src/Pure/Isar/proof.ML
author wenzelm
Sun Mar 01 23:36:12 2009 +0100 (2009-03-01)
changeset 30190 479806475f3c
parent 29581 b3b33e0298eb
child 30211 556d1810cdad
permissions -rw-r--r--
use long names for old-style fold combinators;
     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 add_binds_i: (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     ((binding * attribute list) * (term * term list) list) list -> state -> state
    52   val assume: (Attrib.binding * (string * string list) list) list -> state -> state
    53   val assume_i: ((binding * attribute list) * (term * term list) list) list ->
    54     state -> state
    55   val presume: (Attrib.binding * (string * string list) list) list -> state -> state
    56   val presume_i: ((binding * attribute list) * (term * term list) list) list ->
    57     state -> state
    58   val def: (Attrib.binding * ((binding * mixfix) * (string * string list))) list ->
    59     state -> state
    60   val def_i: ((binding * attribute list) *
    61     ((binding * mixfix) * (term * term list))) list -> state -> state
    62   val chain: state -> state
    63   val chain_facts: thm list -> state -> state
    64   val get_thmss: state -> (Facts.ref * Attrib.src list) list -> thm list
    65   val note_thmss: (Attrib.binding * (Facts.ref * Attrib.src list) list) list -> state -> state
    66   val note_thmss_i: ((binding * attribute list) *
    67     (thm list * attribute list) list) list -> state -> state
    68   val from_thmss: ((Facts.ref * Attrib.src list) list) list -> state -> state
    69   val from_thmss_i: ((thm list * attribute list) list) list -> state -> state
    70   val with_thmss: ((Facts.ref * Attrib.src list) list) list -> state -> state
    71   val with_thmss_i: ((thm list * attribute list) list) list -> state -> state
    72   val using: ((Facts.ref * Attrib.src list) list) list -> state -> state
    73   val using_i: ((thm list * attribute list) list) list -> state -> state
    74   val unfolding: ((Facts.ref * Attrib.src list) list) list -> state -> state
    75   val unfolding_i: ((thm list * attribute list) list) list -> state -> state
    76   val invoke_case: string * string option list * Attrib.src list -> state -> state
    77   val invoke_case_i: string * string option list * attribute list -> state -> state
    78   val begin_block: state -> state
    79   val next_block: state -> state
    80   val end_block: state -> state
    81   val proof: Method.text option -> state -> state Seq.seq
    82   val defer: int option -> state -> state Seq.seq
    83   val prefer: int -> state -> state Seq.seq
    84   val apply: Method.text -> state -> state Seq.seq
    85   val apply_end: Method.text -> state -> state Seq.seq
    86   val local_goal: (context -> ((string * string) * (string * thm list) list) -> unit) ->
    87     (theory -> 'a -> attribute) ->
    88     (context * 'b list -> context * (term list list * (context -> context))) ->
    89     string -> Method.text option -> (thm list list -> state -> state) ->
    90     ((binding * 'a list) * 'b) list -> state -> state
    91   val local_qed: Method.text option * bool -> state -> state
    92   val theorem: Method.text option -> (thm list list -> context -> context) ->
    93     (string * string list) list list -> context -> state
    94   val theorem_i: Method.text option -> (thm list list -> context -> context) ->
    95     (term * term list) list list -> context -> state
    96   val global_qed: Method.text option * bool -> state -> context
    97   val local_terminal_proof: Method.text * Method.text option -> state -> state
    98   val local_default_proof: state -> state
    99   val local_immediate_proof: state -> state
   100   val local_skip_proof: bool -> state -> state
   101   val local_done_proof: state -> state
   102   val global_terminal_proof: Method.text * Method.text option -> state -> context
   103   val global_default_proof: state -> context
   104   val global_immediate_proof: state -> context
   105   val global_skip_proof: bool -> state -> context
   106   val global_done_proof: state -> context
   107   val have: Method.text option -> (thm list list -> state -> state) ->
   108     (Attrib.binding * (string * string list) list) list -> bool -> state -> state
   109   val have_i: Method.text option -> (thm list list -> state -> state) ->
   110     ((binding * attribute list) * (term * term list) list) list -> bool -> state -> state
   111   val show: Method.text option -> (thm list list -> state -> state) ->
   112     (Attrib.binding * (string * string list) list) list -> bool -> state -> state
   113   val show_i: Method.text option -> (thm list list -> state -> state) ->
   114     ((binding * attribute list) * (term * term list) list) list -> bool -> state -> state
   115   val schematic_goal: state -> bool
   116   val is_relevant: state -> bool
   117   val local_future_proof: (state -> ('a * state) Future.future) ->
   118     state -> 'a Future.future * state
   119   val global_future_proof: (state -> ('a * Proof.context) Future.future) ->
   120     state -> 'a Future.future * context
   121   val local_future_terminal_proof: Method.text * Method.text option -> bool -> state -> state
   122   val global_future_terminal_proof: Method.text * Method.text option -> bool -> state -> context
   123 end;
   124 
   125 structure Proof: PROOF =
   126 struct
   127 
   128 type context = Context.proof;
   129 type method = Method.method;
   130 
   131 
   132 (** proof state **)
   133 
   134 (* datatype state *)
   135 
   136 datatype mode = Forward | Chain | Backward;
   137 
   138 datatype state =
   139   State of node Stack.T
   140 and node =
   141   Node of
   142    {context: context,
   143     facts: thm list option,
   144     mode: mode,
   145     goal: goal option}
   146 and goal =
   147   Goal of
   148    {statement: (string * Position.T) * term list list * term,
   149       (*goal kind and statement (starting with vars), initial proposition*)
   150     messages: (unit -> Pretty.T) list,    (*persistent messages (hints etc.)*)
   151     using: thm list,                      (*goal facts*)
   152     goal: thm,                            (*subgoals ==> statement*)
   153     before_qed: Method.text option,
   154     after_qed:
   155       (thm list list -> state -> state) *
   156       (thm list list -> context -> context)};
   157 
   158 fun make_goal (statement, messages, using, goal, before_qed, after_qed) =
   159   Goal {statement = statement, messages = messages, using = using, goal = goal,
   160     before_qed = before_qed, after_qed = after_qed};
   161 
   162 fun make_node (context, facts, mode, goal) =
   163   Node {context = context, facts = facts, mode = mode, goal = goal};
   164 
   165 fun map_node f (Node {context, facts, mode, goal}) =
   166   make_node (f (context, facts, mode, goal));
   167 
   168 val init_context =
   169   ProofContext.set_stmt true #> ProofContext.reset_naming;
   170 
   171 fun init ctxt =
   172   State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
   173 
   174 fun current (State st) = Stack.top st |> (fn Node node => node);
   175 fun map_current f (State st) = State (Stack.map_top (map_node f) st);
   176 fun map_all f (State st) = State (Stack.map_all (map_node f) st);
   177 
   178 
   179 
   180 (** basic proof state operations **)
   181 
   182 (* block structure *)
   183 
   184 fun open_block (State st) = State (Stack.push st);
   185 
   186 fun close_block (State st) = State (Stack.pop st)
   187   handle Empty => error "Unbalanced block parentheses";
   188 
   189 fun level (State st) = Stack.level st;
   190 
   191 fun assert_bottom b state =
   192   let val b' = (level state <= 2) in
   193     if b andalso not b' then error "Not at bottom of proof!"
   194     else if not b andalso b' then error "Already at bottom of proof!"
   195     else state
   196   end;
   197 
   198 
   199 (* context *)
   200 
   201 val context_of = #context o current;
   202 val theory_of = ProofContext.theory_of o context_of;
   203 
   204 fun map_context f =
   205   map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
   206 
   207 fun map_context_result f state =
   208   f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
   209 
   210 fun map_contexts f = map_all (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
   211 
   212 val add_binds_i = map_context o ProofContext.add_binds_i;
   213 val put_thms = map_context oo ProofContext.put_thms;
   214 
   215 
   216 (* facts *)
   217 
   218 val get_facts = #facts o current;
   219 
   220 fun the_facts state =
   221   (case get_facts state of SOME facts => facts
   222   | NONE => error "No current facts available");
   223 
   224 fun the_fact state =
   225   (case the_facts state of [thm] => thm
   226   | _ => error "Single theorem expected");
   227 
   228 fun put_facts facts =
   229   map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
   230   put_thms true (AutoBind.thisN, facts);
   231 
   232 fun these_factss more_facts (named_factss, state) =
   233   (named_factss, state |> put_facts (SOME (maps snd named_factss @ more_facts)));
   234 
   235 fun export_facts inner outer =
   236   (case get_facts inner of
   237     NONE => put_facts NONE outer
   238   | SOME thms =>
   239       thms
   240       |> ProofContext.export (context_of inner) (context_of outer)
   241       |> (fn ths => put_facts (SOME ths) outer));
   242 
   243 
   244 (* mode *)
   245 
   246 val get_mode = #mode o current;
   247 fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
   248 
   249 val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
   250 
   251 fun assert_mode pred state =
   252   let val mode = get_mode state in
   253     if pred mode then state
   254     else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
   255   end;
   256 
   257 val assert_forward = assert_mode (fn mode => mode = Forward);
   258 val assert_chain = assert_mode (fn mode => mode = Chain);
   259 val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
   260 val assert_backward = assert_mode (fn mode => mode = Backward);
   261 val assert_no_chain = assert_mode (fn mode => mode <> Chain);
   262 
   263 val enter_forward = put_mode Forward;
   264 val enter_chain = put_mode Chain;
   265 val enter_backward = put_mode Backward;
   266 
   267 
   268 (* current goal *)
   269 
   270 fun current_goal state =
   271   (case current state of
   272     {context, goal = SOME (Goal goal), ...} => (context, goal)
   273   | _ => error "No current goal!");
   274 
   275 fun assert_current_goal g state =
   276   let val g' = can current_goal state in
   277     if g andalso not g' then error "No goal in this block!"
   278     else if not g andalso g' then error "Goal present in this block!"
   279     else state
   280   end;
   281 
   282 fun put_goal goal = map_current (fn (ctxt, using, mode, _) => (ctxt, using, mode, goal));
   283 
   284 val before_qed = #before_qed o #2 o current_goal;
   285 
   286 
   287 (* nested goal *)
   288 
   289 fun map_goal f g (State (Node {context, facts, mode, goal = SOME goal}, nodes)) =
   290       let
   291         val Goal {statement, messages, using, goal, before_qed, after_qed} = goal;
   292         val goal' = make_goal (g (statement, messages, using, goal, before_qed, after_qed));
   293       in State (make_node (f context, facts, mode, SOME goal'), nodes) end
   294   | map_goal f g (State (nd, node :: nodes)) =
   295       let val State (node', nodes') = map_goal f g (State (node, nodes))
   296       in map_context f (State (nd, node' :: nodes')) end
   297   | map_goal _ _ state = state;
   298 
   299 fun set_goal goal = map_goal I (fn (statement, _, using, _, before_qed, after_qed) =>
   300   (statement, [], using, goal, before_qed, after_qed));
   301 
   302 fun goal_message msg = map_goal I (fn (statement, messages, using, goal, before_qed, after_qed) =>
   303   (statement, msg :: messages, using, goal, before_qed, after_qed));
   304 
   305 fun using_facts using = map_goal I (fn (statement, _, _, goal, before_qed, after_qed) =>
   306   (statement, [], using, goal, before_qed, after_qed));
   307 
   308 local
   309   fun find i state =
   310     (case try current_goal state of
   311       SOME (ctxt, goal) => (ctxt, (i, goal))
   312     | NONE => find (i + 1) (close_block state handle ERROR _ => error "No goal present"));
   313 in val find_goal = find 0 end;
   314 
   315 fun get_goal state =
   316   let val (ctxt, (_, {using, goal, ...})) = find_goal state
   317   in (ctxt, (using, goal)) end;
   318 
   319 
   320 
   321 (** pretty_state **)
   322 
   323 val show_main_goal = ref false;
   324 val verbose = ProofContext.verbose;
   325 
   326 val pretty_goals_local = Display.pretty_goals_aux o Syntax.pp;
   327 
   328 fun pretty_facts _ _ NONE = []
   329   | pretty_facts s ctxt (SOME ths) =
   330       [Pretty.big_list (s ^ "this:") (map (ProofContext.pretty_thm ctxt) ths), Pretty.str ""];
   331 
   332 fun pretty_state nr state =
   333   let
   334     val {context, facts, mode, goal = _} = current state;
   335 
   336     fun levels_up 0 = ""
   337       | levels_up 1 = "1 level up"
   338       | levels_up i = string_of_int i ^ " levels up";
   339 
   340     fun subgoals 0 = ""
   341       | subgoals 1 = "1 subgoal"
   342       | subgoals n = string_of_int n ^ " subgoals";
   343 
   344     fun description strs =
   345       (case filter_out (fn s => s = "") strs of [] => ""
   346       | strs' => enclose " (" ")" (commas strs'));
   347 
   348     fun prt_goal (SOME (ctxt, (i,
   349       {statement = ((_, pos), _, _), messages, using, goal, before_qed = _, after_qed = _}))) =
   350           pretty_facts "using " ctxt
   351             (if mode <> Backward orelse null using then NONE else SOME using) @
   352           [Pretty.str ("goal" ^
   353             description [levels_up (i div 2), subgoals (Thm.nprems_of goal)] ^ ":")] @
   354           pretty_goals_local ctxt Markup.subgoal
   355             (true, ! show_main_goal) (! Display.goals_limit) goal @
   356           (map (fn msg => Position.setmp_thread_data pos msg ()) (rev messages))
   357       | prt_goal NONE = [];
   358 
   359     val prt_ctxt =
   360       if ! verbose orelse mode = Forward then ProofContext.pretty_context context
   361       else if mode = Backward then ProofContext.pretty_ctxt context
   362       else [];
   363   in
   364     [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^
   365       (if ! verbose then ", depth " ^ string_of_int (level state div 2 - 1) else "")),
   366       Pretty.str ""] @
   367     (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
   368     (if ! verbose orelse mode = Forward then
   369        pretty_facts "" context facts @ prt_goal (try find_goal state)
   370      else if mode = Chain then pretty_facts "picking " context facts
   371      else prt_goal (try find_goal state))
   372   end;
   373 
   374 fun pretty_goals main state =
   375   let val (ctxt, (_, goal)) = get_goal state
   376   in pretty_goals_local ctxt Markup.none (false, main) (! Display.goals_limit) goal end;
   377 
   378 
   379 
   380 (** proof steps **)
   381 
   382 (* refine via method *)
   383 
   384 local
   385 
   386 fun goalN i = "goal" ^ string_of_int i;
   387 fun goals st = map goalN (1 upto Thm.nprems_of st);
   388 
   389 fun no_goal_cases st = map (rpair NONE) (goals st);
   390 
   391 fun goal_cases st =
   392   RuleCases.make_common true (Thm.theory_of_thm st, Thm.prop_of st) (map (rpair []) (goals st));
   393 
   394 fun apply_method current_context pos meth state =
   395   let
   396     val (goal_ctxt, (_, {statement, messages = _, using, goal, before_qed, after_qed})) =
   397       find_goal state;
   398     val ctxt = if current_context then context_of state else goal_ctxt;
   399   in
   400     Method.apply pos meth ctxt using goal |> Seq.map (fn (meth_cases, goal') =>
   401       state
   402       |> map_goal
   403           (ProofContext.add_cases false (no_goal_cases goal @ goal_cases goal') #>
   404            ProofContext.add_cases true meth_cases)
   405           (K (statement, [], using, goal', before_qed, after_qed)))
   406   end;
   407 
   408 fun select_goals n meth state =
   409   state
   410   |> (#2 o #2 o get_goal)
   411   |> ALLGOALS Goal.conjunction_tac
   412   |> Seq.maps (fn goal =>
   413     state
   414     |> Seq.lift set_goal (Goal.extract 1 n goal |> Seq.maps (Goal.conjunction_tac 1))
   415     |> Seq.maps meth
   416     |> Seq.maps (fn state' => state'
   417       |> Seq.lift set_goal (Goal.retrofit 1 n (#2 (#2 (get_goal state'))) goal))
   418     |> Seq.maps (apply_method true Position.none (K Method.succeed)));
   419 
   420 fun apply_text cc text state =
   421   let
   422     val thy = theory_of state;
   423     val pos_of = #2 o Args.dest_src;
   424 
   425     fun eval (Method.Basic (m, pos)) = apply_method cc pos m
   426       | eval (Method.Source src) = apply_method cc (pos_of src) (Method.method thy src)
   427       | eval (Method.Source_i src) = apply_method cc (pos_of src) (Method.method_i thy src)
   428       | eval (Method.Then txts) = Seq.EVERY (map eval txts)
   429       | eval (Method.Orelse txts) = Seq.FIRST (map eval txts)
   430       | eval (Method.Try txt) = Seq.TRY (eval txt)
   431       | eval (Method.Repeat1 txt) = Seq.REPEAT1 (eval txt)
   432       | eval (Method.SelectGoals (n, txt)) = select_goals n (eval txt);
   433   in eval text state end;
   434 
   435 in
   436 
   437 val refine = apply_text true;
   438 val refine_end = apply_text false;
   439 
   440 fun refine_insert [] = I
   441   | refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths), Position.none));
   442 
   443 end;
   444 
   445 
   446 (* refine via sub-proof *)
   447 
   448 fun goal_tac rule =
   449   Goal.norm_hhf_tac THEN' Tactic.rtac rule THEN_ALL_NEW
   450     (Goal.norm_hhf_tac THEN' (SUBGOAL (fn (goal, i) =>
   451       if can Logic.unprotect (Logic.strip_assums_concl goal) then
   452         Tactic.etac Drule.protectI i
   453       else all_tac)));
   454 
   455 fun refine_goals print_rule inner raw_rules state =
   456   let
   457     val (outer, (_, goal)) = get_goal state;
   458     fun refine rule st = (print_rule outer rule; FINDGOAL (goal_tac rule) st);
   459   in
   460     raw_rules
   461     |> ProofContext.goal_export inner outer
   462     |> (fn rules => Seq.lift set_goal (EVERY (map refine rules) goal) state)
   463   end;
   464 
   465 
   466 (* conclude_goal *)
   467 
   468 fun conclude_goal ctxt goal propss =
   469   let
   470     val thy = ProofContext.theory_of ctxt;
   471     val string_of_term = Syntax.string_of_term ctxt;
   472     val string_of_thm = ProofContext.string_of_thm ctxt;
   473 
   474     val ngoals = Thm.nprems_of goal;
   475     val _ = ngoals = 0 orelse error (Pretty.string_of (Pretty.chunks
   476       (pretty_goals_local ctxt Markup.none (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 add_fixes args =
   534   assert_forward
   535   #> map_context (snd o add_fixes args)
   536   #> put_facts NONE;
   537 
   538 in
   539 
   540 val fix = gen_fix ProofContext.add_fixes;
   541 val fix_i = gen_fix ProofContext.add_fixes_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 note_ctxt more_facts opt_chain opt_result prep_atts args state =
   623   state
   624   |> assert_forward
   625   |> map_context_result (note_ctxt (Attrib.map_facts (prep_atts (theory_of state)) args))
   626   |> these_factss (more_facts state)
   627   ||> opt_chain
   628   |> opt_result;
   629 
   630 in
   631 
   632 val note_thmss = gen_thmss (ProofContext.note_thmss "") (K []) I #2 Attrib.attribute;
   633 val note_thmss_i = gen_thmss (ProofContext.note_thmss_i "") (K []) I #2 (K I);
   634 
   635 val from_thmss =
   636   gen_thmss (ProofContext.note_thmss "") (K []) chain #2 Attrib.attribute o no_binding;
   637 val from_thmss_i = gen_thmss (ProofContext.note_thmss_i "") (K []) chain #2 (K I) o no_binding;
   638 
   639 val with_thmss =
   640   gen_thmss (ProofContext.note_thmss "") the_facts chain #2 Attrib.attribute o no_binding;
   641 val with_thmss_i = gen_thmss (ProofContext.note_thmss_i "") the_facts chain #2 (K I) o no_binding;
   642 
   643 val local_results =
   644   gen_thmss (ProofContext.note_thmss_i "") (K []) I I (K I) o map (apsnd Thm.simple_fact);
   645 
   646 fun get_thmss state srcs = the_facts (note_thmss [((Binding.empty, []), srcs)] state);
   647 
   648 end;
   649 
   650 
   651 (* using/unfolding *)
   652 
   653 local
   654 
   655 fun gen_using f g note prep_atts args state =
   656   state
   657   |> assert_backward
   658   |> map_context_result
   659     (note "" (Attrib.map_facts (prep_atts (theory_of state)) (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)) ProofContext.note_thmss Attrib.attribute;
   674 val using_i = gen_using append_using (K (K I)) ProofContext.note_thmss_i (K I);
   675 val unfolding = gen_using unfold_using unfold_goals ProofContext.note_thmss Attrib.attribute;
   676 val unfolding_i = gen_using unfold_using unfold_goals ProofContext.note_thmss_i (K I);
   677 
   678 end;
   679 
   680 
   681 (* case *)
   682 
   683 local
   684 
   685 fun gen_invoke_case prep_att (name, xs, raw_atts) state =
   686   let
   687     val atts = map (prep_att (theory_of state)) raw_atts;
   688     val (asms, state') = state |> map_context_result (fn ctxt =>
   689       ctxt |> ProofContext.apply_case (ProofContext.get_case ctxt name xs));
   690     val assumptions = asms |> map (fn (a, ts) => ((Binding.name a, atts), map (rpair []) ts));
   691   in
   692     state'
   693     |> map_context (ProofContext.qualified_names #> ProofContext.no_base_names)
   694     |> assume_i assumptions
   695     |> add_binds_i AutoBind.no_facts
   696     |> map_context (ProofContext.restore_naming (context_of state))
   697     |> `the_facts |-> (fn thms => note_thmss_i [((Binding.name name, []), [(thms, [])])])
   698   end;
   699 
   700 in
   701 
   702 val invoke_case = gen_invoke_case Attrib.attribute;
   703 val invoke_case_i = gen_invoke_case (K I);
   704 
   705 end;
   706 
   707 
   708 
   709 (** proof structure **)
   710 
   711 (* blocks *)
   712 
   713 val begin_block =
   714   assert_forward
   715   #> open_block
   716   #> put_goal NONE
   717   #> open_block;
   718 
   719 val next_block =
   720   assert_forward
   721   #> close_block
   722   #> open_block
   723   #> put_goal NONE
   724   #> put_facts NONE;
   725 
   726 fun end_block state =
   727   state
   728   |> assert_forward
   729   |> close_block
   730   |> assert_current_goal false
   731   |> close_block
   732   |> export_facts state;
   733 
   734 
   735 (* sub-proofs *)
   736 
   737 fun proof opt_text =
   738   assert_backward
   739   #> refine (the_default Method.default_text opt_text)
   740   #> Seq.map (using_facts [] #> enter_forward);
   741 
   742 fun end_proof bot txt state =
   743   state
   744   |> assert_forward
   745   |> assert_bottom bot
   746   |> close_block
   747   |> assert_current_goal true
   748   |> using_facts []
   749   |> `before_qed |-> (refine o the_default Method.succeed_text)
   750   |> Seq.maps (refine (Method.finish_text txt (Position.thread_data ())));
   751 
   752 fun check_result msg sq =
   753   (case Seq.pull sq of
   754     NONE => error msg
   755   | SOME (s, _) => s);
   756 
   757 fun check_finish sq = check_result "Failed to finish proof" sq;
   758 
   759 
   760 (* unstructured refinement *)
   761 
   762 fun defer i = assert_no_chain #> refine (Method.Basic (K (Method.defer i), Position.none));
   763 fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i), Position.none));
   764 
   765 fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);
   766 fun apply_end text = assert_forward #> refine_end text;
   767 
   768 
   769 
   770 (** goals **)
   771 
   772 (* generic goals *)
   773 
   774 local
   775 
   776 fun implicit_vars dest add props =
   777   let
   778     val (explicit_vars, props') = take_prefix (can dest) props |>> map dest;
   779     val vars = rev (subtract (op =) explicit_vars (fold add props []));
   780     val _ =
   781       if null vars then ()
   782       else warning ("Goal statement contains unbound schematic variable(s): " ^
   783         commas_quote (map (Term.string_of_vname o fst) vars));
   784   in (rev vars, props') end;
   785 
   786 fun refine_terms n =
   787   refine (Method.Basic (K (Method.RAW_METHOD
   788     (K (HEADGOAL (PRECISE_CONJUNCTS n
   789       (HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI)))))))), Position.none))
   790   #> Seq.hd;
   791 
   792 in
   793 
   794 fun generic_goal prepp kind before_qed after_qed raw_propp state =
   795   let
   796     val thy = theory_of state;
   797     val cert = Thm.cterm_of thy;
   798     val chaining = can assert_chain state;
   799     val pos = Position.thread_data ();
   800 
   801     val ((propss, after_ctxt), goal_state) =
   802       state
   803       |> assert_forward_or_chain
   804       |> enter_forward
   805       |> open_block
   806       |> map_context_result (fn ctxt => swap (prepp (ctxt, raw_propp)));
   807     val props = flat propss;
   808 
   809     val (_, props') =
   810       implicit_vars (dest_TVar o Logic.dest_type o Logic.dest_term) Term.add_tvars props;
   811     val (vars, _) = implicit_vars (dest_Var o Logic.dest_term) Term.add_vars props';
   812 
   813     val propss' = map (Logic.mk_term o Var) vars :: propss;
   814     val goal_propss = filter_out null propss';
   815     val goal =
   816       cert (Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss))
   817       |> Thm.weaken_sorts (Variable.sorts_of (context_of goal_state));
   818     val statement = ((kind, pos), propss', Thm.term_of goal);
   819     val after_qed' = after_qed |>> (fn after_local =>
   820       fn results => map_context after_ctxt #> after_local results);
   821   in
   822     goal_state
   823     |> map_context (init_context #> Variable.set_body true)
   824     |> put_goal (SOME (make_goal (statement, [], [], Goal.init goal, before_qed, after_qed')))
   825     |> map_context (ProofContext.auto_bind_goal props)
   826     |> chaining ? (`the_facts #-> using_facts)
   827     |> put_facts NONE
   828     |> open_block
   829     |> put_goal NONE
   830     |> enter_backward
   831     |> not (null vars) ? refine_terms (length goal_propss)
   832     |> null props ? (refine (Method.Basic (Method.assumption, Position.none)) #> Seq.hd)
   833   end;
   834 
   835 fun generic_qed after_ctxt state =
   836   let
   837     val (goal_ctxt, {statement, goal, after_qed, ...}) = current_goal state;
   838     val outer_state = state |> close_block;
   839     val outer_ctxt = context_of outer_state;
   840 
   841     val ((_, pos), stmt, _) = statement;
   842     val props =
   843       flat (tl stmt)
   844       |> Variable.exportT_terms goal_ctxt outer_ctxt;
   845     val results =
   846       tl (conclude_goal goal_ctxt goal stmt)
   847       |> burrow (ProofContext.export goal_ctxt outer_ctxt);
   848 
   849     val (after_local, after_global) = after_qed;
   850     fun after_local' x y = Position.setmp_thread_data pos (fn () => after_local x y) ();
   851     fun after_global' x y = Position.setmp_thread_data pos (fn () => after_global x y) ();
   852   in
   853     outer_state
   854     |> map_context (after_ctxt props)
   855     |> pair ((after_local', after_global'), results)
   856   end;
   857 
   858 end;
   859 
   860 
   861 (* local goals *)
   862 
   863 fun local_goal print_results prep_att prepp kind before_qed after_qed stmt state =
   864   let
   865     val thy = theory_of state;
   866     val ((names, attss), propp) =
   867       Attrib.map_specs (prep_att thy) stmt |> split_list |>> split_list;
   868 
   869     fun after_qed' results =
   870       local_results ((names ~~ attss) ~~ results)
   871       #-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
   872       #> after_qed results;
   873   in
   874     state
   875     |> generic_goal prepp kind before_qed (after_qed', K I) propp
   876     |> tap (Variable.warn_extra_tfrees (context_of state) o context_of)
   877   end;
   878 
   879 fun local_qeds txt =
   880   end_proof false txt
   881   #> Seq.map (generic_qed ProofContext.auto_bind_facts #->
   882     (fn ((after_qed, _), results) => after_qed results));
   883 
   884 fun local_qed txt = local_qeds txt #> check_finish;
   885 
   886 
   887 (* global goals *)
   888 
   889 fun global_goal prepp before_qed after_qed propp ctxt =
   890   init ctxt
   891   |> generic_goal (prepp #> ProofContext.auto_fixes) "" before_qed (K I, after_qed) propp;
   892 
   893 val theorem = global_goal ProofContext.bind_propp_schematic;
   894 val theorem_i = global_goal ProofContext.bind_propp_schematic_i;
   895 
   896 fun global_qeds txt =
   897   end_proof true txt
   898   #> Seq.map (generic_qed (K I) #> (fn (((_, after_qed), results), state) =>
   899     after_qed results (context_of state)));
   900 
   901 fun global_qed txt = global_qeds txt #> check_finish;
   902 
   903 
   904 (* concluding steps *)
   905 
   906 fun terminal_proof qed initial terminal =
   907   proof (SOME initial) #> Seq.maps (qed terminal) #> check_finish;
   908 
   909 fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);
   910 val local_default_proof = local_terminal_proof (Method.default_text, NONE);
   911 val local_immediate_proof = local_terminal_proof (Method.this_text, NONE);
   912 fun local_skip_proof int = local_terminal_proof (Method.sorry_text int, NONE);
   913 val local_done_proof = terminal_proof local_qeds Method.done_text (NONE, false);
   914 
   915 fun global_terminal_proof (text, opt_text) = terminal_proof global_qeds text (opt_text, true);
   916 val global_default_proof = global_terminal_proof (Method.default_text, NONE);
   917 val global_immediate_proof = global_terminal_proof (Method.this_text, NONE);
   918 fun global_skip_proof int = global_terminal_proof (Method.sorry_text int, NONE);
   919 val global_done_proof = terminal_proof global_qeds Method.done_text (NONE, false);
   920 
   921 
   922 (* common goal statements *)
   923 
   924 local
   925 
   926 fun gen_have prep_att prepp before_qed after_qed stmt int =
   927   local_goal (ProofDisplay.print_results int) prep_att prepp "have" before_qed after_qed stmt;
   928 
   929 fun gen_show prep_att prepp before_qed after_qed stmt int state =
   930   let
   931     val testing = ref false;
   932     val rule = ref (NONE: thm option);
   933     fun fail_msg ctxt =
   934       "Local statement will fail to refine any pending goal" ::
   935       (case ! rule of NONE => [] | SOME th => [ProofDisplay.string_of_rule ctxt "Failed" th])
   936       |> cat_lines;
   937 
   938     fun print_results ctxt res =
   939       if ! testing then () else ProofDisplay.print_results int ctxt res;
   940     fun print_rule ctxt th =
   941       if ! testing then rule := SOME th
   942       else if int then priority (ProofDisplay.string_of_rule ctxt "Successful" th)
   943       else ();
   944     val test_proof =
   945       try (local_skip_proof true)
   946       |> setmp_noncritical testing true
   947       |> Exn.capture;
   948 
   949     fun after_qed' results =
   950       refine_goals print_rule (context_of state) (flat results)
   951       #> check_result "Failed to refine any pending goal"
   952       #> after_qed results;
   953   in
   954     state
   955     |> local_goal print_results prep_att prepp "show" before_qed after_qed' stmt
   956     |> int ? (fn goal_state =>
   957       (case test_proof goal_state of
   958         Exn.Result (SOME _) => goal_state
   959       | Exn.Result NONE => error (fail_msg (context_of goal_state))
   960       | Exn.Exn Exn.Interrupt => raise Exn.Interrupt
   961       | Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))
   962   end;
   963 
   964 in
   965 
   966 val have = gen_have Attrib.attribute ProofContext.bind_propp;
   967 val have_i = gen_have (K I) ProofContext.bind_propp_i;
   968 val show = gen_show Attrib.attribute ProofContext.bind_propp;
   969 val show_i = gen_show (K I) ProofContext.bind_propp_i;
   970 
   971 end;
   972 
   973 
   974 
   975 (** future proofs **)
   976 
   977 (* relevant proof states *)
   978 
   979 fun is_schematic t =
   980   Term.exists_subterm Term.is_Var t orelse
   981   Term.exists_type (Term.exists_subtype Term.is_TVar) t;
   982 
   983 fun schematic_goal state =
   984   let val (_, (_, {statement = (_, _, prop), ...})) = find_goal state
   985   in is_schematic prop end;
   986 
   987 fun is_relevant state =
   988   (case try find_goal state of
   989     NONE => true
   990   | SOME (_, (_, {statement = (_, _, prop), goal, ...})) =>
   991       is_schematic prop orelse not (Logic.protect prop aconv Thm.concl_of goal));
   992 
   993 
   994 (* full proofs *)
   995 
   996 local
   997 
   998 fun future_proof done get_context fork_proof state =
   999   let
  1000     val _ = assert_backward state;
  1001     val (goal_ctxt, (_, goal)) = find_goal state;
  1002     val {statement as (kind, propss, prop), messages, using, goal, before_qed, after_qed} = goal;
  1003 
  1004     val _ = is_relevant state andalso error "Cannot fork relevant proof";
  1005 
  1006     val prop' = Logic.protect prop;
  1007     val statement' = (kind, [[], [prop']], prop');
  1008     val goal' = Thm.adjust_maxidx_thm (Thm.maxidx_of goal)
  1009       (Drule.comp_no_flatten (goal, Thm.nprems_of goal) 1 Drule.protectI);
  1010 
  1011     fun after_local' [[th]] = put_thms false (AutoBind.thisN, SOME [th]);
  1012     fun after_global' [[th]] = ProofContext.put_thms false (AutoBind.thisN, SOME [th]);
  1013     val after_qed' = (after_local', after_global');
  1014     val this_name = ProofContext.full_bname goal_ctxt AutoBind.thisN;
  1015 
  1016     val result_ctxt =
  1017       state
  1018       |> map_contexts (Variable.declare_term prop)
  1019       |> map_goal I (K (statement', messages, using, goal', before_qed, after_qed'))
  1020       |> fork_proof;
  1021 
  1022     val future_thm = result_ctxt |> Future.map (fn (_, x) =>
  1023       ProofContext.get_fact_single (get_context x) (Facts.named this_name));
  1024     val finished_goal = exception_trace (fn () => Goal.future_result goal_ctxt future_thm prop');
  1025     val state' =
  1026       state
  1027       |> map_goal I (K (statement, messages, using, finished_goal, NONE, after_qed))
  1028       |> done;
  1029   in (Future.map #1 result_ctxt, state') end;
  1030 
  1031 in
  1032 
  1033 fun local_future_proof x = future_proof local_done_proof context_of x;
  1034 fun global_future_proof x = future_proof global_done_proof I x;
  1035 
  1036 end;
  1037 
  1038 
  1039 (* terminal proofs *)
  1040 
  1041 local
  1042 
  1043 fun future_terminal_proof proof1 proof2 meths int state =
  1044   if int orelse is_relevant state orelse not (Goal.future_enabled ())
  1045   then proof1 meths state
  1046   else snd (state |> proof2 (fn state' => Future.fork_pri ~1 (fn () => ((), proof1 meths state'))));
  1047 
  1048 in
  1049 
  1050 fun local_future_terminal_proof x =
  1051   future_terminal_proof local_terminal_proof local_future_proof x;
  1052 
  1053 fun global_future_terminal_proof x =
  1054   future_terminal_proof global_terminal_proof global_future_proof x;
  1055 
  1056 end;
  1057 
  1058 end;
  1059