attrib.binding * (string * string list) list) list ->
    58     state -> state
    59   val assume: (binding * typ option * mixfix) list ->
    60     (term * term list) list list -> (Thm.binding * (term * term list) list) list ->
    61     state -> state
    62   val assume_cmd: (binding * string option * mixfix) list ->
    63     (string * string list) list list -> (Attrib.binding * (string * string list) list) list ->
    64     state -> state
    65   val presume: (binding * typ option * mixfix) list ->
    66     (term * term list) list list -> (Thm.binding * (term * term list) list) list ->
    67     state -> state
    68   val presume_cmd: (binding * string option * mixfix) list ->
    69     (string * string list) list list -> (Attrib.binding * (string * string list) list) list ->
    70     state -> state
    71   val def: (Thm.binding * ((binding * mixfix) * (term * term list))) list -> state -> state
    72   val def_cmd: (Attrib.binding * ((binding * mixfix) * (string * string list))) list -> state -> state
    73   val chain: state -> state
    74   val chain_facts: thm list -> state -> state
    75   val note_thmss: (Thm.binding * (thm list * attribute list) list) list -> state -> state
    76   val note_thmss_cmd: (Attrib.binding * (Facts.ref * Token.src list) list) list -> state -> state
    77   val from_thmss: ((thm list * attribute list) list) list -> state -> state
    78   val from_thmss_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
    79   val with_thmss: ((thm list * attribute list) list) list -> state -> state
    80   val with_thmss_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
    81   val supply: (Thm.binding * (thm list * attribute list) list) list -> state -> state
    82   val supply_cmd: (Attrib.binding * (Facts.ref * Token.src list) list) list -> state -> state
    83   val using: ((thm list * attribute list) list) list -> state -> state
    84   val using_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
    85   val unfolding: ((thm list * attribute list) list) list -> state -> state
    86   val unfolding_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
    87   val case_: Thm.binding * ((string * Position.T) * binding option list) -> state -> state
    88   val case_cmd: Attrib.binding * ((string * Position.T) * binding option list) -> state -> state
    89   val define: (binding * typ option * mixfix) list ->
    90     (binding * typ option * mixfix) list ->
    91     (Thm.binding * (term * term list) list) list -> state -> state
    92   val define_cmd: (binding * string option * mixfix) list ->
    93     (binding * string option * mixfix) list ->
    94     (Attrib.binding * (string * string list) list) list -> state -> state
    95   val begin_block: state -> state
    96   val next_block: state -> state
    97   val end_block: state -> state
    98   val begin_notepad: context -> state
    99   val end_notepad: state -> context
   100   val proof: Method.text_range option -> state -> state Seq.result Seq.seq
   101   val defer: int -> state -> state
   102   val prefer: int -> state -> state
   103   val apply: Method.text_range -> state -> state Seq.result Seq.seq
   104   val apply_end: Method.text_range -> state -> state Seq.result Seq.seq
   105   val local_qed: Method.text_range option * bool -> state -> state
   106   val theorem: Method.text option -> (thm list list -> context -> context) ->
   107     (term * term list) list list -> context -> state
   108   val theorem_cmd: Method.text option -> (thm list list -> context -> context) ->
   109     (string * string list) list list -> context -> state
   110   val global_qed: Method.text_range option * bool -> state -> context
   111   val local_terminal_proof: Method.text_range * Method.text_range option -> state -> state
   112   val local_default_proof: state -> state
   113   val local_immediate_proof: state -> state
   114   val local_skip_proof: bool -> state -> state
   115   val local_done_proof: state -> state
   116   val global_terminal_proof: Method.text_range * Method.text_range option -> state -> context
   117   val global_default_proof: state -> context
   118   val global_immediate_proof: state -> context
   119   val global_skip_proof: bool -> state -> context
   120   val global_done_proof: state -> context
   121   val internal_goal: (context -> (string * string) * (string * thm list) list -> unit) ->
   122     Proof_Context.mode -> bool -> string -> Method.text option ->
   123     (context * thm list list -> state -> state) ->
   124     (binding * typ option * mixfix) list ->
   125     (Thm.binding * (term * term list) list) list ->
   126     (Thm.binding * (term * term list) list) list -> state -> thm list * state
   127   val have: bool -> Method.text option -> (context * thm list list -> state -> state) ->
   128     (binding * typ option * mixfix) list ->
   129     (Thm.binding * (term * term list) list) list ->
   130     (Thm.binding * (term * term list) list) list -> bool -> state -> thm list * state
   131   val have_cmd: bool -> Method.text option -> (context * thm list list -> state -> state) ->
   132     (binding * string option * mixfix) list ->
   133     (Attrib.binding * (string * string list) list) list ->
   134     (Attrib.binding * (string * string list) list) list -> bool -> state -> thm list * state
   135   val show: bool -> Method.text option -> (context * thm list list -> state -> state) ->
   136     (binding * typ option * mixfix) list ->
   137     (Thm.binding * (term * term list) list) list ->
   138     (Thm.binding * (term * term list) list) list -> bool -> state -> thm list * state
   139   val show_cmd: bool -> Method.text option -> (context * thm list list -> state -> state) ->
   140     (binding * string option * mixfix) list ->
   141     (Attrib.binding * (string * string list) list) list ->
   142     (Attrib.binding * (string * string list) list) list -> bool -> state -> thm list * state
   143   val schematic_goal: state -> bool
   144   val is_relevant: state -> bool
   145   val future_proof: (state -> ('a * context) future) -> state -> 'a future * state
   146   val local_future_terminal_proof: Method.text_range * Method.text_range option -> state -> state
   147   val global_future_terminal_proof: Method.text_range * Method.text_range option -> state -> context
   148 end;
   149 
   150 structure Proof: PROOF =
   151 struct
   152 
   153 type context = Proof.context;
   154 type method = Method.method;
   155 
   156 
   157 (** proof state **)
   158 
   159 (* datatype state *)
   160 
   161 datatype mode = Forward | Chain | Backward;
   162 
   163 datatype state =
   164   State of node Stack.T
   165 and node =
   166   Node of
   167    {context: context,
   168     facts: (thm list * bool) option,
   169     mode: mode,
   170     goal: goal option}
   171 and goal =
   172   Goal of
   173    {statement: (string * Position.T) * term list list * term,
   174       (*goal kind and statement (starting with vars), initial proposition*)
   175     using: thm list,                      (*goal facts*)
   176     goal: thm,                            (*subgoals ==> statement*)
   177     before_qed: Method.text option,
   178     after_qed:
   179       (context * thm list list -> state -> state) *
   180       (context * thm list list -> context -> context)};
   181 
   182 val _ =
   183   ML_system_pp (fn _ => fn _ => fn _: state =>
   184     Pretty.to_polyml (Pretty.str "<Proof.state>"));
   185 
   186 fun make_goal (statement, using, goal, before_qed, after_qed) =
   187   Goal {statement = statement, using = using, goal = goal,
   188     before_qed = before_qed, after_qed = after_qed};
   189 
   190 fun make_node (context, facts, mode, goal) =
   191   Node {context = context, facts = facts, mode = mode, goal = goal};
   192 
   193 fun map_node f (Node {context, facts, mode, goal}) =
   194   make_node (f (context, facts, mode, goal));
   195 
   196 val init_context =
   197   Proof_Context.set_stmt true #>
   198   Proof_Context.map_naming (K Name_Space.local_naming);
   199 
   200 fun init ctxt =
   201   State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
   202 
   203 fun top (State stack) = Stack.top stack |> (fn Node node => node);
   204 fun map_top f (State stack) = State (Stack.map_top (map_node f) stack);
   205 fun map_all f (State stack) = State (Stack.map_all (map_node f) stack);
   206 
   207 
   208 
   209 (** basic proof state operations **)
   210 
   211 (* block structure *)
   212 
   213 fun open_block (State stack) = State (Stack.push stack);
   214 
   215 fun close_block (State stack) = State (Stack.pop stack)
   216   handle List.Empty => error "Unbalanced block parentheses";
   217 
   218 fun level (State stack) = Stack.level stack;
   219 
   220 fun assert_bottom b state =
   221   let val b' = level state <= 2 in
   222     if b andalso not b' then error "Not at bottom of proof"
   223     else if not b andalso b' then error "Already at bottom of proof"
   224     else state
   225   end;
   226 
   227 
   228 (* context *)
   229 
   230 val context_of = #context o top;
   231 val theory_of = Proof_Context.theory_of o context_of;
   232 
   233 fun map_context f =
   234   map_top (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
   235 
   236 fun map_context_result f state =
   237   f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
   238 
   239 fun map_contexts f = map_all (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
   240 
   241 fun propagate_ml_env state = map_contexts
   242   (Context.proof_map (ML_Env.inherit (Context.Proof (context_of state)))) state;
   243 
   244 
   245 (* facts *)
   246 
   247 fun report_improper state =
   248   Context_Position.report (context_of state) (Position.thread_data ()) Markup.improper;
   249 
   250 val get_facts = #facts o top;
   251 
   252 fun the_facts state =
   253   (case get_facts state of
   254     SOME (facts, proper) => (if proper then () else report_improper state; facts)
   255   | NONE => error "No current facts available");
   256 
   257 fun the_fact state =
   258   (case the_facts state of
   259     [thm] => thm
   260   | _ => error "Single theorem expected");
   261 
   262 fun put_facts index facts =
   263   map_top (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
   264   map_context (Proof_Context.put_thms index (Auto_Bind.thisN, Option.map #1 facts));
   265 
   266 fun set_facts thms = put_facts false (SOME (thms, true));
   267 val reset_facts = put_facts false NONE;
   268 
   269 fun improper_reset_facts state =
   270   (case get_facts state of
   271     SOME (thms, _) => put_facts false (SOME (thms, false)) state
   272   | NONE => state);
   273 
   274 fun these_factss more_facts (named_factss, state) =
   275   (named_factss, state |> set_facts (maps snd named_factss @ more_facts));
   276 
   277 fun export_facts inner outer =
   278   (case get_facts inner of
   279     NONE => reset_facts outer
   280   | SOME (thms, proper) =>
   281       let val thms' = Proof_Context.export (context_of inner) (context_of outer) thms
   282       in put_facts true (SOME (thms', proper)) outer end);
   283 
   284 
   285 (* mode *)
   286 
   287 val get_mode = #mode o top;
   288 fun put_mode mode = map_top (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
   289 
   290 val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
   291 
   292 fun assert_mode pred state =
   293   let val mode = get_mode state in
   294     if pred mode then state
   295     else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
   296   end;
   297 
   298 val assert_forward = assert_mode (fn mode => mode = Forward);
   299 val assert_chain = assert_mode (fn mode => mode = Chain);
   300 val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
   301 val assert_backward = assert_mode (fn mode => mode = Backward);
   302 val assert_no_chain = assert_mode (fn mode => mode <> Chain);
   303 
   304 val enter_forward = put_mode Forward;
   305 val enter_chain = put_mode Chain;
   306 val enter_backward = put_mode Backward;
   307 
   308 
   309 (* current goal *)
   310 
   311 fun current_goal state =
   312   (case top state of
   313     {context = ctxt, goal = SOME (Goal goal), ...} => (ctxt, goal)
   314   | _ => error "No current goal");
   315 
   316 fun assert_current_goal g state =
   317   let val g' = can current_goal state in
   318     if g andalso not g' then error "No goal in this block"
   319     else if not g andalso g' then error "Goal present in this block"
   320     else state
   321   end;
   322 
   323 fun put_goal goal = map_top (fn (ctxt, facts, mode, _) => (ctxt, facts, mode, goal));
   324 
   325 val set_goal = put_goal o SOME;
   326 val reset_goal = put_goal NONE;
   327 
   328 val before_qed = #before_qed o #2 o current_goal;
   329 
   330 
   331 (* bottom goal *)
   332 
   333 fun has_bottom_goal (State stack) =
   334   let
   335     fun bottom [Node {goal = SOME _, ...}, Node {goal = NONE, ...}] = true
   336       | bottom [Node {goal, ...}] = is_some goal
   337       | bottom [] = false
   338       | bottom (_ :: rest) = bottom rest;
   339   in bottom (op :: (Stack.dest stack)) end;
   340 
   341 
   342 (* nested goal *)
   343 
   344 fun map_goal f (State stack) =
   345   (case Stack.dest stack of
   346     (Node {context = ctxt, facts, mode, goal = SOME goal}, node :: nodes) =>
   347       let
   348         val Goal {statement, using, goal, before_qed, after_qed} = goal;
   349         val (ctxt', statement', using', goal', before_qed', after_qed') =
   350           f (ctxt, statement, using, goal, before_qed, after_qed);
   351         val goal' = make_goal (statement', using', goal', before_qed', after_qed');
   352       in State (Stack.make (make_node (ctxt', facts, mode, SOME goal')) (node :: nodes)) end
   353   | (top_node, node :: nodes) =>
   354       let
   355         val State stack' = map_goal f (State (Stack.make node nodes));
   356         val (node', nodes') = Stack.dest stack';
   357       in State (Stack.make top_node (node' :: nodes')) end
   358   | _ => State stack);
   359 
   360 fun provide_goal goal =
   361   map_goal (fn (ctxt, statement, using, _, before_qed, after_qed) =>
   362     (ctxt, statement, using, goal, before_qed, after_qed));
   363 
   364 fun using_facts using =
   365   map_goal (fn (ctxt, statement, _, goal, before_qed, after_qed) =>
   366     (ctxt, statement, using, goal, before_qed, after_qed));
   367 
   368 fun find_goal state =
   369   (case try current_goal state of
   370     SOME ctxt_goal => ctxt_goal
   371   | NONE => find_goal (close_block state handle ERROR _ => error "No proof goal"));
   372 
   373 fun get_goal state =
   374   let val (ctxt, {using, goal, ...}) = find_goal state
   375   in (ctxt, (using, goal)) end;
   376 
   377 
   378 
   379 (** pretty_state **)
   380 
   381 local
   382 
   383 fun pretty_facts _ _ NONE = []
   384   | pretty_facts ctxt s (SOME ths) = [Proof_Display.pretty_goal_facts ctxt s ths];
   385 
   386 fun pretty_sep prts [] = prts
   387   | pretty_sep [] prts = prts
   388   | pretty_sep prts1 prts2 = prts1 @ [Pretty.str ""] @ prts2;
   389 
   390 in
   391 
   392 fun pretty_state state =
   393   let
   394     val {context = ctxt, facts, mode, goal = _} = top state;
   395     val verbose = Config.get ctxt Proof_Context.verbose;
   396 
   397     fun prt_goal (SOME (_, {statement = _, using, goal, before_qed = _, after_qed = _})) =
   398           pretty_sep
   399             (pretty_facts ctxt "using"
   400               (if mode <> Backward orelse null using then NONE else SOME using))
   401             ([Proof_Display.pretty_goal_header goal] @ Goal_Display.pretty_goals ctxt goal)
   402       | prt_goal NONE = [];
   403 
   404     val prt_ctxt =
   405       if verbose orelse mode = Forward then Proof_Context.pretty_context ctxt
   406       else if mode = Backward then Proof_Context.pretty_ctxt ctxt
   407       else [];
   408 
   409     val position_markup = Position.markup (Position.thread_data ()) Markup.position;
   410   in
   411     [Pretty.block
   412       [Pretty.mark_str (position_markup, "proof"), Pretty.str (" (" ^ mode_name mode ^ ")")]] @
   413     (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
   414     (if verbose orelse mode = Forward then
   415        pretty_sep (pretty_facts ctxt "" (Option.map #1 facts)) (prt_goal (try find_goal state))
   416      else if mode = Chain then pretty_facts ctxt "picking" (Option.map #1 facts)
   417      else prt_goal (try find_goal state))
   418   end;
   419 
   420 end;
   421 
   422 
   423 
   424 (** proof steps **)
   425 
   426 (* refine via method *)
   427 
   428 local
   429 
   430 fun goalN i = "goal" ^ string_of_int i;
   431 fun goals st = map goalN (1 upto Thm.nprems_of st);
   432 
   433 fun no_goal_cases st = map (rpair NONE) (goals st);
   434 
   435 fun goal_cases ctxt st =
   436   Rule_Cases.make_common ctxt (Thm.prop_of st) (map (rpair [] o rpair []) (goals st));
   437 
   438 fun apply_method text ctxt state =
   439   find_goal state |> (fn (goal_ctxt, {statement, using, goal, before_qed, after_qed}) =>
   440     Method.evaluate text ctxt using (goal_ctxt, goal)
   441     |> Seq.map_result (fn (goal_ctxt', goal') =>
   442       let
   443         val goal_ctxt'' = goal_ctxt'
   444           |> Proof_Context.update_cases_legacy (no_goal_cases goal @ goal_cases ctxt goal');
   445         val state' = state
   446           |> map_goal (K (goal_ctxt'', statement, using, goal', before_qed, after_qed));
   447       in state' end));
   448 
   449 in
   450 
   451 fun refine text state = apply_method text (context_of state) state;
   452 fun refine_end text state = apply_method text (#1 (find_goal state)) state;
   453 
   454 fun refine_singleton text = refine text #> Seq.the_result "";
   455 
   456 fun refine_insert ths =
   457   refine_singleton (Method.Basic (K (Method.insert ths)));
   458 
   459 fun refine_primitive r =
   460   refine_singleton (Method.Basic (fn ctxt => fn _ => Method.CONTEXT_TACTIC (PRIMITIVE (r ctxt))));
   461 
   462 end;
   463 
   464 
   465 (* refine via sub-proof *)
   466 
   467 local
   468 
   469 fun finish_tac _ 0 = K all_tac
   470   | finish_tac ctxt n =
   471       Goal.norm_hhf_tac ctxt THEN'
   472       SUBGOAL (fn (goal, i) =>
   473         if can Logic.unprotect (Logic.strip_assums_concl goal) then
   474           eresolve_tac ctxt [Drule.protectI] i THEN finish_tac ctxt (n - 1) i
   475         else finish_tac ctxt (n - 1) (i + 1));
   476 
   477 fun goal_tac ctxt rule =
   478   Goal.norm_hhf_tac ctxt THEN'
   479   resolve_tac ctxt [rule] THEN'
   480   finish_tac ctxt (Thm.nprems_of rule);
   481 
   482 fun FINDGOAL tac st =
   483   let fun find i n = if i > n then Seq.fail else Seq.APPEND (tac i, find (i + 1) n)
   484   in find 1 (Thm.nprems_of st) st end;
   485 
   486 fun protect_prem i th =
   487   Thm.bicompose NONE {flatten = false, match = false, incremented = true}
   488     (false, Drule.incr_indexes th Drule.protectD, 1) i th
   489   |> Seq.hd;
   490 
   491 fun protect_prems th =
   492   fold_rev protect_prem (1 upto Thm.nprems_of th) th;
   493 
   494 in
   495 
   496 fun refine_goals print_rule result_ctxt result state =
   497   let
   498     val (goal_ctxt, (_, goal)) = get_goal state;
   499     fun refine rule st =
   500       (print_rule goal_ctxt rule; FINDGOAL (goal_tac goal_ctxt rule) st);
   501   in
   502     result
   503     |> map (Raw_Simplifier.norm_hhf result_ctxt #> protect_prems)
   504     |> Proof_Context.goal_export result_ctxt goal_ctxt
   505     |> (fn rules => Seq.lift provide_goal (EVERY (map refine rules) goal) state)
   506   end;
   507 
   508 end;
   509 
   510 
   511 (* conclude goal *)
   512 
   513 fun conclude_goal ctxt goal propss =
   514   let
   515     val thy = Proof_Context.theory_of ctxt;
   516 
   517     val _ =
   518       Context.subthy_id (Thm.theory_id_of_thm goal, Context.theory_id thy) orelse
   519         error "Bad background theory of goal state";
   520     val _ = Thm.no_prems goal orelse error (Proof_Display.string_of_goal ctxt goal);
   521 
   522     fun err_lost () = error ("Lost goal structure:\n" ^ Thm.string_of_thm ctxt goal);
   523 
   524     val th =
   525       (Goal.conclude (Thm.close_derivation goal) handle THM _ => err_lost ())
   526       |> Drule.flexflex_unique (SOME ctxt)
   527       |> Thm.check_shyps ctxt
   528       |> Thm.check_hyps (Context.Proof ctxt);
   529 
   530     val goal_propss = filter_out null propss;
   531     val results =
   532       Conjunction.elim_balanced (length goal_propss) th
   533       |> map2 Conjunction.elim_balanced (map length goal_propss)
   534       handle THM _ => err_lost ();
   535     val _ =
   536       Unify.matches_list (Context.Proof ctxt) (flat goal_propss) (map Thm.prop_of (flat results))
   537         orelse error ("Proved a different theorem:\n" ^ Thm.string_of_thm ctxt th);
   538 
   539     fun recover_result ([] :: pss) thss = [] :: recover_result pss thss
   540       | recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss
   541       | recover_result [] [] = []
   542       | recover_result _ _ = err_lost ();
   543   in recover_result propss results end;
   544 
   545 val finished_goal_error = "Failed to finish proof";
   546 
   547 fun finished_goal pos state =
   548   let val (ctxt, (_, goal)) = get_goal state in
   549     if Thm.no_prems goal then Seq.Result state
   550     else
   551       Seq.Error (fn () =>
   552         finished_goal_error ^ Position.here pos ^ ":\n" ^
   553           Proof_Display.string_of_goal ctxt goal)
   554   end;
   555 
   556 
   557 (* goal views -- corresponding to methods *)
   558 
   559 fun raw_goal state =
   560   let val (ctxt, (using, goal)) = get_goal state
   561   in {context = ctxt, facts = using, goal = goal} end;
   562 
   563 val goal = raw_goal o refine_insert [];
   564 
   565 fun simple_goal state =
   566   let
   567     val (_, (using, _)) = get_goal state;
   568     val (ctxt, (_, goal)) = get_goal (refine_insert using state);
   569   in {context = ctxt, goal = goal} end;
   570 
   571 fun method_error kind pos state =
   572   Seq.single (Proof_Display.method_error kind pos (raw_goal state));
   573 
   574 
   575 
   576 (*** structured proof commands ***)
   577 
   578 (** context elements **)
   579 
   580 (* let bindings *)
   581 
   582 local
   583 
   584 fun gen_bind bind args state =
   585   state
   586   |> assert_forward
   587   |> map_context (bind true args #> snd)
   588   |> reset_facts;
   589 
   590 in
   591 
   592 val let_bind = gen_bind Proof_Context.match_bind;
   593 val let_bind_cmd = gen_bind Proof_Context.match_bind_cmd;
   594 
   595 end;
   596 
   597 
   598 (* concrete syntax *)
   599 
   600 local
   601 
   602 fun read_arg (c, mx) ctxt =
   603   (case Proof_Context.read_const {proper = false, strict = false} ctxt c of
   604     Free (x, _) =>
   605       let
   606         val ctxt' =
   607           ctxt |> is_none (Variable.default_type ctxt x) ?
   608             Variable.declare_constraints (Free (x, Mixfix.default_constraint mx));
   609         val t = Free (#1 (Proof_Context.inferred_param x ctxt'));
   610       in ((t, mx), ctxt') end
   611   | t => ((t, mx), ctxt));
   612 
   613 fun gen_write prep_arg mode args =
   614   assert_forward
   615   #> map_context (fold_map prep_arg args #-> Proof_Context.notation true mode)
   616   #> reset_facts;
   617 
   618 in
   619 
   620 val write = gen_write pair;
   621 val write_cmd = gen_write read_arg;
   622 
   623 end;
   624 
   625 
   626 (* fix *)
   627 
   628 local
   629 
   630 fun gen_fix add_fixes raw_fixes =
   631   assert_forward
   632   #> map_context (snd o add_fixes raw_fixes)
   633   #> reset_facts;
   634 
   635 in
   636 
   637 val fix = gen_fix Proof_Context.add_fixes;
   638 val fix_cmd = gen_fix Proof_Context.add_fixes_cmd;
   639 
   640 end;
   641 
   642 
   643 (* assume *)
   644 
   645 local
   646 
   647 fun gen_assume prep_statement prep_att export raw_fixes raw_prems raw_concls state =
   648   let
   649     val ctxt = context_of state;
   650 
   651     val bindings = map (apsnd (map (prep_att ctxt)) o fst) raw_concls;
   652     val ((params, prems_propss, concl_propss, result_binds), _) =
   653       prep_statement raw_fixes raw_prems (map snd raw_concls) ctxt;
   654     val propss = (map o map) (Logic.close_prop params (flat prems_propss)) concl_propss;
   655   in
   656     state
   657     |> assert_forward
   658     |> map_context_result (fn ctxt =>
   659       ctxt
   660       |> (fold o fold) Variable.declare_term propss
   661       |> fold Variable.maybe_bind_term result_binds
   662       |> fold_burrow (Assumption.add_assms export o map (Thm.cterm_of ctxt)) propss
   663       |-> (fn premss =>
   664         Proof_Context.note_thmss "" (bindings ~~ (map o map) (fn th => ([th], [])) premss)))
   665     |> these_factss [] |> #2
   666   end;
   667 
   668 in
   669 
   670 val assm = gen_assume Proof_Context.cert_statement (K I);
   671 val assm_cmd = gen_assume Proof_Context.read_statement Attrib.attribute_cmd;
   672 
   673 val assume = assm Assumption.assume_export;
   674 val assume_cmd = assm_cmd Assumption.assume_export;
   675 
   676 val presume = assm Assumption.presume_export;
   677 val presume_cmd = assm_cmd Assumption.presume_export;
   678 
   679 end;
   680 
   681 
   682 (* def *)
   683 
   684 local
   685 
   686 fun gen_def prep_att prep_var prep_binds args state =
   687   let
   688     val _ = assert_forward state;
   689     val (raw_name_atts, (raw_vars, raw_rhss)) = args |> split_list ||> split_list;
   690     val name_atts = map (apsnd (map (prep_att (context_of state)))) raw_name_atts;
   691   in
   692     state
   693     |> map_context_result (fold_map (fn (x, mx) => prep_var (x, NONE, mx)) raw_vars)
   694     |>> map (fn (x, _, mx) => (x, mx))
   695     |-> (fn vars =>
   696       map_context_result (prep_binds false (map swap raw_rhss))
   697       #-> (fn rhss =>
   698         let
   699           val defs = (vars ~~ (name_atts ~~ rhss)) |> map (fn ((x, mx), ((a, atts), rhs)) =>
   700             ((x, mx), ((Thm.def_binding_optional x a, atts), rhs)));
   701         in map_context_result (Local_Defs.define defs) end))
   702     |-> (set_facts o map (#2 o #2))
   703   end;
   704 
   705 in
   706 
   707 val def = gen_def (K I) Proof_Context.cert_var Proof_Context.match_bind;
   708 val def_cmd = gen_def Attrib.attribute_cmd Proof_Context.read_var Proof_Context.match_bind_cmd;
   709 
   710 end;
   711 
   712 
   713 
   714 (** facts **)
   715 
   716 (* chain *)
   717 
   718 val chain =
   719   assert_forward
   720   #> (fn state => set_facts (Method.clean_facts (the_facts state)) state)
   721   #> enter_chain;
   722 
   723 fun chain_facts facts =
   724   set_facts facts
   725   #> chain;
   726 
   727 
   728 (* note etc. *)
   729 
   730 fun empty_bindings args = map (pair Binding.empty_atts) args;
   731 
   732 local
   733 
   734 fun gen_thmss more_facts opt_chain opt_result prep_atts prep_fact args state =
   735   state
   736   |> assert_forward
   737   |> map_context_result (fn ctxt => ctxt |> Proof_Context.note_thmss ""
   738     (Attrib.map_facts_refs (map (prep_atts ctxt)) (prep_fact ctxt) args))
   739   |> these_factss (more_facts state)
   740   ||> opt_chain
   741   |> opt_result;
   742 
   743 in
   744 
   745 val note_thmss = gen_thmss (K []) I #2 (K I) (K I);
   746 val note_thmss_cmd = gen_thmss (K []) I #2 Attrib.attribute_cmd Proof_Context.get_fact;
   747 
   748 val from_thmss = gen_thmss (K []) chain #2 (K I) (K I) o empty_bindings;
   749 val from_thmss_cmd =
   750   gen_thmss (K []) chain #2 Attrib.attribute_cmd Proof_Context.get_fact o empty_bindings;
   751 
   752 val with_thmss = gen_thmss the_facts chain #2 (K I) (K I) o empty_bindings;
   753 val with_thmss_cmd =
   754   gen_thmss the_facts chain #2 Attrib.attribute_cmd Proof_Context.get_fact o empty_bindings;
   755 
   756 val local_results = gen_thmss (K []) I I (K I) (K I) o map (apsnd Thm.simple_fact);
   757 
   758 end;
   759 
   760 
   761 (* facts during goal refinement *)
   762 
   763 local
   764 
   765 fun gen_supply prep_att prep_fact args state =
   766   state
   767   |> assert_backward
   768   |> map_context (fn ctxt => ctxt |> Proof_Context.note_thmss ""
   769        (Attrib.map_facts_refs (map (prep_att ctxt)) (prep_fact ctxt) args) |> snd);
   770 
   771 in
   772 
   773 val supply = gen_supply (K I) (K I);
   774 val supply_cmd = gen_supply Attrib.attribute_cmd Proof_Context.get_fact;
   775 
   776 end;
   777 
   778 
   779 (* using/unfolding *)
   780 
   781 local
   782 
   783 fun gen_using f g prep_att prep_fact args state =
   784   state
   785   |> assert_backward
   786   |> map_context_result
   787     (fn ctxt => ctxt |> Proof_Context.note_thmss ""
   788       (Attrib.map_facts_refs (map (prep_att ctxt)) (prep_fact ctxt) (empty_bindings args)))
   789   |> (fn (named_facts, state') =>
   790     state' |> map_goal (fn (goal_ctxt, statement, using, goal, before_qed, after_qed) =>
   791       let
   792         val ctxt = context_of state';
   793         val ths = maps snd named_facts;
   794       in (goal_ctxt, statement, f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));
   795 
   796 fun append_using _ ths using = using @ filter_out Thm.is_dummy ths;
   797 fun unfold_using ctxt ths = map (Local_Defs.unfold ctxt ths);
   798 val unfold_goals = Local_Defs.unfold_goals;
   799 
   800 in
   801 
   802 val using = gen_using append_using (K (K I)) (K I) (K I);
   803 val using_cmd = gen_using append_using (K (K I)) Attrib.attribute_cmd Proof_Context.get_fact;
   804 val unfolding = gen_using unfold_using unfold_goals (K I) (K I);
   805 val unfolding_cmd = gen_using unfold_using unfold_goals Attrib.attribute_cmd Proof_Context.get_fact;
   806 
   807 end;
   808 
   809 
   810 (* case *)
   811 
   812 local
   813 
   814 fun gen_case internal prep_att ((raw_binding, raw_atts), ((name, pos), xs)) state =
   815   let
   816     val ctxt = context_of state;
   817 
   818     val binding = if Binding.is_empty raw_binding then Binding.make (name, pos) else raw_binding;
   819     val atts = map (prep_att ctxt) raw_atts;
   820 
   821     val (asms, state') = state |> map_context_result (fn ctxt =>
   822       ctxt |> Proof_Context.apply_case (Proof_Context.check_case ctxt internal (name, pos) xs));
   823     val assumptions =
   824       asms |> map (fn (a, ts) => ((Binding.qualify_name true binding a, []), map (rpair []) ts));
   825   in
   826     state'
   827     |> assume [] [] assumptions
   828     |> map_context (fold Variable.unbind_term Auto_Bind.no_facts)
   829     |> `the_facts |-> (fn thms => note_thmss [((binding, atts), [(thms, [])])])
   830   end;
   831 
   832 in
   833 
   834 val case_ = gen_case true (K I);
   835 val case_cmd = gen_case false Attrib.attribute_cmd;
   836 
   837 end;
   838 
   839 
   840 (* define *)
   841 
   842 local
   843 
   844 fun gen_define prep_stmt prep_att raw_decls raw_fixes raw_defs state =
   845   let
   846     val _ = assert_forward state;
   847     val ctxt = context_of state;
   848 
   849     (*vars*)
   850     val ((vars, propss, _, binds'), vars_ctxt) =
   851       prep_stmt (raw_decls @ raw_fixes) (map snd raw_defs) ctxt;
   852     val (decls, fixes) = chop (length raw_decls) vars;
   853     val show_term = Syntax.string_of_term vars_ctxt;
   854 
   855     (*defs*)
   856     fun match_defs (((b, _, mx), (_, Free (x, T))) :: more_decls) ((((y, U), t), _) :: more_defs) =
   857           if x = y then ((b, mx), (Binding.empty_atts, t)) :: match_defs more_decls more_defs
   858           else
   859             error ("Mismatch of declaration " ^ show_term (Free (x, T)) ^ " wrt. definition " ^
   860               show_term (Free (y, U)))
   861       | match_defs [] [] = []
   862       | match_defs more_decls more_defs =
   863           error ("Mismatch of declarations " ^ commas (map (show_term o #2 o #2) more_decls) ^
   864             (if null more_decls then "" else " ") ^
   865             "wrt. definitions " ^ commas (map (show_term o Free o #1 o #1) more_defs));
   866 
   867     val derived_def = Local_Defs.derived_def ctxt (K  []) {conditional = false};
   868     val defs1 = map (derived_def o Logic.close_prop (map #2 fixes) []) (flat propss);
   869     val defs2 = match_defs decls defs1;
   870     val (defs3, defs_ctxt) = Local_Defs.define defs2 ctxt;
   871 
   872     (*notes*)
   873     val def_thmss =
   874       map (fn (((_, prove), ((b, _), _)), (_, (_, th))) => (b, prove defs_ctxt th))
   875         (defs1 ~~ defs2 ~~ defs3)
   876       |> unflat (map snd raw_defs);
   877     val notes =
   878       map2 (fn ((a, raw_atts), _) => fn def_thms =>
   879         ((Thm.def_binding_optional (Binding.conglomerate (map #1 def_thms)) a,
   880           map (prep_att defs_ctxt) raw_atts), map (fn (_, th) => ([th], [])) def_thms))
   881         raw_defs def_thmss;
   882   in
   883     state
   884     |> map_context (K defs_ctxt #> fold Variable.bind_term binds')
   885     |> note_thmss notes
   886   end;
   887 
   888 in
   889 
   890 val define = gen_define Proof_Context.cert_stmt (K I);
   891 val define_cmd = gen_define Proof_Context.read_stmt Attrib.attribute_cmd;
   892 
   893 end;
   894 
   895 
   896 
   897 (** proof structure **)
   898 
   899 (* blocks *)
   900 
   901 val begin_block =
   902   assert_forward
   903   #> open_block
   904   #> reset_goal
   905   #> open_block;
   906 
   907 val next_block =
   908   assert_forward
   909   #> close_block
   910   #> open_block
   911   #> reset_goal
   912   #> reset_facts;
   913 
   914 fun end_block state =
   915   state
   916   |> assert_forward
   917   |> assert_bottom false
   918   |> close_block
   919   |> assert_current_goal false
   920   |> close_block
   921   |> export_facts state;
   922 
   923 
   924 (* global notepad *)
   925 
   926 val begin_notepad =
   927   init
   928   #> open_block
   929   #> map_context (Variable.set_body true)
   930   #> open_block;
   931 
   932 val end_notepad =
   933   assert_forward
   934   #> assert_bottom true
   935   #> close_block
   936   #> assert_current_goal false
   937   #> close_block
   938   #> context_of;
   939 
   940 
   941 (* sub-proofs *)
   942 
   943 fun proof opt_text =
   944   Seq.APPEND
   945     (assert_backward
   946       #> refine (the_default Method.standard_text (Method.text opt_text))
   947       #> Seq.map_result
   948         (using_facts []
   949           #> enter_forward
   950           #> open_block
   951           #> reset_goal),
   952      method_error "initial" (Method.position opt_text));
   953 
   954 fun end_proof bot (prev_pos, (opt_text, immed)) =
   955   let
   956     val (finish_text, terminal_pos, finished_pos) =
   957       (case opt_text of
   958         NONE => (Method.finish_text (NONE, immed), Position.none, prev_pos)
   959       | SOME (text, (pos, end_pos)) => (Method.finish_text (SOME text, immed), pos, end_pos));
   960   in
   961     Seq.APPEND (fn state =>
   962       state
   963       |> assert_forward
   964       |> assert_bottom bot
   965       |> close_block
   966       |> assert_current_goal true
   967       |> using_facts []
   968       |> `before_qed |-> (refine o the_default Method.succeed_text)
   969       |> Seq.maps_results (refine finish_text),
   970       method_error "terminal" terminal_pos)
   971     #> Seq.maps_results (Seq.single o finished_goal finished_pos)
   972   end;
   973 
   974 fun check_result msg sq =
   975   (case Seq.pull sq of
   976     NONE => error msg
   977   | SOME (s, _) => s);
   978 
   979 
   980 (* unstructured refinement *)
   981 
   982 fun defer i =
   983   assert_no_chain #>
   984   refine_singleton (Method.Basic (fn _ => METHOD (fn _ => ASSERT_SUBGOAL defer_tac i)));
   985 
   986 fun prefer i =
   987   assert_no_chain #>
   988   refine_singleton (Method.Basic (fn _ => METHOD (fn _ => ASSERT_SUBGOAL prefer_tac i)));
   989 
   990 fun apply (text, (pos, _)) =
   991   Seq.APPEND (assert_backward #> refine text #> Seq.map_result (using_facts []),
   992     method_error "" pos);
   993 
   994 fun apply_end (text, (pos, _)) =
   995   Seq.APPEND (assert_forward #> refine_end text, method_error "" pos);
   996 
   997 
   998 
   999 (** goals **)
  1000 
  1001 (* generic goals *)
  1002 
  1003 local
  1004 
  1005 val is_var =
  1006   can (dest_TVar o Logic.dest_type o Logic.dest_term) orf
  1007   can (dest_Var o Logic.dest_term);
  1008 
  1009 fun implicit_vars props =
  1010   let
  1011     val (var_props, _) = take_prefix is_var props;
  1012     val explicit_vars = fold Term.add_vars var_props [];
  1013     val vars = filter_out (member (op =) explicit_vars) (fold Term.add_vars props []);
  1014   in map (Logic.mk_term o Var) vars end;
  1015 
  1016 fun refine_terms n =
  1017   refine_singleton (Method.Basic (fn ctxt => Method.CONTEXT_TACTIC o
  1018     K (HEADGOAL (PRECISE_CONJUNCTS n
  1019       (HEADGOAL (CONJUNCTS (ALLGOALS (resolve_tac ctxt [Drule.termI]))))))));
  1020 
  1021 in
  1022 
  1023 fun generic_goal kind before_qed after_qed goal_ctxt goal_propss result_binds state =
  1024   let
  1025     val chaining = can assert_chain state;
  1026     val pos = Position.thread_data ();
  1027 
  1028     val goal_props = flat goal_propss;
  1029     val vars = implicit_vars goal_props;
  1030     val propss' = vars :: goal_propss;
  1031     val goal_propss = filter_out null propss';
  1032 
  1033     val goal =
  1034       Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss)
  1035       |> Thm.cterm_of goal_ctxt
  1036       |> Thm.weaken_sorts' goal_ctxt;
  1037     val statement = ((kind, pos), propss', Thm.term_of goal);
  1038 
  1039     val after_qed' = after_qed |>> (fn after_local => fn results =>
  1040       map_context (fold Variable.maybe_bind_term result_binds) #> after_local results);
  1041   in
  1042     state
  1043     |> assert_forward_or_chain
  1044     |> enter_forward
  1045     |> open_block
  1046     |> enter_backward
  1047     |> map_context
  1048       (K goal_ctxt
  1049         #> init_context
  1050         #> Variable.set_body true
  1051         #> Proof_Context.auto_bind_goal goal_props)
  1052     |> set_goal (make_goal (statement, [], Goal.init goal, before_qed, after_qed'))
  1053     |> chaining ? (`the_facts #-> using_facts)
  1054     |> reset_facts
  1055     |> not (null vars) ? refine_terms (length goal_propss)
  1056     |> null goal_props ? refine_singleton (Method.Basic Method.assumption)
  1057   end;
  1058 
  1059 fun generic_qed state =
  1060   let
  1061     val (goal_ctxt, {statement = (_, propss, _), goal, after_qed, ...}) =
  1062       current_goal state;
  1063     val results = tl (conclude_goal goal_ctxt goal propss);
  1064   in state |> close_block |> pair (after_qed, (goal_ctxt, results)) end;
  1065 
  1066 end;
  1067 
  1068 
  1069 (* local goals *)
  1070 
  1071 fun local_goal print_results prep_statement prep_att strict_asm
  1072     kind before_qed after_qed raw_fixes raw_assumes raw_shows state =
  1073   let
  1074     val ctxt = context_of state;
  1075 
  1076     val add_assumes =
  1077       Assumption.add_assms
  1078         (if strict_asm then Assumption.assume_export else Assumption.presume_export);
  1079 
  1080     (*params*)
  1081     val ((params, assumes_propss, shows_propss, result_binds), params_ctxt) = ctxt
  1082       |> prep_statement raw_fixes (map snd raw_assumes) (map snd raw_shows);
  1083 
  1084     (*prems*)
  1085     val (assumes_bindings, shows_bindings) =
  1086       apply2 (map (apsnd (map (prep_att ctxt)) o fst)) (raw_assumes, raw_shows);
  1087     val (that_fact, goal_ctxt) = params_ctxt
  1088       |> fold_burrow add_assumes ((map o map) (Thm.cterm_of params_ctxt) assumes_propss)
  1089       |> (fn (premss, ctxt') =>
  1090           let
  1091             val prems = Assumption.local_prems_of ctxt' ctxt;
  1092             val ctxt'' =
  1093               ctxt'
  1094               |> not (null assumes_propss) ?
  1095                 (snd o Proof_Context.note_thmss ""
  1096                   [((Binding.name Auto_Bind.thatN, []), [(prems, [])])])
  1097               |> (snd o Proof_Context.note_thmss ""
  1098                   (assumes_bindings ~~ map (map (fn th => ([th], []))) premss))
  1099           in (prems, ctxt'') end);
  1100 
  1101     (*result*)
  1102     val results_bindings = map (apfst Binding.default_pos) shows_bindings;
  1103     fun after_qed' (result_ctxt, results) state' =
  1104       let
  1105         val ctxt' = context_of state';
  1106         val export0 =
  1107           Assumption.export false result_ctxt ctxt' #>
  1108           fold_rev (fn (x, v) => Thm.forall_intr_name (x, Thm.cterm_of params_ctxt v)) params #>
  1109           Raw_Simplifier.norm_hhf_protect ctxt';
  1110         val export = map export0 #> Variable.export result_ctxt ctxt';
  1111       in
  1112         state'
  1113         |> local_results (results_bindings ~~ burrow export results)
  1114         |-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
  1115         |> after_qed (result_ctxt, results)
  1116       end;
  1117   in
  1118     state
  1119     |> generic_goal kind before_qed (after_qed', K I) goal_ctxt shows_propss result_binds
  1120     |> pair that_fact
  1121   end;
  1122 
  1123 fun local_qeds arg =
  1124   end_proof false arg
  1125   #> Seq.map_result (generic_qed #-> (fn ((after_qed, _), results) => after_qed results));
  1126 
  1127 fun local_qed arg =
  1128   local_qeds (Position.none, arg) #> Seq.the_result finished_goal_error;
  1129 
  1130 
  1131 (* global goals *)
  1132 
  1133 fun global_goal prep_propp before_qed after_qed propp ctxt =
  1134   let
  1135     val (propss, binds) =
  1136       prep_propp (Proof_Context.set_mode Proof_Context.mode_schematic ctxt) propp;
  1137     val goal_ctxt = ctxt
  1138       |> (fold o fold) Variable.auto_fixes propss
  1139       |> fold Variable.bind_term binds;
  1140     fun after_qed' (result_ctxt, results) ctxt' = ctxt'
  1141       |> Proof_Context.restore_naming ctxt
  1142       |> after_qed (burrow (Proof_Context.export result_ctxt ctxt') results);
  1143   in
  1144     ctxt
  1145     |> init
  1146     |> generic_goal "" before_qed (K I, after_qed') goal_ctxt propss []
  1147   end;
  1148 
  1149 val theorem = global_goal Proof_Context.cert_propp;
  1150 val theorem_cmd = global_goal Proof_Context.read_propp;
  1151 
  1152 fun global_qeds arg =
  1153   end_proof true arg
  1154   #> Seq.map_result (generic_qed #> (fn (((_, after_qed), results), state) =>
  1155     after_qed results (context_of state)));
  1156 
  1157 fun global_qed arg =
  1158   global_qeds (Position.none, arg) #> Seq.the_result finished_goal_error;
  1159 
  1160 
  1161 (* terminal proof steps *)
  1162 
  1163 local
  1164 
  1165 fun terminal_proof qeds initial terminal state =
  1166   let
  1167     val ctxt = context_of state;
  1168     val check_closure = Method.check_text ctxt #> Method.map_source (Method.method_closure ctxt);
  1169     val initial' = apfst check_closure initial;
  1170     val terminal' = (apfst o Option.map o apfst) check_closure terminal;
  1171   in
  1172     state
  1173     |> proof (SOME initial')
  1174     |> Seq.maps_results (qeds (#2 (#2 initial), terminal'))
  1175     |> Seq.the_result ""
  1176   end;
  1177 
  1178 in
  1179 
  1180 fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);
  1181 val local_default_proof = local_terminal_proof ((Method.standard_text, Position.no_range), NONE);
  1182 val local_immediate_proof = local_terminal_proof ((Method.this_text, Position.no_range), NONE);
  1183 val local_done_proof = terminal_proof local_qeds (Method.done_text, Position.no_range) (NONE, false);
  1184 
  1185 fun global_terminal_proof (text, opt_text) = terminal_proof global_qeds text (opt_text, true);
  1186 val global_default_proof = global_terminal_proof ((Method.standard_text, Position.no_range), NONE);
  1187 val global_immediate_proof = global_terminal_proof ((Method.this_text, Position.no_range), NONE);
  1188 val global_done_proof = terminal_proof global_qeds (Method.done_text, Position.no_range) (NONE, false);
  1189 
  1190 end;
  1191 
  1192 
  1193 (* skip proofs *)
  1194 
  1195 fun local_skip_proof int state =
  1196   local_terminal_proof ((Method.sorry_text int, Position.no_range), NONE) state before
  1197   Skip_Proof.report (context_of state);
  1198 
  1199 fun global_skip_proof int state =
  1200   global_terminal_proof ((Method.sorry_text int, Position.no_range), NONE) state before
  1201   Skip_Proof.report (context_of state);
  1202 
  1203 
  1204 (* common goal statements *)
  1205 
  1206 fun internal_goal print_results mode =
  1207   local_goal print_results
  1208     (fn a => fn b => fn c => Proof_Context.cert_statement a b c o Proof_Context.set_mode mode) (K I);
  1209 
  1210 local
  1211 
  1212 fun gen_have prep_statement prep_att strict_asm before_qed after_qed fixes assumes shows int =
  1213   local_goal (Proof_Display.print_results int (Position.thread_data ()))
  1214     prep_statement prep_att strict_asm "have" before_qed after_qed fixes assumes shows;
  1215 
  1216 fun gen_show prep_statement prep_att strict_asm before_qed after_qed fixes assumes shows int state =
  1217   let
  1218     val testing = Unsynchronized.ref false;
  1219     val rule = Unsynchronized.ref (NONE: thm option);
  1220     fun fail_msg ctxt =
  1221       "Local statement fails to refine any pending goal" ::
  1222       (case ! rule of NONE => [] | SOME th => [Proof_Display.string_of_rule ctxt "Failed" th])
  1223       |> cat_lines;
  1224 
  1225     val pos = Position.thread_data ();
  1226     fun print_results ctxt res =
  1227       if ! testing then ()
  1228       else Proof_Display.print_results int pos ctxt res;
  1229     fun print_rule ctxt th =
  1230       if ! testing then rule := SOME th
  1231       else if int then
  1232         Proof_Display.string_of_rule ctxt "Successful" th
  1233         |> Markup.markup Markup.text_fold
  1234         |> Output.state
  1235       else ();
  1236     val test_proof =
  1237       local_skip_proof true
  1238       |> Unsynchronized.setmp testing true
  1239       |> Exn.interruptible_capture;
  1240 
  1241     fun after_qed' (result_ctxt, results) state' = state'
  1242       |> refine_goals print_rule result_ctxt (flat results)
  1243       |> check_result "Failed to refine any pending goal"
  1244       |> after_qed (result_ctxt, results);
  1245   in
  1246     state
  1247     |> local_goal print_results prep_statement prep_att strict_asm
  1248       "show" before_qed after_qed' fixes assumes shows
  1249     ||> int ? (fn goal_state =>
  1250       (case test_proof (map_context (Context_Position.set_visible false) goal_state) of
  1251         Exn.Res _ => goal_state
  1252       | Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))
  1253   end;
  1254 
  1255 in
  1256 
  1257 val have = gen_have Proof_Context.cert_statement (K I);
  1258 val have_cmd = gen_have Proof_Context.read_statement Attrib.attribute_cmd;
  1259 val show = gen_show Proof_Context.cert_statement (K I);
  1260 val show_cmd = gen_show Proof_Context.read_statement Attrib.attribute_cmd;
  1261 
  1262 end;
  1263 
  1264 
  1265 
  1266 (** future proofs **)
  1267 
  1268 (* relevant proof states *)
  1269 
  1270 fun schematic_goal state =
  1271   let val (_, {statement = (_, _, prop), ...}) = find_goal state
  1272   in Goal.is_schematic prop end;
  1273 
  1274 fun is_relevant state =
  1275   (case try find_goal state of
  1276     NONE => true
  1277   | SOME (_, {statement = (_, _, prop), goal, ...}) =>
  1278       Goal.is_schematic prop orelse not (Logic.protect prop aconv Thm.concl_of goal));
  1279 
  1280 
  1281 (* full proofs *)
  1282 
  1283 local
  1284 
  1285 structure Result = Proof_Data
  1286 (
  1287   type T = thm option;
  1288   fun init _ = NONE;
  1289 );
  1290 
  1291 fun the_result ctxt =
  1292   (case Result.get ctxt of
  1293     NONE => error "No result of forked proof"
  1294   | SOME th => th);
  1295 
  1296 val set_result = Result.put o SOME;
  1297 val reset_result = Result.put NONE;
  1298 
  1299 in
  1300 
  1301 fun future_proof fork_proof state =
  1302   let
  1303     val _ = assert_backward state;
  1304     val (goal_ctxt, goal_info) = find_goal state;
  1305     val {statement as (kind, _, prop), using, goal, before_qed, after_qed} = goal_info;
  1306 
  1307     val _ = is_relevant state andalso error "Cannot fork relevant proof";
  1308 
  1309     val after_qed' =
  1310       (fn (_, [[th]]) => map_context (set_result th),
  1311        fn (_, [[th]]) => set_result th);
  1312     val result_ctxt =
  1313       state
  1314       |> map_context reset_result
  1315       |> map_goal (K (goal_ctxt, (kind, [[], [prop]], prop), using, goal, before_qed, after_qed'))
  1316       |> fork_proof;
  1317 
  1318     val future_thm = Future.map (the_result o snd) result_ctxt;
  1319     val finished_goal = Goal.protect 0 (Goal.future_result goal_ctxt future_thm prop);
  1320     val state' =
  1321       state
  1322       |> map_goal (K (goal_ctxt, statement, using, finished_goal, NONE, after_qed));
  1323   in (Future.map fst result_ctxt, state') end;
  1324 
  1325 end;
  1326 
  1327 
  1328 (* terminal proofs *)  (* FIXME avoid toplevel imitation -- include in PIDE/document *)
  1329 
  1330 local
  1331 
  1332 fun future_terminal_proof proof1 proof2 done state =
  1333   if Goal.future_enabled 3 andalso not (is_relevant state) then
  1334     state |> future_proof (fn state' =>
  1335       let
  1336         val pos = Position.thread_data ();
  1337         val props = Markup.command_timing :: (Markup.nameN, "by") :: Position.properties_of pos;
  1338       in
  1339         Execution.fork {name = "Proof.future_terminal_proof", pos = pos, pri = ~1}
  1340           (fn () => ((), Timing.protocol props proof2 state'))
  1341       end) |> snd |> done
  1342   else proof1 state;
  1343 
  1344 in
  1345 
  1346 fun local_future_terminal_proof meths =
  1347   future_terminal_proof
  1348     (local_terminal_proof meths)
  1349     (local_terminal_proof meths #> context_of) local_done_proof;
  1350 
  1351 fun global_future_terminal_proof meths =
  1352   future_terminal_proof
  1353     (global_terminal_proof meths)
  1354     (global_terminal_proof meths) global_done_proof;
  1355 
  1356 end;
  1357 
  1358 end;