src/Pure/Tools/find_theorems.ML
 author haftmann Wed Oct 21 08:14:38 2009 +0200 (2009-10-21) changeset 33038 8f9594c31de4 parent 33037 b22e44496dc2 child 33039 5018f6a76b3f permissions -rw-r--r--
dropped redundant gen_ prefix
```     1 (*  Title:      Pure/Tools/find_theorems.ML
```
```     2     Author:     Rafal Kolanski and Gerwin Klein, NICTA
```
```     3
```
```     4 Retrieve theorems from proof context.
```
```     5 *)
```
```     6
```
```     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;
```
```    20
```
```    21 structure FindTheorems: FIND_THEOREMS =
```
```    22 struct
```
```    23
```
```    24 (** search criteria **)
```
```    25
```
```    26 datatype 'term criterion =
```
```    27   Name of string | Intro | IntroIff | Elim | Dest | Solves | Simp of 'term |
```
```    28   Pattern of 'term;
```
```    29
```
```    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
```
```    36   | read_criterion ctxt (Simp str) = Simp (ProofContext.read_term_pattern ctxt str)
```
```    37   | read_criterion ctxt (Pattern str) = Pattern (ProofContext.read_term_pattern ctxt str);
```
```    38
```
```    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;
```
```    55
```
```    56
```
```    57
```
```    58 (** search criterion filters **)
```
```    59
```
```    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 *)
```
```    73
```
```    74
```
```    75 (* matching theorems *)
```
```    76
```
```    77 fun is_nontrivial thy = Term.is_Const o Term.head_of o ObjectLogic.drop_judgment thy;
```
```    78
```
```    79 (*educated guesses on HOL*)  (* FIXME broken *)
```
```    80 val boolT = Type ("bool", []);
```
```    81 val iff_const = Const ("op =", boolT --> boolT --> boolT);
```
```    82
```
```    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;
```
```    90
```
```    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;
```
```   105
```
```   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;
```
```   110
```
```   111     fun bestmatch [] = NONE
```
```   112       | bestmatch xs = SOME (foldr1 Int.min xs);
```
```   113
```
```   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;
```
```   120
```
```   121
```
```   122 (* filter_name *)
```
```   123
```
```   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;
```
```   127
```
```   128
```
```   129 (* filter intro/elim/dest/solves rules *)
```
```   130
```
```   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;
```
```   137
```
```   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;
```
```   147
```
```   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;
```
```   156
```
```   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
```
```   179
```
```   180 val tac_limit = Unsynchronized.ref 5;
```
```   181
```
```   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;
```
```   193
```
```   194
```
```   195 (* filter_simp *)
```
```   196
```
```   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;
```
```   206
```
```   207
```
```   208 (* filter_pattern *)
```
```   209
```
```   210 fun get_names t = Term.add_const_names t (Term.add_free_names t []);
```
```   211 fun get_thm_names (_, thm) = get_names (Thm.full_prop_of thm);
```
```   212
```
```   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.*)
```
```   223
```
```   224 fun filter_pattern ctxt pat =
```
```   225   let
```
```   226     val pat_consts = get_names pat;
```
```   227
```
```   228     fun check (t, NONE) = check (t, SOME (get_thm_names t))
```
```   229       | check ((_, thm), c as SOME thm_consts) =
```
```   230          (if subset (op =) (pat_consts, 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;
```
```   234
```
```   235
```
```   236 (* interpret criteria as filters *)
```
```   237
```
```   238 local
```
```   239
```
```   240 fun err_no_goal c =
```
```   241   error ("Current goal required for " ^ c ^ " search criterion");
```
```   242
```
```   243 val fix_goal = Thm.prop_of;
```
```   244
```
```   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;
```
```   257
```
```   258 fun opt_not x = if is_some x then NONE else SOME (0, 0);
```
```   259
```
```   260 fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int)
```
```   261   | opt_add _ _ = NONE;
```
```   262
```
```   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;
```
```   271
```
```   272
```
```   273 in
```
```   274
```
```   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;
```
```   277
```
```   278 fun sorted_filter filters thms =
```
```   279   let
```
```   280     fun eval_filters thm = app_filters thm (SOME (0, 0), NONE, filters);
```
```   281
```
```   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;
```
```   288
```
```   289 fun lazy_filter filters =
```
```   290   let
```
```   291     fun lazy_match thms = Seq.make (fn () => first_match thms)
```
```   292
```
```   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;
```
```   299
```
```   300 end;
```
```   301
```
```   302
```
```   303 (* removing duplicates, preferring nicer names, roughly n log n *)
```
```   304
```
```   305 local
```
```   306
```
```   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;
```
```   311
```
```   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;
```
```   318
```
```   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;
```
```   328
```
```   329 in
```
```   330
```
```   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));
```
```   335
```
```   336     val shorten =
```
```   337       NameSpace.extern_flags {long_names = false, short_names = false, unique_names = false} space;
```
```   338
```
```   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;
```
```   344
```
```   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;
```
```   351
```
```   352 end;
```
```   353
```
```   354
```
```   355 (* print_theorems *)
```
```   356
```
```   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));
```
```   361
```
```   362 val limit = Unsynchronized.ref 40;
```
```   363
```
```   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;
```
```   371
```
```   372     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
```
```   373     val filters = map (filter_criterion ctxt opt_goal') criteria;
```
```   374
```
```   375     fun find_all facts =
```
```   376       let
```
```   377         val raw_matches = sorted_filter filters facts;
```
```   378
```
```   379         val matches =
```
```   380           if rem_dups
```
```   381           then rem_thm_dups (nicer_shortest ctxt) raw_matches
```
```   382           else raw_matches;
```
```   383
```
```   384         val len = length matches;
```
```   385         val lim = the_default (! limit) opt_limit;
```
```   386       in (SOME len, Library.drop (len - lim, matches)) end;
```
```   387
```
```   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;
```
```   392
```
```   393   in find (all_facts_of ctxt) end;
```
```   394
```
```   395
```
```   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];
```
```   399
```
```   400 fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
```
```   401   let
```
```   402     val start = start_timing ();
```
```   403
```
```   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;
```
```   407
```
```   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 ""));
```
```   416
```
```   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;
```
```   427
```
```   428
```
```   429
```
```   430 (** command syntax **)
```
```   431
```
```   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);
```
```   439
```
```   440 local
```
```   441
```
```   442 structure P = OuterParse and K = OuterKeyword;
```
```   443
```
```   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;
```
```   453
```
```   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
```
```   460
```
```   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));
```
```   465
```
```   466 end;
```
```   467
```
```   468 end;
```