(*  Title:      Pure/Tools/find_theorems.ML

     Author:     Rafal Kolanski and Gerwin Klein, NICTA

 Retrieve theorems from proof context.

 *)

 signature FIND_THEOREMS =

 sig

   datatype 'term criterion =

     Name of string | Intro | IntroIff | Elim | Dest | Solves | Simp of 'term |

     Pattern of 'term

   val tac_limit: int Unsynchronized.ref

   val limit: int Unsynchronized.ref

   val find_theorems: Proof.context -> thm option -> int option -> bool ->

     (bool * string criterion) list -> int option * (Facts.ref * thm) list

   val pretty_thm: Proof.context -> Facts.ref * thm -> Pretty.T

   val print_theorems: Proof.context -> thm option -> int option -> bool ->

     (bool * string criterion) list -> unit

 end;

 structure Find_Theorems: FIND_THEOREMS =

 struct

 (** search criteria **)

 datatype 'term criterion =

   Name of string | Intro | IntroIff | Elim | Dest | Solves | Simp of 'term |

   Pattern of 'term;

 fun apply_dummies tm =

   let

     val (xs, _) = Term.strip_abs tm;

     val tm' = Term.betapplys (tm, map (Term.dummy_pattern o #2) xs);

   in #1 (Term.replace_dummy_patterns tm' 1) end;

 fun parse_pattern ctxt nm =

   let

     val consts = ProofContext.consts_of ctxt;

     val nm' =

       (case Syntax.parse_term ctxt nm of

         Const (c, _) => c

       | _ => Consts.intern consts nm);

   in

     (case try (Consts.the_abbreviation consts) nm' of

       SOME (_, rhs) => apply_dummies (ProofContext.expand_abbrevs ctxt rhs)

     | NONE => ProofContext.read_term_pattern ctxt nm)

   end;

 fun read_criterion _ (Name name) = Name name

   | read_criterion _ Intro = Intro

   | read_criterion _ IntroIff = IntroIff

   | read_criterion _ Elim = Elim

   | read_criterion _ Dest = Dest

   | read_criterion _ Solves = Solves

   | read_criterion ctxt (Simp str) = Simp (ProofContext.read_term_pattern ctxt str)

   | read_criterion ctxt (Pattern str) = Pattern (parse_pattern ctxt str);

 fun pretty_criterion ctxt (b, c) =

   let

     fun prfx s = if b then s else "-" ^ s;

   in

     (case c of

       Name name => Pretty.str (prfx "name: " ^ quote name)

     | Intro => Pretty.str (prfx "intro")

     | IntroIff => Pretty.str (prfx "introiff")

     | Elim => Pretty.str (prfx "elim")

     | Dest => Pretty.str (prfx "dest")

     | Solves => Pretty.str (prfx "solves")

     | Simp pat => Pretty.block [Pretty.str (prfx "simp:"), Pretty.brk 1,

         Pretty.quote (Syntax.pretty_term ctxt (Term.show_dummy_patterns pat))]

     | Pattern pat => Pretty.enclose (prfx " \"") "\""

         [Syntax.pretty_term ctxt (Term.show_dummy_patterns pat)])

   end;

 (** search criterion filters **)

 (*generated filters are to be of the form

   input: (Facts.ref * thm)

   output: (p:int, s:int) option, where

     NONE indicates no match

     p is the primary sorting criterion

       (eg. number of assumptions in the theorem)

     s is the secondary sorting criterion

       (eg. size of the substitution for intro, elim and dest)

   when applying a set of filters to a thm, fold results in:

     (biggest p, sum of all s)

   currently p and s only matter for intro, elim, dest and simp filters,

   otherwise the default ordering is used.

 *)

 (* matching theorems *)

 fun is_nontrivial thy = Term.is_Const o Term.head_of o Object_Logic.drop_judgment thy;

 (*educated guesses on HOL*)  (* FIXME broken *)

 val boolT = Type ("bool", []);

 val iff_const = Const ("op =", boolT --> boolT --> boolT);

 (*extract terms from term_src, refine them to the parts that concern us,

   if po try match them against obj else vice versa.

   trivial matches are ignored.

   returns: smallest substitution size*)

 fun is_matching_thm doiff (extract_terms, refine_term) ctxt po obj term_src =

   let

     val thy = ProofContext.theory_of ctxt;

     fun check_match pat = Pattern.matches thy (if po then (pat, obj) else (obj, pat));

     fun matches pat =

       let

         val jpat = Object_Logic.drop_judgment thy pat;

         val c = Term.head_of jpat;

         val pats =

           if Term.is_Const c

           then

             if doiff andalso c = iff_const then

               (pat :: map (Object_Logic.ensure_propT thy) (snd (strip_comb jpat)))

                 |> filter (is_nontrivial thy)

             else [pat]

           else [];

       in filter check_match pats end;

     fun substsize pat =

       let val (_, subst) =

         Pattern.match thy (if po then (pat, obj) else (obj, pat)) (Vartab.empty, Vartab.empty)

       in Vartab.fold (fn (_, (_, t)) => fn n => size_of_term t + n) subst 0 end;

     fun bestmatch [] = NONE

       | bestmatch xs = SOME (foldl1 Int.min xs);

     val match_thm = matches o refine_term;

   in

     maps match_thm (extract_terms term_src)

     |> map substsize

     |> bestmatch

   end;

 (* filter_name *)

 fun filter_name str_pat (thmref, _) =

   if match_string str_pat (Facts.name_of_ref thmref)

   then SOME (0, 0) else NONE;

 (* filter intro/elim/dest/solves rules *)

 fun filter_dest ctxt goal (_, thm) =

   let

     val extract_dest =

      (fn thm => if Thm.no_prems thm then [] else [Thm.full_prop_of thm],

       hd o Logic.strip_imp_prems);

     val prems = Logic.prems_of_goal goal 1;

     fun try_subst prem = is_matching_thm false extract_dest ctxt true prem thm;

     val successful = prems |> map_filter try_subst;

   in

     (*if possible, keep best substitution (one with smallest size)*)

     (*dest rules always have assumptions, so a dest with one

       assumption is as good as an intro rule with none*)

     if not (null successful)

     then SOME (Thm.nprems_of thm - 1, foldl1 Int.min successful) else NONE

   end;

 fun filter_intro doiff ctxt goal (_, thm) =

   let

     val extract_intro = (single o Thm.full_prop_of, Logic.strip_imp_concl);

     val concl = Logic.concl_of_goal goal 1;

     val ss = is_matching_thm doiff extract_intro ctxt true concl thm;

   in

     if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE

   end;

 fun filter_elim ctxt goal (_, thm) =

   if not (Thm.no_prems thm) then

     let

       val rule = Thm.full_prop_of thm;

       val prems = Logic.prems_of_goal goal 1;

       val goal_concl = Logic.concl_of_goal goal 1;

       val rule_mp = hd (Logic.strip_imp_prems rule);

       val rule_concl = Logic.strip_imp_concl rule;

       fun combine t1 t2 = Const ("*combine*", dummyT --> dummyT) $ (t1 $ t2);

       val rule_tree = combine rule_mp rule_concl;

       fun goal_tree prem = combine prem goal_concl;

       fun try_subst prem =

         is_matching_thm false (single, I) ctxt true (goal_tree prem) rule_tree;

       val successful = prems |> map_filter try_subst;

     in

       (*elim rules always have assumptions, so an elim with one

         assumption is as good as an intro rule with none*)

       if is_nontrivial (ProofContext.theory_of ctxt) (Thm.major_prem_of thm)

         andalso not (null successful)

       then SOME (Thm.nprems_of thm - 1, foldl1 Int.min successful) else NONE

     end

   else NONE

 val tac_limit = Unsynchronized.ref 5;

 fun filter_solves ctxt goal =

   let

     fun etacn thm i = Seq.take (! tac_limit) o etac thm i;

     fun try_thm thm =

       if Thm.no_prems thm then rtac thm 1 goal

       else (etacn thm THEN_ALL_NEW (Goal.norm_hhf_tac THEN' Method.assm_tac ctxt)) 1 goal;

   in

     fn (_, thm) =>

       if is_some (Seq.pull (try_thm thm))

       then SOME (Thm.nprems_of thm, 0) else NONE

   end;

 (* filter_simp *)

 fun filter_simp ctxt t (_, thm) =

   let

     val mksimps = Simplifier.mksimps (simpset_of ctxt);

     val extract_simp =

       (map Thm.full_prop_of o mksimps, #1 o Logic.dest_equals o Logic.strip_imp_concl);

     val ss = is_matching_thm false extract_simp ctxt false t thm;

   in

     if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE

   end;

 (* filter_pattern *)

 fun get_names t = Term.add_const_names t (Term.add_free_names t []);

 fun get_thm_names (_, thm) = get_names (Thm.full_prop_of thm);

 (*Including all constants and frees is only sound because

   matching uses higher-order patterns. If full matching

   were used, then constants that may be subject to

   beta-reduction after substitution of frees should

   not be included for LHS set because they could be

   thrown away by the substituted function.

   e.g. for (?F 1 2) do not include 1 or 2, if it were

        possible for ?F to be (% x y. 3)

   The largest possible set should always be included on

   the RHS.*)

 fun filter_pattern ctxt pat =

   let

     val pat_consts = get_names pat;

     fun check (t, NONE) = check (t, SOME (get_thm_names t))

       | check ((_, thm), c as SOME thm_consts) =

          (if subset (op =) (pat_consts, thm_consts) andalso

             Pattern.matches_subterm (ProofContext.theory_of ctxt) (pat, Thm.full_prop_of thm)

           then SOME (0, 0) else NONE, c);

   in check end;

 (* interpret criteria as filters *)

 local

 fun err_no_goal c =

   error ("Current goal required for " ^ c ^ " search criterion");

 val fix_goal = Thm.prop_of;

 fun filter_crit _ _ (Name name) = apfst (filter_name name)

   | filter_crit _ NONE Intro = err_no_goal "intro"

   | filter_crit _ NONE Elim = err_no_goal "elim"

   | filter_crit _ NONE Dest = err_no_goal "dest"

   | filter_crit _ NONE Solves = err_no_goal "solves"

   | filter_crit ctxt (SOME goal) Intro = apfst (filter_intro false ctxt (fix_goal goal))

   | filter_crit ctxt (SOME goal) IntroIff = apfst (filter_intro true ctxt (fix_goal goal))

   | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt (fix_goal goal))

   | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt (fix_goal goal))

   | filter_crit ctxt (SOME goal) Solves = apfst (filter_solves ctxt goal)

   | filter_crit ctxt _ (Simp pat) = apfst (filter_simp ctxt pat)

   | filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat;

 fun opt_not x = if is_some x then NONE else SOME (0, 0);

 fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int)

   | opt_add _ _ = NONE;

 fun app_filters thm =

   let

     fun app (NONE, _, _) = NONE

       | app (SOME v, _, []) = SOME (v, thm)

       | app (r, consts, f :: fs) =

           let val (r', consts') = f (thm, consts)

           in app (opt_add r r', consts', fs) end;

   in app end;

 in

 fun filter_criterion ctxt opt_goal (b, c) =

   (if b then I else (apfst opt_not)) o filter_crit ctxt opt_goal c;

 fun sorted_filter filters thms =

   let

     fun eval_filters thm = app_filters thm (SOME (0, 0), NONE, filters);

     (*filters return: (number of assumptions, substitution size) option, so

       sort (desc. in both cases) according to number of assumptions first,

       then by the substitution size*)

     fun thm_ord (((p0, s0), _), ((p1, s1), _)) =

       prod_ord int_ord int_ord ((p1, s1), (p0, s0));

   in map_filter eval_filters thms |> sort thm_ord |> map #2 end;

 fun lazy_filter filters =

   let

     fun lazy_match thms = Seq.make (fn () => first_match thms)

     and first_match [] = NONE

       | first_match (thm :: thms) =

           (case app_filters thm (SOME (0, 0), NONE, filters) of

             NONE => first_match thms

           | SOME (_, t) => SOME (t, lazy_match thms));

   in lazy_match end;

 end;

 (* removing duplicates, preferring nicer names, roughly n log n *)

 local

 val index_ord = option_ord (K EQUAL);

 val hidden_ord = bool_ord o pairself Name_Space.is_hidden;

 val qual_ord = int_ord o pairself (length o Long_Name.explode);

 val txt_ord = int_ord o pairself size;

 fun nicer_name (x, i) (y, j) =

   (case hidden_ord (x, y) of EQUAL =>

     (case index_ord (i, j) of EQUAL =>

       (case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord)

     | ord => ord)

   | ord => ord) <> GREATER;

 fun rem_cdups nicer xs =

   let

     fun rem_c rev_seen [] = rev rev_seen

       | rem_c rev_seen [x] = rem_c (x :: rev_seen) []

       | rem_c rev_seen ((x as ((n, t), _)) :: (y as ((n', t'), _)) :: xs) =

           if Thm.eq_thm_prop (t, t')

           then rem_c rev_seen ((if nicer n n' then x else y) :: xs)

           else rem_c (x :: rev_seen) (y :: xs)

   in rem_c [] xs end;

 in

 fun nicer_shortest ctxt =

   let

     (* FIXME global name space!? *)

     val space = Facts.space_of (PureThy.facts_of (ProofContext.theory_of ctxt));

     val shorten =

       Name_Space.extern_flags

         {long_names = false, short_names = false, unique_names = false} space;

     fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =

           nicer_name (shorten x, i) (shorten y, j)

       | nicer (Facts.Fact _) (Facts.Named _) = true

       | nicer (Facts.Named _) (Facts.Fact _) = false;

   in nicer end;

 fun rem_thm_dups nicer xs =

   xs ~~ (1 upto length xs)

   |> sort (Term_Ord.fast_term_ord o pairself (Thm.prop_of o #2 o #1))

   |> rem_cdups nicer

   |> sort (int_ord o pairself #2)

   |> map #1;

 end;

 (* print_theorems *)

 fun all_facts_of ctxt =

   let

     fun visible_facts facts =

       Facts.dest_static [] facts

       |> filter_out (Facts.is_concealed facts o #1);

   in

     maps Facts.selections

      (visible_facts (PureThy.facts_of (ProofContext.theory_of ctxt)) @

       visible_facts (ProofContext.facts_of ctxt))

   end;

 val limit = Unsynchronized.ref 40;

 fun find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =

   let

     val assms =

       ProofContext.get_fact ctxt (Facts.named "local.assms")

         handle ERROR _ => [];

     val add_prems = Seq.hd o TRY (Method.insert_tac assms 1);

     val opt_goal' = Option.map add_prems opt_goal;

     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;

     val filters = map (filter_criterion ctxt opt_goal') criteria;

     fun find_all facts =

       let

         val raw_matches = sorted_filter filters facts;

         val matches =

           if rem_dups

           then rem_thm_dups (nicer_shortest ctxt) raw_matches

           else raw_matches;

         val len = length matches;

         val lim = the_default (! limit) opt_limit;

       in (SOME len, drop (Int.max (len - lim, 0)) matches) end;

     val find =

       if rem_dups orelse is_none opt_limit

       then find_all

       else pair NONE o Seq.list_of o Seq.take (the opt_limit) o lazy_filter filters;

   in find (all_facts_of ctxt) end;

 fun pretty_thm ctxt (thmref, thm) = Pretty.block

   [Pretty.str (Facts.string_of_ref thmref), Pretty.str ":", Pretty.brk 1,

     Display.pretty_thm ctxt thm];

 fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =

   let

     val start = start_timing ();

     val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;

     val (foundo, thms) = find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria;

     val returned = length thms;

     val tally_msg =

       (case foundo of

         NONE => "displaying " ^ string_of_int returned ^ " theorems"

       | SOME found =>

           "found " ^ string_of_int found ^ " theorems" ^

             (if returned < found

              then " (" ^ string_of_int returned ^ " displayed)"

              else ""));

     val end_msg = " in " ^ Time.toString (#cpu (end_timing start)) ^ " secs";

   in

     Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria)

         :: Pretty.str "" ::

      (if null thms then [Pretty.str ("nothing found" ^ end_msg)]

       else

         [Pretty.str (tally_msg ^ end_msg ^ ":"), Pretty.str ""] @

         map (pretty_thm ctxt) thms)

     |> Pretty.chunks |> Pretty.writeln

   end;

 (** command syntax **)

 fun find_theorems_cmd ((opt_lim, rem_dups), spec) =

   Toplevel.unknown_theory o Toplevel.keep (fn state =>

     let

       val proof_state = Toplevel.enter_proof_body state;

       val ctxt = Proof.context_of proof_state;

       val opt_goal = try Proof.simple_goal proof_state |> Option.map #goal;

     in print_theorems ctxt opt_goal opt_lim rem_dups spec end);

 local

 val criterion =

   Parse.reserved "name" |-- Parse.!!! (Parse.$$$ ":" |-- Parse.xname) >> Name ||

   Parse.reserved "intro" >> K Intro ||

   Parse.reserved "introiff" >> K IntroIff ||

   Parse.reserved "elim" >> K Elim ||

   Parse.reserved "dest" >> K Dest ||

   Parse.reserved "solves" >> K Solves ||

   Parse.reserved "simp" |-- Parse.!!! (Parse.$$$ ":" |-- Parse.term) >> Simp ||

   Parse.term >> Pattern;

 val options =

   Scan.optional

     (Parse.$$$ "(" |--

       Parse.!!! (Scan.option Parse.nat -- Scan.optional (Parse.reserved "with_dups" >> K false) true

         --| Parse.$$$ ")")) (NONE, true);

 in

 val _ =

   Outer_Syntax.improper_command "find_theorems" "print theorems meeting specified criteria"

     Keyword.diag

     (options -- Scan.repeat (((Scan.option Parse.minus >> is_none) -- criterion))

       >> (Toplevel.no_timing oo find_theorems_cmd));

 end;

 end;