(*  Title:      Pure/Isar/find_theorems.ML

     ID:         $Id$

     Author:     Rafal Kolanski, NICTA and Tobias Nipkow, TU Muenchen

 Retrieve theorems from proof context.

 *)

 val thms_containing_limit = ref 40;

 signature FIND_THEOREMS =

 sig

   datatype 'term criterion =

     Name of string | Intro | Elim | Dest | Simp of 'term | Pattern of 'term

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

     (bool * string criterion) list -> unit

 end;

 structure FindTheorems: FIND_THEOREMS =

 struct

 (** search criteria **)

 datatype 'term criterion =

   Name of string | Intro | Elim | Dest | Simp of 'term | Pattern of 'term;

 fun read_criterion _ (Name name) = Name name

   | read_criterion _ Intro = Intro

   | read_criterion _ Elim = Elim

   | read_criterion _ Dest = Dest

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

   | read_criterion ctxt (Pattern str) = Pattern (ProofContext.read_term_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")

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

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

     | 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: (thmref * 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 ObjectLogic.drop_judgment thy;

 (*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 (extract_terms, refine_term) ctxt po obj term_src =

   let

     val thy = ProofContext.theory_of ctxt;

     fun matches pat =

       is_nontrivial thy pat andalso

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

     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 (foldr1 Int.min xs);

     val match_thm = matches o refine_term;

   in

     map (substsize o refine_term)

         (filter match_thm (extract_terms term_src)) |> bestmatch

   end;

 (* filter_name *)

 fun match_string pat str =

   let

     fun match [] _ = true

       | match (p :: ps) s =

           size p <= size s andalso

             (case try (unprefix p) s of

               SOME s' => match ps s'

             | NONE => match (p :: ps) (String.substring (s, 1, size s - 1)));

   in match (space_explode "*" pat) str end;

 fun filter_name str_pat (thmref, _) =

   if match_string str_pat (PureThy.name_of_thmref thmref)

   then SOME (0, 0) else NONE;

 (* filter intro/elim/dest 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 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, foldr1 Int.min successful) else NONE

   end;

 fun filter_intro 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 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 o 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 (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, foldr1 Int.min successful) else NONE

     end

   else NONE

 (* filter_simp *)

 fun filter_simp ctxt t (_, thm) =

   let

     val (_, {mk_rews = {mk, ...}, ...}) =

       MetaSimplifier.rep_ss (Simplifier.local_simpset_of ctxt);

     val extract_simp =

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

     val ss = is_matching_thm 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 filter_pattern ctxt pat (_, thm) =

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

   then SOME (0, 0) else NONE;

 (* interpret criteria as filters *)

 local

 fun err_no_goal c =

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

 fun filter_crit _ _ (Name name) = 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 ctxt (SOME goal) Intro = filter_intro ctxt goal

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

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

   | filter_crit ctxt _ (Simp pat) = 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;

 in

 fun filter_criterion ctxt opt_goal (b, c) =

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

 fun all_filters filters thms =

   let

     fun eval_filters filters thm =

       fold opt_add (map (fn f => f thm) filters) (SOME (0, 0));

     (*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 (`(eval_filters filters)) thms

     |> map_filter (fn (SOME x, y) => SOME (x, y) | (NONE, _) => NONE)

     |> sort thm_ord |> map #2

   end;

 end;

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

 fun rem_thm_dups xs =

   let

     fun nicer (Fact x) (Fact y) = size x <= size y

       | nicer (Fact _) _        = true

       | nicer (PureThy.Name x) (PureThy.Name y) = size x <= size y

       | nicer (PureThy.Name _) (Fact _) = false

       | nicer (PureThy.Name _) _ = true

       | nicer (NameSelection (x, _)) (NameSelection (y, _)) = size x <= size y

       | nicer (NameSelection _) _ = false;

     fun rem_cdups 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 if nicer n n'

                  then rem_c rev_seen (x::xs)

                  else rem_c rev_seen (y::xs)

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

       in rem_c [] xs end;

   in ListPair.zip (xs, 1 upto length xs)

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

      |> rem_cdups

      |> sort (int_ord o pairself #2)

      |> map #1

   end;

 (* print_theorems *)

 fun find_thms ctxt spec =

   (PureThy.thms_containing (ProofContext.theory_of ctxt) spec

     |> maps PureThy.selections) @

   (ProofContext.lthms_containing ctxt spec

     |> maps PureThy.selections

     |> distinct (fn ((r1, th1), (r2, th2)) =>

         r1 = r2 andalso Thm.eq_thm_prop (th1, th2)));

 fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =

   let

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

     val filters = map (filter_criterion ctxt opt_goal) criteria;

     val raw_matches = all_filters filters (find_thms ctxt ([], []));

     val matches =

       if rem_dups

       then rem_thm_dups raw_matches

       else raw_matches;

     val len = length matches;

     val limit = the_default (! thms_containing_limit) opt_limit;

     val thms = Library.drop (len - limit, matches);

     fun prt_fact (thmref, thm) =

       ProofContext.pretty_fact ctxt (PureThy.string_of_thmref thmref, [thm]);

   in

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

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

       else

         [Pretty.str ("found " ^ string_of_int len ^ " theorems" ^

           (if len <= limit then "" else " (" ^ string_of_int limit ^ " displayed)") ^ ":"),

          Pretty.str ""] @

         map prt_fact thms)

     |> Pretty.chunks |> Pretty.writeln

   end;

 end;