src/Pure/Tools/find_theorems.ML
 author wenzelm Fri Oct 02 22:02:11 2009 +0200 (2009-10-02) changeset 32859 204f749f35a9 parent 32798 4b85b59a9f66 child 33029 2fefe039edf1 child 33037 b22e44496dc2 permissions -rw-r--r--
replaced Proof.get_goal state by Proof.flat_goal state, which provides the standard view on goals for (semi)automated tools;
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 read_criterion _ (Name name) = Name name
31   | read_criterion _ Intro = Intro
32   | read_criterion _ IntroIff = IntroIff
33   | read_criterion _ Elim = Elim
34   | read_criterion _ Dest = Dest
35   | read_criterion _ Solves = Solves
39 fun pretty_criterion ctxt (b, c) =
40   let
41     fun prfx s = if b then s else "-" ^ s;
42   in
43     (case c of
44       Name name => Pretty.str (prfx "name: " ^ quote name)
45     | Intro => Pretty.str (prfx "intro")
46     | IntroIff => Pretty.str (prfx "introiff")
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 (*educated guesses on HOL*)  (* FIXME broken *)
80 val boolT = Type ("bool", []);
81 val iff_const = Const ("op =", boolT --> boolT --> boolT);
83 (*extract terms from term_src, refine them to the parts that concern us,
84   if po try match them against obj else vice versa.
85   trivial matches are ignored.
86   returns: smallest substitution size*)
87 fun is_matching_thm doiff (extract_terms, refine_term) ctxt po obj term_src =
88   let
89     val thy = ProofContext.theory_of ctxt;
91     fun check_match pat = Pattern.matches thy (if po then (pat, obj) else (obj, pat));
92     fun matches pat =
93       let
94         val jpat = ObjectLogic.drop_judgment thy pat;
95         val c = Term.head_of jpat;
96         val pats =
97           if Term.is_Const c
98           then
99             if doiff andalso c = iff_const then
100               (pat :: map (ObjectLogic.ensure_propT thy) (snd (strip_comb jpat)))
101                 |> filter (is_nontrivial thy)
102             else [pat]
103           else [];
104       in filter check_match pats end;
106     fun substsize pat =
107       let val (_, subst) =
108         Pattern.match thy (if po then (pat, obj) else (obj, pat)) (Vartab.empty, Vartab.empty)
109       in Vartab.fold (fn (_, (_, t)) => fn n => size_of_term t + n) subst 0 end;
111     fun bestmatch [] = NONE
112       | bestmatch xs = SOME (foldr1 Int.min xs);
114     val match_thm = matches o refine_term;
115   in
116     maps match_thm (extract_terms term_src)
117     |> map substsize
118     |> bestmatch
119   end;
122 (* filter_name *)
124 fun filter_name str_pat (thmref, _) =
125   if match_string str_pat (Facts.name_of_ref thmref)
126   then SOME (0, 0) else NONE;
129 (* filter intro/elim/dest/solves rules *)
131 fun filter_dest ctxt goal (_, thm) =
132   let
133     val extract_dest =
134      (fn thm => if Thm.no_prems thm then [] else [Thm.full_prop_of thm],
135       hd o Logic.strip_imp_prems);
136     val prems = Logic.prems_of_goal goal 1;
138     fun try_subst prem = is_matching_thm false extract_dest ctxt true prem thm;
139     val successful = prems |> map_filter try_subst;
140   in
141     (*if possible, keep best substitution (one with smallest size)*)
142     (*dest rules always have assumptions, so a dest with one
143       assumption is as good as an intro rule with none*)
144     if not (null successful)
145     then SOME (Thm.nprems_of thm - 1, foldr1 Int.min successful) else NONE
146   end;
148 fun filter_intro doiff ctxt goal (_, thm) =
149   let
150     val extract_intro = (single o Thm.full_prop_of, Logic.strip_imp_concl);
151     val concl = Logic.concl_of_goal goal 1;
152     val ss = is_matching_thm doiff extract_intro ctxt true concl thm;
153   in
154     if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
155   end;
157 fun filter_elim ctxt goal (_, thm) =
158   if not (Thm.no_prems thm) then
159     let
160       val rule = Thm.full_prop_of thm;
161       val prems = Logic.prems_of_goal goal 1;
162       val goal_concl = Logic.concl_of_goal goal 1;
163       val rule_mp = hd (Logic.strip_imp_prems rule);
164       val rule_concl = Logic.strip_imp_concl rule;
165       fun combine t1 t2 = Const ("*combine*", dummyT --> dummyT) \$ (t1 \$ t2);
166       val rule_tree = combine rule_mp rule_concl;
167       fun goal_tree prem = combine prem goal_concl;
168       fun try_subst prem =
169         is_matching_thm false (single, I) ctxt true (goal_tree prem) rule_tree;
170       val successful = prems |> map_filter try_subst;
171     in
172       (*elim rules always have assumptions, so an elim with one
173         assumption is as good as an intro rule with none*)
174       if is_nontrivial (ProofContext.theory_of ctxt) (Thm.major_prem_of thm)
175         andalso not (null successful)
176       then SOME (Thm.nprems_of thm - 1, foldr1 Int.min successful) else NONE
177     end
178   else NONE
180 val tac_limit = Unsynchronized.ref 5;
182 fun filter_solves ctxt goal =
183   let
184     fun etacn thm i = Seq.take (! tac_limit) o etac thm i;
185     fun try_thm thm =
186       if Thm.no_prems thm then rtac thm 1 goal
187       else (etacn thm THEN_ALL_NEW (Goal.norm_hhf_tac THEN' Method.assm_tac ctxt)) 1 goal;
188   in
189     fn (_, thm) =>
190       if is_some (Seq.pull (try_thm thm))
191       then SOME (Thm.nprems_of thm, 0) else NONE
192   end;
195 (* filter_simp *)
197 fun filter_simp ctxt t (_, thm) =
198   let
199     val mksimps = Simplifier.mksimps (simpset_of ctxt);
200     val extract_simp =
201       (map Thm.full_prop_of o mksimps, #1 o Logic.dest_equals o Logic.strip_imp_concl);
202     val ss = is_matching_thm false extract_simp ctxt false t thm;
203   in
204     if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
205   end;
208 (* filter_pattern *)
211 fun get_thm_names (_, thm) = get_names (Thm.full_prop_of thm);
213 (*Including all constants and frees is only sound because
214   matching uses higher-order patterns. If full matching
215   were used, then constants that may be subject to
216   beta-reduction after substitution of frees should
217   not be included for LHS set because they could be
218   thrown away by the substituted function.
219   e.g. for (?F 1 2) do not include 1 or 2, if it were
220        possible for ?F to be (% x y. 3)
221   The largest possible set should always be included on
222   the RHS.*)
224 fun filter_pattern ctxt pat =
225   let
226     val pat_consts = get_names pat;
228     fun check (t, NONE) = check (t, SOME (get_thm_names t))
229       | check ((_, thm), c as SOME thm_consts) =
230          (if pat_consts subset_string thm_consts andalso
231             Pattern.matches_subterm (ProofContext.theory_of ctxt) (pat, Thm.full_prop_of thm)
232           then SOME (0, 0) else NONE, c);
233   in check end;
236 (* interpret criteria as filters *)
238 local
240 fun err_no_goal c =
241   error ("Current goal required for " ^ c ^ " search criterion");
243 val fix_goal = Thm.prop_of;
245 fun filter_crit _ _ (Name name) = apfst (filter_name name)
246   | filter_crit _ NONE Intro = err_no_goal "intro"
247   | filter_crit _ NONE Elim = err_no_goal "elim"
248   | filter_crit _ NONE Dest = err_no_goal "dest"
249   | filter_crit _ NONE Solves = err_no_goal "solves"
250   | filter_crit ctxt (SOME goal) Intro = apfst (filter_intro false ctxt (fix_goal goal))
251   | filter_crit ctxt (SOME goal) IntroIff = apfst (filter_intro true ctxt (fix_goal goal))
252   | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt (fix_goal goal))
253   | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt (fix_goal goal))
254   | filter_crit ctxt (SOME goal) Solves = apfst (filter_solves ctxt goal)
255   | filter_crit ctxt _ (Simp pat) = apfst (filter_simp ctxt pat)
256   | filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat;
258 fun opt_not x = if is_some x then NONE else SOME (0, 0);
260 fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int)
261   | opt_add _ _ = NONE;
263 fun app_filters thm =
264   let
265     fun app (NONE, _, _) = NONE
266       | app (SOME v, _, []) = SOME (v, thm)
267       | app (r, consts, f :: fs) =
268           let val (r', consts') = f (thm, consts)
269           in app (opt_add r r', consts', fs) end;
270   in app end;
273 in
275 fun filter_criterion ctxt opt_goal (b, c) =
276   (if b then I else (apfst opt_not)) o filter_crit ctxt opt_goal c;
278 fun sorted_filter filters thms =
279   let
280     fun eval_filters thm = app_filters thm (SOME (0, 0), NONE, filters);
282     (*filters return: (number of assumptions, substitution size) option, so
283       sort (desc. in both cases) according to number of assumptions first,
284       then by the substitution size*)
285     fun thm_ord (((p0, s0), _), ((p1, s1), _)) =
286       prod_ord int_ord int_ord ((p1, s1), (p0, s0));
287   in map_filter eval_filters thms |> sort thm_ord |> map #2 end;
289 fun lazy_filter filters =
290   let
291     fun lazy_match thms = Seq.make (fn () => first_match thms)
293     and first_match [] = NONE
294       | first_match (thm :: thms) =
295           (case app_filters thm (SOME (0, 0), NONE, filters) of
296             NONE => first_match thms
297           | SOME (_, t) => SOME (t, lazy_match thms));
298   in lazy_match end;
300 end;
303 (* removing duplicates, preferring nicer names, roughly n log n *)
305 local
307 val index_ord = option_ord (K EQUAL);
308 val hidden_ord = bool_ord o pairself NameSpace.is_hidden;
309 val qual_ord = int_ord o pairself (length o Long_Name.explode);
310 val txt_ord = int_ord o pairself size;
312 fun nicer_name (x, i) (y, j) =
313   (case hidden_ord (x, y) of EQUAL =>
314     (case index_ord (i, j) of EQUAL =>
315       (case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord)
316     | ord => ord)
317   | ord => ord) <> GREATER;
319 fun rem_cdups nicer xs =
320   let
321     fun rem_c rev_seen [] = rev rev_seen
322       | rem_c rev_seen [x] = rem_c (x :: rev_seen) []
323       | rem_c rev_seen ((x as ((n, t), _)) :: (y as ((n', t'), _)) :: xs) =
324           if Thm.eq_thm_prop (t, t')
325           then rem_c rev_seen ((if nicer n n' then x else y) :: xs)
326           else rem_c (x :: rev_seen) (y :: xs)
327   in rem_c [] xs end;
329 in
331 fun nicer_shortest ctxt =
332   let
333     (* FIXME global name space!? *)
334     val space = Facts.space_of (PureThy.facts_of (ProofContext.theory_of ctxt));
336     val shorten =
337       NameSpace.extern_flags {long_names = false, short_names = false, unique_names = false} space;
339     fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =
340           nicer_name (shorten x, i) (shorten y, j)
341       | nicer (Facts.Fact _) (Facts.Named _) = true
342       | nicer (Facts.Named _) (Facts.Fact _) = false;
343   in nicer end;
345 fun rem_thm_dups nicer xs =
346   xs ~~ (1 upto length xs)
347   |> sort (TermOrd.fast_term_ord o pairself (Thm.prop_of o #2 o #1))
348   |> rem_cdups nicer
349   |> sort (int_ord o pairself #2)
350   |> map #1;
352 end;
355 (* print_theorems *)
357 fun all_facts_of ctxt =
358   maps Facts.selections
359    (Facts.dest_static [] (PureThy.facts_of (ProofContext.theory_of ctxt)) @
360     Facts.dest_static [] (ProofContext.facts_of ctxt));
362 val limit = Unsynchronized.ref 40;
364 fun find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
365   let
366     val assms =
367       ProofContext.get_fact ctxt (Facts.named "local.assms")
368         handle ERROR _ => [];
369     val add_prems = Seq.hd o TRY (Method.insert_tac assms 1);
370     val opt_goal' = Option.map add_prems opt_goal;
372     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
373     val filters = map (filter_criterion ctxt opt_goal') criteria;
375     fun find_all facts =
376       let
377         val raw_matches = sorted_filter filters facts;
379         val matches =
380           if rem_dups
381           then rem_thm_dups (nicer_shortest ctxt) raw_matches
382           else raw_matches;
384         val len = length matches;
385         val lim = the_default (! limit) opt_limit;
386       in (SOME len, Library.drop (len - lim, matches)) end;
388     val find =
389       if rem_dups orelse is_none opt_limit
390       then find_all
391       else pair NONE o Seq.list_of o Seq.take (the opt_limit) o lazy_filter filters;
393   in find (all_facts_of ctxt) end;
396 fun pretty_thm ctxt (thmref, thm) = Pretty.block
397   [Pretty.str (Facts.string_of_ref thmref), Pretty.str ":", Pretty.brk 1,
398     Display.pretty_thm ctxt thm];
400 fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
401   let
402     val start = start_timing ();
404     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
405     val (foundo, thms) = find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria;
406     val returned = length thms;
408     val tally_msg =
409       (case foundo of
410         NONE => "displaying " ^ string_of_int returned ^ " theorems"
411       | SOME found =>
412           "found " ^ string_of_int found ^ " theorems" ^
413             (if returned < found
414              then " (" ^ string_of_int returned ^ " displayed)"
415              else ""));
417     val end_msg = " in " ^ Time.toString (#cpu (end_timing start)) ^ " secs";
418   in
419     Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria)
420         :: Pretty.str "" ::
421      (if null thms then [Pretty.str ("nothing found" ^ end_msg)]
422       else
423         [Pretty.str (tally_msg ^ end_msg ^ ":"), Pretty.str ""] @
424         map (pretty_thm ctxt) thms)
425     |> Pretty.chunks |> Pretty.writeln
426   end;
430 (** command syntax **)
432 fun find_theorems_cmd ((opt_lim, rem_dups), spec) =
433   Toplevel.unknown_theory o Toplevel.keep (fn state =>
434     let
435       val proof_state = Toplevel.enter_proof_body state;
436       val ctxt = Proof.context_of proof_state;
437       val opt_goal = try Proof.flat_goal proof_state |> Option.map #2;
438     in print_theorems ctxt opt_goal opt_lim rem_dups spec end);
440 local
442 structure P = OuterParse and K = OuterKeyword;
444 val criterion =
445   P.reserved "name" |-- P.!!! (P.\$\$\$ ":" |-- P.xname) >> Name ||
446   P.reserved "intro" >> K Intro ||
447   P.reserved "introiff" >> K IntroIff ||
448   P.reserved "elim" >> K Elim ||
449   P.reserved "dest" >> K Dest ||
450   P.reserved "solves" >> K Solves ||
451   P.reserved "simp" |-- P.!!! (P.\$\$\$ ":" |-- P.term) >> Simp ||
452   P.term >> Pattern;
454 val options =
455   Scan.optional
456     (P.\$\$\$ "(" |--
457       P.!!! (Scan.option P.nat -- Scan.optional (P.reserved "with_dups" >> K false) true
458         --| P.\$\$\$ ")")) (NONE, true);
459 in
461 val _ =
462   OuterSyntax.improper_command "find_theorems" "print theorems meeting specified criteria" K.diag
463     (options -- Scan.repeat (((Scan.option P.minus >> is_none) -- criterion))
464       >> (Toplevel.no_timing oo find_theorems_cmd));
466 end;
468 end;