(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_fact_filter.ML

     Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA

     Author:     Jasmin Blanchette, TU Muenchen

 *)

 signature SLEDGEHAMMER_FACT_FILTER =

 sig

   type relevance_override =

     {add: Facts.ref list,

      del: Facts.ref list,

      only: bool}

   val trace : bool Unsynchronized.ref

   val name_thm_pairs_from_ref :

     Proof.context -> unit Symtab.table -> thm list -> Facts.ref

     -> ((unit -> string * bool) * (bool * thm)) list

   val relevant_facts :

     bool -> real * real -> int -> bool -> relevance_override

     -> Proof.context * (thm list * 'a) -> term list -> term

     -> ((string * bool) * thm) list

 end;

 structure Sledgehammer_Fact_Filter : SLEDGEHAMMER_FACT_FILTER =

 struct

 open Sledgehammer_Util

 val trace = Unsynchronized.ref false

 fun trace_msg msg = if !trace then tracing (msg ()) else ()

 val respect_no_atp = true

 type relevance_override =

   {add: Facts.ref list,

    del: Facts.ref list,

    only: bool}

 val sledgehammer_prefix = "Sledgehammer" ^ Long_Name.separator

 fun repair_name reserved multi j name =

   (name |> Symtab.defined reserved name ? quote) ^

   (if multi then "(" ^ Int.toString j ^ ")" else "")

 fun name_thm_pairs_from_ref ctxt reserved chained_ths xref =

   let

     val ths = ProofContext.get_fact ctxt xref

     val name = Facts.string_of_ref xref

     val multi = length ths > 1

   in

     fold (fn th => fn (j, rest) =>

              (j + 1, (fn () => (repair_name reserved multi j name,

                                 member Thm.eq_thm chained_ths th),

                       (multi, th)) :: rest))

          ths (1, [])

     |> snd

   end

 (***************************************************************)

 (* Relevance Filtering                                         *)

 (***************************************************************)

 (*** constants with types ***)

 (*An abstraction of Isabelle types*)

 datatype pseudotype = PVar | PType of string * pseudotype list

 fun string_for_pseudotype PVar = "?"

   | string_for_pseudotype (PType (s, Ts)) =

     (case Ts of

        [] => ""

      | [T] => string_for_pseudotype T

      | Ts => string_for_pseudotypes Ts ^ " ") ^ s

 and string_for_pseudotypes Ts =

   "(" ^ commas (map string_for_pseudotype Ts) ^ ")"

 (*Is the second type an instance of the first one?*)

 fun match_pseudotype (PType (a, T), PType (b, U)) =

     a = b andalso match_pseudotypes (T, U)

   | match_pseudotype (PVar, _) = true

   | match_pseudotype (_, PVar) = false

 and match_pseudotypes ([], []) = true

   | match_pseudotypes (T :: Ts, U :: Us) =

     match_pseudotype (T, U) andalso match_pseudotypes (Ts, Us)

 (*Is there a unifiable constant?*)

 fun pseudoconst_mem f const_tab (c, c_typ) =

   exists (curry (match_pseudotypes o f) c_typ)

          (these (Symtab.lookup const_tab c))

 fun pseudotype_for (Type (c,typs)) = PType (c, map pseudotype_for typs)

   | pseudotype_for (TFree _) = PVar

   | pseudotype_for (TVar _) = PVar

 (* Pairs a constant with the list of its type instantiations. *)

 fun pseudoconst_for thy (c, T) =

   (c, map pseudotype_for (Sign.const_typargs thy (c, T)))

   handle TYPE _ => (c, [])  (* Variable (locale constant): monomorphic *)

 fun string_for_pseudoconst (s, []) = s

   | string_for_pseudoconst (s, Ts) = s ^ string_for_pseudotypes Ts

 fun string_for_super_pseudoconst (s, [[]]) = s

   | string_for_super_pseudoconst (s, Tss) =

     s ^ "{" ^ commas (map string_for_pseudotypes Tss) ^ "}"

 (*Add a const/type pair to the table, but a [] entry means a standard connective,

   which we ignore.*)

 fun add_const_to_table (c, ctyps) =

   Symtab.map_default (c, [ctyps])

                      (fn [] => [] | ctypss => insert (op =) ctyps ctypss)

 fun is_formula_type T = (T = HOLogic.boolT orelse T = propT)

 val fresh_prefix = "Sledgehammer.skolem."

 val flip = Option.map not

 (* These are typically simplified away by "Meson.presimplify". *)

 val boring_consts =

   [@{const_name False}, @{const_name True}, @{const_name If}, @{const_name Let}]

 fun get_consts thy pos ts =

   let

     (* We include free variables, as well as constants, to handle locales. For

        each quantifiers that must necessarily be skolemized by the ATP, we

        introduce a fresh constant to simulate the effect of Skolemization. *)

     fun do_term t =

       case t of

         Const x => add_const_to_table (pseudoconst_for thy x)

       | Free (s, _) => add_const_to_table (s, [])

       | t1 $ t2 => fold do_term [t1, t2]

       | Abs (_, _, t') => do_term t'

       | _ => I

     fun do_quantifier will_surely_be_skolemized body_t =

       do_formula pos body_t

       #> (if will_surely_be_skolemized then

             add_const_to_table (gensym fresh_prefix, [])

           else

             I)

     and do_term_or_formula T =

       if is_formula_type T then do_formula NONE else do_term

     and do_formula pos t =

       case t of

         Const (@{const_name all}, _) $ Abs (_, _, body_t) =>

         do_quantifier (pos = SOME false) body_t

       | @{const "==>"} $ t1 $ t2 =>

         do_formula (flip pos) t1 #> do_formula pos t2

       | Const (@{const_name "=="}, Type (_, [T, _])) $ t1 $ t2 =>

         fold (do_term_or_formula T) [t1, t2]

       | @{const Trueprop} $ t1 => do_formula pos t1

       | @{const Not} $ t1 => do_formula (flip pos) t1

       | Const (@{const_name All}, _) $ Abs (_, _, body_t) =>

         do_quantifier (pos = SOME false) body_t

       | Const (@{const_name Ex}, _) $ Abs (_, _, body_t) =>

         do_quantifier (pos = SOME true) body_t

       | @{const "op &"} $ t1 $ t2 => fold (do_formula pos) [t1, t2]

       | @{const "op |"} $ t1 $ t2 => fold (do_formula pos) [t1, t2]

       | @{const "op -->"} $ t1 $ t2 =>

         do_formula (flip pos) t1 #> do_formula pos t2

       | Const (@{const_name "op ="}, Type (_, [T, _])) $ t1 $ t2 =>

         fold (do_term_or_formula T) [t1, t2]

       | Const (@{const_name If}, Type (_, [_, Type (_, [T, _])]))

         $ t1 $ t2 $ t3 =>

         do_formula NONE t1 #> fold (do_term_or_formula T) [t2, t3]

       | Const (@{const_name Ex1}, _) $ Abs (_, _, body_t) =>

         do_quantifier (is_some pos) body_t

       | Const (@{const_name Ball}, _) $ t1 $ Abs (_, _, body_t) =>

         do_quantifier (pos = SOME false)

                       (HOLogic.mk_imp (incr_boundvars 1 t1 $ Bound 0, body_t))

       | Const (@{const_name Bex}, _) $ t1 $ Abs (_, _, body_t) =>

         do_quantifier (pos = SOME true)

                       (HOLogic.mk_conj (incr_boundvars 1 t1 $ Bound 0, body_t))

       | (t0 as Const (_, @{typ bool})) $ t1 =>

         do_term t0 #> do_formula pos t1  (* theory constant *)

       | _ => do_term t

   in

     Symtab.empty |> fold (Symtab.update o rpair []) boring_consts

                  |> fold (do_formula pos) ts

   end

 (*Inserts a dummy "constant" referring to the theory name, so that relevance

   takes the given theory into account.*)

 fun theory_const_prop_of theory_relevant th =

   if theory_relevant then

     let

       val name = Context.theory_name (theory_of_thm th)

       val t = Const (name ^ ". 1", @{typ bool})

     in t $ prop_of th end

   else

     prop_of th

 (**** Constant / Type Frequencies ****)

 (* A two-dimensional symbol table counts frequencies of constants. It's keyed

    first by constant name and second by its list of type instantiations. For the

    latter, we need a linear ordering on "pseudotype list". *)

 fun pseudotype_ord p =

   case p of

     (PVar, PVar) => EQUAL

   | (PVar, PType _) => LESS

   | (PType _, PVar) => GREATER

   | (PType q1, PType q2) =>

     prod_ord fast_string_ord (dict_ord pseudotype_ord) (q1, q2)

 structure CTtab =

   Table(type key = pseudotype list val ord = dict_ord pseudotype_ord)

 fun count_axiom_consts theory_relevant thy (_, th) =

   let

     fun do_const (a, T) =

       let val (c, cts) = pseudoconst_for thy (a, T) in

         (* Two-dimensional table update. Constant maps to types maps to

            count. *)

         CTtab.map_default (cts, 0) (Integer.add 1)

         |> Symtab.map_default (c, CTtab.empty)

       end

     fun do_term (Const x) = do_const x

       | do_term (Free x) = do_const x

       | do_term (t $ u) = do_term t #> do_term u

       | do_term (Abs (_, _, t)) = do_term t

       | do_term _ = I

   in th |> theory_const_prop_of theory_relevant |> do_term end

 (**** Actual Filtering Code ****)

 (*The frequency of a constant is the sum of those of all instances of its type.*)

 fun pseudoconst_freq match const_tab (c, cts) =

   CTtab.fold (fn (cts', m) => match (cts, cts') ? Integer.add m)

              (the (Symtab.lookup const_tab c)) 0

   handle Option.Option => 0

 (* A surprising number of theorems contain only a few significant constants.

    These include all induction rules, and other general theorems. *)

 (* "log" seems best in practice. A constant function of one ignores the constant

    frequencies. *)

 fun rel_log (x : real) = 1.0 + 2.0 / Math.ln (x + 1.0)

 fun irrel_log (x : real) = Math.ln (x + 19.0) / 6.4

 (* Computes a constant's weight, as determined by its frequency. *)

 val rel_weight = rel_log o real oo pseudoconst_freq match_pseudotypes

 val irrel_weight =

   irrel_log o real oo pseudoconst_freq (match_pseudotypes o swap)

 (* fun irrel_weight _ _ = 1.0  FIXME: OLD CODE *)

 fun axiom_weight const_tab relevant_consts axiom_consts =

   case axiom_consts |> List.partition (pseudoconst_mem I relevant_consts)

                     ||> filter_out (pseudoconst_mem swap relevant_consts) of

     ([], []) => 0.0

   | (_, []) => 1.0

   | (rel, irrel) =>

     let

       val rel_weight = fold (curry Real.+ o rel_weight const_tab) rel 0.0

       val irrel_weight = fold (curry Real.+ o irrel_weight const_tab) irrel 0.0

       val res = rel_weight / (rel_weight + irrel_weight)

     in if Real.isFinite res then res else 0.0 end

 fun consts_of_term thy t =

   Symtab.fold (fn (x, ys) => fold (fn y => cons (x, y)) ys)

               (get_consts thy (SOME true) [t]) []

 fun pair_consts_axiom theory_relevant thy axiom =

   (axiom, axiom |> snd |> theory_const_prop_of theory_relevant

                 |> consts_of_term thy)

 type annotated_thm =

   ((unit -> string * bool) * thm) * (string * pseudotype list) list

 fun take_best max (candidates : (annotated_thm * real) list) =

   let

     val ((perfect, more_perfect), imperfect) =

       candidates |> List.partition (fn (_, w) => w > 0.99999) |>> chop (max - 1)

                  ||> sort (Real.compare o swap o pairself snd)

     val (accepts, rejects) =

       case more_perfect @ imperfect of

         [] => (perfect, [])

       | (q :: qs) => (q :: perfect, qs)

   in

     trace_msg (fn () => "Number of candidates: " ^

                         string_of_int (length candidates));

     trace_msg (fn () => "Effective threshold: " ^

                         Real.toString (#2 (hd accepts)));

     trace_msg (fn () => "Actually passed: " ^

         (accepts |> map (fn (((name, _), _), weight) =>

                             fst (name ()) ^ " [" ^ Real.toString weight ^ "]")

                  |> commas));

     (accepts, rejects)

   end

 val threshold_divisor = 2.0

 val ridiculous_threshold = 0.1

 fun relevance_filter ctxt threshold0 decay max_relevant theory_relevant

                      ({add, del, ...} : relevance_override) axioms goal_ts =

   let

     val thy = ProofContext.theory_of ctxt

     val const_tab = fold (count_axiom_consts theory_relevant thy) axioms

                          Symtab.empty

     val add_thms = maps (ProofContext.get_fact ctxt) add

     val del_thms = maps (ProofContext.get_fact ctxt) del

     fun iter j max threshold rel_const_tab hopeless hopeful =

       let

         fun game_over rejects =

           if j = 0 andalso threshold >= ridiculous_threshold then

             (* First iteration? Try again. *)

             iter 0 max (threshold / threshold_divisor) rel_const_tab hopeless

                  hopeful

           else

             (* Add "add:" facts. *)

             if null add_thms then

               []

             else

               map_filter (fn ((p as (_, th), _), _) =>

                              if member Thm.eq_thm add_thms th then SOME p

                              else NONE) rejects

         fun relevant [] rejects [] hopeless =

             (* Nothing has been added this iteration. *)

             game_over (map (apsnd SOME) (rejects @ hopeless))

           | relevant candidates rejects [] hopeless =

             let

               val (accepts, more_rejects) = take_best max candidates

               val rel_const_tab' =

                 rel_const_tab

                 |> fold add_const_to_table (maps (snd o fst) accepts)

               fun is_dirty (c, _) =

                 Symtab.lookup rel_const_tab' c <> Symtab.lookup rel_const_tab c

               val (hopeful_rejects, hopeless_rejects) =

                  (rejects @ hopeless, ([], []))

                  |-> fold (fn (ax as (_, consts), old_weight) =>

                               if exists is_dirty consts then

                                 apfst (cons (ax, NONE))

                               else

                                 apsnd (cons (ax, old_weight)))

                  |>> append (more_rejects

                              |> map (fn (ax as (_, consts), old_weight) =>

                                         (ax, if exists is_dirty consts then NONE

                                              else SOME old_weight)))

               val threshold = threshold + (1.0 - threshold) * decay

               val max = max - length accepts

             in

               trace_msg (fn () => "New or updated constants: " ^

                   commas (rel_const_tab' |> Symtab.dest

                           |> subtract (op =) (Symtab.dest rel_const_tab)

                           |> map string_for_super_pseudoconst));

               map (fst o fst) accepts @

               (if max = 0 then

                  game_over (hopeful_rejects @ map (apsnd SOME) hopeless_rejects)

                else

                  iter (j + 1) max threshold rel_const_tab' hopeless_rejects

                       hopeful_rejects)

             end

           | relevant candidates rejects

                      (((ax as ((name, th), axiom_consts)), cached_weight)

                       :: hopeful) hopeless =

             let

               val weight =

                 case cached_weight of

                   SOME w => w

                 | NONE => axiom_weight const_tab rel_const_tab axiom_consts

             in

               if weight >= threshold then

                 relevant ((ax, weight) :: candidates) rejects hopeful hopeless

               else

                 relevant candidates ((ax, weight) :: rejects) hopeful hopeless

             end

         in

           trace_msg (fn () =>

               "ITERATION " ^ string_of_int j ^ ": current threshold: " ^

               Real.toString threshold ^ ", constants: " ^

               commas (rel_const_tab |> Symtab.dest

                       |> filter (curry (op <>) [] o snd)

                       |> map string_for_super_pseudoconst));

           relevant [] [] hopeful hopeless

         end

   in

     axioms |> filter_out (member Thm.eq_thm del_thms o snd)

            |> map (rpair NONE o pair_consts_axiom theory_relevant thy)

            |> iter 0 max_relevant threshold0

                    (get_consts thy (SOME false) goal_ts) []

            |> tap (fn res => trace_msg (fn () =>

                                 "Total relevant: " ^ Int.toString (length res)))

   end

 (***************************************************************)

 (* Retrieving and filtering lemmas                             *)

 (***************************************************************)

 (*** retrieve lemmas and filter them ***)

 (*Reject theorems with names like "List.filter.filter_list_def" or

   "Accessible_Part.acc.defs", as these are definitions arising from packages.*)

 fun is_package_def a =

   let val names = Long_Name.explode a

   in

      length names > 2 andalso

      not (hd names = "local") andalso

      String.isSuffix "_def" a  orelse  String.isSuffix "_defs" a

   end;

 fun make_fact_table xs =

   fold (Termtab.update o `(prop_of o snd)) xs Termtab.empty

 fun make_unique xs = Termtab.fold (cons o snd) (make_fact_table xs) []

 (* FIXME: put other record thms here, or declare as "no_atp" *)

 val multi_base_blacklist =

   ["defs", "select_defs", "update_defs", "induct", "inducts", "split", "splits",

    "split_asm", "cases", "ext_cases", "eq.simps", "eq.refl", "nchotomy",

    "case_cong", "weak_case_cong"]

   |> map (prefix ".")

 val max_lambda_nesting = 3

 fun term_has_too_many_lambdas max (t1 $ t2) =

     exists (term_has_too_many_lambdas max) [t1, t2]

   | term_has_too_many_lambdas max (Abs (_, _, t)) =

     max = 0 orelse term_has_too_many_lambdas (max - 1) t

   | term_has_too_many_lambdas _ _ = false

 (* Don't count nested lambdas at the level of formulas, since they are

    quantifiers. *)

 fun formula_has_too_many_lambdas Ts (Abs (_, T, t)) =

     formula_has_too_many_lambdas (T :: Ts) t

   | formula_has_too_many_lambdas Ts t =

     if is_formula_type (fastype_of1 (Ts, t)) then

       exists (formula_has_too_many_lambdas Ts) (#2 (strip_comb t))

     else

       term_has_too_many_lambdas max_lambda_nesting t

 (* The max apply depth of any "metis" call in "Metis_Examples" (on 2007-10-31)

    was 11. *)

 val max_apply_depth = 15

 fun apply_depth (f $ t) = Int.max (apply_depth f, apply_depth t + 1)

   | apply_depth (Abs (_, _, t)) = apply_depth t

   | apply_depth _ = 0

 fun is_formula_too_complex t =

   apply_depth t > max_apply_depth orelse formula_has_too_many_lambdas [] t

 val exists_sledgehammer_const =

   exists_Const (fn (s, _) => String.isPrefix sledgehammer_prefix s)

 fun is_strange_theorem th =

   case head_of (concl_of th) of

       Const (a, _) => (a <> @{const_name Trueprop} andalso

                        a <> @{const_name "=="})

     | _ => false

 val type_has_top_sort =

   exists_subtype (fn TFree (_, []) => true | TVar (_, []) => true | _ => false)

 (**** Predicates to detect unwanted facts (prolific or likely to cause

       unsoundness) ****)

 (* Too general means, positive equality literal with a variable X as one

    operand, when X does not occur properly in the other operand. This rules out

    clearly inconsistent facts such as X = a | X = b, though it by no means

    guarantees soundness. *)

 (* Unwanted equalities are those between a (bound or schematic) variable that

    does not properly occur in the second operand. *)

 val is_exhaustive_finite =

   let

     fun is_bad_equal (Var z) t =

         not (exists_subterm (fn Var z' => z = z' | _ => false) t)

       | is_bad_equal (Bound j) t = not (loose_bvar1 (t, j))

       | is_bad_equal _ _ = false

     fun do_equals t1 t2 = is_bad_equal t1 t2 orelse is_bad_equal t2 t1

     fun do_formula pos t =

       case (pos, t) of

         (_, @{const Trueprop} $ t1) => do_formula pos t1

       | (true, Const (@{const_name all}, _) $ Abs (_, _, t')) =>

         do_formula pos t'

       | (true, Const (@{const_name All}, _) $ Abs (_, _, t')) =>

         do_formula pos t'

       | (false, Const (@{const_name Ex}, _) $ Abs (_, _, t')) =>

         do_formula pos t'

       | (_, @{const "==>"} $ t1 $ t2) =>

         do_formula (not pos) t1 andalso

         (t2 = @{prop False} orelse do_formula pos t2)

       | (_, @{const "op -->"} $ t1 $ t2) =>

         do_formula (not pos) t1 andalso

         (t2 = @{const False} orelse do_formula pos t2)

       | (_, @{const Not} $ t1) => do_formula (not pos) t1

       | (true, @{const "op |"} $ t1 $ t2) => forall (do_formula pos) [t1, t2]

       | (false, @{const "op &"} $ t1 $ t2) => forall (do_formula pos) [t1, t2]

       | (true, Const (@{const_name "op ="}, _) $ t1 $ t2) => do_equals t1 t2

       | (true, Const (@{const_name "=="}, _) $ t1 $ t2) => do_equals t1 t2

       | _ => false

   in do_formula true end

 fun has_bound_or_var_of_type tycons =

   exists_subterm (fn Var (_, Type (s, _)) => member (op =) tycons s

                    | Abs (_, Type (s, _), _) => member (op =) tycons s

                    | _ => false)

 (* Facts are forbidden to contain variables of these types. The typical reason

    is that they lead to unsoundness. Note that "unit" satisfies numerous

    equations like "?x = ()". The resulting clauses will have no type constraint,

    yielding false proofs. Even "bool" leads to many unsound proofs, though only

    for higher-order problems. *)

 val dangerous_types = [@{type_name unit}, @{type_name bool}, @{type_name prop}];

 (* Facts containing variables of type "unit" or "bool" or of the form

    "ALL x. x = A | x = B | x = C" are likely to lead to unsound proofs if types

    are omitted. *)

 fun is_dangerous_term full_types t =

   not full_types andalso

   let val t = transform_elim_term t in

     has_bound_or_var_of_type dangerous_types t orelse

     is_exhaustive_finite t

   end

 fun is_theorem_bad_for_atps full_types thm =

   let val t = prop_of thm in

     is_formula_too_complex t orelse exists_type type_has_top_sort t orelse

     is_dangerous_term full_types t orelse exists_sledgehammer_const t orelse

     is_strange_theorem thm

   end

 fun all_name_thms_pairs ctxt reserved full_types add_thms chained_ths =

   let

     val is_chained = member Thm.eq_thm chained_ths

     val global_facts = PureThy.facts_of (ProofContext.theory_of ctxt)

     val local_facts = ProofContext.facts_of ctxt

     val named_locals = local_facts |> Facts.dest_static []

     (* Unnamed, not chained formulas with schematic variables are omitted,

        because they are rejected by the backticks (`...`) parser for some

        reason. *)

     fun is_good_unnamed_local th =

       forall (fn (_, ths) => not (member Thm.eq_thm ths th)) named_locals

       andalso (not (exists_subterm is_Var (prop_of th)) orelse (is_chained th))

     val unnamed_locals =

       local_facts |> Facts.props |> filter is_good_unnamed_local

                   |> map (pair "" o single)

     val full_space =

       Name_Space.merge (Facts.space_of global_facts, Facts.space_of local_facts)

     fun add_valid_facts foldx facts =

       foldx (fn (name0, ths) =>

         if name0 <> "" andalso

            forall (not o member Thm.eq_thm add_thms) ths andalso

            (Facts.is_concealed facts name0 orelse

             (respect_no_atp andalso is_package_def name0) orelse

             exists (fn s => String.isSuffix s name0) multi_base_blacklist orelse

             String.isSuffix "_def_raw" (* FIXME: crude hack *) name0) then

           I

         else

           let

             val multi = length ths > 1

             fun backquotify th =

               "`" ^ Print_Mode.setmp [Print_Mode.input]

                                  (Syntax.string_of_term ctxt) (prop_of th) ^ "`"

               |> String.translate (fn c => if Char.isPrint c then str c else "")

               |> simplify_spaces

             fun check_thms a =

               case try (ProofContext.get_thms ctxt) a of

                 NONE => false

               | SOME ths' => Thm.eq_thms (ths, ths')

           in

             pair 1

             #> fold (fn th => fn (j, rest) =>

                  (j + 1,

                   if is_theorem_bad_for_atps full_types th andalso

                      not (member Thm.eq_thm add_thms th) then

                     rest

                   else

                     (fn () =>

                         (if name0 = "" then

                            th |> backquotify

                          else

                            let

                              val name1 = Facts.extern facts name0

                              val name2 = Name_Space.extern full_space name0

                            in

                              case find_first check_thms [name1, name2, name0] of

                                SOME name => repair_name reserved multi j name

                              | NONE => ""

                            end, is_chained th), (multi, th)) :: rest)) ths

             #> snd

           end)

   in

     [] |> add_valid_facts fold local_facts (unnamed_locals @ named_locals)

        |> add_valid_facts Facts.fold_static global_facts global_facts

   end

 (* The single-name theorems go after the multiple-name ones, so that single

    names are preferred when both are available. *)

 fun name_thm_pairs ctxt respect_no_atp =

   List.partition (fst o snd) #> op @ #> map (apsnd snd)

   #> respect_no_atp ? filter_out (No_ATPs.member ctxt o snd)

 (***************************************************************)

 (* ATP invocation methods setup                                *)

 (***************************************************************)

 fun relevant_facts full_types (threshold0, threshold1) max_relevant

                    theory_relevant (relevance_override as {add, del, only})

                    (ctxt, (chained_ths, _)) hyp_ts concl_t =

   let

     val decay = 1.0 - Math.pow ((1.0 - threshold1) / (1.0 - threshold0),

                                 1.0 / Real.fromInt (max_relevant + 1))

     val add_thms = maps (ProofContext.get_fact ctxt) add

     val reserved = reserved_isar_keyword_table ()

     val axioms =

       (if only then

          maps (name_thm_pairs_from_ref ctxt reserved chained_ths) add

        else

          all_name_thms_pairs ctxt reserved full_types add_thms chained_ths)

       |> name_thm_pairs ctxt (respect_no_atp andalso not only)

       |> make_unique

   in

     trace_msg (fn () => "Considering " ^ Int.toString (length axioms) ^

                         " theorems");

     (if threshold0 > 1.0 orelse threshold0 > threshold1 then

        []

      else if threshold0 < 0.0 then

        axioms

      else

        relevance_filter ctxt threshold0 decay max_relevant theory_relevant

                         relevance_override axioms (concl_t :: hyp_ts))

     |> map (apfst (fn f => f ())) |> sort_wrt (fst o fst)

   end

 end;