--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_filter.ML Tue Aug 31 23:46:23 2010 +0200
@@ -0,0 +1,800 @@
+(* 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
+ datatype locality = General | Intro | Elim | Simp | Local | Chained
+
+ type relevance_override =
+ {add: Facts.ref list,
+ del: Facts.ref list,
+ only: bool}
+
+ val trace : bool Unsynchronized.ref
+ val worse_irrel_freq : real Unsynchronized.ref
+ val higher_order_irrel_weight : real Unsynchronized.ref
+ val abs_rel_weight : real Unsynchronized.ref
+ val abs_irrel_weight : real Unsynchronized.ref
+ val skolem_irrel_weight : real Unsynchronized.ref
+ val intro_bonus : real Unsynchronized.ref
+ val elim_bonus : real Unsynchronized.ref
+ val simp_bonus : real Unsynchronized.ref
+ val local_bonus : real Unsynchronized.ref
+ val chained_bonus : real Unsynchronized.ref
+ val max_imperfect : real Unsynchronized.ref
+ val max_imperfect_exp : real Unsynchronized.ref
+ val threshold_divisor : real Unsynchronized.ref
+ val ridiculous_threshold : real Unsynchronized.ref
+ val name_thm_pairs_from_ref :
+ Proof.context -> unit Symtab.table -> thm list -> Facts.ref
+ -> ((string * locality) * thm) list
+ val relevant_facts :
+ Proof.context -> bool -> real * real -> int -> bool -> relevance_override
+ -> thm list -> term list -> term -> ((string * locality) * 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 ()
+
+(* experimental feature *)
+val term_patterns = false
+
+val respect_no_atp = true
+
+datatype locality = General | Intro | Elim | Simp | Local | Chained
+
+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
+ (ths, (1, []))
+ |-> fold (fn th => fn (j, rest) =>
+ (j + 1, ((repair_name reserved multi j name,
+ if member Thm.eq_thm chained_ths th then Chained
+ else General), th) :: rest))
+ |> snd
+ end
+
+(***************************************************************)
+(* Relevance Filtering *)
+(***************************************************************)
+
+(*** constants with types ***)
+
+fun order_of_type (Type (@{type_name fun}, [T1, @{typ bool}])) =
+ order_of_type T1 (* cheat: pretend sets are first-order *)
+ | 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
+
+fun pterm thy t =
+ case strip_comb t of
+ (Const x, ts) => PApp (pconst thy true x ts)
+ | (Free x, ts) => PApp (pconst thy false x ts)
+ | (Var x, []) => PVar
+ | _ => PApp ("?", []) (* equivalence class of higher-order constructs *)
+(* Pairs a constant with the list of its type instantiations. *)
+and ptype thy const x ts =
+ (if const then map pattern_for_type (these (try (Sign.const_typargs thy) x))
+ else []) @
+ (if term_patterns then map (pterm thy) ts else [])
+and pconst thy const (s, T) ts = (s, ptype thy const (s, T) ts)
+and rich_ptype thy const (s, T) ts =
+ PType (order_of_type T, ptype thy const (s, T) ts)
+and rich_pconst thy const (s, T) ts = (s, rich_ptype thy const (s, T) ts)
+
+fun string_for_hyper_pconst (s, ps) =
+ s ^ "{" ^ commas (map string_for_ptype ps) ^ "}"
+
+val abs_name = "Sledgehammer.abs"
+val skolem_prefix = "Sledgehammer.sko"
+
+(* These are typically simplified away by "Meson.presimplify". Equality is
+ handled specially via "fequal". *)
+val boring_consts =
+ [@{const_name False}, @{const_name True}, @{const_name If}, @{const_name Let},
+ @{const_name HOL.eq}]
+
+(* Add a pconstant to the table, but a [] entry means a standard
+ connective, which we ignore.*)
+fun add_pconst_to_table also_skolem (c, p) =
+ if member (op =) boring_consts c orelse
+ (not also_skolem andalso String.isPrefix skolem_prefix c) then
+ I
+ else
+ Symtab.map_default (c, [p]) (insert (op =) p)
+
+fun is_formula_type T = (T = HOLogic.boolT orelse T = propT)
+
+fun pconsts_in_terms thy also_skolems pos ts =
+ 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 ATP, we
+ introduce a fresh constant to simulate the effect of Skolemization. *)
+ fun do_const const (s, T) ts =
+ add_pconst_to_table also_skolems (rich_pconst thy const (s, T) ts)
+ #> 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, t'), ts) =>
+ (null ts
+ ? add_pconst_to_table true (abs_name, PType (order_of_type T + 1, [])))
+ #> fold do_term (t' :: ts)
+ | (_, ts) => fold do_term 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
+ (gensym skolem_prefix, PType (order_of_type abs_T, []))
+ 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 (_, 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 =>
+ 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 (_, 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 =>
+ 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 (_, 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 t0 #> do_formula pos t1 (* theory constant *)
+ | _ => do_term t
+ in Symtab.empty |> 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 "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_axiom_consts theory_relevant thy =
+ 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) ts, 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 theory_relevant o snd end
+
+
+(**** Actual Filtering Code ****)
+
+fun pow_int x 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 order freq = 1.0 + 2.0 / Math.ln (Real.fromInt freq + 1.0)
+
+(* FUDGE *)
+val worse_irrel_freq = Unsynchronized.ref 100.0
+val higher_order_irrel_weight = Unsynchronized.ref 1.05
+
+(* 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 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
+
+(* FUDGE *)
+val abs_rel_weight = Unsynchronized.ref 0.5
+val abs_irrel_weight = Unsynchronized.ref 2.0
+val skolem_irrel_weight = Unsynchronized.ref 0.75
+
+(* Computes a constant's weight, as determined by its frequency. *)
+fun generic_pconst_weight abs_weight skolem_weight weight_for f const_tab
+ (c as (s, PType (m, _))) =
+ if s = abs_name then abs_weight
+ else if String.isPrefix skolem_prefix s then skolem_weight
+ else weight_for m (pconst_freq (match_ptype o f) const_tab c)
+
+fun rel_pconst_weight const_tab =
+ generic_pconst_weight (!abs_rel_weight) 0.0 rel_weight_for I const_tab
+fun irrel_pconst_weight const_tab =
+ generic_pconst_weight (!abs_irrel_weight) (!skolem_irrel_weight)
+ irrel_weight_for swap const_tab
+
+(* FUDGE *)
+val intro_bonus = Unsynchronized.ref 0.15
+val elim_bonus = Unsynchronized.ref 0.15
+val simp_bonus = Unsynchronized.ref 0.15
+val local_bonus = Unsynchronized.ref 0.55
+val chained_bonus = Unsynchronized.ref 1.5
+
+fun locality_bonus General = 0.0
+ | locality_bonus Intro = !intro_bonus
+ | locality_bonus Elim = !elim_bonus
+ | locality_bonus Simp = !simp_bonus
+ | locality_bonus Local = !local_bonus
+ | locality_bonus Chained = !chained_bonus
+
+fun axiom_weight loc const_tab relevant_consts axiom_consts =
+ case axiom_consts |> List.partition (pconst_hyper_mem I relevant_consts)
+ ||> filter_out (pconst_hyper_mem swap relevant_consts) of
+ ([], _) => 0.0
+ | (rel, irrel) =>
+ let
+ val irrel = irrel |> filter_out (pconst_mem swap rel)
+ val rel_weight =
+ 0.0 |> fold (curry (op +) o rel_pconst_weight const_tab) rel
+ val irrel_weight =
+ ~ (locality_bonus loc)
+ |> fold (curry (op +) o irrel_pconst_weight const_tab) irrel
+ val res = rel_weight / (rel_weight + irrel_weight)
+ in if Real.isFinite res then res else 0.0 end
+
+(* FIXME: experiment
+fun debug_axiom_weight loc const_tab relevant_consts axiom_consts =
+ case axiom_consts |> List.partition (pconst_hyper_mem I relevant_consts)
+ ||> filter_out (pconst_hyper_mem swap relevant_consts) of
+ ([], _) => 0.0
+ | (rel, irrel) =>
+ let
+ val irrel = irrel |> filter_out (pconst_mem swap rel)
+ val rels_weight =
+ 0.0 |> fold (curry (op +) o rel_pconst_weight const_tab) rel
+ val irrels_weight =
+ ~ (locality_bonus loc)
+ |> fold (curry (op +) o irrel_pconst_weight const_tab) irrel
+val _ = tracing (PolyML.makestring ("REL: ", map (`(rel_pconst_weight const_tab)) rel))
+val _ = tracing (PolyML.makestring ("IRREL: ", map (`(irrel_pconst_weight const_tab)) irrel))
+ val res = rels_weight / (rels_weight + irrels_weight)
+ in if Real.isFinite res then res else 0.0 end
+*)
+
+fun pconsts_in_axiom thy t =
+ Symtab.fold (fn (s, pss) => fold (cons o pair s) pss)
+ (pconsts_in_terms thy true (SOME true) [t]) []
+fun pair_consts_axiom theory_relevant thy axiom =
+ case axiom |> snd |> theory_const_prop_of theory_relevant
+ |> pconsts_in_axiom thy of
+ [] => NONE
+ | consts => SOME ((axiom, consts), NONE)
+
+type annotated_thm =
+ (((unit -> string) * locality) * thm) * (string * ptype) list
+
+(* FUDGE *)
+val max_imperfect = Unsynchronized.ref 11.5
+val max_imperfect_exp = Unsynchronized.ref 1.0
+
+fun take_most_relevant max_relevant remaining_max
+ (candidates : (annotated_thm * real) list) =
+ let
+ val max_imperfect =
+ Real.ceil (Math.pow (!max_imperfect,
+ Math.pow (Real.fromInt remaining_max
+ / Real.fromInt max_relevant, !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 (fn () =>
+ "Actually passed (" ^ Int.toString (length accepts) ^ " of " ^
+ Int.toString (length candidates) ^ "): " ^
+ (accepts |> map (fn ((((name, _), _), _), weight) =>
+ name () ^ " [" ^ Real.toString weight ^ "]")
+ |> commas));
+ (accepts, more_rejects @ rejects)
+ end
+
+fun if_empty_replace_with_locality thy axioms loc tab =
+ if Symtab.is_empty tab then
+ pconsts_in_terms thy false (SOME false)
+ (map_filter (fn ((_, loc'), th) =>
+ if loc' = loc then SOME (prop_of th) else NONE) axioms)
+ else
+ tab
+
+(* FUDGE *)
+val threshold_divisor = Unsynchronized.ref 2.0
+val ridiculous_threshold = Unsynchronized.ref 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 goal_const_tab =
+ pconsts_in_terms thy false (SOME false) goal_ts
+ |> fold (if_empty_replace_with_locality thy axioms) [Chained, Local]
+ val add_thms = maps (ProofContext.get_fact ctxt) add
+ val del_thms = maps (ProofContext.get_fact ctxt) del
+ fun iter j remaining_max threshold rel_const_tab hopeless hopeful =
+ let
+ fun game_over rejects =
+ (* 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 [] =
+ (* Nothing has been added this iteration. *)
+ if j = 0 andalso threshold >= !ridiculous_threshold then
+ (* First iteration? Try again. *)
+ iter 0 max_relevant (threshold / !threshold_divisor) rel_const_tab
+ hopeless hopeful
+ else
+ game_over (rejects @ hopeless)
+ | relevant candidates rejects [] =
+ let
+ val (accepts, more_rejects) =
+ take_most_relevant max_relevant remaining_max 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 threshold =
+ 1.0 - (1.0 - threshold)
+ * Math.pow (decay, Real.fromInt (length accepts))
+ val remaining_max = remaining_max - length accepts
+ in
+ trace_msg (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
+ game_over (hopeful_rejects @ map (apsnd SOME) hopeless_rejects)
+ else
+ iter (j + 1) remaining_max threshold rel_const_tab'
+ hopeless_rejects hopeful_rejects)
+ end
+ | relevant candidates rejects
+ (((ax as (((_, loc), th), axiom_consts)), cached_weight)
+ :: hopeful) =
+ let
+ val weight =
+ case cached_weight of
+ SOME w => w
+ | NONE => axiom_weight loc const_tab rel_const_tab axiom_consts
+(* FIXME: experiment
+val name = fst (fst (fst ax)) ()
+val _ = if String.isSubstring "positive_minus" name orelse String.isSubstring "not_exp_le_zero" name then
+tracing ("*** " ^ name ^ PolyML.makestring (debug_axiom_weight loc const_tab rel_const_tab axiom_consts))
+else
+()
+*)
+ in
+ if weight >= threshold then
+ relevant ((ax, weight) :: candidates) rejects hopeful
+ else
+ relevant candidates ((ax, weight) :: rejects) hopeful
+ 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_hyper_pconst));
+ relevant [] [] hopeful
+ end
+ in
+ axioms |> filter_out (member Thm.eq_thm del_thms o snd)
+ |> map_filter (pair_consts_axiom theory_relevant thy)
+ |> iter 0 max_relevant threshold0 goal_const_tab []
+ |> 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 mk_fact_table f xs =
+ fold (Termtab.update o `(prop_of o f)) xs Termtab.empty
+fun uniquify xs = Termtab.fold (cons o snd) (mk_fact_table snd 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)
+
+(* FIXME: make more reliable *)
+val exists_low_level_class_const =
+ exists_Const (fn (s, _) =>
+ String.isSubstring (Long_Name.separator ^ "class" ^ Long_Name.separator) s)
+
+fun is_metastrange_theorem th =
+ case head_of (concl_of th) of
+ Const (a, _) => (a <> @{const_name Trueprop} andalso
+ a <> @{const_name "=="})
+ | _ => false
+
+fun is_that_fact th =
+ String.isSuffix (Long_Name.separator ^ Obtain.thatN) (Thm.get_name_hint th)
+ andalso exists_subterm (fn Free (s, _) => s = Name.skolem Auto_Bind.thesisN
+ | _ => false) (prop_of th)
+
+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 HOL.implies} $ 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 HOL.disj} $ t1 $ t2) => forall (do_formula pos) [t1, t2]
+ | (false, @{const HOL.conj} $ t1 $ t2) => forall (do_formula pos) [t1, t2]
+ | (true, Const (@{const_name HOL.eq}, _) $ 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
+ exists_low_level_class_const t orelse is_metastrange_theorem thm orelse
+ is_that_fact thm
+ end
+
+fun clasimpset_rules_of ctxt =
+ let
+ val {safeIs, safeEs, hazIs, hazEs, ...} = ctxt |> claset_of |> rep_cs
+ val intros = safeIs @ hazIs
+ val elims = map Classical.classical_rule (safeEs @ hazEs)
+ val simps = ctxt |> simpset_of |> dest_ss |> #simps |> map snd
+ in (mk_fact_table I intros, mk_fact_table I elims, mk_fact_table I simps) end
+
+fun all_name_thms_pairs ctxt reserved full_types add_thms chained_ths =
+ let
+ val thy = ProofContext.theory_of ctxt
+ val global_facts = PureThy.facts_of thy
+ val local_facts = ProofContext.facts_of ctxt
+ val named_locals = local_facts |> Facts.dest_static []
+ val is_chained = member Thm.eq_thm chained_ths
+ val (intros, elims, simps) =
+ if exists (curry (op <) 0.0) [!intro_bonus, !elim_bonus, !simp_bonus] then
+ clasimpset_rules_of ctxt
+ else
+ (Termtab.empty, Termtab.empty, Termtab.empty)
+ (* Unnamed nonchained formulas with schematic variables are omitted, because
+ they are rejected by the backticks (`...`) parser for some reason. *)
+ fun is_good_unnamed_local th =
+ not (Thm.has_name_hint th) andalso
+ (not (exists_subterm is_Var (prop_of th)) orelse (is_chained th)) andalso
+ forall (fn (_, ths) => not (member Thm.eq_thm ths th)) named_locals
+ val unnamed_locals =
+ union Thm.eq_thm (Facts.props local_facts) chained_ths
+ |> 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_facts global 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),
+ let val t = prop_of th in
+ if is_chained th then Chained
+ else if not global then Local
+ else if Termtab.defined intros t then Intro
+ else if Termtab.defined elims t then Elim
+ else if Termtab.defined simps t then Simp
+ else General
+ end),
+ (multi, th)) :: rest)) ths
+ #> snd
+ end)
+ in
+ [] |> add_facts false fold local_facts (unnamed_locals @ named_locals)
+ |> add_facts true 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 ctxt full_types (threshold0, threshold1) max_relevant
+ theory_relevant (relevance_override as {add, del, only})
+ chained_ths hyp_ts concl_t =
+ let
+ val decay = 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 (map (fn ((name, loc), th) => ((K name, loc), (true, th)))
+ o 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)
+ |> uniquify
+ 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 (apfst (fn f => f ())))
+ end
+
+end;