src/Pure/Isar/proof.ML
author wenzelm
Thu Jul 23 16:52:16 2009 +0200 (2009-07-23)
changeset 32145 220c9e439d39
parent 32091 30e2ffbba718
child 32167 d32817dda0e6
permissions -rw-r--r--
clarified pretty_goals, pretty_thm_aux: plain context;
explicit pretty_goals_without_context, print_goals_without_context;
tuned;
     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 = Context.proof
    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_contexts: (context -> context) -> state -> state
    20   val bind_terms: (indexname * term option) list -> state -> state
    21   val put_thms: bool -> string * thm list option -> state -> state
    22   val the_facts: state -> thm list
    23   val the_fact: state -> thm
    24   val put_facts: thm list option -> state -> state
    25   val assert_forward: state -> state
    26   val assert_chain: state -> state
    27   val assert_forward_or_chain: state -> state
    28   val assert_backward: state -> state
    29   val assert_no_chain: state -> state
    30   val enter_forward: state -> state
    31   val goal_message: (unit -> Pretty.T) -> state -> state
    32   val get_goal: state -> context * (thm list * thm)
    33   val show_main_goal: bool ref
    34   val verbose: bool ref
    35   val pretty_state: int -> state -> Pretty.T list
    36   val pretty_goals: bool -> state -> Pretty.T list
    37   val refine: Method.text -> state -> state Seq.seq
    38   val refine_end: Method.text -> state -> state Seq.seq
    39   val refine_insert: thm list -> state -> state
    40   val goal_tac: thm -> int -> tactic
    41   val refine_goals: (context -> thm -> unit) -> context -> thm list -> state -> state Seq.seq
    42   val match_bind: (string list * string) list -> state -> state
    43   val match_bind_i: (term list * term) list -> state -> state
    44   val let_bind: (string list * string) list -> state -> state
    45   val let_bind_i: (term list * term) list -> state -> state
    46   val fix: (binding * string option * mixfix) list -> state -> state
    47   val fix_i: (binding * typ option * mixfix) list -> state -> state
    48   val assm: Assumption.export ->
    49     (Attrib.binding * (string * string list) list) list -> state -> state
    50   val assm_i: Assumption.export ->
    51     (Thm.binding * (term * term list) list) list -> state -> state
    52   val assume: (Attrib.binding * (string * string list) list) list -> state -> state
    53   val assume_i: (Thm.binding * (term * term list) list) list -> state -> state
    54   val presume: (Attrib.binding * (string * string list) list) list -> state -> state
    55   val presume_i: (Thm.binding * (term * term list) list) list -> state -> state
    56   val def: (Attrib.binding * ((binding * mixfix) * (string * string list))) list -> state -> state
    57   val def_i: (Thm.binding * ((binding * mixfix) * (term * term list))) list -> state -> state
    58   val chain: state -> state
    59   val chain_facts: thm list -> state -> state
    60   val get_thmss: state -> (Facts.ref * Attrib.src list) list -> thm list
    61   val note_thmss: (Attrib.binding * (Facts.ref * Attrib.src list) list) list -> state -> state
    62   val note_thmss_i: (Thm.binding * (thm list * attribute list) list) list -> state -> state
    63   val from_thmss: ((Facts.ref * Attrib.src list) list) list -> state -> state
    64   val from_thmss_i: ((thm list * attribute list) list) list -> state -> state
    65   val with_thmss: ((Facts.ref * Attrib.src list) list) list -> state -> state
    66   val with_thmss_i: ((thm list * attribute list) list) list -> state -> state
    67   val using: ((Facts.ref * Attrib.src list) list) list -> state -> state
    68   val using_i: ((thm list * attribute list) list) list -> state -> state
    69   val unfolding: ((Facts.ref * Attrib.src list) list) list -> state -> state
    70   val unfolding_i: ((thm list * attribute list) list) list -> state -> state
    71   val invoke_case: string * string option list * Attrib.src list -> state -> state
    72   val invoke_case_i: string * string option list * attribute list -> state -> state
    73   val begin_block: state -> state
    74   val next_block: state -> state
    75   val end_block: state -> state
    76   val proof: Method.text option -> state -> state Seq.seq
    77   val defer: int option -> state -> state Seq.seq
    78   val prefer: int -> state -> state Seq.seq
    79   val apply: Method.text -> state -> state Seq.seq
    80   val apply_end: Method.text -> state -> state Seq.seq
    81   val local_goal: (context -> ((string * string) * (string * thm list) list) -> unit) ->
    82     (theory -> 'a -> attribute) ->
    83     (context * 'b list -> context * (term list list * (context -> context))) ->
    84     string -> Method.text option -> (thm list list -> state -> state) ->
    85     ((binding * 'a list) * 'b) list -> state -> state
    86   val local_qed: Method.text option * bool -> state -> state
    87   val theorem: Method.text option -> (thm list list -> context -> context) ->
    88     (string * string list) list list -> context -> state
    89   val theorem_i: Method.text option -> (thm list list -> context -> context) ->
    90     (term * term list) list list -> context -> state
    91   val global_qed: Method.text option * bool -> state -> context
    92   val local_terminal_proof: Method.text * Method.text option -> state -> state
    93   val local_default_proof: state -> state
    94   val local_immediate_proof: state -> state
    95   val local_skip_proof: bool -> state -> state
    96   val local_done_proof: state -> state
    97   val global_terminal_proof: Method.text * Method.text option -> state -> context
    98   val global_default_proof: state -> context
    99   val global_immediate_proof: state -> context
   100   val global_skip_proof: bool -> state -> context
   101   val global_done_proof: state -> context
   102   val have: Method.text option -> (thm list list -> state -> state) ->
   103     (Attrib.binding * (string * string list) list) list -> bool -> state -> state
   104   val have_i: Method.text option -> (thm list list -> state -> state) ->
   105     (Thm.binding * (term * term list) list) list -> bool -> state -> state
   106   val show: Method.text option -> (thm list list -> state -> state) ->
   107     (Attrib.binding * (string * string list) list) list -> bool -> state -> state
   108   val show_i: Method.text option -> (thm list list -> state -> state) ->
   109     (Thm.binding * (term * term list) list) list -> bool -> state -> state
   110   val schematic_goal: state -> bool
   111   val is_relevant: state -> bool
   112   val local_future_proof: (state -> ('a * state) Future.future) ->
   113     state -> 'a Future.future * state
   114   val global_future_proof: (state -> ('a * Proof.context) Future.future) ->
   115     state -> 'a Future.future * context
   116   val local_future_terminal_proof: Method.text * Method.text option -> bool -> state -> state
   117   val global_future_terminal_proof: Method.text * Method.text option -> bool -> state -> context
   118 end;
   119 
   120 structure Proof: PROOF =
   121 struct
   122 
   123 type context = Context.proof;
   124 type method = Method.method;
   125 
   126 
   127 (** proof state **)
   128 
   129 (* datatype state *)
   130 
   131 datatype mode = Forward | Chain | Backward;
   132 
   133 datatype state =
   134   State of node Stack.T
   135 and node =
   136   Node of
   137    {context: context,
   138     facts: thm list option,
   139     mode: mode,
   140     goal: goal option}
   141 and goal =
   142   Goal of
   143    {statement: (string * Position.T) * term list list * term,
   144       (*goal kind and statement (starting with vars), initial proposition*)
   145     messages: (unit -> Pretty.T) list,    (*persistent messages (hints etc.)*)
   146     using: thm list,                      (*goal facts*)
   147     goal: thm,                            (*subgoals ==> statement*)
   148     before_qed: Method.text option,
   149     after_qed:
   150       (thm list list -> state -> state) *
   151       (thm list list -> context -> context)};
   152 
   153 fun make_goal (statement, messages, using, goal, before_qed, after_qed) =
   154   Goal {statement = statement, messages = messages, using = using, goal = goal,
   155     before_qed = before_qed, after_qed = after_qed};
   156 
   157 fun make_node (context, facts, mode, goal) =
   158   Node {context = context, facts = facts, mode = mode, goal = goal};
   159 
   160 fun map_node f (Node {context, facts, mode, goal}) =
   161   make_node (f (context, facts, mode, goal));
   162 
   163 val init_context =
   164   ProofContext.set_stmt true #> ProofContext.reset_naming;
   165 
   166 fun init ctxt =
   167   State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
   168 
   169 fun current (State st) = Stack.top st |> (fn Node node => node);
   170 fun map_current f (State st) = State (Stack.map_top (map_node f) st);
   171 fun map_all f (State st) = State (Stack.map_all (map_node f) st);
   172 
   173 
   174 
   175 (** basic proof state operations **)
   176 
   177 (* block structure *)
   178 
   179 fun open_block (State st) = State (Stack.push st);
   180 
   181 fun close_block (State st) = State (Stack.pop st)
   182   handle Empty => error "Unbalanced block parentheses";
   183 
   184 fun level (State st) = Stack.level st;
   185 
   186 fun assert_bottom b state =
   187   let val b' = (level state <= 2) in
   188     if b andalso not b' then error "Not at bottom of proof!"
   189     else if not b andalso b' then error "Already at bottom of proof!"
   190     else state
   191   end;
   192 
   193 
   194 (* context *)
   195 
   196 val context_of = #context o current;
   197 val theory_of = ProofContext.theory_of o context_of;
   198 
   199 fun map_context f =
   200   map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
   201 
   202 fun map_context_result f state =
   203   f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
   204 
   205 fun map_contexts f = map_all (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
   206 
   207 val bind_terms = map_context o ProofContext.bind_terms;
   208 val put_thms = map_context oo ProofContext.put_thms;
   209 
   210 
   211 (* facts *)
   212 
   213 val get_facts = #facts o current;
   214 
   215 fun the_facts state =
   216   (case get_facts state of SOME facts => facts
   217   | NONE => error "No current facts available");
   218 
   219 fun the_fact state =
   220   (case the_facts state of [thm] => thm
   221   | _ => error "Single theorem expected");
   222 
   223 fun put_facts facts =
   224   map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
   225   put_thms true (AutoBind.thisN, facts);
   226 
   227 fun these_factss more_facts (named_factss, state) =
   228   (named_factss, state |> put_facts (SOME (maps snd named_factss @ more_facts)));
   229 
   230 fun export_facts inner outer =
   231   (case get_facts inner of
   232     NONE => put_facts NONE outer
   233   | SOME thms =>
   234       thms
   235       |> ProofContext.export (context_of inner) (context_of outer)
   236       |> (fn ths => put_facts (SOME ths) outer));
   237 
   238 
   239 (* mode *)
   240 
   241 val get_mode = #mode o current;
   242 fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
   243 
   244 val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
   245 
   246 fun assert_mode pred state =
   247   let val mode = get_mode state in
   248     if pred mode then state
   249     else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
   250   end;
   251 
   252 val assert_forward = assert_mode (fn mode => mode = Forward);
   253 val assert_chain = assert_mode (fn mode => mode = Chain);
   254 val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
   255 val assert_backward = assert_mode (fn mode => mode = Backward);
   256 val assert_no_chain = assert_mode (fn mode => mode <> Chain);
   257 
   258 val enter_forward = put_mode Forward;
   259 val enter_chain = put_mode Chain;
   260 val enter_backward = put_mode Backward;
   261 
   262 
   263 (* current goal *)
   264 
   265 fun current_goal state =
   266   (case current state of
   267     {context, goal = SOME (Goal goal), ...} => (context, goal)
   268   | _ => error "No current goal!");
   269 
   270 fun assert_current_goal g state =
   271   let val g' = can current_goal state in
   272     if g andalso not g' then error "No goal in this block!"
   273     else if not g andalso g' then error "Goal present in this block!"
   274     else state
   275   end;
   276 
   277 fun put_goal goal = map_current (fn (ctxt, using, mode, _) => (ctxt, using, mode, goal));
   278 
   279 val before_qed = #before_qed o #2 o current_goal;
   280 
   281 
   282 (* nested goal *)
   283 
   284 fun map_goal f g (State (Node {context, facts, mode, goal = SOME goal}, nodes)) =
   285       let
   286         val Goal {statement, messages, using, goal, before_qed, after_qed} = goal;
   287         val goal' = make_goal (g (statement, messages, using, goal, before_qed, after_qed));
   288       in State (make_node (f context, facts, mode, SOME goal'), nodes) end
   289   | map_goal f g (State (nd, node :: nodes)) =
   290       let val State (node', nodes') = map_goal f g (State (node, nodes))
   291       in map_context f (State (nd, node' :: nodes')) end
   292   | map_goal _ _ state = state;
   293 
   294 fun set_goal goal = map_goal I (fn (statement, _, using, _, before_qed, after_qed) =>
   295   (statement, [], using, goal, before_qed, after_qed));
   296 
   297 fun goal_message msg = map_goal I (fn (statement, messages, using, goal, before_qed, after_qed) =>
   298   (statement, msg :: messages, using, goal, before_qed, after_qed));
   299 
   300 fun using_facts using = map_goal I (fn (statement, _, _, goal, before_qed, after_qed) =>
   301   (statement, [], using, goal, before_qed, after_qed));
   302 
   303 local
   304   fun find i state =
   305     (case try current_goal state of
   306       SOME (ctxt, goal) => (ctxt, (i, goal))
   307     | NONE => find (i + 1) (close_block state handle ERROR _ => error "No goal present"));
   308 in val find_goal = find 0 end;
   309 
   310 fun get_goal state =
   311   let val (ctxt, (_, {using, goal, ...})) = find_goal state
   312   in (ctxt, (using, goal)) end;
   313 
   314 
   315 
   316 (** pretty_state **)
   317 
   318 val show_main_goal = ref false;
   319 val verbose = ProofContext.verbose;
   320 
   321 fun pretty_facts _ _ NONE = []
   322   | pretty_facts s ctxt (SOME ths) =
   323       [Pretty.big_list (s ^ "this:") (map (Display.pretty_thm ctxt) ths), Pretty.str ""];
   324 
   325 fun pretty_state nr state =
   326   let
   327     val {context, facts, mode, goal = _} = current state;
   328 
   329     fun levels_up 0 = ""
   330       | levels_up 1 = "1 level up"
   331       | levels_up i = string_of_int i ^ " levels up";
   332 
   333     fun subgoals 0 = ""
   334       | subgoals 1 = "1 subgoal"
   335       | subgoals n = string_of_int n ^ " subgoals";
   336 
   337     fun description strs =
   338       (case filter_out (fn s => s = "") strs of [] => ""
   339       | strs' => enclose " (" ")" (commas strs'));
   340 
   341     fun prt_goal (SOME (ctxt, (i,
   342       {statement = ((_, pos), _, _), messages, using, goal, before_qed = _, after_qed = _}))) =
   343           pretty_facts "using " ctxt
   344             (if mode <> Backward orelse null using then NONE else SOME using) @
   345           [Pretty.str ("goal" ^
   346             description [levels_up (i div 2), subgoals (Thm.nprems_of goal)] ^ ":")] @
   347           Display_Goal.pretty_goals ctxt Markup.subgoal
   348             (true, ! show_main_goal) (! Display.goals_limit) goal @
   349           (map (fn msg => Position.setmp_thread_data pos msg ()) (rev messages))
   350       | prt_goal NONE = [];
   351 
   352     val prt_ctxt =
   353       if ! verbose orelse mode = Forward then ProofContext.pretty_context context
   354       else if mode = Backward then ProofContext.pretty_ctxt context
   355       else [];
   356   in
   357     [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^
   358       (if ! verbose then ", depth " ^ string_of_int (level state div 2 - 1) else "")),
   359       Pretty.str ""] @
   360     (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
   361     (if ! verbose orelse mode = Forward then
   362        pretty_facts "" context facts @ prt_goal (try find_goal state)
   363      else if mode = Chain then pretty_facts "picking " context facts
   364      else prt_goal (try find_goal state))
   365   end;
   366 
   367 fun pretty_goals main state =
   368   let val (ctxt, (_, goal)) = get_goal state
   369   in Display_Goal.pretty_goals ctxt Markup.none (false, main) (! Display.goals_limit) goal end;
   370 
   371 
   372 
   373 (** proof steps **)
   374 
   375 (* refine via method *)
   376 
   377 local
   378 
   379 fun goalN i = "goal" ^ string_of_int i;
   380 fun goals st = map goalN (1 upto Thm.nprems_of st);
   381 
   382 fun no_goal_cases st = map (rpair NONE) (goals st);
   383 
   384 fun goal_cases st =
   385   RuleCases.make_common true (Thm.theory_of_thm st, Thm.prop_of st) (map (rpair []) (goals st));
   386 
   387 fun apply_method current_context pos meth state =
   388   let
   389     val (goal_ctxt, (_, {statement, messages = _, using, goal, before_qed, after_qed})) =
   390       find_goal state;
   391     val ctxt = if current_context then context_of state else goal_ctxt;
   392   in
   393     Method.apply pos meth ctxt using goal |> Seq.map (fn (meth_cases, goal') =>
   394       state
   395       |> map_goal
   396           (ProofContext.add_cases false (no_goal_cases goal @ goal_cases goal') #>
   397            ProofContext.add_cases true meth_cases)
   398           (K (statement, [], using, goal', before_qed, after_qed)))
   399   end;
   400 
   401 fun select_goals n meth state =
   402   state
   403   |> (#2 o #2 o get_goal)
   404   |> ALLGOALS Goal.conjunction_tac
   405   |> Seq.maps (fn goal =>
   406     state
   407     |> Seq.lift set_goal (Goal.extract 1 n goal |> Seq.maps (Goal.conjunction_tac 1))
   408     |> Seq.maps meth
   409     |> Seq.maps (fn state' => state'
   410       |> Seq.lift set_goal (Goal.retrofit 1 n (#2 (#2 (get_goal state'))) goal))
   411     |> Seq.maps (apply_method true Position.none (K Method.succeed)));
   412 
   413 fun apply_text cc text state =
   414   let
   415     val thy = theory_of state;
   416     val pos_of = #2 o Args.dest_src;
   417 
   418     fun eval (Method.Basic (m, pos)) = apply_method cc pos m
   419       | eval (Method.Source src) = apply_method cc (pos_of src) (Method.method thy src)
   420       | eval (Method.Source_i src) = apply_method cc (pos_of src) (Method.method_i thy src)
   421       | eval (Method.Then txts) = Seq.EVERY (map eval txts)
   422       | eval (Method.Orelse txts) = Seq.FIRST (map eval txts)
   423       | eval (Method.Try txt) = Seq.TRY (eval txt)
   424       | eval (Method.Repeat1 txt) = Seq.REPEAT1 (eval txt)
   425       | eval (Method.SelectGoals (n, txt)) = select_goals n (eval txt);
   426   in eval text state end;
   427 
   428 in
   429 
   430 val refine = apply_text true;
   431 val refine_end = apply_text false;
   432 
   433 fun refine_insert [] = I
   434   | refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths), Position.none));
   435 
   436 end;
   437 
   438 
   439 (* refine via sub-proof *)
   440 
   441 fun finish_tac 0 = K all_tac
   442   | finish_tac n =
   443       Goal.norm_hhf_tac THEN'
   444       SUBGOAL (fn (goal, i) =>
   445         if can Logic.unprotect (Logic.strip_assums_concl goal) then
   446           Tactic.etac Drule.protectI i THEN finish_tac (n - 1) i
   447         else finish_tac (n - 1) (i + 1));
   448 
   449 fun goal_tac rule =
   450   Goal.norm_hhf_tac THEN'
   451   Tactic.rtac rule THEN'
   452   finish_tac (Thm.nprems_of rule);
   453 
   454 fun refine_goals print_rule inner raw_rules state =
   455   let
   456     val (outer, (_, goal)) = get_goal state;
   457     fun refine rule st = (print_rule outer rule; FINDGOAL (goal_tac rule) st);
   458   in
   459     raw_rules
   460     |> ProofContext.goal_export inner outer
   461     |> (fn rules => Seq.lift set_goal (EVERY (map refine rules) goal) state)
   462   end;
   463 
   464 
   465 (* conclude_goal *)
   466 
   467 fun conclude_goal ctxt goal propss =
   468   let
   469     val thy = ProofContext.theory_of ctxt;
   470     val string_of_term = Syntax.string_of_term ctxt;
   471     val string_of_thm = Display.string_of_thm ctxt;
   472 
   473     val ngoals = Thm.nprems_of goal;
   474     val _ = ngoals = 0 orelse error (Pretty.string_of (Pretty.chunks
   475       (Display_Goal.pretty_goals ctxt Markup.none
   476           (true, ! show_main_goal) (! Display.goals_limit) goal @
   477         [Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")])));
   478 
   479     val extra_hyps = Assumption.extra_hyps ctxt goal;
   480     val _ = null extra_hyps orelse
   481       error ("Additional hypotheses:\n" ^ cat_lines (map string_of_term extra_hyps));
   482 
   483     fun lost_structure () = error ("Lost goal structure:\n" ^ string_of_thm goal);
   484 
   485     val th = Goal.conclude
   486       (if length (flat propss) > 1 then Thm.norm_proof goal else goal)
   487       handle THM _ => lost_structure ();
   488     val goal_propss = filter_out null propss;
   489     val results =
   490       Conjunction.elim_balanced (length goal_propss) th
   491       |> map2 Conjunction.elim_balanced (map length goal_propss)
   492       handle THM _ => lost_structure ();
   493     val _ = Unify.matches_list thy (flat goal_propss) (map Thm.prop_of (flat results)) orelse
   494       error ("Proved a different theorem:\n" ^ string_of_thm th);
   495     val _ = Thm.check_shyps (Variable.sorts_of ctxt) th;
   496 
   497     fun recover_result ([] :: pss) thss = [] :: recover_result pss thss
   498       | recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss
   499       | recover_result [] [] = []
   500       | recover_result _ _ = lost_structure ();
   501   in recover_result propss results end;
   502 
   503 
   504 
   505 (*** structured proof commands ***)
   506 
   507 (** context elements **)
   508 
   509 (* bindings *)
   510 
   511 local
   512 
   513 fun gen_bind bind args state =
   514   state
   515   |> assert_forward
   516   |> map_context (bind args #> snd)
   517   |> put_facts NONE;
   518 
   519 in
   520 
   521 val match_bind = gen_bind (ProofContext.match_bind false);
   522 val match_bind_i = gen_bind (ProofContext.match_bind_i false);
   523 val let_bind = gen_bind (ProofContext.match_bind true);
   524 val let_bind_i = gen_bind (ProofContext.match_bind_i true);
   525 
   526 end;
   527 
   528 
   529 (* fix *)
   530 
   531 local
   532 
   533 fun gen_fix prep_vars args =
   534   assert_forward
   535   #> map_context (fn ctxt => snd (ProofContext.add_fixes (prep_vars ctxt args) ctxt))
   536   #> put_facts NONE;
   537 
   538 in
   539 
   540 val fix = gen_fix (fn ctxt => fn args => fst (ProofContext.read_vars args ctxt));
   541 val fix_i = gen_fix (K I);
   542 
   543 end;
   544 
   545 
   546 (* assume etc. *)
   547 
   548 local
   549 
   550 fun gen_assume asm prep_att exp args state =
   551   state
   552   |> assert_forward
   553   |> map_context_result (asm exp (Attrib.map_specs (prep_att (theory_of state)) args))
   554   |> these_factss [] |> #2;
   555 
   556 in
   557 
   558 val assm      = gen_assume ProofContext.add_assms Attrib.attribute;
   559 val assm_i    = gen_assume ProofContext.add_assms_i (K I);
   560 val assume    = assm Assumption.assume_export;
   561 val assume_i  = assm_i Assumption.assume_export;
   562 val presume   = assm Assumption.presume_export;
   563 val presume_i = assm_i Assumption.presume_export;
   564 
   565 end;
   566 
   567 
   568 (* def *)
   569 
   570 local
   571 
   572 fun gen_def prep_att prep_vars prep_binds args state =
   573   let
   574     val _ = assert_forward state;
   575     val thy = theory_of state;
   576     val ctxt = context_of state;
   577 
   578     val (raw_name_atts, (raw_vars, raw_rhss)) = args |> split_list ||> split_list;
   579     val name_atts = map (apsnd (map (prep_att thy))) raw_name_atts;
   580   in
   581     state
   582     |> map_context_result (prep_vars (map (fn (x, mx) => (x, NONE, mx)) raw_vars))
   583     |>> map (fn (x, _, mx) => (x, mx))
   584     |-> (fn vars =>
   585       map_context_result (prep_binds false (map swap raw_rhss))
   586       #-> (fn rhss => map_context_result (LocalDefs.add_defs (vars ~~ (name_atts ~~ rhss)))))
   587     |-> (put_facts o SOME o map (#2 o #2))
   588   end;
   589 
   590 in
   591 
   592 val def = gen_def Attrib.attribute ProofContext.read_vars ProofContext.match_bind;
   593 val def_i = gen_def (K I) ProofContext.cert_vars ProofContext.match_bind_i;
   594 
   595 end;
   596 
   597 
   598 
   599 (** facts **)
   600 
   601 (* chain *)
   602 
   603 fun clean_facts ctxt =
   604   put_facts (SOME (filter_out Thm.is_dummy (the_facts ctxt))) ctxt;
   605 
   606 val chain =
   607   assert_forward
   608   #> clean_facts
   609   #> enter_chain;
   610 
   611 fun chain_facts facts =
   612   put_facts (SOME facts)
   613   #> chain;
   614 
   615 
   616 (* note etc. *)
   617 
   618 fun no_binding args = map (pair (Binding.empty, [])) args;
   619 
   620 local
   621 
   622 fun gen_thmss more_facts opt_chain opt_result prep_atts prep_fact args state =
   623   state
   624   |> assert_forward
   625   |> map_context_result (ProofContext.note_thmss ""
   626     (Attrib.map_facts_refs (prep_atts (theory_of state)) (prep_fact (context_of state)) args))
   627   |> these_factss (more_facts state)
   628   ||> opt_chain
   629   |> opt_result;
   630 
   631 in
   632 
   633 val note_thmss = gen_thmss (K []) I #2 Attrib.attribute ProofContext.get_fact;
   634 val note_thmss_i = gen_thmss (K []) I #2 (K I) (K I);
   635 
   636 val from_thmss = gen_thmss (K []) chain #2 Attrib.attribute ProofContext.get_fact o no_binding;
   637 val from_thmss_i = gen_thmss (K []) chain #2 (K I) (K I) o no_binding;
   638 
   639 val with_thmss = gen_thmss the_facts chain #2 Attrib.attribute ProofContext.get_fact o no_binding;
   640 val with_thmss_i = gen_thmss the_facts chain #2 (K I) (K I) o no_binding;
   641 
   642 val local_results = gen_thmss (K []) I I (K I) (K I) o map (apsnd Thm.simple_fact);
   643 
   644 fun get_thmss state srcs = the_facts (note_thmss [((Binding.empty, []), srcs)] state);
   645 
   646 end;
   647 
   648 
   649 (* using/unfolding *)
   650 
   651 local
   652 
   653 fun gen_using f g prep_atts prep_fact args state =
   654   state
   655   |> assert_backward
   656   |> map_context_result
   657     (ProofContext.note_thmss ""
   658       (Attrib.map_facts_refs (prep_atts (theory_of state)) (prep_fact (context_of state))
   659         (no_binding args)))
   660   |> (fn (named_facts, state') =>
   661     state' |> map_goal I (fn (statement, _, using, goal, before_qed, after_qed) =>
   662       let
   663         val ctxt = context_of state';
   664         val ths = maps snd named_facts;
   665       in (statement, [], f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));
   666 
   667 fun append_using _ ths using = using @ filter_out Thm.is_dummy ths;
   668 fun unfold_using ctxt ths = map (LocalDefs.unfold ctxt ths);
   669 val unfold_goals = LocalDefs.unfold_goals;
   670 
   671 in
   672 
   673 val using = gen_using append_using (K (K I)) Attrib.attribute ProofContext.get_fact;
   674 val using_i = gen_using append_using (K (K I)) (K I) (K I);
   675 val unfolding = gen_using unfold_using unfold_goals Attrib.attribute ProofContext.get_fact;
   676 val unfolding_i = gen_using unfold_using unfold_goals (K I) (K I);
   677 
   678 end;
   679 
   680 
   681 (* case *)
   682 
   683 local
   684 
   685 fun qualified_binding a =
   686   Binding.qualify true (Long_Name.qualifier a) (Binding.name (Long_Name.base_name a));
   687 
   688 fun gen_invoke_case prep_att (name, xs, raw_atts) state =
   689   let
   690     val atts = map (prep_att (theory_of state)) raw_atts;
   691     val (asms, state') = state |> map_context_result (fn ctxt =>
   692       ctxt |> ProofContext.apply_case (ProofContext.get_case ctxt name xs));
   693     val assumptions = asms |> map (fn (a, ts) => ((qualified_binding a, atts), map (rpair []) ts));
   694   in
   695     state'
   696     |> assume_i assumptions
   697     |> bind_terms AutoBind.no_facts
   698     |> `the_facts |-> (fn thms => note_thmss_i [((Binding.name name, []), [(thms, [])])])
   699   end;
   700 
   701 in
   702 
   703 val invoke_case = gen_invoke_case Attrib.attribute;
   704 val invoke_case_i = gen_invoke_case (K I);
   705 
   706 end;
   707 
   708 
   709 
   710 (** proof structure **)
   711 
   712 (* blocks *)
   713 
   714 val begin_block =
   715   assert_forward
   716   #> open_block
   717   #> put_goal NONE
   718   #> open_block;
   719 
   720 val next_block =
   721   assert_forward
   722   #> close_block
   723   #> open_block
   724   #> put_goal NONE
   725   #> put_facts NONE;
   726 
   727 fun end_block state =
   728   state
   729   |> assert_forward
   730   |> close_block
   731   |> assert_current_goal false
   732   |> close_block
   733   |> export_facts state;
   734 
   735 
   736 (* sub-proofs *)
   737 
   738 fun proof opt_text =
   739   assert_backward
   740   #> refine (the_default Method.default_text opt_text)
   741   #> Seq.map (using_facts [] #> enter_forward);
   742 
   743 fun end_proof bot txt state =
   744   state
   745   |> assert_forward
   746   |> assert_bottom bot
   747   |> close_block
   748   |> assert_current_goal true
   749   |> using_facts []
   750   |> `before_qed |-> (refine o the_default Method.succeed_text)
   751   |> Seq.maps (refine (Method.finish_text txt (Position.thread_data ())));
   752 
   753 fun check_result msg sq =
   754   (case Seq.pull sq of
   755     NONE => error msg
   756   | SOME (s, _) => s);
   757 
   758 fun check_finish sq = check_result "Failed to finish proof" sq;
   759 
   760 
   761 (* unstructured refinement *)
   762 
   763 fun defer i = assert_no_chain #> refine (Method.Basic (K (Method.defer i), Position.none));
   764 fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i), Position.none));
   765 
   766 fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);
   767 fun apply_end text = assert_forward #> refine_end text;
   768 
   769 
   770 
   771 (** goals **)
   772 
   773 (* generic goals *)
   774 
   775 local
   776 
   777 fun implicit_vars dest add props =
   778   let
   779     val (explicit_vars, props') = take_prefix (can dest) props |>> map dest;
   780     val vars = rev (subtract (op =) explicit_vars (fold add props []));
   781     val _ =
   782       if null vars then ()
   783       else warning ("Goal statement contains unbound schematic variable(s): " ^
   784         commas_quote (map (Term.string_of_vname o fst) vars));
   785   in (rev vars, props') end;
   786 
   787 fun refine_terms n =
   788   refine (Method.Basic (K (RAW_METHOD
   789     (K (HEADGOAL (PRECISE_CONJUNCTS n
   790       (HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI)))))))), Position.none))
   791   #> Seq.hd;
   792 
   793 in
   794 
   795 fun generic_goal prepp kind before_qed after_qed raw_propp state =
   796   let
   797     val thy = theory_of state;
   798     val cert = Thm.cterm_of thy;
   799     val chaining = can assert_chain state;
   800     val pos = Position.thread_data ();
   801 
   802     val ((propss, after_ctxt), goal_state) =
   803       state
   804       |> assert_forward_or_chain
   805       |> enter_forward
   806       |> open_block
   807       |> map_context_result (fn ctxt => swap (prepp (ctxt, raw_propp)));
   808     val props = flat propss;
   809 
   810     val (_, props') =
   811       implicit_vars (dest_TVar o Logic.dest_type o Logic.dest_term) Term.add_tvars props;
   812     val (vars, _) = implicit_vars (dest_Var o Logic.dest_term) Term.add_vars props';
   813 
   814     val propss' = map (Logic.mk_term o Var) vars :: propss;
   815     val goal_propss = filter_out null propss';
   816     val goal =
   817       cert (Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss))
   818       |> Thm.weaken_sorts (Variable.sorts_of (context_of goal_state));
   819     val statement = ((kind, pos), propss', Thm.term_of goal);
   820     val after_qed' = after_qed |>> (fn after_local =>
   821       fn results => map_context after_ctxt #> after_local results);
   822   in
   823     goal_state
   824     |> map_context (init_context #> Variable.set_body true)
   825     |> put_goal (SOME (make_goal (statement, [], [], Goal.init goal, before_qed, after_qed')))
   826     |> map_context (ProofContext.auto_bind_goal props)
   827     |> chaining ? (`the_facts #-> using_facts)
   828     |> put_facts NONE
   829     |> open_block
   830     |> put_goal NONE
   831     |> enter_backward
   832     |> not (null vars) ? refine_terms (length goal_propss)
   833     |> null props ? (refine (Method.Basic (Method.assumption, Position.none)) #> Seq.hd)
   834   end;
   835 
   836 fun generic_qed after_ctxt state =
   837   let
   838     val (goal_ctxt, {statement, goal, after_qed, ...}) = current_goal state;
   839     val outer_state = state |> close_block;
   840     val outer_ctxt = context_of outer_state;
   841 
   842     val ((_, pos), stmt, _) = statement;
   843     val props =
   844       flat (tl stmt)
   845       |> Variable.exportT_terms goal_ctxt outer_ctxt;
   846     val results =
   847       tl (conclude_goal goal_ctxt goal stmt)
   848       |> burrow (ProofContext.export goal_ctxt outer_ctxt);
   849 
   850     val (after_local, after_global) = after_qed;
   851     fun after_local' x y = Position.setmp_thread_data pos (fn () => after_local x y) ();
   852     fun after_global' x y = Position.setmp_thread_data pos (fn () => after_global x y) ();
   853   in
   854     outer_state
   855     |> map_context (after_ctxt props)
   856     |> pair ((after_local', after_global'), results)
   857   end;
   858 
   859 end;
   860 
   861 
   862 (* local goals *)
   863 
   864 fun local_goal print_results prep_att prepp kind before_qed after_qed stmt state =
   865   let
   866     val thy = theory_of state;
   867     val ((names, attss), propp) =
   868       Attrib.map_specs (prep_att thy) stmt |> split_list |>> split_list;
   869 
   870     fun after_qed' results =
   871       local_results ((names ~~ attss) ~~ results)
   872       #-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
   873       #> after_qed results;
   874   in
   875     state
   876     |> generic_goal prepp kind before_qed (after_qed', K I) propp
   877     |> tap (Variable.warn_extra_tfrees (context_of state) o context_of)
   878   end;
   879 
   880 fun local_qeds txt =
   881   end_proof false txt
   882   #> Seq.map (generic_qed ProofContext.auto_bind_facts #->
   883     (fn ((after_qed, _), results) => after_qed results));
   884 
   885 fun local_qed txt = local_qeds txt #> check_finish;
   886 
   887 
   888 (* global goals *)
   889 
   890 fun global_goal prepp before_qed after_qed propp ctxt =
   891   init ctxt
   892   |> generic_goal (prepp #> ProofContext.auto_fixes) "" before_qed (K I, after_qed) propp;
   893 
   894 val theorem = global_goal ProofContext.bind_propp_schematic;
   895 val theorem_i = global_goal ProofContext.bind_propp_schematic_i;
   896 
   897 fun global_qeds txt =
   898   end_proof true txt
   899   #> Seq.map (generic_qed (K I) #> (fn (((_, after_qed), results), state) =>
   900     after_qed results (context_of state)));
   901 
   902 fun global_qed txt = global_qeds txt #> check_finish;
   903 
   904 
   905 (* concluding steps *)
   906 
   907 fun terminal_proof qed initial terminal =
   908   proof (SOME initial) #> Seq.maps (qed terminal) #> check_finish;
   909 
   910 fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);
   911 val local_default_proof = local_terminal_proof (Method.default_text, NONE);
   912 val local_immediate_proof = local_terminal_proof (Method.this_text, NONE);
   913 fun local_skip_proof int = local_terminal_proof (Method.sorry_text int, NONE);
   914 val local_done_proof = terminal_proof local_qeds Method.done_text (NONE, false);
   915 
   916 fun global_terminal_proof (text, opt_text) = terminal_proof global_qeds text (opt_text, true);
   917 val global_default_proof = global_terminal_proof (Method.default_text, NONE);
   918 val global_immediate_proof = global_terminal_proof (Method.this_text, NONE);
   919 fun global_skip_proof int = global_terminal_proof (Method.sorry_text int, NONE);
   920 val global_done_proof = terminal_proof global_qeds Method.done_text (NONE, false);
   921 
   922 
   923 (* common goal statements *)
   924 
   925 local
   926 
   927 fun gen_have prep_att prepp before_qed after_qed stmt int =
   928   local_goal (ProofDisplay.print_results int) prep_att prepp "have" before_qed after_qed stmt;
   929 
   930 fun gen_show prep_att prepp before_qed after_qed stmt int state =
   931   let
   932     val testing = ref false;
   933     val rule = ref (NONE: thm option);
   934     fun fail_msg ctxt =
   935       "Local statement will fail to refine any pending goal" ::
   936       (case ! rule of NONE => [] | SOME th => [ProofDisplay.string_of_rule ctxt "Failed" th])
   937       |> cat_lines;
   938 
   939     fun print_results ctxt res =
   940       if ! testing then () else ProofDisplay.print_results int ctxt res;
   941     fun print_rule ctxt th =
   942       if ! testing then rule := SOME th
   943       else if int then priority (ProofDisplay.string_of_rule ctxt "Successful" th)
   944       else ();
   945     val test_proof =
   946       try (local_skip_proof true)
   947       |> setmp_noncritical testing true
   948       |> Exn.capture;
   949 
   950     fun after_qed' results =
   951       refine_goals print_rule (context_of state) (flat results)
   952       #> check_result "Failed to refine any pending goal"
   953       #> after_qed results;
   954   in
   955     state
   956     |> local_goal print_results prep_att prepp "show" before_qed after_qed' stmt
   957     |> int ? (fn goal_state =>
   958       (case test_proof goal_state of
   959         Exn.Result (SOME _) => goal_state
   960       | Exn.Result NONE => error (fail_msg (context_of goal_state))
   961       | Exn.Exn Exn.Interrupt => raise Exn.Interrupt
   962       | Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))
   963   end;
   964 
   965 in
   966 
   967 val have = gen_have Attrib.attribute ProofContext.bind_propp;
   968 val have_i = gen_have (K I) ProofContext.bind_propp_i;
   969 val show = gen_show Attrib.attribute ProofContext.bind_propp;
   970 val show_i = gen_show (K I) ProofContext.bind_propp_i;
   971 
   972 end;
   973 
   974 
   975 
   976 (** future proofs **)
   977 
   978 (* relevant proof states *)
   979 
   980 fun is_schematic t =
   981   Term.exists_subterm Term.is_Var t orelse
   982   Term.exists_type (Term.exists_subtype Term.is_TVar) t;
   983 
   984 fun schematic_goal state =
   985   let val (_, (_, {statement = (_, _, prop), ...})) = find_goal state
   986   in is_schematic prop end;
   987 
   988 fun is_relevant state =
   989   (case try find_goal state of
   990     NONE => true
   991   | SOME (_, (_, {statement = (_, _, prop), goal, ...})) =>
   992       is_schematic prop orelse not (Logic.protect prop aconv Thm.concl_of goal));
   993 
   994 
   995 (* full proofs *)
   996 
   997 local
   998 
   999 fun future_proof done get_context fork_proof state =
  1000   let
  1001     val _ = assert_backward state;
  1002     val (goal_ctxt, (_, goal)) = find_goal state;
  1003     val {statement as (kind, propss, prop), messages, using, goal, before_qed, after_qed} = goal;
  1004     val goal_txt = prop :: map Thm.term_of (Assumption.all_assms_of goal_ctxt);
  1005 
  1006     val _ = is_relevant state andalso error "Cannot fork relevant proof";
  1007 
  1008     val prop' = Logic.protect prop;
  1009     val statement' = (kind, [[], [prop']], prop');
  1010     val goal' = Thm.adjust_maxidx_thm (Thm.maxidx_of goal)
  1011       (Drule.comp_no_flatten (goal, Thm.nprems_of goal) 1 Drule.protectI);
  1012 
  1013     fun after_local' [[th]] = put_thms false (AutoBind.thisN, SOME [th]);
  1014     fun after_global' [[th]] = ProofContext.put_thms false (AutoBind.thisN, SOME [th]);
  1015     val after_qed' = (after_local', after_global');
  1016     val this_name = ProofContext.full_name goal_ctxt (Binding.name AutoBind.thisN);
  1017 
  1018     val result_ctxt =
  1019       state
  1020       |> map_contexts (fold Variable.declare_term goal_txt)
  1021       |> map_goal I (K (statement', messages, using, goal', before_qed, after_qed'))
  1022       |> fork_proof;
  1023 
  1024     val future_thm = result_ctxt |> Future.map (fn (_, x) =>
  1025       ProofContext.get_fact_single (get_context x) (Facts.named this_name));
  1026     val finished_goal = Goal.future_result goal_ctxt future_thm prop';
  1027     val state' =
  1028       state
  1029       |> map_goal I (K (statement, messages, using, finished_goal, NONE, after_qed))
  1030       |> done;
  1031   in (Future.map #1 result_ctxt, state') end;
  1032 
  1033 in
  1034 
  1035 fun local_future_proof x = future_proof local_done_proof context_of x;
  1036 fun global_future_proof x = future_proof global_done_proof I x;
  1037 
  1038 end;
  1039 
  1040 
  1041 (* terminal proofs *)
  1042 
  1043 local
  1044 
  1045 fun future_terminal_proof proof1 proof2 meths int state =
  1046   if int orelse is_relevant state orelse not (Goal.local_future_enabled ())
  1047   then proof1 meths state
  1048   else snd (proof2 (fn state' => Future.fork_pri ~1 (fn () => ((), proof1 meths state'))) state);
  1049 
  1050 in
  1051 
  1052 fun local_future_terminal_proof x =
  1053   future_terminal_proof local_terminal_proof local_future_proof x;
  1054 
  1055 fun global_future_terminal_proof x =
  1056   future_terminal_proof global_terminal_proof global_future_proof x;
  1057 
  1058 end;
  1059 
  1060 end;
  1061