src/Pure/Tools/find_theorems.ML
 author krauss Mon May 30 17:07:48 2011 +0200 (2011-05-30) changeset 43070 0318781be055 parent 43069 88e45168272c child 43071 c9859f634cef permissions -rw-r--r--
explicit type for search queries
```     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   type 'term query = {
```
```    17     goal: thm option,
```
```    18     limit: int option,
```
```    19     rem_dups: bool,
```
```    20     criteria: (bool * 'term criterion) list
```
```    21   }
```
```    22
```
```    23   val tac_limit: int Unsynchronized.ref
```
```    24   val limit: int Unsynchronized.ref
```
```    25
```
```    26   val read_criterion: Proof.context -> string criterion -> term criterion
```
```    27   val query_parser: (bool * string criterion) list parser
```
```    28
```
```    29   val find_theorems: Proof.context -> thm option -> int option -> bool ->
```
```    30     (bool * term criterion) list -> int option * (Facts.ref * thm) list
```
```    31   val find_theorems_cmd: Proof.context -> thm option -> int option -> bool ->
```
```    32     (bool * string criterion) list -> int option * (Facts.ref * thm) list
```
```    33
```
```    34   val filter_theorems: Proof.context -> theorem list -> term query ->
```
```    35     int option * theorem list
```
```    36   val filter_theorems_cmd: Proof.context -> theorem list -> string query ->
```
```    37     int option * theorem list
```
```    38
```
```    39   val pretty_theorem: Proof.context -> theorem -> Pretty.T
```
```    40   val pretty_thm: Proof.context -> Facts.ref * thm -> Pretty.T
```
```    41
```
```    42 end;
```
```    43
```
```    44 structure Find_Theorems: FIND_THEOREMS =
```
```    45 struct
```
```    46
```
```    47 (** search criteria **)
```
```    48
```
```    49 datatype 'term criterion =
```
```    50   Name of string | Intro | IntroIff | Elim | Dest | Solves | Simp of 'term |
```
```    51   Pattern of 'term;
```
```    52
```
```    53 fun apply_dummies tm =
```
```    54   let
```
```    55     val (xs, _) = Term.strip_abs tm;
```
```    56     val tm' = Term.betapplys (tm, map (Term.dummy_pattern o #2) xs);
```
```    57   in #1 (Term.replace_dummy_patterns tm' 1) end;
```
```    58
```
```    59 fun parse_pattern ctxt nm =
```
```    60   let
```
```    61     val consts = Proof_Context.consts_of ctxt;
```
```    62     val nm' =
```
```    63       (case Syntax.parse_term ctxt nm of
```
```    64         Const (c, _) => c
```
```    65       | _ => Consts.intern consts nm);
```
```    66   in
```
```    67     (case try (Consts.the_abbreviation consts) nm' of
```
```    68       SOME (_, rhs) => apply_dummies (Proof_Context.expand_abbrevs ctxt rhs)
```
```    69     | NONE => Proof_Context.read_term_pattern ctxt nm)
```
```    70   end;
```
```    71
```
```    72 fun read_criterion _ (Name name) = Name name
```
```    73   | read_criterion _ Intro = Intro
```
```    74   | read_criterion _ IntroIff = IntroIff
```
```    75   | read_criterion _ Elim = Elim
```
```    76   | read_criterion _ Dest = Dest
```
```    77   | read_criterion _ Solves = Solves
```
```    78   | read_criterion ctxt (Simp str) = Simp (Proof_Context.read_term_pattern ctxt str)
```
```    79   | read_criterion ctxt (Pattern str) = Pattern (parse_pattern ctxt str);
```
```    80
```
```    81 fun pretty_criterion ctxt (b, c) =
```
```    82   let
```
```    83     fun prfx s = if b then s else "-" ^ s;
```
```    84   in
```
```    85     (case c of
```
```    86       Name name => Pretty.str (prfx "name: " ^ quote name)
```
```    87     | Intro => Pretty.str (prfx "intro")
```
```    88     | IntroIff => Pretty.str (prfx "introiff")
```
```    89     | Elim => Pretty.str (prfx "elim")
```
```    90     | Dest => Pretty.str (prfx "dest")
```
```    91     | Solves => Pretty.str (prfx "solves")
```
```    92     | Simp pat => Pretty.block [Pretty.str (prfx "simp:"), Pretty.brk 1,
```
```    93         Pretty.quote (Syntax.pretty_term ctxt (Term.show_dummy_patterns pat))]
```
```    94     | Pattern pat => Pretty.enclose (prfx " \"") "\""
```
```    95         [Syntax.pretty_term ctxt (Term.show_dummy_patterns pat)])
```
```    96   end;
```
```    97
```
```    98
```
```    99 (** queries **)
```
```   100
```
```   101 type 'term query = {
```
```   102   goal: thm option,
```
```   103   limit: int option,
```
```   104   rem_dups: bool,
```
```   105   criteria: (bool * 'term criterion) list
```
```   106 };
```
```   107
```
```   108 fun map_criteria f {goal, limit, rem_dups, criteria} =
```
```   109   {goal=goal, limit=limit, rem_dups=rem_dups, criteria=f criteria};
```
```   110
```
```   111
```
```   112 (** theorems, either internal or external (without proof) **)
```
```   113
```
```   114 datatype theorem =
```
```   115   Internal of Facts.ref * thm |
```
```   116   External of Facts.ref * term;
```
```   117
```
```   118 fun prop_of (Internal (_, thm)) = Thm.full_prop_of thm
```
```   119   | prop_of (External (_, prop)) = prop;
```
```   120
```
```   121 fun nprems_of (Internal (_, thm)) = Thm.nprems_of thm
```
```   122   | nprems_of (External (_, prop)) = Logic.count_prems prop;
```
```   123
```
```   124 fun major_prem_of (Internal (_, thm)) = Thm.major_prem_of thm
```
```   125   | major_prem_of (External (_, prop)) =
```
```   126       Logic.strip_assums_concl (hd (Logic.strip_imp_prems prop));
```
```   127
```
```   128 fun fact_ref_of (Internal (fact_ref, _)) = fact_ref
```
```   129   | fact_ref_of (External (fact_ref, _)) = fact_ref;
```
```   130
```
```   131 (** search criterion filters **)
```
```   132
```
```   133 (*generated filters are to be of the form
```
```   134   input: theorem
```
```   135   output: (p:int, s:int) option, where
```
```   136     NONE indicates no match
```
```   137     p is the primary sorting criterion
```
```   138       (eg. number of assumptions in the theorem)
```
```   139     s is the secondary sorting criterion
```
```   140       (eg. size of the substitution for intro, elim and dest)
```
```   141   when applying a set of filters to a thm, fold results in:
```
```   142     (biggest p, sum of all s)
```
```   143   currently p and s only matter for intro, elim, dest and simp filters,
```
```   144   otherwise the default ordering is used.
```
```   145 *)
```
```   146
```
```   147
```
```   148 (* matching theorems *)
```
```   149
```
```   150 fun is_nontrivial thy = Term.is_Const o Term.head_of o Object_Logic.drop_judgment thy;
```
```   151
```
```   152 (*educated guesses on HOL*)  (* FIXME broken *)
```
```   153 val boolT = Type ("bool", []);
```
```   154 val iff_const = Const ("op =", boolT --> boolT --> boolT);
```
```   155
```
```   156 (*extract terms from term_src, refine them to the parts that concern us,
```
```   157   if po try match them against obj else vice versa.
```
```   158   trivial matches are ignored.
```
```   159   returns: smallest substitution size*)
```
```   160 fun is_matching_thm doiff (extract_terms, refine_term) ctxt po obj term_src =
```
```   161   let
```
```   162     val thy = Proof_Context.theory_of ctxt;
```
```   163
```
```   164     fun check_match pat = Pattern.matches thy (if po then (pat, obj) else (obj, pat));
```
```   165     fun matches pat =
```
```   166       let
```
```   167         val jpat = Object_Logic.drop_judgment thy pat;
```
```   168         val c = Term.head_of jpat;
```
```   169         val pats =
```
```   170           if Term.is_Const c
```
```   171           then
```
```   172             if doiff andalso c = iff_const then
```
```   173               (pat :: map (Object_Logic.ensure_propT thy) (snd (strip_comb jpat)))
```
```   174                 |> filter (is_nontrivial thy)
```
```   175             else [pat]
```
```   176           else [];
```
```   177       in filter check_match pats end;
```
```   178
```
```   179     fun substsize pat =
```
```   180       let val (_, subst) =
```
```   181         Pattern.match thy (if po then (pat, obj) else (obj, pat)) (Vartab.empty, Vartab.empty)
```
```   182       in Vartab.fold (fn (_, (_, t)) => fn n => size_of_term t + n) subst 0 end;
```
```   183
```
```   184     fun bestmatch [] = NONE
```
```   185       | bestmatch xs = SOME (foldl1 Int.min xs);
```
```   186
```
```   187     val match_thm = matches o refine_term;
```
```   188   in
```
```   189     maps match_thm (extract_terms term_src)
```
```   190     |> map substsize
```
```   191     |> bestmatch
```
```   192   end;
```
```   193
```
```   194
```
```   195 (* filter_name *)
```
```   196
```
```   197 fun filter_name str_pat theorem =
```
```   198   if match_string str_pat (Facts.name_of_ref (fact_ref_of theorem))
```
```   199   then SOME (0, 0) else NONE;
```
```   200
```
```   201
```
```   202 (* filter intro/elim/dest/solves rules *)
```
```   203
```
```   204 fun filter_dest ctxt goal theorem =
```
```   205   let
```
```   206     val extract_dest =
```
```   207      (fn theorem => if nprems_of theorem = 0 then [] else [prop_of theorem],
```
```   208       hd o Logic.strip_imp_prems);
```
```   209     val prems = Logic.prems_of_goal goal 1;
```
```   210
```
```   211     fun try_subst prem = is_matching_thm false extract_dest ctxt true prem theorem;
```
```   212     val successful = prems |> map_filter try_subst;
```
```   213   in
```
```   214     (*if possible, keep best substitution (one with smallest size)*)
```
```   215     (*dest rules always have assumptions, so a dest with one
```
```   216       assumption is as good as an intro rule with none*)
```
```   217     if not (null successful)
```
```   218     then SOME (nprems_of theorem - 1, foldl1 Int.min successful) else NONE
```
```   219   end;
```
```   220
```
```   221 fun filter_intro doiff ctxt goal theorem =
```
```   222   let
```
```   223     val extract_intro = (single o prop_of, Logic.strip_imp_concl);
```
```   224     val concl = Logic.concl_of_goal goal 1;
```
```   225     val ss = is_matching_thm doiff extract_intro ctxt true concl theorem;
```
```   226   in
```
```   227     if is_some ss then SOME (nprems_of theorem, the ss) else NONE
```
```   228   end;
```
```   229
```
```   230 fun filter_elim ctxt goal theorem =
```
```   231   if nprems_of theorem > 0 then
```
```   232     let
```
```   233       val rule = prop_of theorem;
```
```   234       val prems = Logic.prems_of_goal goal 1;
```
```   235       val goal_concl = Logic.concl_of_goal goal 1;
```
```   236       val rule_mp = hd (Logic.strip_imp_prems rule);
```
```   237       val rule_concl = Logic.strip_imp_concl rule;
```
```   238       fun combine t1 t2 = Const ("*combine*", dummyT --> dummyT) \$ (t1 \$ t2);
```
```   239       val rule_tree = combine rule_mp rule_concl;
```
```   240       fun goal_tree prem = combine prem goal_concl;
```
```   241       fun try_subst prem =
```
```   242         is_matching_thm false (single, I) ctxt true (goal_tree prem) rule_tree;
```
```   243       val successful = prems |> map_filter try_subst;
```
```   244     in
```
```   245       (*elim rules always have assumptions, so an elim with one
```
```   246         assumption is as good as an intro rule with none*)
```
```   247       if is_nontrivial (Proof_Context.theory_of ctxt) (major_prem_of theorem)
```
```   248         andalso not (null successful)
```
```   249       then SOME (nprems_of theorem - 1, foldl1 Int.min successful) else NONE
```
```   250     end
```
```   251   else NONE
```
```   252
```
```   253 val tac_limit = Unsynchronized.ref 5;
```
```   254
```
```   255 fun filter_solves ctxt goal =
```
```   256   let
```
```   257     fun etacn thm i = Seq.take (! tac_limit) o etac thm i;
```
```   258     fun try_thm thm =
```
```   259       if Thm.no_prems thm then rtac thm 1 goal
```
```   260       else (etacn thm THEN_ALL_NEW (Goal.norm_hhf_tac THEN' Method.assm_tac ctxt)) 1 goal;
```
```   261   in
```
```   262     fn Internal (_, thm) =>
```
```   263       if is_some (Seq.pull (try_thm thm))
```
```   264       then SOME (Thm.nprems_of thm, 0) else NONE
```
```   265      | External _ => NONE
```
```   266   end;
```
```   267
```
```   268
```
```   269 (* filter_simp *)
```
```   270
```
```   271 fun filter_simp ctxt t (Internal (_, thm)) =
```
```   272       let
```
```   273         val mksimps = Simplifier.mksimps (simpset_of ctxt);
```
```   274         val extract_simp =
```
```   275           (map Thm.full_prop_of o mksimps, #1 o Logic.dest_equals o Logic.strip_imp_concl);
```
```   276         val ss = is_matching_thm false extract_simp ctxt false t thm;
```
```   277       in
```
```   278         if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
```
```   279       end
```
```   280   | filter_simp _ _ (External _) = NONE;
```
```   281
```
```   282
```
```   283 (* filter_pattern *)
```
```   284
```
```   285 fun get_names t = Term.add_const_names t (Term.add_free_names t []);
```
```   286
```
```   287 (*Including all constants and frees is only sound because
```
```   288   matching uses higher-order patterns. If full matching
```
```   289   were used, then constants that may be subject to
```
```   290   beta-reduction after substitution of frees should
```
```   291   not be included for LHS set because they could be
```
```   292   thrown away by the substituted function.
```
```   293   e.g. for (?F 1 2) do not include 1 or 2, if it were
```
```   294        possible for ?F to be (% x y. 3)
```
```   295   The largest possible set should always be included on
```
```   296   the RHS.*)
```
```   297
```
```   298 fun filter_pattern ctxt pat =
```
```   299   let
```
```   300     val pat_consts = get_names pat;
```
```   301
```
```   302     fun check (theorem, NONE) = check (theorem, SOME (get_names (prop_of theorem)))
```
```   303       | check (theorem, c as SOME thm_consts) =
```
```   304          (if subset (op =) (pat_consts, thm_consts) andalso
```
```   305             Pattern.matches_subterm (Proof_Context.theory_of ctxt) (pat, prop_of theorem)
```
```   306           then SOME (0, 0) else NONE, c);
```
```   307   in check end;
```
```   308
```
```   309
```
```   310 (* interpret criteria as filters *)
```
```   311
```
```   312 local
```
```   313
```
```   314 fun err_no_goal c =
```
```   315   error ("Current goal required for " ^ c ^ " search criterion");
```
```   316
```
```   317 val fix_goal = Thm.prop_of;
```
```   318
```
```   319 fun filter_crit _ _ (Name name) = apfst (filter_name name)
```
```   320   | filter_crit _ NONE Intro = err_no_goal "intro"
```
```   321   | filter_crit _ NONE IntroIff = err_no_goal "introiff"
```
```   322   | filter_crit _ NONE Elim = err_no_goal "elim"
```
```   323   | filter_crit _ NONE Dest = err_no_goal "dest"
```
```   324   | filter_crit _ NONE Solves = err_no_goal "solves"
```
```   325   | filter_crit ctxt (SOME goal) Intro = apfst (filter_intro false ctxt (fix_goal goal))
```
```   326   | filter_crit ctxt (SOME goal) IntroIff = apfst (filter_intro true ctxt (fix_goal goal))
```
```   327   | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt (fix_goal goal))
```
```   328   | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt (fix_goal goal))
```
```   329   | filter_crit ctxt (SOME goal) Solves = apfst (filter_solves ctxt goal)
```
```   330   | filter_crit ctxt _ (Simp pat) = apfst (filter_simp ctxt pat)
```
```   331   | filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat;
```
```   332
```
```   333 fun opt_not x = if is_some x then NONE else SOME (0, 0);
```
```   334
```
```   335 fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int)
```
```   336   | opt_add _ _ = NONE;
```
```   337
```
```   338 fun app_filters thm =
```
```   339   let
```
```   340     fun app (NONE, _, _) = NONE
```
```   341       | app (SOME v, _, []) = SOME (v, thm)
```
```   342       | app (r, consts, f :: fs) =
```
```   343           let val (r', consts') = f (thm, consts)
```
```   344           in app (opt_add r r', consts', fs) end;
```
```   345   in app end;
```
```   346
```
```   347
```
```   348 in
```
```   349
```
```   350 fun filter_criterion ctxt opt_goal (b, c) =
```
```   351   (if b then I else (apfst opt_not)) o filter_crit ctxt opt_goal c;
```
```   352
```
```   353 fun sorted_filter filters theorems =
```
```   354   let
```
```   355     fun eval_filters theorem = app_filters theorem (SOME (0, 0), NONE, filters);
```
```   356
```
```   357     (*filters return: (number of assumptions, substitution size) option, so
```
```   358       sort (desc. in both cases) according to number of assumptions first,
```
```   359       then by the substitution size*)
```
```   360     fun result_ord (((p0, s0), _), ((p1, s1), _)) =
```
```   361       prod_ord int_ord int_ord ((p1, s1), (p0, s0));
```
```   362   in map_filter eval_filters theorems |> sort result_ord |> map #2 end;
```
```   363
```
```   364 fun lazy_filter filters =
```
```   365   let
```
```   366     fun lazy_match thms = Seq.make (fn () => first_match thms)
```
```   367
```
```   368     and first_match [] = NONE
```
```   369       | first_match (thm :: thms) =
```
```   370           (case app_filters thm (SOME (0, 0), NONE, filters) of
```
```   371             NONE => first_match thms
```
```   372           | SOME (_, t) => SOME (t, lazy_match thms));
```
```   373   in lazy_match end;
```
```   374
```
```   375 end;
```
```   376
```
```   377
```
```   378 (* removing duplicates, preferring nicer names, roughly n log n *)
```
```   379
```
```   380 local
```
```   381
```
```   382 val index_ord = option_ord (K EQUAL);
```
```   383 val hidden_ord = bool_ord o pairself Name_Space.is_hidden;
```
```   384 val qual_ord = int_ord o pairself (length o Long_Name.explode);
```
```   385 val txt_ord = int_ord o pairself size;
```
```   386
```
```   387 fun nicer_name (x, i) (y, j) =
```
```   388   (case hidden_ord (x, y) of EQUAL =>
```
```   389     (case index_ord (i, j) of EQUAL =>
```
```   390       (case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord)
```
```   391     | ord => ord)
```
```   392   | ord => ord) <> GREATER;
```
```   393
```
```   394 fun rem_cdups nicer xs =
```
```   395   let
```
```   396     fun rem_c rev_seen [] = rev rev_seen
```
```   397       | rem_c rev_seen [x] = rem_c (x :: rev_seen) []
```
```   398       | rem_c rev_seen ((x as (t, _)) :: (y as (t', _)) :: xs) =
```
```   399           if (prop_of t) aconv (prop_of t')
```
```   400           then rem_c rev_seen ((if nicer (fact_ref_of t) (fact_ref_of t') then x else y) :: xs)
```
```   401           else rem_c (x :: rev_seen) (y :: xs)
```
```   402   in rem_c [] xs end;
```
```   403
```
```   404 in
```
```   405
```
```   406 fun nicer_shortest ctxt =
```
```   407   let
```
```   408     (* FIXME global name space!? *)
```
```   409     val space = Facts.space_of (Global_Theory.facts_of (Proof_Context.theory_of ctxt));
```
```   410
```
```   411     val shorten =
```
```   412       Name_Space.extern
```
```   413         (ctxt
```
```   414           |> Config.put Name_Space.names_long false
```
```   415           |> Config.put Name_Space.names_short false
```
```   416           |> Config.put Name_Space.names_unique false) space;
```
```   417
```
```   418     fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =
```
```   419           nicer_name (shorten x, i) (shorten y, j)
```
```   420       | nicer (Facts.Fact _) (Facts.Named _) = true
```
```   421       | nicer (Facts.Named _) (Facts.Fact _) = false;
```
```   422   in nicer end;
```
```   423
```
```   424 fun rem_thm_dups nicer xs =
```
```   425   xs ~~ (1 upto length xs)
```
```   426   |> sort (Term_Ord.fast_term_ord o pairself (prop_of o #1))
```
```   427   |> rem_cdups nicer
```
```   428   |> sort (int_ord o pairself #2)
```
```   429   |> map #1;
```
```   430
```
```   431 end;
```
```   432
```
```   433
```
```   434 (* print_theorems *)
```
```   435
```
```   436 fun all_facts_of ctxt =
```
```   437   let
```
```   438     fun visible_facts facts =
```
```   439       Facts.dest_static [] facts
```
```   440       |> filter_out (Facts.is_concealed facts o #1);
```
```   441   in
```
```   442     maps Facts.selections
```
```   443      (visible_facts (Global_Theory.facts_of (Proof_Context.theory_of ctxt)) @
```
```   444
```
```   445
```
```   446       visible_facts (Proof_Context.facts_of ctxt))
```
```   447   end;
```
```   448
```
```   449 val limit = Unsynchronized.ref 40;
```
```   450
```
```   451 fun filter_theorems ctxt theorems query =
```
```   452   let
```
```   453     val {goal=opt_goal, limit=opt_limit, rem_dups, criteria} = query
```
```   454     val filters = map (filter_criterion ctxt opt_goal) criteria;
```
```   455
```
```   456     fun find_all theorems =
```
```   457       let
```
```   458         val raw_matches = sorted_filter filters theorems;
```
```   459
```
```   460         val matches =
```
```   461           if rem_dups
```
```   462           then rem_thm_dups (nicer_shortest ctxt) raw_matches
```
```   463           else raw_matches;
```
```   464
```
```   465         val len = length matches;
```
```   466         val lim = the_default (! limit) opt_limit;
```
```   467       in (SOME len, drop (Int.max (len - lim, 0)) matches) end;
```
```   468
```
```   469     val find =
```
```   470       if rem_dups orelse is_none opt_limit
```
```   471       then find_all
```
```   472       else pair NONE o Seq.list_of o Seq.take (the opt_limit) o lazy_filter filters;
```
```   473
```
```   474   in find theorems end;
```
```   475
```
```   476 fun filter_theorems_cmd ctxt theorems raw_query =
```
```   477   filter_theorems ctxt theorems (map_criteria
```
```   478     (map (apsnd (read_criterion ctxt))) raw_query);
```
```   479
```
```   480 fun gen_find_theorems filter ctxt opt_goal opt_limit rem_dups raw_criteria =
```
```   481   let
```
```   482     val assms =
```
```   483       Proof_Context.get_fact ctxt (Facts.named "local.assms")
```
```   484         handle ERROR _ => [];
```
```   485     val add_prems = Seq.hd o TRY (Method.insert_tac assms 1);
```
```   486     val opt_goal' = Option.map add_prems opt_goal;
```
```   487   in
```
```   488     filter ctxt (map Internal (all_facts_of ctxt))
```
```   489       {goal=opt_goal', limit=opt_limit, rem_dups=rem_dups, criteria=raw_criteria}
```
```   490     |> apsnd (map (fn Internal f => f))
```
```   491   end;
```
```   492
```
```   493 val find_theorems = gen_find_theorems filter_theorems;
```
```   494 val find_theorems_cmd = gen_find_theorems filter_theorems_cmd;
```
```   495
```
```   496 fun pretty_theorem ctxt (Internal (thmref, thm)) = Pretty.block
```
```   497       [Pretty.str (Facts.string_of_ref thmref), Pretty.str ":", Pretty.brk 1,
```
```   498         Display.pretty_thm ctxt thm]
```
```   499   | pretty_theorem ctxt (External (thmref, prop)) = Pretty.block
```
```   500       [Pretty.str (Facts.string_of_ref thmref), Pretty.str ":", Pretty.brk 1,
```
```   501         Syntax.unparse_term ctxt prop];
```
```   502
```
```   503 fun pretty_thm ctxt (thmref, thm) = pretty_theorem ctxt (Internal (thmref, thm));
```
```   504
```
```   505 fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
```
```   506   let
```
```   507     val start = Timing.start ();
```
```   508
```
```   509     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
```
```   510     val (foundo, theorems) = filter_theorems ctxt (map Internal (all_facts_of ctxt))
```
```   511       {goal=opt_goal, limit=opt_limit, rem_dups=rem_dups, criteria=criteria};
```
```   512     val returned = length theorems;
```
```   513
```
```   514     val tally_msg =
```
```   515       (case foundo of
```
```   516         NONE => "displaying " ^ string_of_int returned ^ " theorem(s)"
```
```   517       | SOME found =>
```
```   518           "found " ^ string_of_int found ^ " theorem(s)" ^
```
```   519             (if returned < found
```
```   520              then " (" ^ string_of_int returned ^ " displayed)"
```
```   521              else ""));
```
```   522
```
```   523     val end_msg = " in " ^ Time.toString (#cpu (Timing.result start)) ^ " secs";
```
```   524   in
```
```   525     Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria) ::
```
```   526     Pretty.str "" ::
```
```   527     (if null theorems then [Pretty.str ("nothing found" ^ end_msg)]
```
```   528      else
```
```   529       [Pretty.str (tally_msg ^ end_msg ^ ":"), Pretty.str ""] @
```
```   530         map (pretty_theorem ctxt) theorems)
```
```   531   end |> Pretty.chunks |> Pretty.writeln;
```
```   532
```
```   533
```
```   534
```
```   535 (** command syntax **)
```
```   536
```
```   537 local
```
```   538
```
```   539 val criterion =
```
```   540   Parse.reserved "name" |-- Parse.!!! (Parse.\$\$\$ ":" |-- Parse.xname) >> Name ||
```
```   541   Parse.reserved "intro" >> K Intro ||
```
```   542   Parse.reserved "introiff" >> K IntroIff ||
```
```   543   Parse.reserved "elim" >> K Elim ||
```
```   544   Parse.reserved "dest" >> K Dest ||
```
```   545   Parse.reserved "solves" >> K Solves ||
```
```   546   Parse.reserved "simp" |-- Parse.!!! (Parse.\$\$\$ ":" |-- Parse.term) >> Simp ||
```
```   547   Parse.term >> Pattern;
```
```   548
```
```   549 val options =
```
```   550   Scan.optional
```
```   551     (Parse.\$\$\$ "(" |--
```
```   552       Parse.!!! (Scan.option Parse.nat -- Scan.optional (Parse.reserved "with_dups" >> K false) true
```
```   553         --| Parse.\$\$\$ ")")) (NONE, true);
```
```   554 in
```
```   555
```
```   556 val query_parser = Scan.repeat (((Scan.option Parse.minus >> is_none) -- criterion));
```
```   557
```
```   558 val _ =
```
```   559   Outer_Syntax.improper_command "find_theorems" "print theorems meeting specified criteria"
```
```   560     Keyword.diag
```
```   561     (options -- query_parser
```
```   562       >> (fn ((opt_lim, rem_dups), spec) =>
```
```   563         Toplevel.no_timing o
```
```   564         Toplevel.keep (fn state =>
```
```   565           let
```
```   566             val ctxt = Toplevel.context_of state;
```
```   567             val opt_goal = try (Proof.simple_goal o Toplevel.proof_of) state |> Option.map #goal;
```
```   568           in print_theorems ctxt opt_goal opt_lim rem_dups spec end)));
```
```   569
```
```   570 end;
```
```   571
```
```   572 end;
```