src/Pure/Tools/find_theorems.ML
 author kleing Sat Sep 14 20:56:12 2013 +1000 (2013-09-14) changeset 53632 96808429b9ec parent 52982 8e78bd316a53 child 53633 69f1221fc892 permissions -rw-r--r--
more useful sorting of find_thms results
```     1 (*  Title:      Pure/Tools/find_theorems.ML
```
```     2     Author:     Rafal Kolanski and Gerwin Klein, NICTA
```
```     3     Author:     Lars Noschinski and Alexander Krauss, TU Muenchen
```
```     4
```
```     5 Retrieve theorems from proof context.
```
```     6 *)
```
```     7
```
```     8 signature FIND_THEOREMS =
```
```     9 sig
```
```    10   datatype 'term criterion =
```
```    11     Name of string | Intro | Elim | Dest | Solves | Simp of 'term | Pattern of 'term
```
```    12   type 'term query = {
```
```    13     goal: thm option,
```
```    14     limit: int option,
```
```    15     rem_dups: bool,
```
```    16     criteria: (bool * 'term criterion) list
```
```    17   }
```
```    18   val read_query: Position.T -> string -> (bool * string criterion) list
```
```    19   val find_theorems: Proof.context -> thm option -> int option -> bool ->
```
```    20     (bool * term criterion) list -> int option * (Facts.ref * thm) list
```
```    21   val find_theorems_cmd: Proof.context -> thm option -> int option -> bool ->
```
```    22     (bool * string criterion) list -> int option * (Facts.ref * thm) list
```
```    23   val pretty_thm: Proof.context -> Facts.ref * thm -> Pretty.T
```
```    24 end;
```
```    25
```
```    26 structure Find_Theorems: FIND_THEOREMS =
```
```    27 struct
```
```    28
```
```    29 (** search criteria **)
```
```    30
```
```    31 datatype 'term criterion =
```
```    32   Name of string | Intro | Elim | Dest | Solves | Simp of 'term | Pattern of 'term;
```
```    33
```
```    34 fun apply_dummies tm =
```
```    35   let
```
```    36     val (xs, _) = Term.strip_abs tm;
```
```    37     val tm' = Term.betapplys (tm, map (Term.dummy_pattern o #2) xs);
```
```    38   in #1 (Term.replace_dummy_patterns tm' 1) end;
```
```    39
```
```    40 fun parse_pattern ctxt nm =
```
```    41   let
```
```    42     val consts = Proof_Context.consts_of ctxt;
```
```    43     val nm' =
```
```    44       (case Syntax.parse_term ctxt nm of
```
```    45         Const (c, _) => c
```
```    46       | _ => Consts.intern consts nm);
```
```    47   in
```
```    48     (case try (Consts.the_abbreviation consts) nm' of
```
```    49       SOME (_, rhs) => apply_dummies (Proof_Context.expand_abbrevs ctxt rhs)
```
```    50     | NONE => Proof_Context.read_term_pattern ctxt nm)
```
```    51   end;
```
```    52
```
```    53 fun read_criterion _ (Name name) = Name name
```
```    54   | read_criterion _ Intro = Intro
```
```    55   | read_criterion _ Elim = Elim
```
```    56   | read_criterion _ Dest = Dest
```
```    57   | read_criterion _ Solves = Solves
```
```    58   | read_criterion ctxt (Simp str) = Simp (Proof_Context.read_term_pattern ctxt str)
```
```    59   | read_criterion ctxt (Pattern str) = Pattern (parse_pattern ctxt str);
```
```    60
```
```    61 fun pretty_criterion ctxt (b, c) =
```
```    62   let
```
```    63     fun prfx s = if b then s else "-" ^ s;
```
```    64   in
```
```    65     (case c of
```
```    66       Name name => Pretty.str (prfx "name: " ^ quote name)
```
```    67     | Intro => Pretty.str (prfx "intro")
```
```    68     | Elim => Pretty.str (prfx "elim")
```
```    69     | Dest => Pretty.str (prfx "dest")
```
```    70     | Solves => Pretty.str (prfx "solves")
```
```    71     | Simp pat => Pretty.block [Pretty.str (prfx "simp:"), Pretty.brk 1,
```
```    72         Pretty.quote (Syntax.pretty_term ctxt (Term.show_dummy_patterns pat))]
```
```    73     | Pattern pat => Pretty.enclose (prfx " \"") "\""
```
```    74         [Syntax.pretty_term ctxt (Term.show_dummy_patterns pat)])
```
```    75   end;
```
```    76
```
```    77
```
```    78
```
```    79 (** queries **)
```
```    80
```
```    81 type 'term query = {
```
```    82   goal: thm option,
```
```    83   limit: int option,
```
```    84   rem_dups: bool,
```
```    85   criteria: (bool * 'term criterion) list
```
```    86 };
```
```    87
```
```    88 fun map_criteria f {goal, limit, rem_dups, criteria} =
```
```    89   {goal = goal, limit = limit, rem_dups = rem_dups, criteria = f criteria};
```
```    90
```
```    91
```
```    92
```
```    93 (** theorems, either internal or external (without proof) **)
```
```    94
```
```    95 datatype theorem =
```
```    96   Internal of Facts.ref * thm |
```
```    97   External of Facts.ref * term; (* FIXME: Facts.ref not appropriate *)
```
```    98
```
```    99 fun fact_ref_markup (Facts.Named ((name, pos), SOME [Facts.Single i])) =
```
```   100       Position.markup pos o Markup.properties [("name", name), ("index", Markup.print_int i)]
```
```   101   | fact_ref_markup (Facts.Named ((name, pos), NONE)) =
```
```   102       Position.markup pos o Markup.properties [("name", name)]
```
```   103   | fact_ref_markup fact_ref = raise Fail "bad fact ref";
```
```   104
```
```   105 fun prop_of (Internal (_, thm)) = Thm.full_prop_of thm
```
```   106   | prop_of (External (_, prop)) = prop;
```
```   107
```
```   108 fun nprems_of (Internal (_, thm)) = Thm.nprems_of thm
```
```   109   | nprems_of (External (_, prop)) = Logic.count_prems prop;
```
```   110
```
```   111 fun size_of (Internal (_, thm)) = size_of_term (Thm.prop_of thm)
```
```   112   | size_of (External (_, prop)) = size_of_term prop;
```
```   113
```
```   114 fun major_prem_of (Internal (_, thm)) = Thm.major_prem_of thm
```
```   115   | major_prem_of (External (_, prop)) =
```
```   116       Logic.strip_assums_concl (hd (Logic.strip_imp_prems prop));
```
```   117
```
```   118 fun fact_ref_of (Internal (fact_ref, _)) = fact_ref
```
```   119   | fact_ref_of (External (fact_ref, _)) = fact_ref;
```
```   120
```
```   121
```
```   122
```
```   123 (** search criterion filters **)
```
```   124
```
```   125 (*generated filters are to be of the form
```
```   126   input: theorem
```
```   127   output: (p:int, s:int, t:int) option, where
```
```   128     NONE indicates no match
```
```   129     p is the primary sorting criterion
```
```   130       (eg. size of term)
```
```   131     s is the secondary sorting criterion
```
```   132       (eg. number of assumptions in the theorem)
```
```   133     t is the tertiary sorting criterion
```
```   134       (eg. size of the substitution for intro, elim and dest)
```
```   135   when applying a set of filters to a thm, fold results in:
```
```   136     (max p, max s, sum of all t)
```
```   137 *)
```
```   138
```
```   139
```
```   140 (* matching theorems *)
```
```   141
```
```   142 fun is_nontrivial thy = Term.is_Const o Term.head_of o Object_Logic.drop_judgment thy;
```
```   143
```
```   144 (*extract terms from term_src, refine them to the parts that concern us,
```
```   145   if po try match them against obj else vice versa.
```
```   146   trivial matches are ignored.
```
```   147   returns: smallest substitution size*)
```
```   148 fun is_matching_thm (extract_terms, refine_term) ctxt po obj term_src =
```
```   149   let
```
```   150     val thy = Proof_Context.theory_of ctxt;
```
```   151
```
```   152     fun matches pat =
```
```   153       is_nontrivial thy pat andalso
```
```   154       Pattern.matches thy (if po then (pat, obj) else (obj, pat));
```
```   155
```
```   156     fun subst_size pat =
```
```   157       let val (_, subst) =
```
```   158         Pattern.match thy (if po then (pat, obj) else (obj, pat)) (Vartab.empty, Vartab.empty)
```
```   159       in Vartab.fold (fn (_, (_, t)) => fn n => size_of_term t + n) subst 0 end;
```
```   160
```
```   161     fun best_match [] = NONE
```
```   162       | best_match xs = SOME (foldl1 Int.min xs);
```
```   163
```
```   164     val match_thm = matches o refine_term;
```
```   165   in
```
```   166     map (subst_size o refine_term) (filter match_thm (extract_terms term_src))
```
```   167     |> best_match
```
```   168   end;
```
```   169
```
```   170
```
```   171 (* filter_name *)
```
```   172
```
```   173 fun filter_name str_pat theorem =
```
```   174   if match_string str_pat (Facts.name_of_ref (fact_ref_of theorem))
```
```   175   then SOME (0, 0, 0) else NONE;
```
```   176
```
```   177
```
```   178 (* filter intro/elim/dest/solves rules *)
```
```   179
```
```   180 fun filter_dest ctxt goal theorem =
```
```   181   let
```
```   182     val extract_dest =
```
```   183      (fn theorem => if nprems_of theorem = 0 then [] else [prop_of theorem],
```
```   184       hd o Logic.strip_imp_prems);
```
```   185     val prems = Logic.prems_of_goal goal 1;
```
```   186
```
```   187     fun try_subst prem = is_matching_thm extract_dest ctxt true prem theorem;
```
```   188     val successful = prems |> map_filter try_subst;
```
```   189   in
```
```   190     (*if possible, keep best substitution (one with smallest size)*)
```
```   191     (*dest rules always have assumptions, so a dest with one
```
```   192       assumption is as good as an intro rule with none*)
```
```   193     if not (null successful)
```
```   194     then SOME (size_of theorem, nprems_of theorem - 1, foldl1 Int.min successful) else NONE
```
```   195   end;
```
```   196
```
```   197 fun filter_intro ctxt goal theorem =
```
```   198   let
```
```   199     val extract_intro = (single o prop_of, Logic.strip_imp_concl);
```
```   200     val concl = Logic.concl_of_goal goal 1;
```
```   201     val ss = is_matching_thm extract_intro ctxt true concl theorem;
```
```   202   in
```
```   203     if is_some ss then SOME (size_of theorem, nprems_of theorem, the ss) else NONE
```
```   204   end;
```
```   205
```
```   206 fun filter_elim ctxt goal theorem =
```
```   207   if nprems_of theorem > 0 then
```
```   208     let
```
```   209       val rule = prop_of theorem;
```
```   210       val prems = Logic.prems_of_goal goal 1;
```
```   211       val goal_concl = Logic.concl_of_goal goal 1;
```
```   212       val rule_mp = hd (Logic.strip_imp_prems rule);
```
```   213       val rule_concl = Logic.strip_imp_concl rule;
```
```   214       fun combine t1 t2 = Const ("*combine*", dummyT --> dummyT) \$ (t1 \$ t2);  (* FIXME ?? *)
```
```   215       val rule_tree = combine rule_mp rule_concl;
```
```   216       fun goal_tree prem = combine prem goal_concl;
```
```   217       fun try_subst prem = is_matching_thm (single, I) ctxt true (goal_tree prem) rule_tree;
```
```   218       val successful = prems |> map_filter try_subst;
```
```   219     in
```
```   220       (*elim rules always have assumptions, so an elim with one
```
```   221         assumption is as good as an intro rule with none*)
```
```   222       if is_nontrivial (Proof_Context.theory_of ctxt) (major_prem_of theorem)
```
```   223         andalso not (null successful)
```
```   224       then SOME (size_of theorem, nprems_of theorem - 1, foldl1 Int.min successful) else NONE
```
```   225     end
```
```   226   else NONE;
```
```   227
```
```   228 fun filter_solves ctxt goal =
```
```   229   let
```
```   230     val thy' =
```
```   231       Proof_Context.theory_of ctxt
```
```   232       |> Context_Position.set_visible_global (Context_Position.is_visible ctxt);
```
```   233     val ctxt' = Proof_Context.transfer thy' ctxt;
```
```   234     val goal' = Thm.transfer thy' goal;
```
```   235
```
```   236     fun limited_etac thm i =
```
```   237       Seq.take (Options.default_int @{option find_theorems_tac_limit}) o etac thm i;
```
```   238     fun try_thm thm =
```
```   239       if Thm.no_prems thm then rtac thm 1 goal'
```
```   240       else (limited_etac thm THEN_ALL_NEW (Goal.norm_hhf_tac THEN' Method.assm_tac ctxt')) 1 goal';
```
```   241   in
```
```   242     fn Internal (_, thm) =>
```
```   243         if is_some (Seq.pull (try_thm thm))
```
```   244         then SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, 0) else NONE
```
```   245      | External _ => NONE
```
```   246   end;
```
```   247
```
```   248
```
```   249 (* filter_simp *)
```
```   250
```
```   251 fun filter_simp ctxt t (Internal (_, thm)) =
```
```   252       let
```
```   253         val mksimps = Simplifier.mksimps ctxt;
```
```   254         val extract_simp =
```
```   255           (map Thm.full_prop_of o mksimps, #1 o Logic.dest_equals o Logic.strip_imp_concl);
```
```   256         val ss = is_matching_thm extract_simp ctxt false t thm;
```
```   257       in
```
```   258         if is_some ss
```
```   259         then SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, the ss)
```
```   260         else NONE
```
```   261       end
```
```   262   | filter_simp _ _ (External _) = NONE;
```
```   263
```
```   264
```
```   265 (* filter_pattern *)
```
```   266
```
```   267 fun get_names t = Term.add_const_names t (Term.add_free_names t []);
```
```   268
```
```   269 (*Including all constants and frees is only sound because matching
```
```   270   uses higher-order patterns. If full matching were used, then
```
```   271   constants that may be subject to beta-reduction after substitution
```
```   272   of frees should not be included for LHS set because they could be
```
```   273   thrown away by the substituted function.  E.g. for (?F 1 2) do not
```
```   274   include 1 or 2, if it were possible for ?F to be (%x y. 3).  The
```
```   275   largest possible set should always be included on the RHS.*)
```
```   276
```
```   277 fun filter_pattern ctxt pat =
```
```   278   let
```
```   279     val pat_consts = get_names pat;
```
```   280
```
```   281     fun check (theorem, NONE) = check (theorem, SOME (get_names (prop_of theorem)))
```
```   282       | check (theorem, c as SOME thm_consts) =
```
```   283          (if subset (op =) (pat_consts, thm_consts) andalso
```
```   284             Pattern.matches_subterm (Proof_Context.theory_of ctxt) (pat, prop_of theorem)
```
```   285           then SOME (size_of theorem, nprems_of theorem, 0) else NONE, c);
```
```   286   in check end;
```
```   287
```
```   288
```
```   289 (* interpret criteria as filters *)
```
```   290
```
```   291 local
```
```   292
```
```   293 fun err_no_goal c =
```
```   294   error ("Current goal required for " ^ c ^ " search criterion");
```
```   295
```
```   296 fun filter_crit _ _ (Name name) = apfst (filter_name name)
```
```   297   | filter_crit _ NONE Intro = err_no_goal "intro"
```
```   298   | filter_crit _ NONE Elim = err_no_goal "elim"
```
```   299   | filter_crit _ NONE Dest = err_no_goal "dest"
```
```   300   | filter_crit _ NONE Solves = err_no_goal "solves"
```
```   301   | filter_crit ctxt (SOME goal) Intro = apfst (filter_intro ctxt (Thm.prop_of goal))
```
```   302   | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt (Thm.prop_of goal))
```
```   303   | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt (Thm.prop_of goal))
```
```   304   | filter_crit ctxt (SOME goal) Solves = apfst (filter_solves ctxt goal)
```
```   305   | filter_crit ctxt _ (Simp pat) = apfst (filter_simp ctxt pat)
```
```   306   | filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat;
```
```   307
```
```   308 fun opt_not x = if is_some x then NONE else SOME (0, 0, 0);
```
```   309
```
```   310 fun opt_add (SOME (a, c, x)) (SOME (b, d, y)) = SOME (Int.max (a,b), Int.max (c, d), x + y : int)
```
```   311   | opt_add _ _ = NONE;
```
```   312
```
```   313 fun app_filters thm =
```
```   314   let
```
```   315     fun app (NONE, _, _) = NONE
```
```   316       | app (SOME v, _, []) = SOME (v, thm)
```
```   317       | app (r, consts, f :: fs) =
```
```   318           let val (r', consts') = f (thm, consts)
```
```   319           in app (opt_add r r', consts', fs) end;
```
```   320   in app end;
```
```   321
```
```   322 in
```
```   323
```
```   324 fun filter_criterion ctxt opt_goal (b, c) =
```
```   325   (if b then I else (apfst opt_not)) o filter_crit ctxt opt_goal c;
```
```   326
```
```   327 fun sorted_filter filters theorems =
```
```   328   let
```
```   329     fun eval_filters theorem = app_filters theorem (SOME (0, 0, 0), NONE, filters);
```
```   330
```
```   331     (*filters return: (thm size, number of assumptions, substitution size) option, so
```
```   332       sort according to size of thm first, then number of assumptions,
```
```   333       then by the substitution size, then by term order *)
```
```   334     fun result_ord (((p0, s0, t0), thm0), ((p1, s1, t1), thm1)) =
```
```   335       prod_ord int_ord (prod_ord int_ord (prod_ord int_ord Term_Ord.term_ord))
```
```   336          ((p1, (s1, (t1, prop_of thm1))), (p0, (s0, (t0, prop_of thm0))));
```
```   337   in
```
```   338     grouped 100 Par_List.map eval_filters theorems
```
```   339     |> map_filter I |> sort result_ord |> map #2
```
```   340   end;
```
```   341
```
```   342 fun lazy_filter filters =
```
```   343   let
```
```   344     fun lazy_match thms = Seq.make (fn () => first_match thms)
```
```   345     and first_match [] = NONE
```
```   346       | first_match (thm :: thms) =
```
```   347           (case app_filters thm (SOME (0, 0, 0), NONE, filters) of
```
```   348             NONE => first_match thms
```
```   349           | SOME (_, t) => SOME (t, lazy_match thms));
```
```   350   in lazy_match end;
```
```   351
```
```   352 end;
```
```   353
```
```   354
```
```   355 (* removing duplicates, preferring nicer names, roughly O(n log n) *)
```
```   356
```
```   357 local
```
```   358
```
```   359 val index_ord = option_ord (K EQUAL);
```
```   360 val hidden_ord = bool_ord o pairself Name_Space.is_hidden;
```
```   361 val qual_ord = int_ord o pairself (length o Long_Name.explode);
```
```   362 val txt_ord = int_ord o pairself size;
```
```   363
```
```   364 fun nicer_name (x, i) (y, j) =
```
```   365   (case hidden_ord (x, y) of EQUAL =>
```
```   366     (case index_ord (i, j) of EQUAL =>
```
```   367       (case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord)
```
```   368     | ord => ord)
```
```   369   | ord => ord) <> GREATER;
```
```   370
```
```   371 fun rem_cdups nicer xs =
```
```   372   let
```
```   373     fun rem_c rev_seen [] = rev rev_seen
```
```   374       | rem_c rev_seen [x] = rem_c (x :: rev_seen) []
```
```   375       | rem_c rev_seen ((x as (t, _)) :: (y as (t', _)) :: xs) =
```
```   376           if (prop_of t) aconv (prop_of t')
```
```   377           then rem_c rev_seen ((if nicer (fact_ref_of t) (fact_ref_of t') then x else y) :: xs)
```
```   378           else rem_c (x :: rev_seen) (y :: xs)
```
```   379   in rem_c [] xs end;
```
```   380
```
```   381 in
```
```   382
```
```   383 fun nicer_shortest ctxt =
```
```   384   let
```
```   385     val space = Facts.space_of (Proof_Context.facts_of ctxt);
```
```   386
```
```   387     val shorten =
```
```   388       Name_Space.extern
```
```   389         (ctxt
```
```   390           |> Config.put Name_Space.names_long false
```
```   391           |> Config.put Name_Space.names_short false
```
```   392           |> Config.put Name_Space.names_unique false) space;
```
```   393
```
```   394     fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =
```
```   395           nicer_name (shorten x, i) (shorten y, j)
```
```   396       | nicer (Facts.Fact _) (Facts.Named _) = true
```
```   397       | nicer (Facts.Named _) (Facts.Fact _) = false;
```
```   398   in nicer end;
```
```   399
```
```   400 fun rem_thm_dups nicer xs =
```
```   401   (xs ~~ (1 upto length xs))
```
```   402   |> sort (Term_Ord.fast_term_ord o pairself (prop_of o #1))
```
```   403   |> rem_cdups nicer
```
```   404   |> sort (int_ord o pairself #2)
```
```   405   |> map #1;
```
```   406
```
```   407 end;
```
```   408
```
```   409
```
```   410
```
```   411 (** main operations **)
```
```   412
```
```   413 (* filter_theorems *)
```
```   414
```
```   415 fun all_facts_of ctxt =
```
```   416   let
```
```   417     fun visible_facts facts =
```
```   418       Facts.dest_static [] facts
```
```   419       |> filter_out (Facts.is_concealed facts o #1);
```
```   420   in
```
```   421     maps Facts.selections
```
```   422      (visible_facts (Proof_Context.facts_of ctxt) @
```
```   423       visible_facts (Global_Theory.facts_of (Proof_Context.theory_of ctxt)))
```
```   424   end;
```
```   425
```
```   426 fun filter_theorems ctxt theorems query =
```
```   427   let
```
```   428     val {goal = opt_goal, limit = opt_limit, rem_dups, criteria} = query;
```
```   429     val filters = map (filter_criterion ctxt opt_goal) criteria;
```
```   430
```
```   431     fun find_all theorems =
```
```   432       let
```
```   433         val raw_matches = sorted_filter filters theorems;
```
```   434
```
```   435         val matches =
```
```   436           if rem_dups
```
```   437           then rem_thm_dups (nicer_shortest ctxt) raw_matches
```
```   438           else raw_matches;
```
```   439
```
```   440         val len = length matches;
```
```   441         val lim = the_default (Options.default_int @{option find_theorems_limit}) opt_limit;
```
```   442       in (SOME len, drop (Int.max (len - lim, 0)) matches) end;
```
```   443
```
```   444     val find =
```
```   445       if rem_dups orelse is_none opt_limit
```
```   446       then find_all
```
```   447       else pair NONE o Seq.list_of o Seq.take (the opt_limit) o lazy_filter filters;
```
```   448
```
```   449   in find theorems end;
```
```   450
```
```   451 fun filter_theorems_cmd ctxt theorems raw_query =
```
```   452   filter_theorems ctxt theorems (map_criteria (map (apsnd (read_criterion ctxt))) raw_query);
```
```   453
```
```   454
```
```   455 (* find_theorems *)
```
```   456
```
```   457 local
```
```   458
```
```   459 fun gen_find_theorems filter ctxt opt_goal opt_limit rem_dups raw_criteria =
```
```   460   let
```
```   461     val assms =
```
```   462       Proof_Context.get_fact ctxt (Facts.named "local.assms")
```
```   463         handle ERROR _ => [];
```
```   464     val add_prems = Seq.hd o TRY (Method.insert_tac assms 1);
```
```   465     val opt_goal' = Option.map add_prems opt_goal;
```
```   466   in
```
```   467     filter ctxt (map Internal (all_facts_of ctxt))
```
```   468       {goal = opt_goal', limit = opt_limit, rem_dups = rem_dups, criteria = raw_criteria}
```
```   469     |> apsnd (map (fn Internal f => f))
```
```   470   end;
```
```   471
```
```   472 in
```
```   473
```
```   474 val find_theorems = gen_find_theorems filter_theorems;
```
```   475 val find_theorems_cmd = gen_find_theorems filter_theorems_cmd;
```
```   476
```
```   477 end;
```
```   478
```
```   479
```
```   480 (* pretty_theorems *)
```
```   481
```
```   482 local
```
```   483
```
```   484 fun pretty_ref ctxt thmref =
```
```   485   let
```
```   486     val (name, sel) =
```
```   487       (case thmref of
```
```   488         Facts.Named ((name, _), sel) => (name, sel)
```
```   489       | Facts.Fact _ => raise Fail "Illegal literal fact");
```
```   490   in
```
```   491     [Pretty.mark (Proof_Context.markup_fact ctxt name) (Pretty.str name),
```
```   492       Pretty.str (Facts.string_of_selection sel), Pretty.str ":", Pretty.brk 1]
```
```   493   end;
```
```   494
```
```   495 fun pretty_theorem ctxt (Internal (thmref, thm)) =
```
```   496       Pretty.block (pretty_ref ctxt thmref @ [Display.pretty_thm ctxt thm])
```
```   497   | pretty_theorem ctxt (External (thmref, prop)) =
```
```   498       Pretty.block (pretty_ref ctxt thmref @ [Syntax.unparse_term ctxt prop]);
```
```   499
```
```   500 in
```
```   501
```
```   502 fun pretty_thm ctxt (thmref, thm) = pretty_theorem ctxt (Internal (thmref, thm));
```
```   503
```
```   504 fun pretty_theorems state opt_limit rem_dups raw_criteria =
```
```   505   let
```
```   506     val ctxt = Proof.context_of state;
```
```   507     val opt_goal = try Proof.simple_goal state |> Option.map #goal;
```
```   508     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
```
```   509
```
```   510     val (opt_found, theorems) =
```
```   511       filter_theorems ctxt (map Internal (all_facts_of ctxt))
```
```   512         {goal = opt_goal, limit = opt_limit, rem_dups = rem_dups, criteria = criteria};
```
```   513     val returned = length theorems;
```
```   514
```
```   515     val tally_msg =
```
```   516       (case opt_found of
```
```   517         NONE => "displaying " ^ string_of_int returned ^ " theorem(s)"
```
```   518       | SOME found =>
```
```   519           "found " ^ string_of_int found ^ " theorem(s)" ^
```
```   520             (if returned < found
```
```   521              then " (" ^ string_of_int returned ^ " displayed)"
```
```   522              else ""));
```
```   523   in
```
```   524     Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria) ::
```
```   525     Pretty.str "" ::
```
```   526     (if null theorems then [Pretty.str "nothing found"]
```
```   527      else
```
```   528       [Pretty.str (tally_msg ^ ":"), Pretty.str ""] @
```
```   529         grouped 10 Par_List.map (Pretty.item o single o pretty_theorem ctxt) theorems)
```
```   530   end |> Pretty.fbreaks |> curry Pretty.blk 0;
```
```   531
```
```   532 end;
```
```   533
```
```   534
```
```   535
```
```   536 (** Isar command syntax **)
```
```   537
```
```   538 fun proof_state st =
```
```   539   (case try Toplevel.proof_of st of
```
```   540     SOME state => state
```
```   541   | NONE => Proof.init (Toplevel.context_of st));
```
```   542
```
```   543 local
```
```   544
```
```   545 val criterion =
```
```   546   Parse.reserved "name" |-- Parse.!!! (Parse.\$\$\$ ":" |-- Parse.xname) >> Name ||
```
```   547   Parse.reserved "intro" >> K Intro ||
```
```   548   Parse.reserved "elim" >> K Elim ||
```
```   549   Parse.reserved "dest" >> K Dest ||
```
```   550   Parse.reserved "solves" >> K Solves ||
```
```   551   Parse.reserved "simp" |-- Parse.!!! (Parse.\$\$\$ ":" |-- Parse.term) >> Simp ||
```
```   552   Parse.term >> Pattern;
```
```   553
```
```   554 val options =
```
```   555   Scan.optional
```
```   556     (Parse.\$\$\$ "(" |--
```
```   557       Parse.!!! (Scan.option Parse.nat -- Scan.optional (Parse.reserved "with_dups" >> K false) true
```
```   558         --| Parse.\$\$\$ ")")) (NONE, true);
```
```   559
```
```   560 val query = Scan.repeat ((Scan.option Parse.minus >> is_none) -- criterion);
```
```   561
```
```   562 in
```
```   563
```
```   564 fun read_query pos str =
```
```   565   Outer_Syntax.scan pos str
```
```   566   |> filter Token.is_proper
```
```   567   |> Scan.error (Scan.finite Token.stopper (Parse.!!! (query --| Scan.ahead Parse.eof)))
```
```   568   |> #1;
```
```   569
```
```   570 val _ =
```
```   571   Outer_Syntax.improper_command @{command_spec "find_theorems"}
```
```   572     "find theorems meeting specified criteria"
```
```   573     (options -- query >> (fn ((opt_lim, rem_dups), spec) =>
```
```   574       Toplevel.keep (fn st =>
```
```   575         Pretty.writeln (pretty_theorems (proof_state st) opt_lim rem_dups spec))));
```
```   576
```
```   577 end;
```
```   578
```
```   579
```
```   580
```
```   581 (** PIDE query operation **)
```
```   582
```
```   583 val _ =
```
```   584   Query_Operation.register "find_theorems" (fn {state = st, args, output_result} =>
```
```   585     if can Toplevel.context_of st then
```
```   586       let
```
```   587         val [limit_arg, allow_dups_arg, context_arg, query_arg] = args;
```
```   588         val state =
```
```   589           if context_arg = "" then proof_state st
```
```   590           else Proof.init (Proof_Context.init_global (Thy_Info.get_theory context_arg));
```
```   591         val opt_limit = Int.fromString limit_arg;
```
```   592         val rem_dups = allow_dups_arg = "false";
```
```   593         val criteria = read_query Position.none query_arg;
```
```   594       in output_result (Pretty.string_of (pretty_theorems state opt_limit rem_dups criteria)) end
```
```   595     else error "Unknown context");
```
```   596
```
```   597 end;
```