src/Pure/Tools/find_theorems.ML
 author Timothy Bourke Mon Mar 30 12:25:52 2009 +1100 (2009-03-30) changeset 30785 15f64e05e703 parent 30693 c672c8162f4b child 30822 8aac4b974280 permissions -rw-r--r--
Limit the number of results returned by auto_solves.
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 | Elim | Dest | Solves | Simp of 'term |
11     Pattern of 'term
12   val tac_limit: int ref
13   val limit: int 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 FindTheorems: FIND_THEOREMS =
22 struct
24 (** search criteria **)
26 datatype 'term criterion =
27   Name of string | Intro | Elim | Dest | Solves | Simp of 'term |
28   Pattern of 'term;
30 fun read_criterion _ (Name name) = Name name
31   | read_criterion _ Intro = Intro
32   | read_criterion _ Elim = Elim
33   | read_criterion _ Dest = Dest
34   | read_criterion _ Solves = Solves
35   | read_criterion ctxt (Simp str) = Simp (ProofContext.read_term_pattern ctxt str)
36   | read_criterion ctxt (Pattern str) = Pattern (ProofContext.read_term_pattern ctxt str);
38 fun pretty_criterion ctxt (b, c) =
39   let
40     fun prfx s = if b then s else "-" ^ s;
41   in
42     (case c of
43       Name name => Pretty.str (prfx "name: " ^ quote name)
44     | Intro => Pretty.str (prfx "intro")
45     | Elim => Pretty.str (prfx "elim")
46     | Dest => Pretty.str (prfx "dest")
47     | Solves => Pretty.str (prfx "solves")
48     | Simp pat => Pretty.block [Pretty.str (prfx "simp:"), Pretty.brk 1,
49         Pretty.quote (Syntax.pretty_term ctxt (Term.show_dummy_patterns pat))]
50     | Pattern pat => Pretty.enclose (prfx " \"") "\""
51         [Syntax.pretty_term ctxt (Term.show_dummy_patterns pat)])
52   end;
56 (** search criterion filters **)
58 (*generated filters are to be of the form
59   input: (Facts.ref * thm)
60   output: (p:int, s:int) option, where
61     NONE indicates no match
62     p is the primary sorting criterion
63       (eg. number of assumptions in the theorem)
64     s is the secondary sorting criterion
65       (eg. size of the substitution for intro, elim and dest)
66   when applying a set of filters to a thm, fold results in:
67     (biggest p, sum of all s)
68   currently p and s only matter for intro, elim, dest and simp filters,
69   otherwise the default ordering is used.
70 *)
73 (* matching theorems *)
75 fun is_nontrivial thy = Term.is_Const o Term.head_of o ObjectLogic.drop_judgment thy;
77 (*extract terms from term_src, refine them to the parts that concern us,
78   if po try match them against obj else vice versa.
79   trivial matches are ignored.
80   returns: smallest substitution size*)
81 fun is_matching_thm (extract_terms, refine_term) ctxt po obj term_src =
82   let
83     val thy = ProofContext.theory_of ctxt;
85     fun matches pat =
86       is_nontrivial thy pat andalso
87       Pattern.matches thy (if po then (pat, obj) else (obj, pat));
89     fun substsize pat =
90       let val (_, subst) =
91         Pattern.match thy (if po then (pat, obj) else (obj, pat)) (Vartab.empty, Vartab.empty)
92       in Vartab.fold (fn (_, (_, t)) => fn n => size_of_term t + n) subst 0 end;
94     fun bestmatch [] = NONE
95      |  bestmatch xs = SOME (foldr1 Int.min xs);
97     val match_thm = matches o refine_term;
98   in
99     map (substsize o refine_term) (filter match_thm (extract_terms term_src))
100     |> bestmatch
101   end;
104 (* filter_name *)
106 fun filter_name str_pat (thmref, _) =
107   if match_string str_pat (Facts.name_of_ref thmref)
108   then SOME (0, 0) else NONE;
111 (* filter intro/elim/dest/solves rules *)
113 fun filter_dest ctxt goal (_, thm) =
114   let
115     val extract_dest =
116      (fn thm => if Thm.no_prems thm then [] else [Thm.full_prop_of thm],
117       hd o Logic.strip_imp_prems);
118     val prems = Logic.prems_of_goal goal 1;
120     fun try_subst prem = is_matching_thm extract_dest ctxt true prem thm;
121     val successful = prems |> map_filter try_subst;
122   in
123     (*if possible, keep best substitution (one with smallest size)*)
124     (*dest rules always have assumptions, so a dest with one
125       assumption is as good as an intro rule with none*)
126     if not (null successful)
127     then SOME (Thm.nprems_of thm - 1, foldr1 Int.min successful) else NONE
128   end;
130 fun filter_intro ctxt goal (_, thm) =
131   let
132     val extract_intro = (single o Thm.full_prop_of, Logic.strip_imp_concl);
133     val concl = Logic.concl_of_goal goal 1;
134     val ss = is_matching_thm extract_intro ctxt true concl thm;
135   in
136     if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
137   end;
139 fun filter_elim ctxt goal (_, thm) =
140   if not (Thm.no_prems thm) then
141     let
142       val rule = Thm.full_prop_of thm;
143       val prems = Logic.prems_of_goal goal 1;
144       val goal_concl = Logic.concl_of_goal goal 1;
145       val rule_mp = hd (Logic.strip_imp_prems rule);
146       val rule_concl = Logic.strip_imp_concl rule;
147       fun combine t1 t2 = Const ("*combine*", dummyT --> dummyT) \$ (t1 \$ t2);
148       val rule_tree = combine rule_mp rule_concl;
149       fun goal_tree prem = combine prem goal_concl;
150       fun try_subst prem =
151         is_matching_thm (single, I) ctxt true (goal_tree prem) rule_tree;
152       val successful = prems |> map_filter try_subst;
153     in
154     (*elim rules always have assumptions, so an elim with one
155       assumption is as good as an intro rule with none*)
156       if is_nontrivial (ProofContext.theory_of ctxt) (Thm.major_prem_of thm)
157         andalso not (null successful)
158       then SOME (Thm.nprems_of thm - 1, foldr1 Int.min successful) else NONE
159     end
160   else NONE
162 val tac_limit = ref 5;
164 fun filter_solves ctxt goal =
165   let
166     val baregoal = Logic.get_goal (Thm.prop_of goal) 1;
168     fun etacn thm i = Seq.take (! tac_limit) o etac thm i;
169     fun try_thm thm =
170       if Thm.no_prems thm then rtac thm 1 goal
171       else (etacn thm THEN_ALL_NEW (Goal.norm_hhf_tac THEN' Method.assm_tac ctxt)) 1 goal;
172   in
173     fn (_, thm) =>
174       if (is_some o Seq.pull o try_thm) thm
175       then SOME (Thm.nprems_of thm, 0) else NONE
176   end;
179 (* filter_simp *)
181 fun filter_simp ctxt t (_, thm) =
182   let
183     val mksimps = Simplifier.mksimps (Simplifier.local_simpset_of ctxt);
184     val extract_simp =
185       (map Thm.full_prop_of o mksimps, #1 o Logic.dest_equals o Logic.strip_imp_concl);
186     val ss = is_matching_thm extract_simp ctxt false t thm;
187   in
188     if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
189   end;
192 (* filter_pattern *)
194 fun get_names t = (Term.add_const_names t []) union (Term.add_free_names t []);
195 fun get_thm_names (_, thm) = get_names (Thm.full_prop_of thm);
197 (*Including all constants and frees is only sound because
198   matching uses higher-order patterns. If full matching
199   were used, then constants that may be subject to
200   beta-reduction after substitution of frees should
201   not be included for LHS set because they could be
202   thrown away by the substituted function.
203   e.g. for (?F 1 2) do not include 1 or 2, if it were
204        possible for ?F to be (% x y. 3)
205   The largest possible set should always be included on
206   the RHS.*)
208 fun filter_pattern ctxt pat =
209   let
210     val pat_consts = get_names pat;
212     fun check (t, NONE) = check (t, SOME (get_thm_names t))
213       | check ((_, thm), c as SOME thm_consts) =
214           (if pat_consts subset_string thm_consts
215               andalso (Pattern.matches_subterm (ProofContext.theory_of ctxt)
216                                                (pat, Thm.full_prop_of thm))
217            then SOME (0, 0) else NONE, c);
218   in check end;
221 (* interpret criteria as filters *)
223 local
225 fun err_no_goal c =
226   error ("Current goal required for " ^ c ^ " search criterion");
228 val fix_goal = Thm.prop_of;
229 val fix_goalo = Option.map fix_goal;
231 fun filter_crit _ _ (Name name) = apfst (filter_name name)
232   | filter_crit _ NONE Intro = err_no_goal "intro"
233   | filter_crit _ NONE Elim = err_no_goal "elim"
234   | filter_crit _ NONE Dest = err_no_goal "dest"
235   | filter_crit _ NONE Solves = err_no_goal "solves"
236   | filter_crit ctxt (SOME goal) Intro = apfst (filter_intro ctxt (fix_goal goal))
237   | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt (fix_goal goal))
238   | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt (fix_goal goal))
239   | filter_crit ctxt (SOME goal) Solves = apfst (filter_solves ctxt goal)
240   | filter_crit ctxt _ (Simp pat) = apfst (filter_simp ctxt pat)
241   | filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat;
243 fun opt_not x = if is_some x then NONE else SOME (0, 0);
245 fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int)
246   | opt_add _ _ = NONE;
248 fun app_filters thm =
249   let
250     fun app (NONE, _, _) = NONE
251       | app (SOME v, consts, []) = SOME (v, thm)
252       | app (r, consts, f :: fs) =
253           let val (r', consts') = f (thm, consts)
254           in app (opt_add r r', consts', fs) end;
255   in app end;
258 in
260 fun filter_criterion ctxt opt_goal (b, c) =
261   (if b then I else (apfst opt_not)) o filter_crit ctxt opt_goal c;
263 fun sorted_filter filters thms =
264   let
265     fun eval_filters thm = app_filters thm (SOME (0, 0), NONE, filters);
267     (*filters return: (number of assumptions, substitution size) option, so
268       sort (desc. in both cases) according to number of assumptions first,
269       then by the substitution size*)
270     fun thm_ord (((p0, s0), _), ((p1, s1), _)) =
271       prod_ord int_ord int_ord ((p1, s1), (p0, s0));
272   in map_filter eval_filters thms |> sort thm_ord |> map #2 end;
274 fun lazy_filter filters = let
275     fun lazy_match thms = Seq.make (fn () => first_match thms)
277     and first_match [] = NONE
278       | first_match (thm::thms) =
279           case app_filters thm (SOME (0, 0), NONE, filters) of
280             NONE => first_match thms
281           | SOME (_, t) => SOME (t, lazy_match thms);
282   in lazy_match end;
283 end;
286 (* removing duplicates, preferring nicer names, roughly n log n *)
288 local
290 val index_ord = option_ord (K EQUAL);
291 val hidden_ord = bool_ord o pairself NameSpace.is_hidden;
292 val qual_ord = int_ord o pairself (length o Long_Name.explode);
293 val txt_ord = int_ord o pairself size;
295 fun nicer_name (x, i) (y, j) =
296   (case hidden_ord (x, y) of EQUAL =>
297     (case index_ord (i, j) of EQUAL =>
298       (case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord)
299     | ord => ord)
300   | ord => ord) <> GREATER;
302 fun rem_cdups nicer xs =
303   let
304     fun rem_c rev_seen [] = rev rev_seen
305       | rem_c rev_seen [x] = rem_c (x :: rev_seen) []
306       | rem_c rev_seen ((x as ((n, t), _)) :: (y as ((n', t'), _)) :: xs) =
307         if Thm.eq_thm_prop (t, t')
308         then rem_c rev_seen ((if nicer n n' then x else y) :: xs)
309         else rem_c (x :: rev_seen) (y :: xs)
310   in rem_c [] xs end;
312 in
314 fun nicer_shortest ctxt =
315   let
316     (* FIXME global name space!? *)
317     val space = Facts.space_of (PureThy.facts_of (ProofContext.theory_of ctxt));
319     val shorten =
320       NameSpace.extern_flags {long_names = false, short_names = false, unique_names = false} space;
322     fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =
323           nicer_name (shorten x, i) (shorten y, j)
324       | nicer (Facts.Fact _) (Facts.Named _) = true
325       | nicer (Facts.Named _) (Facts.Fact _) = false;
326   in nicer end;
328 fun rem_thm_dups nicer xs =
329   xs ~~ (1 upto length xs)
330   |> sort (TermOrd.fast_term_ord o pairself (Thm.prop_of o #2 o #1))
331   |> rem_cdups nicer
332   |> sort (int_ord o pairself #2)
333   |> map #1;
335 end;
338 (* print_theorems *)
340 fun all_facts_of ctxt =
341   maps Facts.selections
342    (Facts.dest_static [] (PureThy.facts_of (ProofContext.theory_of ctxt)) @
343     Facts.dest_static [] (ProofContext.facts_of ctxt));
345 val limit = ref 40;
347 fun find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
348   let
349     val assms = ProofContext.get_fact ctxt (Facts.named "local.assms")
350                 handle ERROR _ => [];
351     val add_prems = Seq.hd o (TRY (Method.insert_tac assms 1));
352     val opt_goal' = Option.map add_prems opt_goal;
354     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
355     val filters = map (filter_criterion ctxt opt_goal') criteria;
357     fun find_all facts =
358       let
359         val raw_matches = sorted_filter filters facts;
361         val matches =
362           if rem_dups
363           then rem_thm_dups (nicer_shortest ctxt) raw_matches
364           else raw_matches;
366         val len = length matches;
367         val lim = the_default (! limit) opt_limit;
368       in (SOME len, Library.drop (len - lim, matches)) end;
370     val find =
371       if rem_dups orelse is_none opt_limit
372       then find_all
373       else pair NONE o Seq.list_of o Seq.take (the opt_limit) o lazy_filter filters
375   in find (all_facts_of ctxt) end;
378 fun pretty_thm ctxt (thmref, thm) = Pretty.block
379   [Pretty.str (Facts.string_of_ref thmref), Pretty.str ":", Pretty.brk 1,
380     ProofContext.pretty_thm ctxt thm];
382 fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
383   let
384     val start = start_timing ();
386     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
387     val (foundo, thms) = find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria;
388     val returned = length thms;
390     val tally_msg =
391       case foundo of
392         NONE => "displaying " ^ string_of_int returned ^ " theorems"
393       | SOME found => "found " ^ string_of_int found ^ " theorems" ^
394                       (if returned < found
395                        then " (" ^ string_of_int returned ^ " displayed)"
396                        else "");
398     val end_msg = " in " ^ Time.toString (#all (end_timing start)) ^ " secs";
399   in
400     Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria)
401         :: Pretty.str "" ::
402      (if null thms then [Pretty.str ("nothing found" ^ end_msg)]
403       else
404         [Pretty.str (tally_msg ^ end_msg ^ ":"), Pretty.str ""] @
405         map (pretty_thm ctxt) thms)
406     |> Pretty.chunks |> Pretty.writeln
407   end;
410 (** command syntax **)
412 fun find_theorems_cmd ((opt_lim, rem_dups), spec) =
413   Toplevel.unknown_theory o Toplevel.keep (fn state =>
414   let
415     val proof_state = Toplevel.enter_proof_body state;
416     val ctxt = Proof.context_of proof_state;
417     val opt_goal = try Proof.get_goal proof_state |> Option.map (#2 o #2);
418   in print_theorems ctxt opt_goal opt_lim rem_dups spec end);
420 local
422 structure P = OuterParse and K = OuterKeyword;
424 val criterion =
425   P.reserved "name" |-- P.!!! (P.\$\$\$ ":" |-- P.xname) >> Name ||
426   P.reserved "intro" >> K Intro ||
427   P.reserved "elim" >> K Elim ||
428   P.reserved "dest" >> K Dest ||
429   P.reserved "solves" >> K Solves ||
430   P.reserved "simp" |-- P.!!! (P.\$\$\$ ":" |-- P.term) >> Simp ||
431   P.term >> Pattern;
433 val options =
434   Scan.optional
435     (P.\$\$\$ "(" |--
436       P.!!! (Scan.option P.nat -- Scan.optional (P.reserved "with_dups" >> K false) true
437         --| P.\$\$\$ ")")) (NONE, true);
438 in
440 val _ =
441   OuterSyntax.improper_command "find_theorems" "print theorems meeting specified criteria" K.diag
442     (options -- Scan.repeat (((Scan.option P.minus >> is_none) -- criterion))
443       >> (Toplevel.no_timing oo find_theorems_cmd));
445 end;
447 end;