[isabelle-dev] Abbreviations and find_theorems

Florian Haftmann florian.haftmann at informatik.tu-muenchen.de
Wed Nov 26 19:40:09 CET 2014


The following is based against 43e07797269b.  If you do not want apply
the patched just copy find_theorems.ML to src/Pure/Tools.

I merely implemented that patterns which are abstractions (after
eta-contraction!) are implicitly expanded with schematic parameters.

Hence

  inj ~> %f. inj_on f UNIV ~> inj_on _ UNIV

This seems a quite reasonable, generic approach to give semantics to
search patterns.

@Timothy: in the progress of investigating I stumbled over your
changeset (c61fe520602b, actually brought in by Gerwin) and dismantled
it.  Do you remember what it had been intended for resp. by which
criterion we can decide whether the dismantling is really admissible?
Before going ahead and pushing something, I would like to resolve this
question.

Thanks a lot,
	Florian

-- 

PGP available:
http://home.informatik.tu-muenchen.de/haftmann/pgp/florian_haftmann_at_informatik_tu_muenchen_de
-------------- next part --------------
# HG changeset patch
# Parent 504998921f0f5bed09e6809138cb65a01e294a41
turn application-specific Pattern.matches_subterm into an application-private function

diff -r 504998921f0f src/Pure/Tools/find_theorems.ML
--- a/src/Pure/Tools/find_theorems.ML	Wed Nov 26 16:15:33 2014 +0100
+++ b/src/Pure/Tools/find_theorems.ML	Wed Nov 26 16:19:37 2014 +0100
@@ -239,6 +239,16 @@
 
 fun get_names t = Term.add_const_names t (Term.add_free_names t []);
 
+(* Does pat match a subterm of obj? *)
+fun matches_subterm thy (pat, obj) =
+  let
+    fun msub bounds obj = Pattern.matches thy (pat, obj) orelse
+      (case obj of
+        Abs (x, T, t) => msub (bounds + 1) (snd (Term.dest_abs (Name.bound bounds, T, t)))
+      | t $ u => msub bounds t orelse msub bounds u
+      | _ => false)
+  in msub 0 obj end;
+
 (*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
@@ -254,7 +264,7 @@
     fun check ((x, thm), NONE) = check ((x, thm), SOME (get_names (Thm.full_prop_of thm)))
       | check ((_, thm), c as SOME thm_consts) =
          (if subset (op =) (pat_consts, thm_consts) andalso
-            Pattern.matches_subterm (Proof_Context.theory_of ctxt) (pat, Thm.full_prop_of thm)
+            matches_subterm (Proof_Context.theory_of ctxt) (pat, Thm.full_prop_of thm)
           then SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, 0) else NONE, c);
   in check end;
 
diff -r 504998921f0f src/Pure/more_pattern.ML
--- a/src/Pure/more_pattern.ML	Wed Nov 26 16:15:33 2014 +0100
+++ b/src/Pure/more_pattern.ML	Wed Nov 26 16:19:37 2014 +0100
@@ -11,7 +11,6 @@
   val matches: theory -> term * term -> bool
   val matchess: theory -> term list * term list -> bool
   val equiv: theory -> term * term -> bool
-  val matches_subterm: theory -> term * term -> bool
   val first_order: term -> bool
   val pattern: term -> bool
   val match_rew: theory -> term -> term * term -> (term * term) option
@@ -32,17 +31,6 @@
 
 fun equiv thy (t, u) = matches thy (t, u) andalso matches thy (u, t);
 
-
-(* Does pat match a subterm of obj? *)
-fun matches_subterm thy (pat, obj) =
-  let
-    fun msub bounds obj = matches thy (pat, obj) orelse
-      (case obj of
-        Abs (x, T, t) => msub (bounds + 1) (snd (Term.dest_abs (Name.bound bounds, T, t)))
-      | t $ u => msub bounds t orelse msub bounds u
-      | _ => false)
-  in msub 0 obj end;
-
 fun first_order (Abs (_, _, t)) = first_order t
   | first_order (Var _ $ _) = false
   | first_order (t $ u) = first_order t andalso first_order u
-------------- next part --------------
# HG changeset patch
# Parent 99edc21bcc93c81a1b4256cb469652b2ed3bff6e
tuned variable names

diff -r 99edc21bcc93 -r 11e79e9d8857 src/Pure/Tools/find_theorems.ML
--- a/src/Pure/Tools/find_theorems.ML	Wed Nov 26 16:19:37 2014 +0100
+++ b/src/Pure/Tools/find_theorems.ML	Wed Nov 26 16:34:52 2014 +0100
@@ -170,7 +170,7 @@
     val concl = Logic.concl_of_goal goal 1;
   in
     (case is_matching_thm extract_intro ctxt true concl thm of
-      SOME ss => SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, ss)
+      SOME k => SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, k)
     | NONE => NONE)
   end;
 
@@ -244,7 +244,7 @@
   let
     fun msub bounds obj = Pattern.matches thy (pat, obj) orelse
       (case obj of
-        Abs (x, T, t) => msub (bounds + 1) (snd (Term.dest_abs (Name.bound bounds, T, t)))
+        Abs (_, T, t) => msub (bounds + 1) (snd (Term.dest_abs (Name.bound bounds, T, t)))
       | t $ u => msub bounds t orelse msub bounds u
       | _ => false)
   in msub 0 obj end;
@@ -572,3 +572,4 @@
     else error "Unknown context");
 
 end;
+
-------------- next part --------------
# HG changeset patch
# Parent 11e79e9d8857e7d69d9c97de69d60b3dc6efffc1
revert Ā»betterĀ« handling of abbreviation from c61fe520602b

diff -r 11e79e9d8857 -r 3f2424c95d87 src/Pure/Tools/find_theorems.ML
--- a/src/Pure/Tools/find_theorems.ML	Wed Nov 26 16:34:52 2014 +0100
+++ b/src/Pure/Tools/find_theorems.ML	Wed Nov 26 16:56:09 2014 +0100
@@ -31,32 +31,13 @@
 datatype 'term criterion =
   Name of string | Intro | 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 = Proof_Context.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 (Proof_Context.expand_abbrevs ctxt rhs)
-    | NONE => Proof_Context.read_term_pattern ctxt nm)
-  end;
-
 fun read_criterion _ (Name name) = Name name
   | read_criterion _ Intro = Intro
   | read_criterion _ Elim = Elim
   | read_criterion _ Dest = Dest
   | read_criterion _ Solves = Solves
   | read_criterion ctxt (Simp str) = Simp (Proof_Context.read_term_pattern ctxt str)
-  | read_criterion ctxt (Pattern str) = Pattern (parse_pattern ctxt str);
+  | read_criterion ctxt (Pattern str) = Pattern (Proof_Context.read_term_pattern ctxt str);
 
 fun pretty_criterion ctxt (b, c) =
   let
-------------- next part --------------
# HG changeset patch
# Parent 3f2424c95d874f929ee704a180dc1bfe63839ba8
eta-expand all search patterns using schematic place holders

diff -r 3f2424c95d87 src/Pure/Tools/find_theorems.ML
--- a/src/Pure/Tools/find_theorems.ML	Wed Nov 26 16:56:09 2014 +0100
+++ b/src/Pure/Tools/find_theorems.ML	Wed Nov 26 19:29:12 2014 +0100
@@ -218,6 +218,13 @@
 
 (* filter_pattern *)
 
+fun expand_abs t =
+  let
+    val m = Term.maxidx_of_term t + 1;
+    val vs = strip_abs_vars t;
+    val ts = map_index (fn (k, (_, T)) => Var ((Name.aT, m + k), T)) vs;
+  in betapplys (t, ts) end;
+
 fun get_names t = Term.add_const_names t (Term.add_free_names t []);
 
 (* Does pat match a subterm of obj? *)
@@ -240,12 +247,12 @@
 
 fun filter_pattern ctxt pat =
   let
-    val pat_consts = get_names pat;
-
+    val pat' = (expand_abs o Envir.eta_contract) pat;
+    val pat_consts = get_names pat';
     fun check ((x, thm), NONE) = check ((x, thm), SOME (get_names (Thm.full_prop_of thm)))
       | check ((_, thm), c as SOME thm_consts) =
          (if subset (op =) (pat_consts, thm_consts) andalso
-            matches_subterm (Proof_Context.theory_of ctxt) (pat, Thm.full_prop_of thm)
+            matches_subterm (Proof_Context.theory_of ctxt) (pat', Thm.full_prop_of thm)
           then SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, 0) else NONE, c);
   in check end;
 
-------------- next part --------------
(*  Title:      Pure/Tools/find_theorems.ML
    Author:     Rafal Kolanski and Gerwin Klein, NICTA
    Author:     Lars Noschinski and Alexander Krauss, TU Muenchen

Retrieve theorems from proof context.
*)

signature FIND_THEOREMS =
sig
  datatype 'term criterion =
    Name of string | Intro | Elim | Dest | Solves | Simp of 'term | Pattern of 'term
  type 'term query = {
    goal: thm option,
    limit: int option,
    rem_dups: bool,
    criteria: (bool * 'term criterion) list
  }
  val read_query: Position.T -> string -> (bool * string criterion) list
  val find_theorems: Proof.context -> thm option -> int option -> bool ->
    (bool * term criterion) list -> int option * (Facts.ref * thm) list
  val find_theorems_cmd: 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
end;

structure Find_Theorems: FIND_THEOREMS =
struct

(** search criteria **)

datatype 'term criterion =
  Name of string | Intro | Elim | Dest | Solves | 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 _ Solves = Solves
  | read_criterion ctxt (Simp str) = Simp (Proof_Context.read_term_pattern ctxt str)
  | read_criterion ctxt (Pattern str) = Pattern (Proof_Context.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")
    | 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;



(** queries **)

type 'term query = {
  goal: thm option,
  limit: int option,
  rem_dups: bool,
  criteria: (bool * 'term criterion) list
};

fun map_criteria f {goal, limit, rem_dups, criteria} =
  {goal = goal, limit = limit, rem_dups = rem_dups, criteria = f criteria};


(** search criterion filters **)

(*generated filters are to be of the form
  input: (Facts.ref * thm)
  output: (p:int, s:int, t:int) option, where
    NONE indicates no match
    p is the primary sorting criterion
      (eg. size of term)
    s is the secondary sorting criterion
      (eg. number of assumptions in the theorem)
    t is the tertiary sorting criterion
      (eg. size of the substitution for intro, elim and dest)
  when applying a set of filters to a thm, fold results in:
    (max p, max s, sum of all t)
*)


(* matching theorems *)

fun is_nontrivial thy = Term.is_Const o Term.head_of o Object_Logic.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 = Proof_Context.theory_of ctxt;

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

    fun subst_size 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 best_match [] = NONE
      | best_match xs = SOME (foldl1 Int.min xs);

    val match_thm = matches o refine_term;
  in
    map (subst_size o refine_term) (filter match_thm (extract_terms term_src))
    |> best_match
  end;


(* filter_name *)

fun filter_name str_pat (thmref, _) =
  if match_string str_pat (Facts.name_of_ref thmref)
  then SOME (0, 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 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 (size_of_term (Thm.prop_of thm), Thm.nprems_of thm - 1, foldl1 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;
  in
    (case is_matching_thm extract_intro ctxt true concl thm of
      SOME k => SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, k)
    | NONE => NONE)
  end;

fun filter_elim ctxt goal (_, thm) =
  if Thm.nprems_of thm > 0 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);  (* FIXME ?!? *)
      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 (Proof_Context.theory_of ctxt) (Thm.major_prem_of thm)
          andalso not (null successful) then
        SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm - 1, foldl1 Int.min successful)
      else NONE
    end
  else NONE;

fun filter_solves ctxt goal =
  let
    val thy' =
      Proof_Context.theory_of ctxt
      |> Context_Position.set_visible_global (Context_Position.is_visible ctxt);
    val ctxt' = Proof_Context.transfer thy' ctxt;
    val goal' = Thm.transfer thy' goal;

    fun limited_etac thm i =
      Seq.take (Options.default_int @{system_option find_theorems_tactic_limit}) o
        eresolve_tac [thm] i;
    fun try_thm thm =
      if Thm.no_prems thm then resolve_tac [thm] 1 goal'
      else
        (limited_etac thm THEN_ALL_NEW (Goal.norm_hhf_tac ctxt' THEN' Method.assm_tac ctxt'))
          1 goal';
  in
    fn (_, thm) =>
      if is_some (Seq.pull (try_thm thm))
      then SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, 0)
      else NONE
  end;


(* filter_simp *)

fun filter_simp ctxt t (_, thm) =
  let
    val mksimps = Simplifier.mksimps ctxt;
    val extract_simp =
      (map Thm.full_prop_of o mksimps, #1 o Logic.dest_equals o Logic.strip_imp_concl);
  in
    (case is_matching_thm extract_simp ctxt false t thm of
      SOME ss => SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, ss)
    | NONE => NONE)
  end;


(* filter_pattern *)

fun expand_abs t =
  let
    val m = Term.maxidx_of_term t + 1;
    val vs = strip_abs_vars t;
    val ts = map_index (fn (k, (_, T)) => Var ((Name.aT, m + k), T)) vs;
  in betapplys (t, ts) end;

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

(* Does pat match a subterm of obj? *)
fun matches_subterm thy (pat, obj) =
  let
    fun msub bounds obj = Pattern.matches thy (pat, obj) orelse
      (case obj of
        Abs (_, T, t) => msub (bounds + 1) (snd (Term.dest_abs (Name.bound bounds, T, t)))
      | t $ u => msub bounds t orelse msub bounds u
      | _ => false)
  in msub 0 obj end;

(*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' = (expand_abs o Envir.eta_contract) pat;
    val pat_consts = get_names pat';
    fun check ((x, thm), NONE) = check ((x, thm), SOME (get_names (Thm.full_prop_of thm)))
      | check ((_, thm), c as SOME thm_consts) =
         (if subset (op =) (pat_consts, thm_consts) andalso
            matches_subterm (Proof_Context.theory_of ctxt) (pat', Thm.full_prop_of thm)
          then SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, 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");

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 ctxt (Thm.prop_of goal))
  | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt (Thm.prop_of goal))
  | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt (Thm.prop_of 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, 0);

fun opt_add (SOME (a, c, x)) (SOME (b, d, y)) = SOME (Int.max (a,b), Int.max (c, d), 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, 0), NONE, filters);

    (*filters return: (thm size, number of assumptions, substitution size) option, so
      sort according to size of thm first, then number of assumptions,
      then by the substitution size, then by term order *)
    fun result_ord (((p0, s0, t0), (_, thm0)), ((p1, s1, t1), (_, thm1))) =
      prod_ord int_ord (prod_ord int_ord (prod_ord int_ord Term_Ord.term_ord))
         ((p1, (s1, (t1, Thm.full_prop_of thm1))), (p0, (s0, (t0, Thm.full_prop_of thm0))));
  in
    grouped 100 Par_List.map eval_filters thms
    |> map_filter I |> sort result_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, 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 O(n log n) *)

local

val index_ord = option_ord (K EQUAL);
val hidden_ord = bool_ord o pairself Long_Name.is_hidden;
val qual_ord = int_ord o pairself Long_Name.qualification;
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, thm), _)) :: (y as ((n', thm'), _)) :: rest) =
          if Thm.eq_thm_prop (thm, thm')
          then rem_c rev_seen ((if nicer n n' then x else y) :: rest)
          else rem_c (x :: rev_seen) (y :: rest);
  in rem_c [] xs end;

in

fun nicer_shortest ctxt =
  let
    fun extern_shortest name =
      Name_Space.extern_shortest ctxt
        (Facts.space_of (Proof_Context.facts_of_fact ctxt name)) name;

    fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =
          nicer_name (extern_shortest x, i) (extern_shortest y, j)
      | nicer (Facts.Fact _) (Facts.Named _) = true
      | nicer (Facts.Named _) (Facts.Fact _) = false
      | nicer (Facts.Fact _) (Facts.Fact _) = true;
  in nicer end;

fun rem_thm_dups nicer xs =
  (xs ~~ (1 upto length xs))
  |> sort (Term_Ord.fast_term_ord o pairself (Thm.full_prop_of o #2 o #1))
  |> rem_cdups nicer
  |> sort (int_ord o pairself #2)
  |> map #1;

end;



(** main operations **)

(* filter_theorems *)

fun all_facts_of ctxt =
  let
    val local_facts = Proof_Context.facts_of ctxt;
    val global_facts = Global_Theory.facts_of (Proof_Context.theory_of ctxt);
  in
    maps Facts.selections
     (Facts.dest_static false [global_facts] local_facts @
      Facts.dest_static false [] global_facts)
  end;

fun filter_theorems ctxt theorems query =
  let
    val {goal = opt_goal, limit = opt_limit, rem_dups, criteria} = query;
    val filters = map (filter_criterion ctxt opt_goal) criteria;

    fun find_all theorems =
      let
        val raw_matches = sorted_filter filters theorems;

        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 (Options.default_int @{system_option find_theorems_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 theorems end;

fun filter_theorems_cmd ctxt theorems raw_query =
  filter_theorems ctxt theorems (map_criteria (map (apsnd (read_criterion ctxt))) raw_query);


(* find_theorems *)

local

fun gen_find_theorems filter ctxt opt_goal opt_limit rem_dups raw_criteria =
  let
    val assms =
      Proof_Context.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;
  in
    filter ctxt (all_facts_of ctxt)
      {goal = opt_goal', limit = opt_limit, rem_dups = rem_dups, criteria = raw_criteria}
  end;

in

val find_theorems = gen_find_theorems filter_theorems;
val find_theorems_cmd = gen_find_theorems filter_theorems_cmd;

end;


(* pretty_theorems *)

local

fun pretty_ref ctxt thmref =
  let
    val (name, sel) =
      (case thmref of
        Facts.Named ((name, _), sel) => (name, sel)
      | Facts.Fact _ => raise Fail "Illegal literal fact");
  in
    [Pretty.mark (#1 (Proof_Context.markup_extern_fact ctxt name)) (Pretty.str name),
      Pretty.str (Facts.string_of_selection sel), Pretty.str ":", Pretty.brk 1]
  end;

in

fun pretty_thm ctxt (thmref, thm) =
  Pretty.block (pretty_ref ctxt thmref @ [Display.pretty_thm ctxt thm]);

fun pretty_theorems state opt_limit rem_dups raw_criteria =
  let
    val ctxt = Proof.context_of state;
    val opt_goal = try Proof.simple_goal state |> Option.map #goal;
    val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;

    val (opt_found, theorems) =
      filter_theorems ctxt (all_facts_of ctxt)
        {goal = opt_goal, limit = opt_limit, rem_dups = rem_dups, criteria = criteria};
    val returned = length theorems;

    val tally_msg =
      (case opt_found of
        NONE => "displaying " ^ string_of_int returned ^ " theorem(s)"
      | SOME found =>
          "found " ^ string_of_int found ^ " theorem(s)" ^
            (if returned < found
             then " (" ^ string_of_int returned ^ " displayed)"
             else ""));
    val position_markup = Position.markup (Position.thread_data ()) Markup.position;
  in
    Pretty.block
      (Pretty.fbreaks
        (Pretty.mark position_markup (Pretty.keyword1 "find_theorems") ::
          map (pretty_criterion ctxt) criteria)) ::
    Pretty.str "" ::
    (if null theorems then [Pretty.str "found nothing"]
     else
       Pretty.str (tally_msg ^ ":") ::
       grouped 10 Par_List.map (Pretty.item o single o pretty_thm ctxt) (rev theorems))
  end |> Pretty.fbreaks |> curry Pretty.blk 0;

end;



(** Isar command syntax **)

fun proof_state st =
  (case try Toplevel.proof_of st of
    SOME state => state
  | NONE => Proof.init (Toplevel.context_of st));

local

val criterion =
  Parse.reserved "name" |-- Parse.!!! (Parse.$$$ ":" |-- Parse.xname) >> Name ||
  Parse.reserved "intro" >> K Intro ||
  Parse.reserved "elim" >> K Elim ||
  Parse.reserved "dest" >> K Dest ||
  Parse.reserved "solves" >> K Solves ||
  Parse.reserved "simp" |-- Parse.!!! (Parse.$$$ ":" |-- 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);

val query = Scan.repeat ((Scan.option Parse.minus >> is_none) -- criterion);

val query_keywords = Keyword.add_keywords [(":", NONE)] Keyword.empty_keywords;

in

fun read_query pos str =
  Outer_Syntax.scan query_keywords pos str
  |> filter Token.is_proper
  |> Scan.error (Scan.finite Token.stopper (Parse.!!! (query --| Scan.ahead Parse.eof)))
  |> #1;

val _ =
  Outer_Syntax.command @{command_spec "find_theorems"}
    "find theorems meeting specified criteria"
    (options -- query >> (fn ((opt_lim, rem_dups), spec) =>
      Toplevel.keep (fn st =>
        Pretty.writeln (pretty_theorems (proof_state st) opt_lim rem_dups spec))));

end;



(** PIDE query operation **)

val _ =
  Query_Operation.register "find_theorems" (fn {state = st, args, output_result} =>
    if can Toplevel.context_of st then
      let
        val [limit_arg, allow_dups_arg, query_arg] = args;
        val state = proof_state st;
        val opt_limit = Int.fromString limit_arg;
        val rem_dups = allow_dups_arg = "false";
        val criteria = read_query Position.none query_arg;
      in output_result (Pretty.string_of (pretty_theorems state opt_limit rem_dups criteria)) end
    else error "Unknown context");

end;

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