src/HOL/Tools/Sledgehammer/sledgehammer_mepo.ML
changeset 48380 d4b7c7be3116
parent 48308 89674e5a4d35
child 48381 1b7d798460bb
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_mepo.ML	Fri Jul 20 22:19:45 2012 +0200
@@ -0,0 +1,537 @@
+(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_mepo.ML
+    Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA
+    Author:     Jasmin Blanchette, TU Muenchen
+
+Sledgehammer's iterative relevance filter (MePo = Meng-Paulson).
+*)
+
+signature SLEDGEHAMMER_FILTER_ITER =
+sig
+  type stature = ATP_Problem_Generate.stature
+  type fact = Sledgehammer_Fact.fact
+  type params = Sledgehammer_Provers.params
+  type relevance_fudge = Sledgehammer_Provers.relevance_fudge
+
+  val trace : bool Config.T
+  val pseudo_abs_name : string
+  val pseudo_skolem_prefix : string
+  val const_names_in_fact :
+    theory -> (string * typ -> term list -> bool * term list) -> term
+    -> string list
+  val iterative_relevant_facts :
+    Proof.context -> params -> string -> int -> relevance_fudge option
+    -> term list -> term -> fact list -> fact list
+end;
+
+structure Sledgehammer_Filter_Iter : SLEDGEHAMMER_FILTER_ITER =
+struct
+
+open ATP_Problem_Generate
+open Sledgehammer_Fact
+open Sledgehammer_Provers
+
+val trace =
+  Attrib.setup_config_bool @{binding sledgehammer_filter_iter_trace} (K false)
+fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else ()
+
+val sledgehammer_prefix = "Sledgehammer" ^ Long_Name.separator
+val pseudo_abs_name = sledgehammer_prefix ^ "abs"
+val pseudo_skolem_prefix = sledgehammer_prefix ^ "sko"
+val theory_const_suffix = Long_Name.separator ^ " 1"
+
+fun order_of_type (Type (@{type_name fun}, [T1, T2])) =
+    Int.max (order_of_type T1 + 1, order_of_type T2)
+  | order_of_type (Type (_, Ts)) = fold (Integer.max o order_of_type) Ts 0
+  | order_of_type _ = 0
+
+(* An abstraction of Isabelle types and first-order terms *)
+datatype pattern = PVar | PApp of string * pattern list
+datatype ptype = PType of int * pattern list
+
+fun string_for_pattern PVar = "_"
+  | string_for_pattern (PApp (s, ps)) =
+    if null ps then s else s ^ string_for_patterns ps
+and string_for_patterns ps = "(" ^ commas (map string_for_pattern ps) ^ ")"
+fun string_for_ptype (PType (_, ps)) = string_for_patterns ps
+
+(*Is the second type an instance of the first one?*)
+fun match_pattern (PVar, _) = true
+  | match_pattern (PApp _, PVar) = false
+  | match_pattern (PApp (s, ps), PApp (t, qs)) =
+    s = t andalso match_patterns (ps, qs)
+and match_patterns (_, []) = true
+  | match_patterns ([], _) = false
+  | match_patterns (p :: ps, q :: qs) =
+    match_pattern (p, q) andalso match_patterns (ps, qs)
+fun match_ptype (PType (_, ps), PType (_, qs)) = match_patterns (ps, qs)
+
+(* Is there a unifiable constant? *)
+fun pconst_mem f consts (s, ps) =
+  exists (curry (match_ptype o f) ps)
+         (map snd (filter (curry (op =) s o fst) consts))
+fun pconst_hyper_mem f const_tab (s, ps) =
+  exists (curry (match_ptype o f) ps) (these (Symtab.lookup const_tab s))
+
+fun pattern_for_type (Type (s, Ts)) = PApp (s, map pattern_for_type Ts)
+  | pattern_for_type (TFree (s, _)) = PApp (s, [])
+  | pattern_for_type (TVar _) = PVar
+
+(* Pairs a constant with the list of its type instantiations. *)
+fun ptype thy const x =
+  (if const then map pattern_for_type (these (try (Sign.const_typargs thy) x))
+   else [])
+fun rich_ptype thy const (s, T) =
+  PType (order_of_type T, ptype thy const (s, T))
+fun rich_pconst thy const (s, T) = (s, rich_ptype thy const (s, T))
+
+fun string_for_hyper_pconst (s, ps) =
+  s ^ "{" ^ commas (map string_for_ptype ps) ^ "}"
+
+(* Add a pconstant to the table, but a [] entry means a standard
+   connective, which we ignore.*)
+fun add_pconst_to_table also_skolem (s, p) =
+  if (not also_skolem andalso String.isPrefix pseudo_skolem_prefix s) then I
+  else Symtab.map_default (s, [p]) (insert (op =) p)
+
+(* Set constants tend to pull in too many irrelevant facts. We limit the damage
+   by treating them more or less as if they were built-in but add their
+   axiomatization at the end. *)
+val set_consts = [@{const_name Collect}, @{const_name Set.member}]
+val set_thms = @{thms Collect_mem_eq mem_Collect_eq Collect_cong}
+
+fun add_pconsts_in_term thy is_built_in_const also_skolems pos =
+  let
+    val flip = Option.map not
+    (* We include free variables, as well as constants, to handle locales. For
+       each quantifiers that must necessarily be skolemized by the automatic
+       prover, we introduce a fresh constant to simulate the effect of
+       Skolemization. *)
+    fun do_const const ext_arg (x as (s, _)) ts =
+      let val (built_in, ts) = is_built_in_const x ts in
+        if member (op =) set_consts s then
+          fold (do_term ext_arg) ts
+        else
+          (not built_in
+           ? add_pconst_to_table also_skolems (rich_pconst thy const x))
+          #> fold (do_term false) ts
+      end
+    and do_term ext_arg t =
+      case strip_comb t of
+        (Const x, ts) => do_const true ext_arg x ts
+      | (Free x, ts) => do_const false ext_arg x ts
+      | (Abs (_, T, t'), ts) =>
+        ((null ts andalso not ext_arg)
+         (* Since lambdas on the right-hand side of equalities are usually
+            extensionalized later by "abs_extensionalize_term", we don't
+            penalize them here. *)
+         ? add_pconst_to_table true (pseudo_abs_name,
+                                     PType (order_of_type T + 1, [])))
+        #> fold (do_term false) (t' :: ts)
+      | (_, ts) => fold (do_term false) ts
+    fun do_quantifier will_surely_be_skolemized abs_T body_t =
+      do_formula pos body_t
+      #> (if also_skolems andalso will_surely_be_skolemized then
+            add_pconst_to_table true (pseudo_skolem_prefix ^ serial_string (),
+                                      PType (order_of_type abs_T, []))
+          else
+            I)
+    and do_term_or_formula ext_arg T =
+      if T = HOLogic.boolT then do_formula NONE else do_term ext_arg
+    and do_formula pos t =
+      case t of
+        Const (@{const_name all}, _) $ Abs (_, T, t') =>
+        do_quantifier (pos = SOME false) T t'
+      | @{const "==>"} $ t1 $ t2 =>
+        do_formula (flip pos) t1 #> do_formula pos t2
+      | Const (@{const_name "=="}, Type (_, [T, _])) $ t1 $ t2 =>
+        do_term_or_formula false T t1 #> do_term_or_formula true T t2
+      | @{const Trueprop} $ t1 => do_formula pos t1
+      | @{const False} => I
+      | @{const True} => I
+      | @{const Not} $ t1 => do_formula (flip pos) t1
+      | Const (@{const_name All}, _) $ Abs (_, T, t') =>
+        do_quantifier (pos = SOME false) T t'
+      | Const (@{const_name Ex}, _) $ Abs (_, T, t') =>
+        do_quantifier (pos = SOME true) T t'
+      | @{const HOL.conj} $ t1 $ t2 => fold (do_formula pos) [t1, t2]
+      | @{const HOL.disj} $ t1 $ t2 => fold (do_formula pos) [t1, t2]
+      | @{const HOL.implies} $ t1 $ t2 =>
+        do_formula (flip pos) t1 #> do_formula pos t2
+      | Const (@{const_name HOL.eq}, Type (_, [T, _])) $ t1 $ t2 =>
+        do_term_or_formula false T t1 #> do_term_or_formula true T t2
+      | Const (@{const_name If}, Type (_, [_, Type (_, [T, _])]))
+        $ t1 $ t2 $ t3 =>
+        do_formula NONE t1 #> fold (do_term_or_formula false T) [t2, t3]
+      | Const (@{const_name Ex1}, _) $ Abs (_, T, t') =>
+        do_quantifier (is_some pos) T t'
+      | Const (@{const_name Ball}, _) $ t1 $ Abs (_, T, t') =>
+        do_quantifier (pos = SOME false) T
+                      (HOLogic.mk_imp (incr_boundvars 1 t1 $ Bound 0, t'))
+      | Const (@{const_name Bex}, _) $ t1 $ Abs (_, T, t') =>
+        do_quantifier (pos = SOME true) T
+                      (HOLogic.mk_conj (incr_boundvars 1 t1 $ Bound 0, t'))
+      | (t0 as Const (_, @{typ bool})) $ t1 =>
+        do_term false t0 #> do_formula pos t1  (* theory constant *)
+      | _ => do_term false t
+  in do_formula pos end
+
+fun pconsts_in_fact thy is_built_in_const t =
+  Symtab.fold (fn (s, pss) => fold (cons o pair s) pss)
+              (Symtab.empty |> add_pconsts_in_term thy is_built_in_const true
+                                                   (SOME true) t) []
+
+val const_names_in_fact = map fst ooo pconsts_in_fact
+
+(* Inserts a dummy "constant" referring to the theory name, so that relevance
+   takes the given theory into account. *)
+fun theory_constify ({theory_const_rel_weight, theory_const_irrel_weight, ...}
+                     : relevance_fudge) thy_name t =
+  if exists (curry (op <) 0.0) [theory_const_rel_weight,
+                                theory_const_irrel_weight] then
+    Const (thy_name ^ theory_const_suffix, @{typ bool}) $ t
+  else
+    t
+
+fun theory_const_prop_of fudge th =
+  theory_constify fudge (Context.theory_name (theory_of_thm th)) (prop_of th)
+
+fun pair_consts_fact thy is_built_in_const fudge fact =
+  case fact |> snd |> theory_const_prop_of fudge
+            |> pconsts_in_fact thy is_built_in_const of
+    [] => NONE
+  | consts => SOME ((fact, consts), NONE)
+
+(* 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 "pattern list". *)
+
+fun pattern_ord p =
+  case p of
+    (PVar, PVar) => EQUAL
+  | (PVar, PApp _) => LESS
+  | (PApp _, PVar) => GREATER
+  | (PApp q1, PApp q2) =>
+    prod_ord fast_string_ord (dict_ord pattern_ord) (q1, q2)
+fun ptype_ord (PType p, PType q) =
+  prod_ord (dict_ord pattern_ord) int_ord (swap p, swap q)
+
+structure PType_Tab = Table(type key = ptype val ord = ptype_ord)
+
+fun count_fact_consts thy fudge =
+  let
+    fun do_const const (s, T) ts =
+      (* Two-dimensional table update. Constant maps to types maps to count. *)
+      PType_Tab.map_default (rich_ptype thy const (s, T), 0) (Integer.add 1)
+      |> Symtab.map_default (s, PType_Tab.empty)
+      #> fold do_term ts
+    and do_term t =
+      case strip_comb t of
+        (Const x, ts) => do_const true x ts
+      | (Free x, ts) => do_const false x ts
+      | (Abs (_, _, t'), ts) => fold do_term (t' :: ts)
+      | (_, ts) => fold do_term ts
+  in do_term o theory_const_prop_of fudge o snd end
+
+fun pow_int _ 0 = 1.0
+  | pow_int x 1 = x
+  | pow_int x n = if n > 0 then x * pow_int x (n - 1) else pow_int x (n + 1) / x
+
+(*The frequency of a constant is the sum of those of all instances of its type.*)
+fun pconst_freq match const_tab (c, ps) =
+  PType_Tab.fold (fn (qs, m) => match (ps, qs) ? Integer.add m)
+                 (the (Symtab.lookup const_tab c)) 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. Rare constants give more points if they are relevant than less
+   rare ones. *)
+fun rel_weight_for _ freq = 1.0 + 2.0 / Math.ln (Real.fromInt freq + 1.0)
+
+(* Irrelevant constants are treated differently. We associate lower penalties to
+   very rare constants and very common ones -- the former because they can't
+   lead to the inclusion of too many new facts, and the latter because they are
+   so common as to be of little interest. *)
+fun irrel_weight_for ({worse_irrel_freq, higher_order_irrel_weight, ...}
+                      : relevance_fudge) order freq =
+  let val (k, x) = worse_irrel_freq |> `Real.ceil in
+    (if freq < k then Math.ln (Real.fromInt (freq + 1)) / Math.ln x
+     else rel_weight_for order freq / rel_weight_for order k)
+    * pow_int higher_order_irrel_weight (order - 1)
+  end
+
+fun multiplier_for_const_name local_const_multiplier s =
+  if String.isSubstring "." s then 1.0 else local_const_multiplier
+
+(* Computes a constant's weight, as determined by its frequency. *)
+fun generic_pconst_weight local_const_multiplier abs_weight skolem_weight
+                          theory_const_weight chained_const_weight weight_for f
+                          const_tab chained_const_tab (c as (s, PType (m, _))) =
+  if s = pseudo_abs_name then
+    abs_weight
+  else if String.isPrefix pseudo_skolem_prefix s then
+    skolem_weight
+  else if String.isSuffix theory_const_suffix s then
+    theory_const_weight
+  else
+    multiplier_for_const_name local_const_multiplier s
+    * weight_for m (pconst_freq (match_ptype o f) const_tab c)
+    |> (if chained_const_weight < 1.0 andalso
+           pconst_hyper_mem I chained_const_tab c then
+          curry (op *) chained_const_weight
+        else
+          I)
+
+fun rel_pconst_weight ({local_const_multiplier, abs_rel_weight,
+                        theory_const_rel_weight, ...} : relevance_fudge)
+                      const_tab =
+  generic_pconst_weight local_const_multiplier abs_rel_weight 0.0
+                        theory_const_rel_weight 0.0 rel_weight_for I const_tab
+                        Symtab.empty
+
+fun irrel_pconst_weight (fudge as {local_const_multiplier, abs_irrel_weight,
+                                   skolem_irrel_weight,
+                                   theory_const_irrel_weight,
+                                   chained_const_irrel_weight, ...})
+                        const_tab chained_const_tab =
+  generic_pconst_weight local_const_multiplier abs_irrel_weight
+                        skolem_irrel_weight theory_const_irrel_weight
+                        chained_const_irrel_weight (irrel_weight_for fudge) swap
+                        const_tab chained_const_tab
+
+fun stature_bonus ({intro_bonus, ...} : relevance_fudge) (_, Intro) =
+    intro_bonus
+  | stature_bonus {elim_bonus, ...} (_, Elim) = elim_bonus
+  | stature_bonus {simp_bonus, ...} (_, Simp) = simp_bonus
+  | stature_bonus {local_bonus, ...} (Local, _) = local_bonus
+  | stature_bonus {assum_bonus, ...} (Assum, _) = assum_bonus
+  | stature_bonus {chained_bonus, ...} (Chained, _) = chained_bonus
+  | stature_bonus _ _ = 0.0
+
+fun is_odd_const_name s =
+  s = pseudo_abs_name orelse String.isPrefix pseudo_skolem_prefix s orelse
+  String.isSuffix theory_const_suffix s
+
+fun fact_weight fudge stature const_tab relevant_consts chained_consts
+                fact_consts =
+  case fact_consts |> List.partition (pconst_hyper_mem I relevant_consts)
+                   ||> filter_out (pconst_hyper_mem swap relevant_consts) of
+    ([], _) => 0.0
+  | (rel, irrel) =>
+    if forall (forall (is_odd_const_name o fst)) [rel, irrel] then
+      0.0
+    else
+      let
+        val irrel = irrel |> filter_out (pconst_mem swap rel)
+        val rel_weight =
+          0.0 |> fold (curry (op +) o rel_pconst_weight fudge const_tab) rel
+        val irrel_weight =
+          ~ (stature_bonus fudge stature)
+          |> fold (curry (op +)
+                   o irrel_pconst_weight fudge const_tab chained_consts) irrel
+        val res = rel_weight / (rel_weight + irrel_weight)
+      in if Real.isFinite res then res else 0.0 end
+
+fun take_most_relevant ctxt max_facts remaining_max
+        ({max_imperfect, max_imperfect_exp, ...} : relevance_fudge)
+        (candidates : ((fact * (string * ptype) list) * real) list) =
+  let
+    val max_imperfect =
+      Real.ceil (Math.pow (max_imperfect,
+                    Math.pow (Real.fromInt remaining_max
+                              / Real.fromInt max_facts, max_imperfect_exp)))
+    val (perfect, imperfect) =
+      candidates |> sort (Real.compare o swap o pairself snd)
+                 |> take_prefix (fn (_, w) => w > 0.99999)
+    val ((accepts, more_rejects), rejects) =
+      chop max_imperfect imperfect |>> append perfect |>> chop remaining_max
+  in
+    trace_msg ctxt (fn () =>
+        "Actually passed (" ^ string_of_int (length accepts) ^ " of " ^
+        string_of_int (length candidates) ^ "): " ^
+        (accepts |> map (fn ((((name, _), _), _), weight) =>
+                            name () ^ " [" ^ Real.toString weight ^ "]")
+                 |> commas));
+    (accepts, more_rejects @ rejects)
+  end
+
+fun if_empty_replace_with_scope thy is_built_in_const facts sc tab =
+  if Symtab.is_empty tab then
+    Symtab.empty
+    |> fold (add_pconsts_in_term thy is_built_in_const false (SOME false))
+            (map_filter (fn ((_, (sc', _)), th) =>
+                            if sc' = sc then SOME (prop_of th) else NONE) facts)
+  else
+    tab
+
+fun consider_arities is_built_in_const th =
+  let
+    fun aux _ _ NONE = NONE
+      | aux t args (SOME tab) =
+        case t of
+          t1 $ t2 => SOME tab |> aux t1 (t2 :: args) |> aux t2 []
+        | Const (x as (s, _)) =>
+          (if is_built_in_const x args |> fst then
+             SOME tab
+           else case Symtab.lookup tab s of
+             NONE => SOME (Symtab.update (s, length args) tab)
+           | SOME n => if n = length args then SOME tab else NONE)
+        | _ => SOME tab
+  in aux (prop_of th) [] end
+
+(* FIXME: This is currently only useful for polymorphic type encodings. *)
+fun could_benefit_from_ext is_built_in_const facts =
+  fold (consider_arities is_built_in_const o snd) facts (SOME Symtab.empty)
+  |> is_none
+
+(* High enough so that it isn't wrongly considered as very relevant (e.g., for E
+   weights), but low enough so that it is unlikely to be truncated away if few
+   facts are included. *)
+val special_fact_index = 75
+
+fun relevance_filter ctxt thres0 decay max_facts is_built_in_const
+        (fudge as {threshold_divisor, ridiculous_threshold, ...}) facts hyp_ts
+        concl_t =
+  let
+    val thy = Proof_Context.theory_of ctxt
+    val const_tab = fold (count_fact_consts thy fudge) facts Symtab.empty
+    val add_pconsts = add_pconsts_in_term thy is_built_in_const false o SOME
+    val chained_ts =
+      facts |> map_filter (fn ((_, (Chained, _)), th) => SOME (prop_of th)
+                            | _ => NONE)
+    val chained_const_tab = Symtab.empty |> fold (add_pconsts true) chained_ts
+    val goal_const_tab =
+      Symtab.empty |> fold (add_pconsts true) hyp_ts
+                   |> add_pconsts false concl_t
+      |> (fn tab => if Symtab.is_empty tab then chained_const_tab else tab)
+      |> fold (if_empty_replace_with_scope thy is_built_in_const facts)
+              [Chained, Assum, Local]
+    fun iter j remaining_max thres rel_const_tab hopeless hopeful =
+      let
+        fun relevant [] _ [] =
+            (* Nothing has been added this iteration. *)
+            if j = 0 andalso thres >= ridiculous_threshold then
+              (* First iteration? Try again. *)
+              iter 0 max_facts (thres / threshold_divisor) rel_const_tab
+                   hopeless hopeful
+            else
+              []
+          | relevant candidates rejects [] =
+            let
+              val (accepts, more_rejects) =
+                take_most_relevant ctxt max_facts remaining_max fudge candidates
+              val rel_const_tab' =
+                rel_const_tab
+                |> fold (add_pconst_to_table false) (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 thres =
+                1.0 - (1.0 - thres)
+                      * Math.pow (decay, Real.fromInt (length accepts))
+              val remaining_max = remaining_max - length accepts
+            in
+              trace_msg ctxt (fn () => "New or updated constants: " ^
+                  commas (rel_const_tab' |> Symtab.dest
+                          |> subtract (op =) (rel_const_tab |> Symtab.dest)
+                          |> map string_for_hyper_pconst));
+              map (fst o fst) accepts @
+              (if remaining_max = 0 then
+                 []
+               else
+                 iter (j + 1) remaining_max thres rel_const_tab'
+                      hopeless_rejects hopeful_rejects)
+            end
+          | relevant candidates rejects
+                     (((ax as (((_, stature), _), fact_consts)), cached_weight)
+                      :: hopeful) =
+            let
+              val weight =
+                case cached_weight of
+                  SOME w => w
+                | NONE => fact_weight fudge stature const_tab rel_const_tab
+                                      chained_const_tab fact_consts
+            in
+              if weight >= thres then
+                relevant ((ax, weight) :: candidates) rejects hopeful
+              else
+                relevant candidates ((ax, weight) :: rejects) hopeful
+            end
+        in
+          trace_msg ctxt (fn () =>
+              "ITERATION " ^ string_of_int j ^ ": current threshold: " ^
+              Real.toString thres ^ ", constants: " ^
+              commas (rel_const_tab |> Symtab.dest
+                      |> filter (curry (op <>) [] o snd)
+                      |> map string_for_hyper_pconst));
+          relevant [] [] hopeful
+        end
+    fun uses_const s t =
+      fold_aterms (curry (fn (Const (s', _), false) => s' = s | (_, b) => b)) t
+                  false
+    fun uses_const_anywhere accepts s =
+      exists (uses_const s o prop_of o snd) accepts orelse
+      exists (uses_const s) (concl_t :: hyp_ts)
+    fun add_set_const_thms accepts =
+      exists (uses_const_anywhere accepts) set_consts ? append set_thms
+    fun insert_into_facts accepts [] = accepts
+      | insert_into_facts accepts ths =
+        let
+          val add = facts |> filter (member Thm.eq_thm_prop ths o snd)
+          val (bef, after) =
+            accepts |> filter_out (member Thm.eq_thm_prop ths o snd)
+                    |> take (max_facts - length add)
+                    |> chop special_fact_index
+        in bef @ add @ after end
+    fun insert_special_facts accepts =
+       (* FIXME: get rid of "ext" here once it is treated as a helper *)
+       [] |> could_benefit_from_ext is_built_in_const accepts ? cons @{thm ext}
+          |> add_set_const_thms accepts
+          |> insert_into_facts accepts
+  in
+    facts |> map_filter (pair_consts_fact thy is_built_in_const fudge)
+          |> iter 0 max_facts thres0 goal_const_tab []
+          |> insert_special_facts
+          |> tap (fn accepts => trace_msg ctxt (fn () =>
+                      "Total relevant: " ^ string_of_int (length accepts)))
+  end
+
+fun iterative_relevant_facts ctxt
+        ({fact_thresholds = (thres0, thres1), ...} : params) prover
+        max_facts fudge hyp_ts concl_t facts =
+  let
+    val thy = Proof_Context.theory_of ctxt
+    val is_built_in_const =
+      Sledgehammer_Provers.is_built_in_const_for_prover ctxt prover
+    val fudge =
+      case fudge of
+        SOME fudge => fudge
+      | NONE => Sledgehammer_Provers.relevance_fudge_for_prover ctxt prover
+    val decay = Math.pow ((1.0 - thres1) / (1.0 - thres0),
+                          1.0 / Real.fromInt (max_facts + 1))
+  in
+    trace_msg ctxt (fn () => "Considering " ^ string_of_int (length facts) ^
+                             " facts");
+    (if thres1 < 0.0 then
+       facts
+     else if thres0 > 1.0 orelse thres0 > thres1 then
+       []
+     else
+       relevance_filter ctxt thres0 decay max_facts is_built_in_const fudge
+           facts hyp_ts
+           (concl_t |> theory_constify fudge (Context.theory_name thy)))
+  end
+
+end;