src/Pure/Isar/proof.ML
author wenzelm
Mon May 03 14:25:56 2010 +0200 (2010-05-03)
changeset 36610 bafd82950e24
parent 36507 c966a1aab860
child 37186 349e9223c685
permissions -rw-r--r--
renamed ProofContext.init to ProofContext.init_global to emphasize that this is not the real thing;
     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_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 show_main_goal: bool Unsynchronized.ref
    33   val verbose: bool Unsynchronized.ref
    34   val pretty_state: int -> state -> Pretty.T list
    35   val pretty_goals: bool -> state -> Pretty.T list
    36   val refine: Method.text -> state -> state Seq.seq
    37   val refine_end: Method.text -> state -> state Seq.seq
    38   val refine_insert: thm list -> state -> state
    39   val goal_tac: thm -> int -> tactic
    40   val refine_goals: (context -> thm -> unit) -> context -> thm list -> state -> state Seq.seq
    41   val raw_goal: state -> {context: context, facts: thm list, goal: thm}
    42   val goal: state -> {context: context, facts: thm list, goal: thm}
    43   val simple_goal: state -> {context: context, goal: thm}
    44   val let_bind: (term list * term) list -> state -> state
    45   val let_bind_cmd: (string list * string) list -> state -> state
    46   val write: Syntax.mode -> (term * mixfix) list -> state -> state
    47   val write_cmd: Syntax.mode -> (string * mixfix) list -> state -> state
    48   val fix: (binding * typ option * mixfix) list -> state -> state
    49   val fix_cmd: (binding * string option * mixfix) list -> state -> state
    50   val assm: Assumption.export ->
    51     (Thm.binding * (term * term list) list) list -> state -> state
    52   val assm_cmd: Assumption.export ->
    53     (Attrib.binding * (string * string list) list) list -> state -> state
    54   val assume: (Thm.binding * (term * term list) list) list -> state -> state
    55   val assume_cmd: (Attrib.binding * (string * string list) list) list -> state -> state
    56   val presume: (Thm.binding * (term * term list) list) list -> state -> state
    57   val presume_cmd: (Attrib.binding * (string * string list) list) list -> state -> state
    58   val def: (Thm.binding * ((binding * mixfix) * (term * term list))) list -> state -> state
    59   val def_cmd: (Attrib.binding * ((binding * mixfix) * (string * string list))) list -> state -> state
    60   val chain: state -> state
    61   val chain_facts: thm list -> state -> state
    62   val get_thmss_cmd: state -> (Facts.ref * Attrib.src list) list -> thm list
    63   val note_thmss: (Thm.binding * (thm list * attribute list) list) list -> state -> state
    64   val note_thmss_cmd: (Attrib.binding * (Facts.ref * Attrib.src list) list) list -> state -> state
    65   val from_thmss: ((thm list * attribute list) list) list -> state -> state
    66   val from_thmss_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
    67   val with_thmss: ((thm list * attribute list) list) list -> state -> state
    68   val with_thmss_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
    69   val using: ((thm list * attribute list) list) list -> state -> state
    70   val using_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
    71   val unfolding: ((thm list * attribute list) list) list -> state -> state
    72   val unfolding_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
    73   val invoke_case: string * string option list * attribute list -> state -> state
    74   val invoke_case_cmd: string * string option list * Attrib.src list -> state -> state
    75   val begin_block: state -> state
    76   val next_block: state -> state
    77   val end_block: state -> state
    78   val proof: Method.text option -> state -> state Seq.seq
    79   val defer: int option -> state -> state Seq.seq
    80   val prefer: int -> state -> state Seq.seq
    81   val apply: Method.text -> state -> state Seq.seq
    82   val apply_end: Method.text -> state -> state Seq.seq
    83   val local_goal: (context -> ((string * string) * (string * thm list) list) -> unit) ->
    84     (theory -> 'a -> attribute) ->
    85     (context * 'b list -> context * (term list list * (context -> context))) ->
    86     string -> Method.text option -> (thm list list -> state -> state) ->
    87     ((binding * 'a list) * 'b) list -> state -> state
    88   val local_qed: Method.text option * bool -> state -> state
    89   val theorem: Method.text option -> (thm list list -> context -> context) ->
    90     (term * term list) list list -> context -> state
    91   val theorem_cmd: Method.text option -> (thm list list -> context -> context) ->
    92     (string * string list) list list -> context -> state
    93   val global_qed: Method.text option * bool -> state -> context
    94   val local_terminal_proof: Method.text * Method.text option -> state -> state
    95   val local_default_proof: state -> state
    96   val local_immediate_proof: state -> state
    97   val local_skip_proof: bool -> state -> state
    98   val local_done_proof: state -> state
    99   val global_terminal_proof: Method.text * Method.text option -> state -> context
   100   val global_default_proof: state -> context
   101   val global_immediate_proof: state -> context
   102   val global_skip_proof: bool -> state -> context
   103   val global_done_proof: state -> context
   104   val have: Method.text option -> (thm list list -> state -> state) ->
   105     (Thm.binding * (term * term list) list) list -> bool -> state -> state
   106   val have_cmd: Method.text option -> (thm list list -> state -> state) ->
   107     (Attrib.binding * (string * string list) list) list -> bool -> state -> state
   108   val show: Method.text option -> (thm list list -> state -> state) ->
   109     (Thm.binding * (term * term list) list) list -> bool -> state -> state
   110   val show_cmd: Method.text option -> (thm list list -> state -> state) ->
   111     (Attrib.binding * (string * string list) list) list -> bool -> state -> state
   112   val schematic_goal: state -> bool
   113   val is_relevant: state -> bool
   114   val local_future_proof: (state -> ('a * state) Future.future) ->
   115     state -> 'a Future.future * state
   116   val global_future_proof: (state -> ('a * Proof.context) Future.future) ->
   117     state -> 'a Future.future * context
   118   val local_future_terminal_proof: Method.text * Method.text option -> bool -> state -> state
   119   val global_future_terminal_proof: Method.text * Method.text option -> bool -> state -> context
   120 end;
   121 
   122 structure Proof: PROOF =
   123 struct
   124 
   125 type context = Proof.context;
   126 type method = Method.method;
   127 
   128 
   129 (** proof state **)
   130 
   131 (* datatype state *)
   132 
   133 datatype mode = Forward | Chain | Backward;
   134 
   135 datatype state =
   136   State of node Stack.T
   137 and node =
   138   Node of
   139    {context: context,
   140     facts: thm list option,
   141     mode: mode,
   142     goal: goal option}
   143 and goal =
   144   Goal of
   145    {statement: (string * Position.T) * term list list * term,
   146       (*goal kind and statement (starting with vars), initial proposition*)
   147     messages: (unit -> Pretty.T) list,    (*persistent messages (hints etc.)*)
   148     using: thm list,                      (*goal facts*)
   149     goal: thm,                            (*subgoals ==> statement*)
   150     before_qed: Method.text option,
   151     after_qed:
   152       (thm list list -> state -> state) *
   153       (thm list list -> context -> context)};
   154 
   155 fun make_goal (statement, messages, using, goal, before_qed, after_qed) =
   156   Goal {statement = statement, messages = messages, using = using, goal = goal,
   157     before_qed = before_qed, after_qed = after_qed};
   158 
   159 fun make_node (context, facts, mode, goal) =
   160   Node {context = context, facts = facts, mode = mode, goal = goal};
   161 
   162 fun map_node f (Node {context, facts, mode, goal}) =
   163   make_node (f (context, facts, mode, goal));
   164 
   165 val init_context =
   166   ProofContext.set_stmt true #>
   167   ProofContext.map_naming (K ProofContext.local_naming);
   168 
   169 fun init ctxt =
   170   State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
   171 
   172 fun current (State st) = Stack.top st |> (fn Node node => node);
   173 fun map_current f (State st) = State (Stack.map_top (map_node f) st);
   174 fun map_all f (State st) = State (Stack.map_all (map_node f) st);
   175 
   176 
   177 
   178 (** basic proof state operations **)
   179 
   180 (* block structure *)
   181 
   182 fun open_block (State st) = State (Stack.push st);
   183 
   184 fun close_block (State st) = State (Stack.pop st)
   185   handle Empty => error "Unbalanced block parentheses";
   186 
   187 fun level (State st) = Stack.level st;
   188 
   189 fun assert_bottom b state =
   190   let val b' = (level state <= 2) in
   191     if b andalso not b' then error "Not at bottom of proof!"
   192     else if not b andalso b' then error "Already at bottom of proof!"
   193     else state
   194   end;
   195 
   196 
   197 (* context *)
   198 
   199 val context_of = #context o current;
   200 val theory_of = ProofContext.theory_of o context_of;
   201 
   202 fun map_context f =
   203   map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
   204 
   205 fun map_context_result f state =
   206   f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
   207 
   208 fun map_contexts f = map_all (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
   209 
   210 val bind_terms = map_context o ProofContext.bind_terms;
   211 val put_thms = map_context oo ProofContext.put_thms;
   212 
   213 
   214 (* facts *)
   215 
   216 val get_facts = #facts o current;
   217 
   218 fun the_facts state =
   219   (case get_facts state of SOME facts => facts
   220   | NONE => error "No current facts available");
   221 
   222 fun the_fact state =
   223   (case the_facts state of [thm] => thm
   224   | _ => error "Single theorem expected");
   225 
   226 fun put_facts facts =
   227   map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
   228   put_thms true (Auto_Bind.thisN, facts);
   229 
   230 fun these_factss more_facts (named_factss, state) =
   231   (named_factss, state |> put_facts (SOME (maps snd named_factss @ more_facts)));
   232 
   233 fun export_facts inner outer =
   234   (case get_facts inner of
   235     NONE => put_facts NONE outer
   236   | SOME thms =>
   237       thms
   238       |> ProofContext.export (context_of inner) (context_of outer)
   239       |> (fn ths => put_facts (SOME ths) outer));
   240 
   241 
   242 (* mode *)
   243 
   244 val get_mode = #mode o current;
   245 fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
   246 
   247 val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
   248 
   249 fun assert_mode pred state =
   250   let val mode = get_mode state in
   251     if pred mode then state
   252     else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
   253   end;
   254 
   255 val assert_forward = assert_mode (fn mode => mode = Forward);
   256 val assert_chain = assert_mode (fn mode => mode = Chain);
   257 val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
   258 val assert_backward = assert_mode (fn mode => mode = Backward);
   259 val assert_no_chain = assert_mode (fn mode => mode <> Chain);
   260 
   261 val enter_forward = put_mode Forward;
   262 val enter_chain = put_mode Chain;
   263 val enter_backward = put_mode Backward;
   264 
   265 
   266 (* current goal *)
   267 
   268 fun current_goal state =
   269   (case current state of
   270     {context, goal = SOME (Goal goal), ...} => (context, goal)
   271   | _ => error "No current goal!");
   272 
   273 fun assert_current_goal g state =
   274   let val g' = can current_goal state in
   275     if g andalso not g' then error "No goal in this block!"
   276     else if not g andalso g' then error "Goal present in this block!"
   277     else state
   278   end;
   279 
   280 fun put_goal goal = map_current (fn (ctxt, using, mode, _) => (ctxt, using, mode, goal));
   281 
   282 val before_qed = #before_qed o #2 o current_goal;
   283 
   284 
   285 (* nested goal *)
   286 
   287 fun map_goal f g (State (Node {context, facts, mode, goal = SOME goal}, nodes)) =
   288       let
   289         val Goal {statement, messages, using, goal, before_qed, after_qed} = goal;
   290         val goal' = make_goal (g (statement, messages, using, goal, before_qed, after_qed));
   291       in State (make_node (f context, facts, mode, SOME goal'), nodes) end
   292   | map_goal f g (State (nd, node :: nodes)) =
   293       let val State (node', nodes') = map_goal f g (State (node, nodes))
   294       in map_context f (State (nd, node' :: nodes')) end
   295   | map_goal _ _ state = state;
   296 
   297 fun set_goal goal = map_goal I (fn (statement, _, using, _, before_qed, after_qed) =>
   298   (statement, [], using, goal, before_qed, after_qed));
   299 
   300 fun goal_message msg = map_goal I (fn (statement, messages, using, goal, before_qed, after_qed) =>
   301   (statement, msg :: messages, using, goal, before_qed, after_qed));
   302 
   303 fun using_facts using = map_goal I (fn (statement, _, _, goal, before_qed, after_qed) =>
   304   (statement, [], using, goal, before_qed, after_qed));
   305 
   306 local
   307   fun find i state =
   308     (case try current_goal state of
   309       SOME (ctxt, goal) => (ctxt, (i, goal))
   310     | NONE => find (i + 1) (close_block state handle ERROR _ => error "No goal present"));
   311 in val find_goal = find 0 end;
   312 
   313 fun get_goal state =
   314   let val (ctxt, (_, {using, goal, ...})) = find_goal state
   315   in (ctxt, (using, goal)) end;
   316 
   317 
   318 
   319 (** pretty_state **)
   320 
   321 val show_main_goal = Unsynchronized.ref false;
   322 val verbose = ProofContext.verbose;
   323 
   324 fun pretty_facts _ _ NONE = []
   325   | pretty_facts s ctxt (SOME ths) =
   326       [Pretty.big_list (s ^ "this:") (map (Display.pretty_thm ctxt) ths), Pretty.str ""];
   327 
   328 fun pretty_state nr state =
   329   let
   330     val {context, facts, mode, goal = _} = current state;
   331 
   332     fun levels_up 0 = ""
   333       | levels_up 1 = "1 level up"
   334       | levels_up i = string_of_int i ^ " levels up";
   335 
   336     fun subgoals 0 = ""
   337       | subgoals 1 = "1 subgoal"
   338       | subgoals n = string_of_int n ^ " subgoals";
   339 
   340     fun description strs =
   341       (case filter_out (fn s => s = "") strs of [] => ""
   342       | strs' => enclose " (" ")" (commas strs'));
   343 
   344     fun prt_goal (SOME (ctxt, (i,
   345       {statement = ((_, pos), _, _), messages, using, goal, before_qed = _, after_qed = _}))) =
   346           pretty_facts "using " ctxt
   347             (if mode <> Backward orelse null using then NONE else SOME using) @
   348           [Pretty.str ("goal" ^
   349             description [levels_up (i div 2), subgoals (Thm.nprems_of goal)] ^ ":")] @
   350           Goal_Display.pretty_goals ctxt
   351             {total = true, main = ! show_main_goal, maxgoals = ! Display.goals_limit} goal @
   352           (map (fn msg => Position.setmp_thread_data pos msg ()) (rev messages))
   353       | prt_goal NONE = [];
   354 
   355     val prt_ctxt =
   356       if ! verbose orelse mode = Forward then ProofContext.pretty_context context
   357       else if mode = Backward then ProofContext.pretty_ctxt context
   358       else [];
   359   in
   360     [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^
   361       (if ! verbose then ", depth " ^ string_of_int (level state div 2 - 1) else "")),
   362       Pretty.str ""] @
   363     (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
   364     (if ! verbose orelse mode = Forward then
   365        pretty_facts "" context facts @ prt_goal (try find_goal state)
   366      else if mode = Chain then pretty_facts "picking " context facts
   367      else prt_goal (try find_goal state))
   368   end;
   369 
   370 fun pretty_goals main state =
   371   let val (ctxt, (_, goal)) = get_goal state in
   372     Goal_Display.pretty_goals ctxt
   373       {total = false, main = main, maxgoals = ! Display.goals_limit} goal
   374   end;
   375 
   376 
   377 
   378 (** proof steps **)
   379 
   380 (* refine via method *)
   381 
   382 local
   383 
   384 fun goalN i = "goal" ^ string_of_int i;
   385 fun goals st = map goalN (1 upto Thm.nprems_of st);
   386 
   387 fun no_goal_cases st = map (rpair NONE) (goals st);
   388 
   389 fun goal_cases st =
   390   Rule_Cases.make_common (Thm.theory_of_thm st, Thm.prop_of st) (map (rpair []) (goals st));
   391 
   392 fun apply_method current_context meth state =
   393   let
   394     val (goal_ctxt, (_, {statement, messages = _, using, goal, before_qed, after_qed})) =
   395       find_goal state;
   396     val ctxt = if current_context then context_of state else goal_ctxt;
   397   in
   398     Method.apply meth ctxt using goal |> Seq.map (fn (meth_cases, goal') =>
   399       state
   400       |> map_goal
   401           (ProofContext.add_cases false (no_goal_cases goal @ goal_cases goal') #>
   402            ProofContext.add_cases true meth_cases)
   403           (K (statement, [], using, goal', before_qed, after_qed)))
   404   end;
   405 
   406 fun select_goals n meth state =
   407   state
   408   |> (#2 o #2 o get_goal)
   409   |> ALLGOALS Goal.conjunction_tac
   410   |> Seq.maps (fn goal =>
   411     state
   412     |> Seq.lift set_goal (Goal.extract 1 n goal |> Seq.maps (Goal.conjunction_tac 1))
   413     |> Seq.maps meth
   414     |> Seq.maps (fn state' => state'
   415       |> Seq.lift set_goal (Goal.retrofit 1 n (#2 (#2 (get_goal state'))) goal))
   416     |> Seq.maps (apply_method true (K Method.succeed)));
   417 
   418 fun apply_text cc text state =
   419   let
   420     val thy = theory_of state;
   421 
   422     fun eval (Method.Basic m) = apply_method cc m
   423       | eval (Method.Source src) = apply_method cc (Method.method thy src)
   424       | eval (Method.Source_i src) = apply_method cc (Method.method_i thy src)
   425       | eval (Method.Then txts) = Seq.EVERY (map eval txts)
   426       | eval (Method.Orelse txts) = Seq.FIRST (map eval txts)
   427       | eval (Method.Try txt) = Seq.TRY (eval txt)
   428       | eval (Method.Repeat1 txt) = Seq.REPEAT1 (eval txt)
   429       | eval (Method.SelectGoals (n, txt)) = select_goals n (eval txt);
   430   in eval text state end;
   431 
   432 in
   433 
   434 val refine = apply_text true;
   435 val refine_end = apply_text false;
   436 fun refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths)));
   437 
   438 end;
   439 
   440 
   441 (* refine via sub-proof *)
   442 
   443 fun finish_tac 0 = K all_tac
   444   | finish_tac n =
   445       Goal.norm_hhf_tac THEN'
   446       SUBGOAL (fn (goal, i) =>
   447         if can Logic.unprotect (Logic.strip_assums_concl goal) then
   448           Tactic.etac Drule.protectI i THEN finish_tac (n - 1) i
   449         else finish_tac (n - 1) (i + 1));
   450 
   451 fun goal_tac rule =
   452   Goal.norm_hhf_tac THEN'
   453   Tactic.rtac rule THEN'
   454   finish_tac (Thm.nprems_of rule);
   455 
   456 fun refine_goals print_rule inner raw_rules state =
   457   let
   458     val (outer, (_, goal)) = get_goal state;
   459     fun refine rule st = (print_rule outer rule; FINDGOAL (goal_tac rule) st);
   460   in
   461     raw_rules
   462     |> ProofContext.goal_export inner outer
   463     |> (fn rules => Seq.lift set_goal (EVERY (map refine rules) goal) state)
   464   end;
   465 
   466 
   467 (* conclude_goal *)
   468 
   469 fun conclude_goal ctxt goal propss =
   470   let
   471     val thy = ProofContext.theory_of ctxt;
   472     val string_of_term = Syntax.string_of_term ctxt;
   473     val string_of_thm = Display.string_of_thm ctxt;
   474 
   475     val ngoals = Thm.nprems_of goal;
   476     val _ = ngoals = 0 orelse error (Pretty.string_of (Pretty.chunks
   477       (Goal_Display.pretty_goals ctxt
   478           {total = true, main = ! show_main_goal, maxgoals = ! Display.goals_limit} goal @
   479         [Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")])));
   480 
   481     val extra_hyps = Assumption.extra_hyps ctxt goal;
   482     val _ = null extra_hyps orelse
   483       error ("Additional hypotheses:\n" ^ cat_lines (map string_of_term extra_hyps));
   484 
   485     fun lost_structure () = error ("Lost goal structure:\n" ^ string_of_thm goal);
   486 
   487     val th = Goal.conclude
   488       (if length (flat propss) > 1 then Thm.norm_proof goal else goal)
   489       handle THM _ => lost_structure ();
   490     val goal_propss = filter_out null propss;
   491     val results =
   492       Conjunction.elim_balanced (length goal_propss) th
   493       |> map2 Conjunction.elim_balanced (map length goal_propss)
   494       handle THM _ => lost_structure ();
   495     val _ = Unify.matches_list thy (flat goal_propss) (map Thm.prop_of (flat results)) orelse
   496       error ("Proved a different theorem:\n" ^ string_of_thm th);
   497     val _ = Thm.check_shyps (Variable.sorts_of ctxt) th;
   498 
   499     fun recover_result ([] :: pss) thss = [] :: recover_result pss thss
   500       | recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss
   501       | recover_result [] [] = []
   502       | recover_result _ _ = lost_structure ();
   503   in recover_result propss results end;
   504 
   505 
   506 (* goal views -- corresponding to methods *)
   507 
   508 fun raw_goal state =
   509   let val (ctxt, (facts, goal)) = get_goal state
   510   in {context = ctxt, facts = facts, goal = goal} end;
   511 
   512 val goal = raw_goal o refine_insert [];
   513 
   514 fun simple_goal state =
   515   let
   516     val (_, (facts, _)) = get_goal state;
   517     val (ctxt, (_, goal)) = get_goal (refine_insert facts state);
   518   in {context = ctxt, goal = goal} end;
   519 
   520 
   521 
   522 (*** structured proof commands ***)
   523 
   524 (** context elements **)
   525 
   526 (* let bindings *)
   527 
   528 local
   529 
   530 fun gen_bind bind args state =
   531   state
   532   |> assert_forward
   533   |> map_context (bind true args #> snd)
   534   |> put_facts NONE;
   535 
   536 in
   537 
   538 val let_bind = gen_bind ProofContext.match_bind_i;
   539 val let_bind_cmd = gen_bind ProofContext.match_bind;
   540 
   541 end;
   542 
   543 
   544 (* concrete syntax *)
   545 
   546 local
   547 
   548 fun gen_write prep_arg mode args =
   549   assert_forward
   550   #> map_context (fn ctxt => ctxt |> ProofContext.notation true mode (map (prep_arg ctxt) args))
   551   #> put_facts NONE;
   552 
   553 in
   554 
   555 val write = gen_write (K I);
   556 
   557 val write_cmd =
   558   gen_write (fn ctxt => fn (c, mx) =>
   559     (ProofContext.read_const ctxt false (Syntax.mixfixT mx) c, mx));
   560 
   561 end;
   562 
   563 
   564 (* fix *)
   565 
   566 local
   567 
   568 fun gen_fix prep_vars args =
   569   assert_forward
   570   #> map_context (fn ctxt => snd (ProofContext.add_fixes (prep_vars ctxt args) ctxt))
   571   #> put_facts NONE;
   572 
   573 in
   574 
   575 val fix = gen_fix (K I);
   576 val fix_cmd = gen_fix (fn ctxt => fn args => fst (ProofContext.read_vars args ctxt));
   577 
   578 end;
   579 
   580 
   581 (* assume etc. *)
   582 
   583 local
   584 
   585 fun gen_assume asm prep_att exp args state =
   586   state
   587   |> assert_forward
   588   |> map_context_result (asm exp (Attrib.map_specs (prep_att (theory_of state)) args))
   589   |> these_factss [] |> #2;
   590 
   591 in
   592 
   593 val assm = gen_assume ProofContext.add_assms_i (K I);
   594 val assm_cmd = gen_assume ProofContext.add_assms Attrib.attribute;
   595 val assume = assm Assumption.assume_export;
   596 val assume_cmd = assm_cmd Assumption.assume_export;
   597 val presume = assm Assumption.presume_export;
   598 val presume_cmd = assm_cmd Assumption.presume_export;
   599 
   600 end;
   601 
   602 
   603 (* def *)
   604 
   605 local
   606 
   607 fun gen_def prep_att prep_vars prep_binds args state =
   608   let
   609     val _ = assert_forward state;
   610     val thy = theory_of state;
   611 
   612     val (raw_name_atts, (raw_vars, raw_rhss)) = args |> split_list ||> split_list;
   613     val name_atts = map (apsnd (map (prep_att thy))) raw_name_atts;
   614   in
   615     state
   616     |> map_context_result (prep_vars (map (fn (x, mx) => (x, NONE, mx)) raw_vars))
   617     |>> map (fn (x, _, mx) => (x, mx))
   618     |-> (fn vars =>
   619       map_context_result (prep_binds false (map swap raw_rhss))
   620       #-> (fn rhss => map_context_result (Local_Defs.add_defs (vars ~~ (name_atts ~~ rhss)))))
   621     |-> (put_facts o SOME o map (#2 o #2))
   622   end;
   623 
   624 in
   625 
   626 val def = gen_def (K I) ProofContext.cert_vars ProofContext.match_bind_i;
   627 val def_cmd = gen_def Attrib.attribute ProofContext.read_vars ProofContext.match_bind;
   628 
   629 end;
   630 
   631 
   632 
   633 (** facts **)
   634 
   635 (* chain *)
   636 
   637 fun clean_facts ctxt =
   638   put_facts (SOME (filter_out Thm.is_dummy (the_facts ctxt))) ctxt;
   639 
   640 val chain =
   641   assert_forward
   642   #> clean_facts
   643   #> enter_chain;
   644 
   645 fun chain_facts facts =
   646   put_facts (SOME facts)
   647   #> chain;
   648 
   649 
   650 (* note etc. *)
   651 
   652 fun no_binding args = map (pair (Binding.empty, [])) args;
   653 
   654 local
   655 
   656 fun gen_thmss more_facts opt_chain opt_result prep_atts prep_fact args state =
   657   state
   658   |> assert_forward
   659   |> map_context_result (ProofContext.note_thmss ""
   660     (Attrib.map_facts_refs (prep_atts (theory_of state)) (prep_fact (context_of state)) args))
   661   |> these_factss (more_facts state)
   662   ||> opt_chain
   663   |> opt_result;
   664 
   665 in
   666 
   667 val note_thmss = gen_thmss (K []) I #2 (K I) (K I);
   668 val note_thmss_cmd = gen_thmss (K []) I #2 Attrib.attribute ProofContext.get_fact;
   669 
   670 val from_thmss = gen_thmss (K []) chain #2 (K I) (K I) o no_binding;
   671 val from_thmss_cmd = gen_thmss (K []) chain #2 Attrib.attribute ProofContext.get_fact o no_binding;
   672 
   673 val with_thmss = gen_thmss the_facts chain #2 (K I) (K I) o no_binding;
   674 val with_thmss_cmd = gen_thmss the_facts chain #2 Attrib.attribute ProofContext.get_fact o no_binding;
   675 
   676 val local_results = gen_thmss (K []) I I (K I) (K I) o map (apsnd Thm.simple_fact);
   677 
   678 fun get_thmss_cmd state srcs = the_facts (note_thmss_cmd [((Binding.empty, []), srcs)] state);
   679 
   680 end;
   681 
   682 
   683 (* using/unfolding *)
   684 
   685 local
   686 
   687 fun gen_using f g prep_atts prep_fact args state =
   688   state
   689   |> assert_backward
   690   |> map_context_result
   691     (ProofContext.note_thmss ""
   692       (Attrib.map_facts_refs (prep_atts (theory_of state)) (prep_fact (context_of state))
   693         (no_binding args)))
   694   |> (fn (named_facts, state') =>
   695     state' |> map_goal I (fn (statement, _, using, goal, before_qed, after_qed) =>
   696       let
   697         val ctxt = context_of state';
   698         val ths = maps snd named_facts;
   699       in (statement, [], f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));
   700 
   701 fun append_using _ ths using = using @ filter_out Thm.is_dummy ths;
   702 fun unfold_using ctxt ths = map (Local_Defs.unfold ctxt ths);
   703 val unfold_goals = Local_Defs.unfold_goals;
   704 
   705 in
   706 
   707 val using = gen_using append_using (K (K I)) (K I) (K I);
   708 val using_cmd = gen_using append_using (K (K I)) Attrib.attribute ProofContext.get_fact;
   709 val unfolding = gen_using unfold_using unfold_goals (K I) (K I);
   710 val unfolding_cmd = gen_using unfold_using unfold_goals Attrib.attribute ProofContext.get_fact;
   711 
   712 end;
   713 
   714 
   715 (* case *)
   716 
   717 local
   718 
   719 fun qualified_binding a =
   720   Binding.qualify true (Long_Name.qualifier a) (Binding.name (Long_Name.base_name a));
   721 
   722 fun gen_invoke_case prep_att (name, xs, raw_atts) state =
   723   let
   724     val atts = map (prep_att (theory_of state)) raw_atts;
   725     val (asms, state') = state |> map_context_result (fn ctxt =>
   726       ctxt |> ProofContext.apply_case (ProofContext.get_case ctxt name xs));
   727     val assumptions = asms |> map (fn (a, ts) => ((qualified_binding a, atts), map (rpair []) ts));
   728   in
   729     state'
   730     |> assume assumptions
   731     |> bind_terms Auto_Bind.no_facts
   732     |> `the_facts |-> (fn thms => note_thmss [((Binding.name name, []), [(thms, [])])])
   733   end;
   734 
   735 in
   736 
   737 val invoke_case = gen_invoke_case (K I);
   738 val invoke_case_cmd = gen_invoke_case Attrib.attribute;
   739 
   740 end;
   741 
   742 
   743 
   744 (** proof structure **)
   745 
   746 (* blocks *)
   747 
   748 val begin_block =
   749   assert_forward
   750   #> open_block
   751   #> put_goal NONE
   752   #> open_block;
   753 
   754 val next_block =
   755   assert_forward
   756   #> close_block
   757   #> open_block
   758   #> put_goal NONE
   759   #> put_facts NONE;
   760 
   761 fun end_block state =
   762   state
   763   |> assert_forward
   764   |> close_block
   765   |> assert_current_goal false
   766   |> close_block
   767   |> export_facts state;
   768 
   769 
   770 (* sub-proofs *)
   771 
   772 fun proof opt_text =
   773   assert_backward
   774   #> refine (the_default Method.default_text opt_text)
   775   #> Seq.map (using_facts [] #> enter_forward);
   776 
   777 fun end_proof bot txt state =
   778   state
   779   |> assert_forward
   780   |> assert_bottom bot
   781   |> close_block
   782   |> assert_current_goal true
   783   |> using_facts []
   784   |> `before_qed |-> (refine o the_default Method.succeed_text)
   785   |> Seq.maps (refine (Method.finish_text txt));
   786 
   787 fun check_result msg sq =
   788   (case Seq.pull sq of
   789     NONE => error msg
   790   | SOME (s, _) => s);
   791 
   792 fun check_finish sq = check_result "Failed to finish proof" sq;
   793 
   794 
   795 (* unstructured refinement *)
   796 
   797 fun defer i = assert_no_chain #> refine (Method.Basic (K (Method.defer i)));
   798 fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i)));
   799 
   800 fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);
   801 fun apply_end text = assert_forward #> refine_end text;
   802 
   803 
   804 
   805 (** goals **)
   806 
   807 (* generic goals *)
   808 
   809 local
   810 
   811 val is_var =
   812   can (dest_TVar o Logic.dest_type o Logic.dest_term) orf
   813   can (dest_Var o Logic.dest_term);
   814 
   815 fun implicit_vars props =
   816   let
   817     val (var_props, _) = take_prefix is_var props;
   818     val explicit_vars = fold Term.add_vars var_props [];
   819     val vars = filter_out (member (op =) explicit_vars) (fold Term.add_vars props []);
   820   in map (Logic.mk_term o Var) vars end;
   821 
   822 fun refine_terms n =
   823   refine (Method.Basic (K (RAW_METHOD
   824     (K (HEADGOAL (PRECISE_CONJUNCTS n
   825       (HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI))))))))))
   826   #> Seq.hd;
   827 
   828 in
   829 
   830 fun generic_goal prepp kind before_qed after_qed raw_propp state =
   831   let
   832     val thy = theory_of state;
   833     val cert = Thm.cterm_of thy;
   834     val chaining = can assert_chain state;
   835     val pos = Position.thread_data ();
   836 
   837     val ((propss, after_ctxt), goal_state) =
   838       state
   839       |> assert_forward_or_chain
   840       |> enter_forward
   841       |> open_block
   842       |> map_context_result (fn ctxt => swap (prepp (ctxt, raw_propp)));
   843     val props = flat propss;
   844 
   845     val vars = implicit_vars props;
   846     val propss' = vars :: propss;
   847     val goal_propss = filter_out null propss';
   848     val goal =
   849       cert (Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss))
   850       |> Thm.weaken_sorts (Variable.sorts_of (context_of goal_state));
   851     val statement = ((kind, pos), propss', Thm.term_of goal);
   852     val after_qed' = after_qed |>> (fn after_local =>
   853       fn results => map_context after_ctxt #> after_local results);
   854   in
   855     goal_state
   856     |> map_context (init_context #> Variable.set_body true)
   857     |> put_goal (SOME (make_goal (statement, [], [], Goal.init goal, before_qed, after_qed')))
   858     |> map_context (ProofContext.auto_bind_goal props)
   859     |> chaining ? (`the_facts #-> using_facts)
   860     |> put_facts NONE
   861     |> open_block
   862     |> put_goal NONE
   863     |> enter_backward
   864     |> not (null vars) ? refine_terms (length goal_propss)
   865     |> null props ? (refine (Method.Basic Method.assumption) #> Seq.hd)
   866   end;
   867 
   868 fun generic_qed after_ctxt state =
   869   let
   870     val (goal_ctxt, {statement = (_, stmt, _), goal, after_qed, ...}) = current_goal state;
   871     val outer_state = state |> close_block;
   872     val outer_ctxt = context_of outer_state;
   873 
   874     val props =
   875       flat (tl stmt)
   876       |> Variable.exportT_terms goal_ctxt outer_ctxt;
   877     val results =
   878       tl (conclude_goal goal_ctxt goal stmt)
   879       |> burrow (ProofContext.export goal_ctxt outer_ctxt);
   880   in
   881     outer_state
   882     |> map_context (after_ctxt props)
   883     |> pair (after_qed, results)
   884   end;
   885 
   886 end;
   887 
   888 
   889 (* local goals *)
   890 
   891 fun local_goal print_results prep_att prepp kind before_qed after_qed stmt state =
   892   let
   893     val thy = theory_of state;
   894     val ((names, attss), propp) =
   895       Attrib.map_specs (prep_att thy) stmt |> split_list |>> split_list;
   896 
   897     fun after_qed' results =
   898       local_results ((names ~~ attss) ~~ results)
   899       #-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
   900       #> after_qed results;
   901   in
   902     state
   903     |> generic_goal prepp kind before_qed (after_qed', K I) propp
   904     |> tap (Variable.warn_extra_tfrees (context_of state) o context_of)
   905   end;
   906 
   907 fun local_qeds txt =
   908   end_proof false txt
   909   #> Seq.map (generic_qed ProofContext.auto_bind_facts #->
   910     (fn ((after_qed, _), results) => after_qed results));
   911 
   912 fun local_qed txt = local_qeds txt #> check_finish;
   913 
   914 
   915 (* global goals *)
   916 
   917 fun global_goal prepp before_qed after_qed propp ctxt =
   918   init ctxt
   919   |> generic_goal (prepp #> ProofContext.auto_fixes) "" before_qed (K I, after_qed) propp;
   920 
   921 val theorem = global_goal ProofContext.bind_propp_schematic_i;
   922 val theorem_cmd = global_goal ProofContext.bind_propp_schematic;
   923 
   924 fun global_qeds txt =
   925   end_proof true txt
   926   #> Seq.map (generic_qed (K I) #> (fn (((_, after_qed), results), state) =>
   927     after_qed results (context_of state)));
   928 
   929 fun global_qed txt = global_qeds txt #> check_finish;
   930 
   931 
   932 (* concluding steps *)
   933 
   934 fun terminal_proof qed initial terminal =
   935   proof (SOME initial) #> Seq.maps (qed terminal) #> check_finish;
   936 
   937 fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);
   938 val local_default_proof = local_terminal_proof (Method.default_text, NONE);
   939 val local_immediate_proof = local_terminal_proof (Method.this_text, NONE);
   940 fun local_skip_proof int = local_terminal_proof (Method.sorry_text int, NONE);
   941 val local_done_proof = terminal_proof local_qeds Method.done_text (NONE, false);
   942 
   943 fun global_terminal_proof (text, opt_text) = terminal_proof global_qeds text (opt_text, true);
   944 val global_default_proof = global_terminal_proof (Method.default_text, NONE);
   945 val global_immediate_proof = global_terminal_proof (Method.this_text, NONE);
   946 fun global_skip_proof int = global_terminal_proof (Method.sorry_text int, NONE);
   947 val global_done_proof = terminal_proof global_qeds Method.done_text (NONE, false);
   948 
   949 
   950 (* common goal statements *)
   951 
   952 local
   953 
   954 fun gen_have prep_att prepp before_qed after_qed stmt int =
   955   local_goal (Proof_Display.print_results int) prep_att prepp "have" before_qed after_qed stmt;
   956 
   957 fun gen_show prep_att prepp before_qed after_qed stmt int state =
   958   let
   959     val testing = Unsynchronized.ref false;
   960     val rule = Unsynchronized.ref (NONE: thm option);
   961     fun fail_msg ctxt =
   962       "Local statement will fail to refine any pending goal" ::
   963       (case ! rule of NONE => [] | SOME th => [Proof_Display.string_of_rule ctxt "Failed" th])
   964       |> cat_lines;
   965 
   966     fun print_results ctxt res =
   967       if ! testing then () else Proof_Display.print_results int ctxt res;
   968     fun print_rule ctxt th =
   969       if ! testing then rule := SOME th
   970       else if int then priority (Proof_Display.string_of_rule ctxt "Successful" th)
   971       else ();
   972     val test_proof =
   973       try (local_skip_proof true)
   974       |> setmp_noncritical testing true
   975       |> Exn.capture;
   976 
   977     fun after_qed' results =
   978       refine_goals print_rule (context_of state) (flat results)
   979       #> check_result "Failed to refine any pending goal"
   980       #> after_qed results;
   981   in
   982     state
   983     |> local_goal print_results prep_att prepp "show" before_qed after_qed' stmt
   984     |> int ? (fn goal_state =>
   985       (case test_proof goal_state of
   986         Exn.Result (SOME _) => goal_state
   987       | Exn.Result NONE => error (fail_msg (context_of goal_state))
   988       | Exn.Exn Exn.Interrupt => raise Exn.Interrupt
   989       | Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))
   990   end;
   991 
   992 in
   993 
   994 val have = gen_have (K I) ProofContext.bind_propp_i;
   995 val have_cmd = gen_have Attrib.attribute ProofContext.bind_propp;
   996 val show = gen_show (K I) ProofContext.bind_propp_i;
   997 val show_cmd = gen_show Attrib.attribute ProofContext.bind_propp;
   998 
   999 end;
  1000 
  1001 
  1002 
  1003 (** future proofs **)
  1004 
  1005 (* relevant proof states *)
  1006 
  1007 fun is_schematic t =
  1008   Term.exists_subterm Term.is_Var t orelse
  1009   Term.exists_type (Term.exists_subtype Term.is_TVar) t;
  1010 
  1011 fun schematic_goal state =
  1012   let val (_, (_, {statement = (_, _, prop), ...})) = find_goal state
  1013   in is_schematic prop end;
  1014 
  1015 fun is_relevant state =
  1016   (case try find_goal state of
  1017     NONE => true
  1018   | SOME (_, (_, {statement = (_, _, prop), goal, ...})) =>
  1019       is_schematic prop orelse not (Logic.protect prop aconv Thm.concl_of goal));
  1020 
  1021 
  1022 (* full proofs *)
  1023 
  1024 local
  1025 
  1026 fun future_proof done get_context fork_proof state =
  1027   let
  1028     val _ = assert_backward state;
  1029     val (goal_ctxt, (_, goal)) = find_goal state;
  1030     val {statement as (kind, _, prop), messages, using, goal, before_qed, after_qed} = goal;
  1031     val goal_txt = prop :: map Thm.term_of (Assumption.all_assms_of goal_ctxt);
  1032 
  1033     val _ = is_relevant state andalso error "Cannot fork relevant proof";
  1034 
  1035     val prop' = Logic.protect prop;
  1036     val statement' = (kind, [[], [prop']], prop');
  1037     val goal' = Thm.adjust_maxidx_thm (Thm.maxidx_of goal)
  1038       (Drule.comp_no_flatten (goal, Thm.nprems_of goal) 1 Drule.protectI);
  1039 
  1040     fun after_local' [[th]] = put_thms false (Auto_Bind.thisN, SOME [th]);
  1041     fun after_global' [[th]] = ProofContext.put_thms false (Auto_Bind.thisN, SOME [th]);
  1042     val after_qed' = (after_local', after_global');
  1043     val this_name = ProofContext.full_name goal_ctxt (Binding.name Auto_Bind.thisN);
  1044 
  1045     val result_ctxt =
  1046       state
  1047       |> map_contexts (fold Variable.declare_term goal_txt)
  1048       |> map_goal I (K (statement', messages, using, goal', before_qed, after_qed'))
  1049       |> fork_proof;
  1050 
  1051     val future_thm = result_ctxt |> Future.map (fn (_, x) =>
  1052       ProofContext.get_fact_single (get_context x) (Facts.named this_name));
  1053     val finished_goal = Goal.future_result goal_ctxt future_thm prop';
  1054     val state' =
  1055       state
  1056       |> map_goal I (K (statement, messages, using, finished_goal, NONE, after_qed))
  1057       |> done;
  1058   in (Future.map #1 result_ctxt, state') end;
  1059 
  1060 in
  1061 
  1062 fun local_future_proof x = future_proof local_done_proof context_of x;
  1063 fun global_future_proof x = future_proof global_done_proof I x;
  1064 
  1065 end;
  1066 
  1067 
  1068 (* terminal proofs *)
  1069 
  1070 local
  1071 
  1072 fun future_terminal_proof proof1 proof2 meths int state =
  1073   if int orelse is_relevant state orelse not (Goal.local_future_enabled ())
  1074   then proof1 meths state
  1075   else snd (proof2 (fn state' => Future.fork_pri ~1 (fn () => ((), proof1 meths state'))) state);
  1076 
  1077 in
  1078 
  1079 fun local_future_terminal_proof x =
  1080   future_terminal_proof local_terminal_proof local_future_proof x;
  1081 
  1082 fun global_future_terminal_proof x =
  1083   future_terminal_proof global_terminal_proof global_future_proof x;
  1084 
  1085 end;
  1086 
  1087 end;
  1088