src/Pure/Tools/find_theorems.ML
 author wenzelm Sat Mar 20 17:33:11 2010 +0100 (2010-03-20) changeset 35845 e5980f0ad025 parent 35625 9c818cab0dd0 child 36950 75b8f26f2f07 permissions -rw-r--r--
renamed varify/unvarify operations to varify_global/unvarify_global to emphasize that these only work in a global situation;
1 (*  Title:      Pure/Tools/find_theorems.ML
2     Author:     Rafal Kolanski and Gerwin Klein, NICTA
4 Retrieve theorems from proof context.
5 *)
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   val tac_limit: int Unsynchronized.ref
13   val limit: int Unsynchronized.ref
14   val find_theorems: Proof.context -> thm option -> int option -> bool ->
15     (bool * string criterion) list -> int option * (Facts.ref * thm) list
16   val pretty_thm: Proof.context -> Facts.ref * thm -> Pretty.T
17   val print_theorems: Proof.context -> thm option -> int option -> bool ->
18     (bool * string criterion) list -> unit
19 end;
21 structure Find_Theorems: FIND_THEOREMS =
22 struct
24 (** search criteria **)
26 datatype 'term criterion =
27   Name of string | Intro | IntroIff | Elim | Dest | Solves | Simp of 'term |
28   Pattern of 'term;
30 fun apply_dummies tm =
31   let
32     val (xs, _) = Term.strip_abs tm;
33     val tm' = Term.betapplys (tm, map (Term.dummy_pattern o #2) xs);
34   in #1 (Term.replace_dummy_patterns tm' 1) end;
36 fun parse_pattern ctxt nm =
37   let
38     val consts = ProofContext.consts_of ctxt;
39     val nm' =
40       (case Syntax.parse_term ctxt nm of
41         Const (c, _) => c
42       | _ => Consts.intern consts nm);
43   in
44     (case try (Consts.the_abbreviation consts) nm' of
45       SOME (_, rhs) => apply_dummies (ProofContext.expand_abbrevs ctxt rhs)
46     | NONE => ProofContext.read_term_pattern ctxt nm)
47   end;
49 fun read_criterion _ (Name name) = Name name
50   | read_criterion _ Intro = Intro
51   | read_criterion _ IntroIff = IntroIff
52   | read_criterion _ Elim = Elim
53   | read_criterion _ Dest = Dest
54   | read_criterion _ Solves = Solves
55   | read_criterion ctxt (Simp str) = Simp (ProofContext.read_term_pattern ctxt str)
56   | read_criterion ctxt (Pattern str) = Pattern (parse_pattern ctxt str);
58 fun pretty_criterion ctxt (b, c) =
59   let
60     fun prfx s = if b then s else "-" ^ s;
61   in
62     (case c of
63       Name name => Pretty.str (prfx "name: " ^ quote name)
64     | Intro => Pretty.str (prfx "intro")
65     | IntroIff => Pretty.str (prfx "introiff")
66     | Elim => Pretty.str (prfx "elim")
67     | Dest => Pretty.str (prfx "dest")
68     | Solves => Pretty.str (prfx "solves")
69     | Simp pat => Pretty.block [Pretty.str (prfx "simp:"), Pretty.brk 1,
70         Pretty.quote (Syntax.pretty_term ctxt (Term.show_dummy_patterns pat))]
71     | Pattern pat => Pretty.enclose (prfx " \"") "\""
72         [Syntax.pretty_term ctxt (Term.show_dummy_patterns pat)])
73   end;
77 (** search criterion filters **)
79 (*generated filters are to be of the form
80   input: (Facts.ref * thm)
81   output: (p:int, s:int) option, where
82     NONE indicates no match
83     p is the primary sorting criterion
84       (eg. number of assumptions in the theorem)
85     s is the secondary sorting criterion
86       (eg. size of the substitution for intro, elim and dest)
87   when applying a set of filters to a thm, fold results in:
88     (biggest p, sum of all s)
89   currently p and s only matter for intro, elim, dest and simp filters,
90   otherwise the default ordering is used.
91 *)
94 (* matching theorems *)
96 fun is_nontrivial thy = Term.is_Const o Term.head_of o Object_Logic.drop_judgment thy;
98 (*educated guesses on HOL*)  (* FIXME broken *)
99 val boolT = Type ("bool", []);
100 val iff_const = Const ("op =", boolT --> boolT --> boolT);
102 (*extract terms from term_src, refine them to the parts that concern us,
103   if po try match them against obj else vice versa.
104   trivial matches are ignored.
105   returns: smallest substitution size*)
106 fun is_matching_thm doiff (extract_terms, refine_term) ctxt po obj term_src =
107   let
108     val thy = ProofContext.theory_of ctxt;
110     fun check_match pat = Pattern.matches thy (if po then (pat, obj) else (obj, pat));
111     fun matches pat =
112       let
113         val jpat = Object_Logic.drop_judgment thy pat;
114         val c = Term.head_of jpat;
115         val pats =
116           if Term.is_Const c
117           then
118             if doiff andalso c = iff_const then
119               (pat :: map (Object_Logic.ensure_propT thy) (snd (strip_comb jpat)))
120                 |> filter (is_nontrivial thy)
121             else [pat]
122           else [];
123       in filter check_match pats end;
125     fun substsize pat =
126       let val (_, subst) =
127         Pattern.match thy (if po then (pat, obj) else (obj, pat)) (Vartab.empty, Vartab.empty)
128       in Vartab.fold (fn (_, (_, t)) => fn n => size_of_term t + n) subst 0 end;
130     fun bestmatch [] = NONE
131       | bestmatch xs = SOME (foldl1 Int.min xs);
133     val match_thm = matches o refine_term;
134   in
135     maps match_thm (extract_terms term_src)
136     |> map substsize
137     |> bestmatch
138   end;
141 (* filter_name *)
143 fun filter_name str_pat (thmref, _) =
144   if match_string str_pat (Facts.name_of_ref thmref)
145   then SOME (0, 0) else NONE;
148 (* filter intro/elim/dest/solves rules *)
150 fun filter_dest ctxt goal (_, thm) =
151   let
152     val extract_dest =
153      (fn thm => if Thm.no_prems thm then [] else [Thm.full_prop_of thm],
154       hd o Logic.strip_imp_prems);
155     val prems = Logic.prems_of_goal goal 1;
157     fun try_subst prem = is_matching_thm false extract_dest ctxt true prem thm;
158     val successful = prems |> map_filter try_subst;
159   in
160     (*if possible, keep best substitution (one with smallest size)*)
161     (*dest rules always have assumptions, so a dest with one
162       assumption is as good as an intro rule with none*)
163     if not (null successful)
164     then SOME (Thm.nprems_of thm - 1, foldl1 Int.min successful) else NONE
165   end;
167 fun filter_intro doiff ctxt goal (_, thm) =
168   let
169     val extract_intro = (single o Thm.full_prop_of, Logic.strip_imp_concl);
170     val concl = Logic.concl_of_goal goal 1;
171     val ss = is_matching_thm doiff extract_intro ctxt true concl thm;
172   in
173     if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
174   end;
176 fun filter_elim ctxt goal (_, thm) =
177   if not (Thm.no_prems thm) then
178     let
179       val rule = Thm.full_prop_of thm;
180       val prems = Logic.prems_of_goal goal 1;
181       val goal_concl = Logic.concl_of_goal goal 1;
182       val rule_mp = hd (Logic.strip_imp_prems rule);
183       val rule_concl = Logic.strip_imp_concl rule;
184       fun combine t1 t2 = Const ("*combine*", dummyT --> dummyT) \$ (t1 \$ t2);
185       val rule_tree = combine rule_mp rule_concl;
186       fun goal_tree prem = combine prem goal_concl;
187       fun try_subst prem =
188         is_matching_thm false (single, I) ctxt true (goal_tree prem) rule_tree;
189       val successful = prems |> map_filter try_subst;
190     in
191       (*elim rules always have assumptions, so an elim with one
192         assumption is as good as an intro rule with none*)
193       if is_nontrivial (ProofContext.theory_of ctxt) (Thm.major_prem_of thm)
194         andalso not (null successful)
195       then SOME (Thm.nprems_of thm - 1, foldl1 Int.min successful) else NONE
196     end
197   else NONE
199 val tac_limit = Unsynchronized.ref 5;
201 fun filter_solves ctxt goal =
202   let
203     fun etacn thm i = Seq.take (! tac_limit) o etac thm i;
204     fun try_thm thm =
205       if Thm.no_prems thm then rtac thm 1 goal
206       else (etacn thm THEN_ALL_NEW (Goal.norm_hhf_tac THEN' Method.assm_tac ctxt)) 1 goal;
207   in
208     fn (_, thm) =>
209       if is_some (Seq.pull (try_thm thm))
210       then SOME (Thm.nprems_of thm, 0) else NONE
211   end;
214 (* filter_simp *)
216 fun filter_simp ctxt t (_, thm) =
217   let
218     val mksimps = Simplifier.mksimps (simpset_of ctxt);
219     val extract_simp =
220       (map Thm.full_prop_of o mksimps, #1 o Logic.dest_equals o Logic.strip_imp_concl);
221     val ss = is_matching_thm false extract_simp ctxt false t thm;
222   in
223     if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
224   end;
227 (* filter_pattern *)
229 fun get_names t = Term.add_const_names t (Term.add_free_names t []);
230 fun get_thm_names (_, thm) = get_names (Thm.full_prop_of thm);
232 (*Including all constants and frees is only sound because
233   matching uses higher-order patterns. If full matching
234   were used, then constants that may be subject to
235   beta-reduction after substitution of frees should
236   not be included for LHS set because they could be
237   thrown away by the substituted function.
238   e.g. for (?F 1 2) do not include 1 or 2, if it were
239        possible for ?F to be (% x y. 3)
240   The largest possible set should always be included on
241   the RHS.*)
243 fun filter_pattern ctxt pat =
244   let
245     val pat_consts = get_names pat;
247     fun check (t, NONE) = check (t, SOME (get_thm_names t))
248       | check ((_, thm), c as SOME thm_consts) =
249          (if subset (op =) (pat_consts, thm_consts) andalso
250             Pattern.matches_subterm (ProofContext.theory_of ctxt) (pat, Thm.full_prop_of thm)
251           then SOME (0, 0) else NONE, c);
252   in check end;
255 (* interpret criteria as filters *)
257 local
259 fun err_no_goal c =
260   error ("Current goal required for " ^ c ^ " search criterion");
262 val fix_goal = Thm.prop_of;
264 fun filter_crit _ _ (Name name) = apfst (filter_name name)
265   | filter_crit _ NONE Intro = err_no_goal "intro"
266   | filter_crit _ NONE Elim = err_no_goal "elim"
267   | filter_crit _ NONE Dest = err_no_goal "dest"
268   | filter_crit _ NONE Solves = err_no_goal "solves"
269   | filter_crit ctxt (SOME goal) Intro = apfst (filter_intro false ctxt (fix_goal goal))
270   | filter_crit ctxt (SOME goal) IntroIff = apfst (filter_intro true ctxt (fix_goal goal))
271   | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt (fix_goal goal))
272   | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt (fix_goal goal))
273   | filter_crit ctxt (SOME goal) Solves = apfst (filter_solves ctxt goal)
274   | filter_crit ctxt _ (Simp pat) = apfst (filter_simp ctxt pat)
275   | filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat;
277 fun opt_not x = if is_some x then NONE else SOME (0, 0);
279 fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int)
280   | opt_add _ _ = NONE;
282 fun app_filters thm =
283   let
284     fun app (NONE, _, _) = NONE
285       | app (SOME v, _, []) = SOME (v, thm)
286       | app (r, consts, f :: fs) =
287           let val (r', consts') = f (thm, consts)
288           in app (opt_add r r', consts', fs) end;
289   in app end;
292 in
294 fun filter_criterion ctxt opt_goal (b, c) =
295   (if b then I else (apfst opt_not)) o filter_crit ctxt opt_goal c;
297 fun sorted_filter filters thms =
298   let
299     fun eval_filters thm = app_filters thm (SOME (0, 0), NONE, filters);
301     (*filters return: (number of assumptions, substitution size) option, so
302       sort (desc. in both cases) according to number of assumptions first,
303       then by the substitution size*)
304     fun thm_ord (((p0, s0), _), ((p1, s1), _)) =
305       prod_ord int_ord int_ord ((p1, s1), (p0, s0));
306   in map_filter eval_filters thms |> sort thm_ord |> map #2 end;
308 fun lazy_filter filters =
309   let
310     fun lazy_match thms = Seq.make (fn () => first_match thms)
312     and first_match [] = NONE
313       | first_match (thm :: thms) =
314           (case app_filters thm (SOME (0, 0), NONE, filters) of
315             NONE => first_match thms
316           | SOME (_, t) => SOME (t, lazy_match thms));
317   in lazy_match end;
319 end;
322 (* removing duplicates, preferring nicer names, roughly n log n *)
324 local
326 val index_ord = option_ord (K EQUAL);
327 val hidden_ord = bool_ord o pairself Name_Space.is_hidden;
328 val qual_ord = int_ord o pairself (length o Long_Name.explode);
329 val txt_ord = int_ord o pairself size;
331 fun nicer_name (x, i) (y, j) =
332   (case hidden_ord (x, y) of EQUAL =>
333     (case index_ord (i, j) of EQUAL =>
334       (case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord)
335     | ord => ord)
336   | ord => ord) <> GREATER;
338 fun rem_cdups nicer xs =
339   let
340     fun rem_c rev_seen [] = rev rev_seen
341       | rem_c rev_seen [x] = rem_c (x :: rev_seen) []
342       | rem_c rev_seen ((x as ((n, t), _)) :: (y as ((n', t'), _)) :: xs) =
343           if Thm.eq_thm_prop (t, t')
344           then rem_c rev_seen ((if nicer n n' then x else y) :: xs)
345           else rem_c (x :: rev_seen) (y :: xs)
346   in rem_c [] xs end;
348 in
350 fun nicer_shortest ctxt =
351   let
352     (* FIXME global name space!? *)
353     val space = Facts.space_of (PureThy.facts_of (ProofContext.theory_of ctxt));
355     val shorten =
356       Name_Space.extern_flags
357         {long_names = false, short_names = false, unique_names = false} space;
359     fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =
360           nicer_name (shorten x, i) (shorten y, j)
361       | nicer (Facts.Fact _) (Facts.Named _) = true
362       | nicer (Facts.Named _) (Facts.Fact _) = false;
363   in nicer end;
365 fun rem_thm_dups nicer xs =
366   xs ~~ (1 upto length xs)
367   |> sort (Term_Ord.fast_term_ord o pairself (Thm.prop_of o #2 o #1))
368   |> rem_cdups nicer
369   |> sort (int_ord o pairself #2)
370   |> map #1;
372 end;
375 (* print_theorems *)
377 fun all_facts_of ctxt =
378   let
379     fun visible_facts facts =
380       Facts.dest_static [] facts
381       |> filter_out (Facts.is_concealed facts o #1);
382   in
383     maps Facts.selections
384      (visible_facts (PureThy.facts_of (ProofContext.theory_of ctxt)) @
385       visible_facts (ProofContext.facts_of ctxt))
386   end;
388 val limit = Unsynchronized.ref 40;
390 fun find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
391   let
392     val assms =
393       ProofContext.get_fact ctxt (Facts.named "local.assms")
394         handle ERROR _ => [];
395     val add_prems = Seq.hd o TRY (Method.insert_tac assms 1);
396     val opt_goal' = Option.map add_prems opt_goal;
398     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
399     val filters = map (filter_criterion ctxt opt_goal') criteria;
401     fun find_all facts =
402       let
403         val raw_matches = sorted_filter filters facts;
405         val matches =
406           if rem_dups
407           then rem_thm_dups (nicer_shortest ctxt) raw_matches
408           else raw_matches;
410         val len = length matches;
411         val lim = the_default (! limit) opt_limit;
412       in (SOME len, drop (Int.max (len - lim, 0)) matches) end;
414     val find =
415       if rem_dups orelse is_none opt_limit
416       then find_all
417       else pair NONE o Seq.list_of o Seq.take (the opt_limit) o lazy_filter filters;
419   in find (all_facts_of ctxt) end;
422 fun pretty_thm ctxt (thmref, thm) = Pretty.block
423   [Pretty.str (Facts.string_of_ref thmref), Pretty.str ":", Pretty.brk 1,
424     Display.pretty_thm ctxt thm];
426 fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
427   let
428     val start = start_timing ();
430     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
431     val (foundo, thms) = find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria;
432     val returned = length thms;
434     val tally_msg =
435       (case foundo of
436         NONE => "displaying " ^ string_of_int returned ^ " theorems"
437       | SOME found =>
438           "found " ^ string_of_int found ^ " theorems" ^
439             (if returned < found
440              then " (" ^ string_of_int returned ^ " displayed)"
441              else ""));
443     val end_msg = " in " ^ Time.toString (#cpu (end_timing start)) ^ " secs";
444   in
445     Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria)
446         :: Pretty.str "" ::
447      (if null thms then [Pretty.str ("nothing found" ^ end_msg)]
448       else
449         [Pretty.str (tally_msg ^ end_msg ^ ":"), Pretty.str ""] @
450         map (pretty_thm ctxt) thms)
451     |> Pretty.chunks |> Pretty.writeln
452   end;
456 (** command syntax **)
458 fun find_theorems_cmd ((opt_lim, rem_dups), spec) =
459   Toplevel.unknown_theory o Toplevel.keep (fn state =>
460     let
461       val proof_state = Toplevel.enter_proof_body state;
462       val ctxt = Proof.context_of proof_state;
463       val opt_goal = try Proof.simple_goal proof_state |> Option.map #goal;
464     in print_theorems ctxt opt_goal opt_lim rem_dups spec end);
466 local
468 structure P = OuterParse and K = OuterKeyword;
470 val criterion =
471   P.reserved "name" |-- P.!!! (P.\$\$\$ ":" |-- P.xname) >> Name ||
472   P.reserved "intro" >> K Intro ||
473   P.reserved "introiff" >> K IntroIff ||
474   P.reserved "elim" >> K Elim ||
475   P.reserved "dest" >> K Dest ||
476   P.reserved "solves" >> K Solves ||
477   P.reserved "simp" |-- P.!!! (P.\$\$\$ ":" |-- P.term) >> Simp ||
478   P.term >> Pattern;
480 val options =
481   Scan.optional
482     (P.\$\$\$ "(" |--
483       P.!!! (Scan.option P.nat -- Scan.optional (P.reserved "with_dups" >> K false) true
484         --| P.\$\$\$ ")")) (NONE, true);
485 in
487 val _ =
488   OuterSyntax.improper_command "find_theorems" "print theorems meeting specified criteria" K.diag
489     (options -- Scan.repeat (((Scan.option P.minus >> is_none) -- criterion))
490       >> (Toplevel.no_timing oo find_theorems_cmd));
492 end;
494 end;