src/Pure/Tools/find_theorems.ML
 author krauss Fri Feb 25 16:57:44 2011 +0100 (2011-02-25) changeset 41845 6611b9cef38b parent 41844 b933142e02d0 child 42012 2c3fe3cbebae permissions -rw-r--r--
reactivate time measurement (partly reverting c27b0b37041a);
export pretty_theorem, to display both internal or external facts
```     1 (*  Title:      Pure/Tools/find_theorems.ML
```
```     2     Author:     Rafal Kolanski and Gerwin Klein, NICTA
```
```     3
```
```     4 Retrieve theorems from proof context.
```
```     5 *)
```
```     6
```
```     7 signature FIND_THEOREMS =
```
```     8 sig
```
```     9   datatype 'term criterion =
```
```    10     Name of string | Intro | IntroIff | Elim | Dest | Solves | Simp of 'term |
```
```    11     Pattern of 'term
```
```    12
```
```    13   datatype theorem =
```
```    14     Internal of Facts.ref * thm | External of Facts.ref * term
```
```    15
```
```    16   val tac_limit: int Unsynchronized.ref
```
```    17   val limit: int Unsynchronized.ref
```
```    18   val find_theorems: Proof.context -> thm option -> int option -> bool ->
```
```    19     (bool * string criterion) list -> int option * (Facts.ref * thm) list
```
```    20   val filter_theorems: Proof.context -> theorem list -> thm option ->
```
```    21     int option -> bool -> (bool * string criterion) list ->
```
```    22     int option * theorem list
```
```    23
```
```    24   val pretty_theorem: Proof.context -> theorem -> Pretty.T
```
```    25   val pretty_thm: Proof.context -> Facts.ref * thm -> Pretty.T
```
```    26
```
```    27 end;
```
```    28
```
```    29 structure Find_Theorems: FIND_THEOREMS =
```
```    30 struct
```
```    31
```
```    32 (** search criteria **)
```
```    33
```
```    34 datatype 'term criterion =
```
```    35   Name of string | Intro | IntroIff | Elim | Dest | Solves | Simp of 'term |
```
```    36   Pattern of 'term;
```
```    37
```
```    38 fun apply_dummies tm =
```
```    39   let
```
```    40     val (xs, _) = Term.strip_abs tm;
```
```    41     val tm' = Term.betapplys (tm, map (Term.dummy_pattern o #2) xs);
```
```    42   in #1 (Term.replace_dummy_patterns tm' 1) end;
```
```    43
```
```    44 fun parse_pattern ctxt nm =
```
```    45   let
```
```    46     val consts = ProofContext.consts_of ctxt;
```
```    47     val nm' =
```
```    48       (case Syntax.parse_term ctxt nm of
```
```    49         Const (c, _) => c
```
```    50       | _ => Consts.intern consts nm);
```
```    51   in
```
```    52     (case try (Consts.the_abbreviation consts) nm' of
```
```    53       SOME (_, rhs) => apply_dummies (ProofContext.expand_abbrevs ctxt rhs)
```
```    54     | NONE => ProofContext.read_term_pattern ctxt nm)
```
```    55   end;
```
```    56
```
```    57 fun read_criterion _ (Name name) = Name name
```
```    58   | read_criterion _ Intro = Intro
```
```    59   | read_criterion _ IntroIff = IntroIff
```
```    60   | read_criterion _ Elim = Elim
```
```    61   | read_criterion _ Dest = Dest
```
```    62   | read_criterion _ Solves = Solves
```
```    63   | read_criterion ctxt (Simp str) = Simp (ProofContext.read_term_pattern ctxt str)
```
```    64   | read_criterion ctxt (Pattern str) = Pattern (parse_pattern ctxt str);
```
```    65
```
```    66 fun pretty_criterion ctxt (b, c) =
```
```    67   let
```
```    68     fun prfx s = if b then s else "-" ^ s;
```
```    69   in
```
```    70     (case c of
```
```    71       Name name => Pretty.str (prfx "name: " ^ quote name)
```
```    72     | Intro => Pretty.str (prfx "intro")
```
```    73     | IntroIff => Pretty.str (prfx "introiff")
```
```    74     | Elim => Pretty.str (prfx "elim")
```
```    75     | Dest => Pretty.str (prfx "dest")
```
```    76     | Solves => Pretty.str (prfx "solves")
```
```    77     | Simp pat => Pretty.block [Pretty.str (prfx "simp:"), Pretty.brk 1,
```
```    78         Pretty.quote (Syntax.pretty_term ctxt (Term.show_dummy_patterns pat))]
```
```    79     | Pattern pat => Pretty.enclose (prfx " \"") "\""
```
```    80         [Syntax.pretty_term ctxt (Term.show_dummy_patterns pat)])
```
```    81   end;
```
```    82
```
```    83
```
```    84 (** theorems, either internal or external (without proof) **)
```
```    85
```
```    86 datatype theorem =
```
```    87   Internal of Facts.ref * thm |
```
```    88   External of Facts.ref * term;
```
```    89
```
```    90 fun prop_of (Internal (_, thm)) = Thm.full_prop_of thm
```
```    91   | prop_of (External (_, prop)) = prop;
```
```    92
```
```    93 fun nprems_of (Internal (_, thm)) = Thm.nprems_of thm
```
```    94   | nprems_of (External (_, prop)) = Logic.count_prems prop;
```
```    95
```
```    96 fun major_prem_of (Internal (_, thm)) = Thm.major_prem_of thm
```
```    97   | major_prem_of (External (_, prop)) =
```
```    98       Logic.strip_assums_concl (hd (Logic.strip_imp_prems prop));
```
```    99
```
```   100 fun fact_ref_of (Internal (fact_ref, _)) = fact_ref
```
```   101   | fact_ref_of (External (fact_ref, _)) = fact_ref;
```
```   102
```
```   103 (** search criterion filters **)
```
```   104
```
```   105 (*generated filters are to be of the form
```
```   106   input: theorem
```
```   107   output: (p:int, s:int) option, where
```
```   108     NONE indicates no match
```
```   109     p is the primary sorting criterion
```
```   110       (eg. number of assumptions in the theorem)
```
```   111     s is the secondary sorting criterion
```
```   112       (eg. size of the substitution for intro, elim and dest)
```
```   113   when applying a set of filters to a thm, fold results in:
```
```   114     (biggest p, sum of all s)
```
```   115   currently p and s only matter for intro, elim, dest and simp filters,
```
```   116   otherwise the default ordering is used.
```
```   117 *)
```
```   118
```
```   119
```
```   120 (* matching theorems *)
```
```   121
```
```   122 fun is_nontrivial thy = Term.is_Const o Term.head_of o Object_Logic.drop_judgment thy;
```
```   123
```
```   124 (*educated guesses on HOL*)  (* FIXME broken *)
```
```   125 val boolT = Type ("bool", []);
```
```   126 val iff_const = Const ("op =", boolT --> boolT --> boolT);
```
```   127
```
```   128 (*extract terms from term_src, refine them to the parts that concern us,
```
```   129   if po try match them against obj else vice versa.
```
```   130   trivial matches are ignored.
```
```   131   returns: smallest substitution size*)
```
```   132 fun is_matching_thm doiff (extract_terms, refine_term) ctxt po obj term_src =
```
```   133   let
```
```   134     val thy = ProofContext.theory_of ctxt;
```
```   135
```
```   136     fun check_match pat = Pattern.matches thy (if po then (pat, obj) else (obj, pat));
```
```   137     fun matches pat =
```
```   138       let
```
```   139         val jpat = Object_Logic.drop_judgment thy pat;
```
```   140         val c = Term.head_of jpat;
```
```   141         val pats =
```
```   142           if Term.is_Const c
```
```   143           then
```
```   144             if doiff andalso c = iff_const then
```
```   145               (pat :: map (Object_Logic.ensure_propT thy) (snd (strip_comb jpat)))
```
```   146                 |> filter (is_nontrivial thy)
```
```   147             else [pat]
```
```   148           else [];
```
```   149       in filter check_match pats end;
```
```   150
```
```   151     fun substsize pat =
```
```   152       let val (_, subst) =
```
```   153         Pattern.match thy (if po then (pat, obj) else (obj, pat)) (Vartab.empty, Vartab.empty)
```
```   154       in Vartab.fold (fn (_, (_, t)) => fn n => size_of_term t + n) subst 0 end;
```
```   155
```
```   156     fun bestmatch [] = NONE
```
```   157       | bestmatch xs = SOME (foldl1 Int.min xs);
```
```   158
```
```   159     val match_thm = matches o refine_term;
```
```   160   in
```
```   161     maps match_thm (extract_terms term_src)
```
```   162     |> map substsize
```
```   163     |> bestmatch
```
```   164   end;
```
```   165
```
```   166
```
```   167 (* filter_name *)
```
```   168
```
```   169 fun filter_name str_pat theorem =
```
```   170   if match_string str_pat (Facts.name_of_ref (fact_ref_of theorem))
```
```   171   then SOME (0, 0) else NONE;
```
```   172
```
```   173
```
```   174 (* filter intro/elim/dest/solves rules *)
```
```   175
```
```   176 fun filter_dest ctxt goal theorem =
```
```   177   let
```
```   178     val extract_dest =
```
```   179      (fn theorem => if nprems_of theorem = 0 then [] else [prop_of theorem],
```
```   180       hd o Logic.strip_imp_prems);
```
```   181     val prems = Logic.prems_of_goal goal 1;
```
```   182
```
```   183     fun try_subst prem = is_matching_thm false extract_dest ctxt true prem theorem;
```
```   184     val successful = prems |> map_filter try_subst;
```
```   185   in
```
```   186     (*if possible, keep best substitution (one with smallest size)*)
```
```   187     (*dest rules always have assumptions, so a dest with one
```
```   188       assumption is as good as an intro rule with none*)
```
```   189     if not (null successful)
```
```   190     then SOME (nprems_of theorem - 1, foldl1 Int.min successful) else NONE
```
```   191   end;
```
```   192
```
```   193 fun filter_intro doiff ctxt goal theorem =
```
```   194   let
```
```   195     val extract_intro = (single o prop_of, Logic.strip_imp_concl);
```
```   196     val concl = Logic.concl_of_goal goal 1;
```
```   197     val ss = is_matching_thm doiff extract_intro ctxt true concl theorem;
```
```   198   in
```
```   199     if is_some ss then SOME (nprems_of theorem, the ss) else NONE
```
```   200   end;
```
```   201
```
```   202 fun filter_elim ctxt goal theorem =
```
```   203   if nprems_of theorem > 0 then
```
```   204     let
```
```   205       val rule = prop_of theorem;
```
```   206       val prems = Logic.prems_of_goal goal 1;
```
```   207       val goal_concl = Logic.concl_of_goal goal 1;
```
```   208       val rule_mp = hd (Logic.strip_imp_prems rule);
```
```   209       val rule_concl = Logic.strip_imp_concl rule;
```
```   210       fun combine t1 t2 = Const ("*combine*", dummyT --> dummyT) \$ (t1 \$ t2);
```
```   211       val rule_tree = combine rule_mp rule_concl;
```
```   212       fun goal_tree prem = combine prem goal_concl;
```
```   213       fun try_subst prem =
```
```   214         is_matching_thm false (single, I) ctxt true (goal_tree prem) rule_tree;
```
```   215       val successful = prems |> map_filter try_subst;
```
```   216     in
```
```   217       (*elim rules always have assumptions, so an elim with one
```
```   218         assumption is as good as an intro rule with none*)
```
```   219       if is_nontrivial (ProofContext.theory_of ctxt) (major_prem_of theorem)
```
```   220         andalso not (null successful)
```
```   221       then SOME (nprems_of theorem - 1, foldl1 Int.min successful) else NONE
```
```   222     end
```
```   223   else NONE
```
```   224
```
```   225 val tac_limit = Unsynchronized.ref 5;
```
```   226
```
```   227 fun filter_solves ctxt goal =
```
```   228   let
```
```   229     fun etacn thm i = Seq.take (! tac_limit) o etac thm i;
```
```   230     fun try_thm thm =
```
```   231       if Thm.no_prems thm then rtac thm 1 goal
```
```   232       else (etacn thm THEN_ALL_NEW (Goal.norm_hhf_tac THEN' Method.assm_tac ctxt)) 1 goal;
```
```   233   in
```
```   234     fn Internal (_, thm) =>
```
```   235       if is_some (Seq.pull (try_thm thm))
```
```   236       then SOME (Thm.nprems_of thm, 0) else NONE
```
```   237      | External _ => NONE
```
```   238   end;
```
```   239
```
```   240
```
```   241 (* filter_simp *)
```
```   242
```
```   243 fun filter_simp ctxt t (Internal (_, thm)) =
```
```   244       let
```
```   245         val mksimps = Simplifier.mksimps (simpset_of ctxt);
```
```   246         val extract_simp =
```
```   247           (map Thm.full_prop_of o mksimps, #1 o Logic.dest_equals o Logic.strip_imp_concl);
```
```   248         val ss = is_matching_thm false extract_simp ctxt false t thm;
```
```   249       in
```
```   250         if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
```
```   251       end
```
```   252   | filter_simp _ _ (External _) = NONE;
```
```   253
```
```   254
```
```   255 (* filter_pattern *)
```
```   256
```
```   257 fun get_names t = Term.add_const_names t (Term.add_free_names t []);
```
```   258
```
```   259 (*Including all constants and frees is only sound because
```
```   260   matching uses higher-order patterns. If full matching
```
```   261   were used, then constants that may be subject to
```
```   262   beta-reduction after substitution of frees should
```
```   263   not be included for LHS set because they could be
```
```   264   thrown away by the substituted function.
```
```   265   e.g. for (?F 1 2) do not include 1 or 2, if it were
```
```   266        possible for ?F to be (% x y. 3)
```
```   267   The largest possible set should always be included on
```
```   268   the RHS.*)
```
```   269
```
```   270 fun filter_pattern ctxt pat =
```
```   271   let
```
```   272     val pat_consts = get_names pat;
```
```   273
```
```   274     fun check (theorem, NONE) = check (theorem, SOME (get_names (prop_of theorem)))
```
```   275       | check (theorem, c as SOME thm_consts) =
```
```   276          (if subset (op =) (pat_consts, thm_consts) andalso
```
```   277             Pattern.matches_subterm (ProofContext.theory_of ctxt) (pat, prop_of theorem)
```
```   278           then SOME (0, 0) else NONE, c);
```
```   279   in check end;
```
```   280
```
```   281
```
```   282 (* interpret criteria as filters *)
```
```   283
```
```   284 local
```
```   285
```
```   286 fun err_no_goal c =
```
```   287   error ("Current goal required for " ^ c ^ " search criterion");
```
```   288
```
```   289 val fix_goal = Thm.prop_of;
```
```   290
```
```   291 fun filter_crit _ _ (Name name) = apfst (filter_name name)
```
```   292   | filter_crit _ NONE Intro = err_no_goal "intro"
```
```   293   | filter_crit _ NONE IntroIff = err_no_goal "introiff"
```
```   294   | filter_crit _ NONE Elim = err_no_goal "elim"
```
```   295   | filter_crit _ NONE Dest = err_no_goal "dest"
```
```   296   | filter_crit _ NONE Solves = err_no_goal "solves"
```
```   297   | filter_crit ctxt (SOME goal) Intro = apfst (filter_intro false ctxt (fix_goal goal))
```
```   298   | filter_crit ctxt (SOME goal) IntroIff = apfst (filter_intro true ctxt (fix_goal goal))
```
```   299   | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt (fix_goal goal))
```
```   300   | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt (fix_goal goal))
```
```   301   | filter_crit ctxt (SOME goal) Solves = apfst (filter_solves ctxt goal)
```
```   302   | filter_crit ctxt _ (Simp pat) = apfst (filter_simp ctxt pat)
```
```   303   | filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat;
```
```   304
```
```   305 fun opt_not x = if is_some x then NONE else SOME (0, 0);
```
```   306
```
```   307 fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int)
```
```   308   | opt_add _ _ = NONE;
```
```   309
```
```   310 fun app_filters thm =
```
```   311   let
```
```   312     fun app (NONE, _, _) = NONE
```
```   313       | app (SOME v, _, []) = SOME (v, thm)
```
```   314       | app (r, consts, f :: fs) =
```
```   315           let val (r', consts') = f (thm, consts)
```
```   316           in app (opt_add r r', consts', fs) end;
```
```   317   in app end;
```
```   318
```
```   319
```
```   320 in
```
```   321
```
```   322 fun filter_criterion ctxt opt_goal (b, c) =
```
```   323   (if b then I else (apfst opt_not)) o filter_crit ctxt opt_goal c;
```
```   324
```
```   325 fun sorted_filter filters theorems =
```
```   326   let
```
```   327     fun eval_filters theorem = app_filters theorem (SOME (0, 0), NONE, filters);
```
```   328
```
```   329     (*filters return: (number of assumptions, substitution size) option, so
```
```   330       sort (desc. in both cases) according to number of assumptions first,
```
```   331       then by the substitution size*)
```
```   332     fun result_ord (((p0, s0), _), ((p1, s1), _)) =
```
```   333       prod_ord int_ord int_ord ((p1, s1), (p0, s0));
```
```   334   in map_filter eval_filters theorems |> sort result_ord |> map #2 end;
```
```   335
```
```   336 fun lazy_filter filters =
```
```   337   let
```
```   338     fun lazy_match thms = Seq.make (fn () => first_match thms)
```
```   339
```
```   340     and first_match [] = NONE
```
```   341       | first_match (thm :: thms) =
```
```   342           (case app_filters thm (SOME (0, 0), NONE, filters) of
```
```   343             NONE => first_match thms
```
```   344           | SOME (_, t) => SOME (t, lazy_match thms));
```
```   345   in lazy_match end;
```
```   346
```
```   347 end;
```
```   348
```
```   349
```
```   350 (* removing duplicates, preferring nicer names, roughly n log n *)
```
```   351
```
```   352 local
```
```   353
```
```   354 val index_ord = option_ord (K EQUAL);
```
```   355 val hidden_ord = bool_ord o pairself Name_Space.is_hidden;
```
```   356 val qual_ord = int_ord o pairself (length o Long_Name.explode);
```
```   357 val txt_ord = int_ord o pairself size;
```
```   358
```
```   359 fun nicer_name (x, i) (y, j) =
```
```   360   (case hidden_ord (x, y) of EQUAL =>
```
```   361     (case index_ord (i, j) of EQUAL =>
```
```   362       (case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord)
```
```   363     | ord => ord)
```
```   364   | ord => ord) <> GREATER;
```
```   365
```
```   366 fun rem_cdups nicer xs =
```
```   367   let
```
```   368     fun rem_c rev_seen [] = rev rev_seen
```
```   369       | rem_c rev_seen [x] = rem_c (x :: rev_seen) []
```
```   370       | rem_c rev_seen ((x as (t, _)) :: (y as (t', _)) :: xs) =
```
```   371           if (prop_of t) aconv (prop_of t')
```
```   372           then rem_c rev_seen ((if nicer (fact_ref_of t) (fact_ref_of t') then x else y) :: xs)
```
```   373           else rem_c (x :: rev_seen) (y :: xs)
```
```   374   in rem_c [] xs end;
```
```   375
```
```   376 in
```
```   377
```
```   378 fun nicer_shortest ctxt =
```
```   379   let
```
```   380     (* FIXME global name space!? *)
```
```   381     val space = Facts.space_of (Global_Theory.facts_of (ProofContext.theory_of ctxt));
```
```   382
```
```   383     val shorten =
```
```   384       Name_Space.extern_flags
```
```   385         {long_names = false, short_names = false, unique_names = false} space;
```
```   386
```
```   387     fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =
```
```   388           nicer_name (shorten x, i) (shorten y, j)
```
```   389       | nicer (Facts.Fact _) (Facts.Named _) = true
```
```   390       | nicer (Facts.Named _) (Facts.Fact _) = false;
```
```   391   in nicer end;
```
```   392
```
```   393 fun rem_thm_dups nicer xs =
```
```   394   xs ~~ (1 upto length xs)
```
```   395   |> sort (Term_Ord.fast_term_ord o pairself (prop_of o #1))
```
```   396   |> rem_cdups nicer
```
```   397   |> sort (int_ord o pairself #2)
```
```   398   |> map #1;
```
```   399
```
```   400 end;
```
```   401
```
```   402
```
```   403 (* print_theorems *)
```
```   404
```
```   405 fun all_facts_of ctxt =
```
```   406   let
```
```   407     fun visible_facts facts =
```
```   408       Facts.dest_static [] facts
```
```   409       |> filter_out (Facts.is_concealed facts o #1);
```
```   410   in
```
```   411     maps Facts.selections
```
```   412      (visible_facts (Global_Theory.facts_of (ProofContext.theory_of ctxt)) @
```
```   413
```
```   414
```
```   415       visible_facts (ProofContext.facts_of ctxt))
```
```   416   end;
```
```   417
```
```   418 val limit = Unsynchronized.ref 40;
```
```   419
```
```   420 fun filter_theorems ctxt theorems opt_goal opt_limit rem_dups raw_criteria =
```
```   421   let
```
```   422     val assms =
```
```   423       ProofContext.get_fact ctxt (Facts.named "local.assms")
```
```   424         handle ERROR _ => [];
```
```   425     val add_prems = Seq.hd o TRY (Method.insert_tac assms 1);
```
```   426     val opt_goal' = Option.map add_prems opt_goal;
```
```   427
```
```   428     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
```
```   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 (! 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 find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
```
```   452   filter_theorems ctxt (map Internal (all_facts_of ctxt)) opt_goal opt_limit
```
```   453      rem_dups raw_criteria
```
```   454   |> apsnd (map (fn Internal f => f));
```
```   455
```
```   456 fun pretty_theorem ctxt (Internal (thmref, thm)) = Pretty.block
```
```   457       [Pretty.str (Facts.string_of_ref thmref), Pretty.str ":", Pretty.brk 1,
```
```   458         Display.pretty_thm ctxt thm]
```
```   459   | pretty_theorem ctxt (External (thmref, prop)) = Pretty.block
```
```   460       [Pretty.str (Facts.string_of_ref thmref), Pretty.str ":", Pretty.brk 1,
```
```   461         Syntax.unparse_term ctxt prop];
```
```   462
```
```   463 fun pretty_thm ctxt (thmref, thm) = pretty_theorem ctxt (Internal (thmref, thm));
```
```   464
```
```   465 fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
```
```   466   let
```
```   467     val start = start_timing ();
```
```   468
```
```   469     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
```
```   470     val (foundo, theorems) = filter_theorems ctxt (map Internal (all_facts_of ctxt))
```
```   471       opt_goal opt_limit rem_dups raw_criteria;
```
```   472     val returned = length theorems;
```
```   473
```
```   474     val tally_msg =
```
```   475       (case foundo of
```
```   476         NONE => "displaying " ^ string_of_int returned ^ " theorem(s)"
```
```   477       | SOME found =>
```
```   478           "found " ^ string_of_int found ^ " theorem(s)" ^
```
```   479             (if returned < found
```
```   480              then " (" ^ string_of_int returned ^ " displayed)"
```
```   481              else ""));
```
```   482
```
```   483     val end_msg = " in " ^ Time.toString (#cpu (end_timing start)) ^ " secs";
```
```   484   in
```
```   485     Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria) ::
```
```   486     Pretty.str "" ::
```
```   487     (if null theorems then [Pretty.str ("nothing found" ^ end_msg)]
```
```   488      else
```
```   489       [Pretty.str (tally_msg ^ end_msg ^ ":"), Pretty.str ""] @
```
```   490         map (pretty_theorem ctxt) theorems)
```
```   491   end |> Pretty.chunks |> Pretty.writeln;
```
```   492
```
```   493
```
```   494
```
```   495 (** command syntax **)
```
```   496
```
```   497 local
```
```   498
```
```   499 val criterion =
```
```   500   Parse.reserved "name" |-- Parse.!!! (Parse.\$\$\$ ":" |-- Parse.xname) >> Name ||
```
```   501   Parse.reserved "intro" >> K Intro ||
```
```   502   Parse.reserved "introiff" >> K IntroIff ||
```
```   503   Parse.reserved "elim" >> K Elim ||
```
```   504   Parse.reserved "dest" >> K Dest ||
```
```   505   Parse.reserved "solves" >> K Solves ||
```
```   506   Parse.reserved "simp" |-- Parse.!!! (Parse.\$\$\$ ":" |-- Parse.term) >> Simp ||
```
```   507   Parse.term >> Pattern;
```
```   508
```
```   509 val options =
```
```   510   Scan.optional
```
```   511     (Parse.\$\$\$ "(" |--
```
```   512       Parse.!!! (Scan.option Parse.nat -- Scan.optional (Parse.reserved "with_dups" >> K false) true
```
```   513         --| Parse.\$\$\$ ")")) (NONE, true);
```
```   514 in
```
```   515
```
```   516 val _ =
```
```   517   Outer_Syntax.improper_command "find_theorems" "print theorems meeting specified criteria"
```
```   518     Keyword.diag
```
```   519     (options -- Scan.repeat (((Scan.option Parse.minus >> is_none) -- criterion))
```
```   520       >> (fn ((opt_lim, rem_dups), spec) =>
```
```   521         Toplevel.no_timing o
```
```   522         Toplevel.keep (fn state =>
```
```   523           let
```
```   524             val ctxt = Toplevel.context_of state;
```
```   525             val opt_goal = try (Proof.simple_goal o Toplevel.proof_of) state |> Option.map #goal;
```
```   526           in print_theorems ctxt opt_goal opt_lim rem_dups spec end)));
```
```   527
```
```   528 end;
```
```   529
```
```   530 end;
```