src/Pure/Tools/find_theorems.ML
 author kleing Wed Oct 21 16:41:22 2009 +1100 (2009-10-21) changeset 33036 c61fe520602b parent 33029 2fefe039edf1 child 33039 5018f6a76b3f permissions -rw-r--r--
find_theorems: better handling of abbreviations (by Timothy Bourke)
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 FindTheorems: 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   strip_abs tm
32   |> fst
33   |> map (Term.dummy_pattern o snd)
34   |> betapplys o pair tm
35   |> (fn x => Term.replace_dummy_patterns x 1)
36   |> fst;
38 fun parse_pattern ctxt nm =
39   let
40     val nm' = case Syntax.parse_term ctxt nm of Const (n, _) => n | _ => nm;
41     val consts = ProofContext.consts_of ctxt;
42   in
43     nm'
44     |> Consts.intern consts
45     |> Consts.the_abbreviation consts
46     |> snd
47     |> apply_dummies
48     handle TYPE _ => ProofContext.read_term_pattern ctxt nm
49   end;
51 fun read_criterion _ (Name name) = Name name
52   | read_criterion _ Intro = Intro
53   | read_criterion _ IntroIff = IntroIff
54   | read_criterion _ Elim = Elim
55   | read_criterion _ Dest = Dest
56   | read_criterion _ Solves = Solves
57   | read_criterion ctxt (Simp str) = Simp (ProofContext.read_term_pattern ctxt str)
58   | read_criterion ctxt (Pattern str) = Pattern (parse_pattern ctxt str);
60 fun pretty_criterion ctxt (b, c) =
61   let
62     fun prfx s = if b then s else "-" ^ s;
63   in
64     (case c of
65       Name name => Pretty.str (prfx "name: " ^ quote name)
66     | Intro => Pretty.str (prfx "intro")
67     | IntroIff => Pretty.str (prfx "introiff")
68     | Elim => Pretty.str (prfx "elim")
69     | Dest => Pretty.str (prfx "dest")
70     | Solves => Pretty.str (prfx "solves")
71     | Simp pat => Pretty.block [Pretty.str (prfx "simp:"), Pretty.brk 1,
72         Pretty.quote (Syntax.pretty_term ctxt (Term.show_dummy_patterns pat))]
73     | Pattern pat => Pretty.enclose (prfx " \"") "\""
74         [Syntax.pretty_term ctxt (Term.show_dummy_patterns pat)])
75   end;
79 (** search criterion filters **)
81 (*generated filters are to be of the form
82   input: (Facts.ref * thm)
83   output: (p:int, s:int) option, where
84     NONE indicates no match
85     p is the primary sorting criterion
86       (eg. number of assumptions in the theorem)
87     s is the secondary sorting criterion
88       (eg. size of the substitution for intro, elim and dest)
89   when applying a set of filters to a thm, fold results in:
90     (biggest p, sum of all s)
91   currently p and s only matter for intro, elim, dest and simp filters,
92   otherwise the default ordering is used.
93 *)
96 (* matching theorems *)
98 fun is_nontrivial thy = Term.is_Const o Term.head_of o ObjectLogic.drop_judgment thy;
100 (*educated guesses on HOL*)  (* FIXME broken *)
101 val boolT = Type ("bool", []);
102 val iff_const = Const ("op =", boolT --> boolT --> boolT);
104 (*extract terms from term_src, refine them to the parts that concern us,
105   if po try match them against obj else vice versa.
106   trivial matches are ignored.
107   returns: smallest substitution size*)
108 fun is_matching_thm doiff (extract_terms, refine_term) ctxt po obj term_src =
109   let
110     val thy = ProofContext.theory_of ctxt;
112     fun check_match pat = Pattern.matches thy (if po then (pat, obj) else (obj, pat));
113     fun matches pat =
114       let
115         val jpat = ObjectLogic.drop_judgment thy pat;
116         val c = Term.head_of jpat;
117         val pats =
118           if Term.is_Const c
119           then
120             if doiff andalso c = iff_const then
121               (pat :: map (ObjectLogic.ensure_propT thy) (snd (strip_comb jpat)))
122                 |> filter (is_nontrivial thy)
123             else [pat]
124           else [];
125       in filter check_match pats end;
127     fun substsize pat =
128       let val (_, subst) =
129         Pattern.match thy (if po then (pat, obj) else (obj, pat)) (Vartab.empty, Vartab.empty)
130       in Vartab.fold (fn (_, (_, t)) => fn n => size_of_term t + n) subst 0 end;
132     fun bestmatch [] = NONE
133       | bestmatch xs = SOME (foldl1 Int.min xs);
135     val match_thm = matches o refine_term;
136   in
137     maps match_thm (extract_terms term_src)
138     |> map substsize
139     |> bestmatch
140   end;
143 (* filter_name *)
145 fun filter_name str_pat (thmref, _) =
146   if match_string str_pat (Facts.name_of_ref thmref)
147   then SOME (0, 0) else NONE;
150 (* filter intro/elim/dest/solves rules *)
152 fun filter_dest ctxt goal (_, thm) =
153   let
154     val extract_dest =
155      (fn thm => if Thm.no_prems thm then [] else [Thm.full_prop_of thm],
156       hd o Logic.strip_imp_prems);
157     val prems = Logic.prems_of_goal goal 1;
159     fun try_subst prem = is_matching_thm false extract_dest ctxt true prem thm;
160     val successful = prems |> map_filter try_subst;
161   in
162     (*if possible, keep best substitution (one with smallest size)*)
163     (*dest rules always have assumptions, so a dest with one
164       assumption is as good as an intro rule with none*)
165     if not (null successful)
166     then SOME (Thm.nprems_of thm - 1, foldl1 Int.min successful) else NONE
167   end;
169 fun filter_intro doiff ctxt goal (_, thm) =
170   let
171     val extract_intro = (single o Thm.full_prop_of, Logic.strip_imp_concl);
172     val concl = Logic.concl_of_goal goal 1;
173     val ss = is_matching_thm doiff extract_intro ctxt true concl thm;
174   in
175     if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
176   end;
178 fun filter_elim ctxt goal (_, thm) =
179   if not (Thm.no_prems thm) then
180     let
181       val rule = Thm.full_prop_of thm;
182       val prems = Logic.prems_of_goal goal 1;
183       val goal_concl = Logic.concl_of_goal goal 1;
184       val rule_mp = hd (Logic.strip_imp_prems rule);
185       val rule_concl = Logic.strip_imp_concl rule;
186       fun combine t1 t2 = Const ("*combine*", dummyT --> dummyT) \$ (t1 \$ t2);
187       val rule_tree = combine rule_mp rule_concl;
188       fun goal_tree prem = combine prem goal_concl;
189       fun try_subst prem =
190         is_matching_thm false (single, I) ctxt true (goal_tree prem) rule_tree;
191       val successful = prems |> map_filter try_subst;
192     in
193       (*elim rules always have assumptions, so an elim with one
194         assumption is as good as an intro rule with none*)
195       if is_nontrivial (ProofContext.theory_of ctxt) (Thm.major_prem_of thm)
196         andalso not (null successful)
197       then SOME (Thm.nprems_of thm - 1, foldl1 Int.min successful) else NONE
198     end
199   else NONE
201 val tac_limit = Unsynchronized.ref 5;
203 fun filter_solves ctxt goal =
204   let
205     fun etacn thm i = Seq.take (! tac_limit) o etac thm i;
206     fun try_thm thm =
207       if Thm.no_prems thm then rtac thm 1 goal
208       else (etacn thm THEN_ALL_NEW (Goal.norm_hhf_tac THEN' Method.assm_tac ctxt)) 1 goal;
209   in
210     fn (_, thm) =>
211       if is_some (Seq.pull (try_thm thm))
212       then SOME (Thm.nprems_of thm, 0) else NONE
213   end;
216 (* filter_simp *)
218 fun filter_simp ctxt t (_, thm) =
219   let
220     val mksimps = Simplifier.mksimps (simpset_of ctxt);
221     val extract_simp =
222       (map Thm.full_prop_of o mksimps, #1 o Logic.dest_equals o Logic.strip_imp_concl);
223     val ss = is_matching_thm false extract_simp ctxt false t thm;
224   in
225     if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
226   end;
229 (* filter_pattern *)
231 fun get_names t = Term.add_const_names t (Term.add_free_names t []);
232 fun get_thm_names (_, thm) = get_names (Thm.full_prop_of thm);
234 (*Including all constants and frees is only sound because
235   matching uses higher-order patterns. If full matching
236   were used, then constants that may be subject to
237   beta-reduction after substitution of frees should
238   not be included for LHS set because they could be
239   thrown away by the substituted function.
240   e.g. for (?F 1 2) do not include 1 or 2, if it were
241        possible for ?F to be (% x y. 3)
242   The largest possible set should always be included on
243   the RHS.*)
245 fun filter_pattern ctxt pat =
246   let
247     val pat_consts = get_names pat;
249     fun check (t, NONE) = check (t, SOME (get_thm_names t))
250       | check ((_, thm), c as SOME thm_consts) =
251          (if pat_consts subset_string thm_consts andalso
252             Pattern.matches_subterm (ProofContext.theory_of ctxt) (pat, Thm.full_prop_of thm)
253           then SOME (0, 0) else NONE, c);
254   in check end;
257 (* interpret criteria as filters *)
259 local
261 fun err_no_goal c =
262   error ("Current goal required for " ^ c ^ " search criterion");
264 val fix_goal = Thm.prop_of;
266 fun filter_crit _ _ (Name name) = apfst (filter_name name)
267   | filter_crit _ NONE Intro = err_no_goal "intro"
268   | filter_crit _ NONE Elim = err_no_goal "elim"
269   | filter_crit _ NONE Dest = err_no_goal "dest"
270   | filter_crit _ NONE Solves = err_no_goal "solves"
271   | filter_crit ctxt (SOME goal) Intro = apfst (filter_intro false ctxt (fix_goal goal))
272   | filter_crit ctxt (SOME goal) IntroIff = apfst (filter_intro true ctxt (fix_goal goal))
273   | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt (fix_goal goal))
274   | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt (fix_goal goal))
275   | filter_crit ctxt (SOME goal) Solves = apfst (filter_solves ctxt goal)
276   | filter_crit ctxt _ (Simp pat) = apfst (filter_simp ctxt pat)
277   | filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat;
279 fun opt_not x = if is_some x then NONE else SOME (0, 0);
281 fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int)
282   | opt_add _ _ = NONE;
284 fun app_filters thm =
285   let
286     fun app (NONE, _, _) = NONE
287       | app (SOME v, _, []) = SOME (v, thm)
288       | app (r, consts, f :: fs) =
289           let val (r', consts') = f (thm, consts)
290           in app (opt_add r r', consts', fs) end;
291   in app end;
294 in
296 fun filter_criterion ctxt opt_goal (b, c) =
297   (if b then I else (apfst opt_not)) o filter_crit ctxt opt_goal c;
299 fun sorted_filter filters thms =
300   let
301     fun eval_filters thm = app_filters thm (SOME (0, 0), NONE, filters);
303     (*filters return: (number of assumptions, substitution size) option, so
304       sort (desc. in both cases) according to number of assumptions first,
305       then by the substitution size*)
306     fun thm_ord (((p0, s0), _), ((p1, s1), _)) =
307       prod_ord int_ord int_ord ((p1, s1), (p0, s0));
308   in map_filter eval_filters thms |> sort thm_ord |> map #2 end;
310 fun lazy_filter filters =
311   let
312     fun lazy_match thms = Seq.make (fn () => first_match thms)
314     and first_match [] = NONE
315       | first_match (thm :: thms) =
316           (case app_filters thm (SOME (0, 0), NONE, filters) of
317             NONE => first_match thms
318           | SOME (_, t) => SOME (t, lazy_match thms));
319   in lazy_match end;
321 end;
324 (* removing duplicates, preferring nicer names, roughly n log n *)
326 local
328 val index_ord = option_ord (K EQUAL);
329 val hidden_ord = bool_ord o pairself NameSpace.is_hidden;
330 val qual_ord = int_ord o pairself (length o Long_Name.explode);
331 val txt_ord = int_ord o pairself size;
333 fun nicer_name (x, i) (y, j) =
334   (case hidden_ord (x, y) of EQUAL =>
335     (case index_ord (i, j) of EQUAL =>
336       (case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord)
337     | ord => ord)
338   | ord => ord) <> GREATER;
340 fun rem_cdups nicer xs =
341   let
342     fun rem_c rev_seen [] = rev rev_seen
343       | rem_c rev_seen [x] = rem_c (x :: rev_seen) []
344       | rem_c rev_seen ((x as ((n, t), _)) :: (y as ((n', t'), _)) :: xs) =
345           if Thm.eq_thm_prop (t, t')
346           then rem_c rev_seen ((if nicer n n' then x else y) :: xs)
347           else rem_c (x :: rev_seen) (y :: xs)
348   in rem_c [] xs end;
350 in
352 fun nicer_shortest ctxt =
353   let
354     (* FIXME global name space!? *)
355     val space = Facts.space_of (PureThy.facts_of (ProofContext.theory_of ctxt));
357     val shorten =
358       NameSpace.extern_flags {long_names = false, short_names = false, unique_names = false} space;
360     fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =
361           nicer_name (shorten x, i) (shorten y, j)
362       | nicer (Facts.Fact _) (Facts.Named _) = true
363       | nicer (Facts.Named _) (Facts.Fact _) = false;
364   in nicer end;
366 fun rem_thm_dups nicer xs =
367   xs ~~ (1 upto length xs)
368   |> sort (TermOrd.fast_term_ord o pairself (Thm.prop_of o #2 o #1))
369   |> rem_cdups nicer
370   |> sort (int_ord o pairself #2)
371   |> map #1;
373 end;
376 (* print_theorems *)
378 fun all_facts_of ctxt =
379   maps Facts.selections
380    (Facts.dest_static [] (PureThy.facts_of (ProofContext.theory_of ctxt)) @
381     Facts.dest_static [] (ProofContext.facts_of ctxt));
383 val limit = Unsynchronized.ref 40;
385 fun find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
386   let
387     val assms =
388       ProofContext.get_fact ctxt (Facts.named "local.assms")
389         handle ERROR _ => [];
390     val add_prems = Seq.hd o TRY (Method.insert_tac assms 1);
391     val opt_goal' = Option.map add_prems opt_goal;
393     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
394     val filters = map (filter_criterion ctxt opt_goal') criteria;
396     fun find_all facts =
397       let
398         val raw_matches = sorted_filter filters facts;
400         val matches =
401           if rem_dups
402           then rem_thm_dups (nicer_shortest ctxt) raw_matches
403           else raw_matches;
405         val len = length matches;
406         val lim = the_default (! limit) opt_limit;
407       in (SOME len, Library.drop (len - lim, matches)) end;
409     val find =
410       if rem_dups orelse is_none opt_limit
411       then find_all
412       else pair NONE o Seq.list_of o Seq.take (the opt_limit) o lazy_filter filters;
414   in find (all_facts_of ctxt) end;
417 fun pretty_thm ctxt (thmref, thm) = Pretty.block
418   [Pretty.str (Facts.string_of_ref thmref), Pretty.str ":", Pretty.brk 1,
419     Display.pretty_thm ctxt thm];
421 fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
422   let
423     val start = start_timing ();
425     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
426     val (foundo, thms) = find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria;
427     val returned = length thms;
429     val tally_msg =
430       (case foundo of
431         NONE => "displaying " ^ string_of_int returned ^ " theorems"
432       | SOME found =>
433           "found " ^ string_of_int found ^ " theorems" ^
434             (if returned < found
435              then " (" ^ string_of_int returned ^ " displayed)"
436              else ""));
438     val end_msg = " in " ^ Time.toString (#cpu (end_timing start)) ^ " secs";
439   in
440     Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria)
441         :: Pretty.str "" ::
442      (if null thms then [Pretty.str ("nothing found" ^ end_msg)]
443       else
444         [Pretty.str (tally_msg ^ end_msg ^ ":"), Pretty.str ""] @
445         map (pretty_thm ctxt) thms)
446     |> Pretty.chunks |> Pretty.writeln
447   end;
451 (** command syntax **)
453 fun find_theorems_cmd ((opt_lim, rem_dups), spec) =
454   Toplevel.unknown_theory o Toplevel.keep (fn state =>
455     let
456       val proof_state = Toplevel.enter_proof_body state;
457       val ctxt = Proof.context_of proof_state;
458       val opt_goal = try Proof.flat_goal proof_state |> Option.map #2;
459     in print_theorems ctxt opt_goal opt_lim rem_dups spec end);
461 local
463 structure P = OuterParse and K = OuterKeyword;
465 val criterion =
466   P.reserved "name" |-- P.!!! (P.\$\$\$ ":" |-- P.xname) >> Name ||
467   P.reserved "intro" >> K Intro ||
468   P.reserved "introiff" >> K IntroIff ||
469   P.reserved "elim" >> K Elim ||
470   P.reserved "dest" >> K Dest ||
471   P.reserved "solves" >> K Solves ||
472   P.reserved "simp" |-- P.!!! (P.\$\$\$ ":" |-- P.term) >> Simp ||
473   P.term >> Pattern;
475 val options =
476   Scan.optional
477     (P.\$\$\$ "(" |--
478       P.!!! (Scan.option P.nat -- Scan.optional (P.reserved "with_dups" >> K false) true
479         --| P.\$\$\$ ")")) (NONE, true);
480 in
482 val _ =
483   OuterSyntax.improper_command "find_theorems" "print theorems meeting specified criteria" K.diag
484     (options -- Scan.repeat (((Scan.option P.minus >> is_none) -- criterion))
485       >> (Toplevel.no_timing oo find_theorems_cmd));
487 end;
489 end;