src/Pure/Tools/find_theorems.ML
 author wenzelm Fri Feb 27 15:46:22 2009 +0100 (2009-02-27) changeset 30142 8d6145694bb5 parent 29882 src/Pure/Isar/find_theorems.ML@29154e67731d child 30143 98a986b02022 permissions -rw-r--r--
moved find_theorems.ML and find_consts.ML to Pure/Tools, collecting main implementation in one place each;
1 (*  Title:      Pure/Isar/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   val limit: int ref
10   val tac_limit: int ref
12   datatype 'term criterion =
13     Name of string | Intro | Elim | Dest | Solves | Simp of 'term |
14     Pattern of 'term
16   val find_theorems: Proof.context -> thm option -> bool ->
17     (bool * string criterion) list -> (Facts.ref * thm) list
19   val print_theorems: Proof.context -> thm option -> int option -> bool ->
20     (bool * string criterion) list -> unit
21 end;
23 structure FindTheorems: FIND_THEOREMS =
24 struct
26 (** search criteria **)
28 datatype 'term criterion =
29   Name of string | Intro | Elim | Dest | Solves | Simp of 'term |
30   Pattern of 'term;
32 fun read_criterion _ (Name name) = Name name
33   | read_criterion _ Intro = Intro
34   | read_criterion _ Elim = Elim
35   | read_criterion _ Dest = Dest
36   | read_criterion _ Solves = Solves
37   | read_criterion ctxt (Simp str) = Simp (ProofContext.read_term_pattern ctxt str)
38   | read_criterion ctxt (Pattern str) = Pattern (ProofContext.read_term_pattern ctxt str);
40 fun pretty_criterion ctxt (b, c) =
41   let
42     fun prfx s = if b then s else "-" ^ s;
43   in
44     (case c of
45       Name name => Pretty.str (prfx "name: " ^ quote name)
46     | Intro => Pretty.str (prfx "intro")
47     | Elim => Pretty.str (prfx "elim")
48     | Dest => Pretty.str (prfx "dest")
49     | Solves => Pretty.str (prfx "solves")
50     | Simp pat => Pretty.block [Pretty.str (prfx "simp:"), Pretty.brk 1,
51         Pretty.quote (Syntax.pretty_term ctxt (Term.show_dummy_patterns pat))]
52     | Pattern pat => Pretty.enclose (prfx " \"") "\""
53         [Syntax.pretty_term ctxt (Term.show_dummy_patterns pat)])
54   end;
58 (** search criterion filters **)
60 (*generated filters are to be of the form
61   input: (Facts.ref * thm)
62   output: (p:int, s:int) option, where
63     NONE indicates no match
64     p is the primary sorting criterion
65       (eg. number of assumptions in the theorem)
66     s is the secondary sorting criterion
67       (eg. size of the substitution for intro, elim and dest)
68   when applying a set of filters to a thm, fold results in:
69     (biggest p, sum of all s)
70   currently p and s only matter for intro, elim, dest and simp filters,
71   otherwise the default ordering is used.
72 *)
75 (* matching theorems *)
77 fun is_nontrivial thy = Term.is_Const o Term.head_of o ObjectLogic.drop_judgment thy;
79 (*extract terms from term_src, refine them to the parts that concern us,
80   if po try match them against obj else vice versa.
81   trivial matches are ignored.
82   returns: smallest substitution size*)
83 fun is_matching_thm (extract_terms, refine_term) ctxt po obj term_src =
84   let
85     val thy = ProofContext.theory_of ctxt;
87     fun matches pat =
88       is_nontrivial thy pat andalso
89       Pattern.matches thy (if po then (pat, obj) else (obj, pat));
91     fun substsize pat =
92       let val (_, subst) =
93         Pattern.match thy (if po then (pat, obj) else (obj, pat)) (Vartab.empty, Vartab.empty)
94       in Vartab.fold (fn (_, (_, t)) => fn n => size_of_term t + n) subst 0 end;
96     fun bestmatch [] = NONE
97      |  bestmatch xs = SOME (foldr1 Int.min xs);
99     val match_thm = matches o refine_term;
100   in
101     map (substsize o refine_term) (filter match_thm (extract_terms term_src))
102     |> bestmatch
103   end;
106 (* filter_name *)
108 fun filter_name str_pat (thmref, _) =
109   if match_string str_pat (Facts.name_of_ref thmref)
110   then SOME (0, 0) else NONE;
113 (* filter intro/elim/dest/solves rules *)
115 fun filter_dest ctxt goal (_, thm) =
116   let
117     val extract_dest =
118      (fn thm => if Thm.no_prems thm then [] else [Thm.full_prop_of thm],
119       hd o Logic.strip_imp_prems);
120     val prems = Logic.prems_of_goal goal 1;
122     fun try_subst prem = is_matching_thm extract_dest ctxt true prem thm;
123     val successful = prems |> map_filter try_subst;
124   in
125     (*if possible, keep best substitution (one with smallest size)*)
126     (*dest rules always have assumptions, so a dest with one
127       assumption is as good as an intro rule with none*)
128     if not (null successful)
129     then SOME (Thm.nprems_of thm - 1, foldr1 Int.min successful) else NONE
130   end;
132 fun filter_intro ctxt goal (_, thm) =
133   let
134     val extract_intro = (single o Thm.full_prop_of, Logic.strip_imp_concl);
135     val concl = Logic.concl_of_goal goal 1;
136     val ss = is_matching_thm extract_intro ctxt true concl thm;
137   in
138     if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
139   end;
141 fun filter_elim ctxt goal (_, thm) =
142   if not (Thm.no_prems thm) then
143     let
144       val rule = Thm.full_prop_of thm;
145       val prems = Logic.prems_of_goal goal 1;
146       val goal_concl = Logic.concl_of_goal goal 1;
147       val rule_mp = hd (Logic.strip_imp_prems rule);
148       val rule_concl = Logic.strip_imp_concl rule;
149       fun combine t1 t2 = Const ("*combine*", dummyT --> dummyT) \$ (t1 \$ t2);
150       val rule_tree = combine rule_mp rule_concl;
151       fun goal_tree prem = combine prem goal_concl;
152       fun try_subst prem =
153         is_matching_thm (single, I) ctxt true (goal_tree prem) rule_tree;
154       val successful = prems |> map_filter try_subst;
155     in
156     (*elim rules always have assumptions, so an elim with one
157       assumption is as good as an intro rule with none*)
158       if is_nontrivial (ProofContext.theory_of ctxt) (Thm.major_prem_of thm)
159         andalso not (null successful)
160       then SOME (Thm.nprems_of thm - 1, foldr1 Int.min successful) else NONE
161     end
162   else NONE
164 val tac_limit = ref 5;
166 fun filter_solves ctxt goal = let
167     val baregoal = Logic.get_goal (prop_of goal) 1;
169     fun etacn thm i = Seq.take (!tac_limit) o etac thm i;
170     fun try_thm thm = if Thm.no_prems thm then rtac thm 1 goal
171                       else (etacn thm THEN_ALL_NEW
172                              (Goal.norm_hhf_tac THEN'
173                                Method.assumption_tac ctxt)) 1 goal;
174   in
175     fn (_, thm) => if (is_some o Seq.pull o try_thm) thm
176                    then SOME (Thm.nprems_of thm, 0) else NONE
177   end;
180 (* filter_simp *)
182 fun filter_simp ctxt t (_, thm) =
183   let
184     val (_, {mk_rews = {mk, ...}, ...}) =
185       Simplifier.rep_ss (Simplifier.local_simpset_of ctxt);
186     val extract_simp =
187       (map Thm.full_prop_of o mk, #1 o Logic.dest_equals o Logic.strip_imp_concl);
188     val ss = is_matching_thm extract_simp ctxt false t thm
189   in
190     if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
191   end;
194 (* filter_pattern *)
196 fun get_names t = (Term.add_const_names t []) union (Term.add_free_names t []);
197 fun get_thm_names (_, thm) = get_names (Thm.full_prop_of thm);
198   (* Including all constants and frees is only sound because
199      matching uses higher-order patterns. If full matching
200      were used, then constants that may be subject to
201      beta-reduction after substitution of frees should
202      not be included for LHS set because they could be
203      thrown away by the substituted function.
204      e.g. for (?F 1 2) do not include 1 or 2, if it were
205           possible for ?F to be (% x y. 3)
206      The largest possible set should always be included on
207      the RHS. *)
209 fun filter_pattern ctxt pat = 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
237                                                   (fix_goal goal))
238   | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt
239                                                   (fix_goal goal))
240   | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt
241                                                   (fix_goal goal))
242   | filter_crit ctxt (SOME goal) Solves = apfst (filter_solves ctxt goal)
243   | filter_crit ctxt _ (Simp pat) = apfst (filter_simp ctxt pat)
244   | filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat;
246 fun opt_not x = if is_some x then NONE else SOME (0, 0);
248 fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int)
249   | opt_add _ _ = NONE;
251 fun app_filters thm = let
252     fun app (NONE, _, _) = NONE
253       | app (SOME v, consts, []) = SOME (v, thm)
254       | app (r, consts, f::fs) = let val (r', consts') = f (thm, consts)
255                                  in app (opt_add r r', consts', fs) end;
256   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 all_filters 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 end;
277 (* removing duplicates, preferring nicer names, roughly n log n *)
279 local
281 val index_ord = option_ord (K EQUAL);
282 val hidden_ord = bool_ord o pairself NameSpace.is_hidden;
283 val qual_ord = int_ord o pairself (length o NameSpace.explode);
284 val txt_ord = int_ord o pairself size;
286 fun nicer_name (x, i) (y, j) =
287   (case hidden_ord (x, y) of EQUAL =>
288     (case index_ord (i, j) of EQUAL =>
289       (case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord)
290     | ord => ord)
291   | ord => ord) <> GREATER;
293 fun rem_cdups nicer xs =
294   let
295     fun rem_c rev_seen [] = rev rev_seen
296       | rem_c rev_seen [x] = rem_c (x :: rev_seen) []
297       | rem_c rev_seen ((x as ((n, t), _)) :: (y as ((n', t'), _)) :: xs) =
298         if Thm.eq_thm_prop (t, t')
299         then rem_c rev_seen ((if nicer n n' then x else y) :: xs)
300         else rem_c (x :: rev_seen) (y :: xs)
301   in rem_c [] xs end;
303 in
305 fun nicer_shortest ctxt = let
306     val ns = ProofContext.theory_of ctxt
307              |> PureThy.facts_of
308              |> Facts.space_of;
310     val len_sort = sort (int_ord o (pairself size));
311     fun shorten s = (case len_sort (NameSpace.get_accesses ns s) of
312                        [] => s
313                      | s'::_ => s');
315     fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =
316           nicer_name (shorten x, i) (shorten y, j)
317       | nicer (Facts.Fact _) (Facts.Named _) = true
318       | nicer (Facts.Named _) (Facts.Fact _) = false;
319   in nicer end;
321 fun rem_thm_dups nicer xs =
322   xs ~~ (1 upto length xs)
323   |> sort (TermOrd.fast_term_ord o pairself (Thm.prop_of o #2 o #1))
324   |> rem_cdups nicer
325   |> sort (int_ord o pairself #2)
326   |> map #1;
328 end;
331 (* print_theorems *)
333 fun all_facts_of ctxt =
334   maps Facts.selections
335    (Facts.dest_static [] (PureThy.facts_of (ProofContext.theory_of ctxt)) @
336     Facts.dest_static [] (ProofContext.facts_of ctxt));
338 val limit = ref 40;
340 fun find_theorems ctxt opt_goal rem_dups raw_criteria =
341   let
342     val add_prems = Seq.hd o (TRY (Method.insert_tac
343                                      (Assumption.prems_of ctxt) 1));
344     val opt_goal' = Option.map add_prems opt_goal;
346     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
347     val filters = map (filter_criterion ctxt opt_goal') criteria;
349     val raw_matches = all_filters filters (all_facts_of ctxt);
351     val matches =
352       if rem_dups
353       then rem_thm_dups (nicer_shortest ctxt) raw_matches
354       else raw_matches;
355   in matches end;
357 fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria = let
358     val start = start_timing ();
360     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
361     val matches = find_theorems ctxt opt_goal rem_dups raw_criteria;
363     val len = length matches;
364     val lim = the_default (! limit) opt_limit;
365     val thms = Library.drop (len - lim, matches);
367     val end_msg = " in " ^
368                   (List.nth (String.tokens Char.isSpace (end_timing start), 3))
369                   ^ " secs"
370   in
371     Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria)
372         :: Pretty.str "" ::
373      (if null thms then [Pretty.str ("nothing found" ^ end_msg)]
374       else
375         [Pretty.str ("found " ^ string_of_int len ^ " theorems" ^
376           (if len <= lim then ""
377            else " (" ^ string_of_int lim ^ " displayed)")
378            ^ end_msg ^ ":"), Pretty.str ""] @
379         map Display.pretty_fact thms)
380     |> Pretty.chunks |> Pretty.writeln
381   end;
385 (** command syntax **)
387 fun find_theorems_cmd ((opt_lim, rem_dups), spec) =
388   Toplevel.unknown_theory o Toplevel.keep (fn state =>
389   let
390     val proof_state = Toplevel.enter_proof_body state;
391     val ctxt = Proof.context_of proof_state;
392     val opt_goal = try Proof.get_goal proof_state |> Option.map (#2 o #2);
393   in print_theorems ctxt opt_goal opt_lim rem_dups spec end);
395 local
397 structure P = OuterParse and K = OuterKeyword;
399 val criterion =
400   P.reserved "name" |-- P.!!! (P.\$\$\$ ":" |-- P.xname) >> Name ||
401   P.reserved "intro" >> K Intro ||
402   P.reserved "elim" >> K Elim ||
403   P.reserved "dest" >> K Dest ||
404   P.reserved "solves" >> K Solves ||
405   P.reserved "simp" |-- P.!!! (P.\$\$\$ ":" |-- P.term) >> Simp ||
406   P.term >> Pattern;
408 val options =
409   Scan.optional
410     (P.\$\$\$ "(" |--
411       P.!!! (Scan.option P.nat -- Scan.optional (P.reserved "with_dups" >> K false) true
412         --| P.\$\$\$ ")")) (NONE, true);
413 in
415 val _ =
416   OuterSyntax.improper_command "find_theorems" "print theorems meeting specified criteria" K.diag
417     (options -- Scan.repeat (((Scan.option P.minus >> is_none) -- criterion))
418       >> (Toplevel.no_timing oo find_theorems_cmd));
420 end;
422 end;