--- /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;