(* Title: HOL/Tools/Sledgehammer/sledgehammer_fact_filter.ML
Author: Jia Meng, Cambridge University Computer Laboratory, 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 chained_prefix : string
val name_thms_pair_from_ref :
Proof.context -> thm list -> Facts.ref -> string * thm list
val relevant_facts :
bool -> real -> real -> bool -> int -> bool -> relevance_override
-> Proof.context * (thm list * 'a) -> term list -> term
-> (string * thm) list
end;
structure Sledgehammer_Fact_Filter : SLEDGEHAMMER_FACT_FILTER =
struct
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
(* Used to label theorems chained into the goal. *)
val chained_prefix = sledgehammer_prefix ^ "chained_"
fun name_thms_pair_from_ref ctxt chained_ths xref =
let
val ths = ProofContext.get_fact ctxt xref
val name = Facts.string_of_ref xref
|> forall (member Thm.eq_thm chained_ths) ths
? prefix chained_prefix
in (name, ths) end
(***************************************************************)
(* Relevance Filtering *)
(***************************************************************)
fun strip_Trueprop (@{const Trueprop} $ t) = t
| strip_Trueprop t = t;
(*** constants with types ***)
(*An abstraction of Isabelle types*)
datatype const_typ = CTVar | CType of string * const_typ list
(*Is the second type an instance of the first one?*)
fun match_type (CType(con1,args1)) (CType(con2,args2)) =
con1=con2 andalso match_types args1 args2
| match_type CTVar _ = true
| match_type _ CTVar = false
and match_types [] [] = true
| match_types (a1::as1) (a2::as2) = match_type a1 a2 andalso match_types as1 as2;
(*Is there a unifiable constant?*)
fun uni_mem goal_const_tab (c, c_typ) =
exists (match_types c_typ) (these (Symtab.lookup goal_const_tab c))
(*Maps a "real" type to a const_typ*)
fun const_typ_of (Type (c,typs)) = CType (c, map const_typ_of typs)
| const_typ_of (TFree _) = CTVar
| const_typ_of (TVar _) = CTVar
(*Pairs a constant with the list of its type instantiations (using const_typ)*)
fun const_with_typ thy (c,typ) =
let val tvars = Sign.const_typargs thy (c,typ)
in (c, map const_typ_of tvars) end
handle TYPE _ => (c,[]); (*Variable (locale constant): monomorphic*)
(*Add a const/type pair to the table, but a [] entry means a standard connective,
which we ignore.*)
fun add_const_type_to_table (c, ctyps) =
Symtab.map_default (c, [ctyps])
(fn [] => [] | ctypss => insert (op =) ctyps ctypss)
val fresh_prefix = "Sledgehammer.Fresh."
val flip = Option.map not
val boring_natural_consts = [@{const_name If}]
(* Including equality in this list might be expected to stop rules like
subset_antisym from being chosen, but for some reason filtering works better
with them listed. The logical signs All, Ex, &, and --> are omitted for CNF
because any remaining occurrences must be within comprehensions. *)
val boring_cnf_consts =
[@{const_name Trueprop}, @{const_name "==>"}, @{const_name all},
@{const_name "=="}, @{const_name "op |"}, @{const_name Not},
@{const_name "op ="}]
fun get_consts_typs thy pos ts =
let
(* Free variables are included, as well as constants, to handle locales.
"skolem_id" is included to increase the complexity of theorems containing
Skolem functions. In non-CNF form, "Ex" is included but each occurrence
is considered fresh, to simulate the effect of Skolemization. *)
fun do_term t =
case t of
Const x => add_const_type_to_table (const_with_typ thy x)
| Free x => add_const_type_to_table (const_with_typ thy x)
| (t as Const (@{const_name skolem_id}, _)) $ _ => do_term t
| t1 $ t2 => do_term t1 #> do_term t2
| Abs (_, _, t) =>
(* Abstractions lead to combinators, so we add a penalty for them. *)
add_const_type_to_table (gensym fresh_prefix, [])
#> do_term t
| _ => I
fun do_quantifier sweet_pos pos body_t =
do_formula pos body_t
#> (if pos = SOME sweet_pos then I
else add_const_type_to_table (gensym fresh_prefix, []))
and do_equality T t1 t2 =
fold (if T = @{typ bool} orelse T = @{typ prop} then do_formula NONE
else do_term) [t1, t2]
and do_formula pos t =
case t of
Const (@{const_name all}, _) $ Abs (_, _, body_t) =>
do_quantifier false pos body_t
| @{const "==>"} $ t1 $ t2 =>
do_formula (flip pos) t1 #> do_formula pos t2
| Const (@{const_name "=="}, Type (_, [T, _])) $ t1 $ t2 =>
do_equality 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 false pos body_t
| Const (@{const_name Ex}, _) $ Abs (_, _, body_t) =>
do_quantifier true pos 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 =>
do_equality T t1 t2
| (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_natural_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 type const_typ list.*)
local
fun cons_nr CTVar = 0
| cons_nr (CType _) = 1;
in
fun const_typ_ord TU =
case TU of
(CType (a, Ts), CType (b, Us)) =>
(case fast_string_ord(a,b) of EQUAL => dict_ord const_typ_ord (Ts,Us) | ord => ord)
| (T, U) => int_ord (cons_nr T, cons_nr U);
end;
structure CTtab = Table(type key = const_typ list val ord = dict_ord const_typ_ord);
fun count_axiom_consts theory_relevant thy (_, th) =
let
fun do_const (a, T) =
let val (c, cts) = const_with_typ 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 (Const (x as (@{const_name skolem_id}, _)) $ _) = 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 const_frequency const_tab (c, cts) =
CTtab.fold (fn (cts', m) => match_types cts cts' ? Integer.add m)
(the (Symtab.lookup const_tab c)
handle Option.Option => raise Fail ("Const: " ^ c)) 0
(*A surprising number of theorems contain only a few significant constants.
These include all induction rules, and other general theorems. Filtering
theorems in clause form reveals these complexities in the form of Skolem
functions. If we were instead to filter theorems in their natural form,
some other method of measuring theorem complexity would become necessary.*)
(* "log" seems best in practice. A constant function of one ignores the constant
frequencies. *)
fun log_weight2 (x:real) = 1.0 + 2.0 / Math.ln (x + 1.0)
(* Computes a constant's weight, as determined by its frequency. *)
val ct_weight = log_weight2 o real oo const_frequency
(*Relevant constants are weighted according to frequency,
but irrelevant constants are simply counted. Otherwise, Skolem functions,
which are rare, would harm a clause's chances of being picked.*)
fun clause_weight const_tab gctyps consts_typs =
let val rel = filter (uni_mem gctyps) consts_typs
val rel_weight = fold (curry Real.+ o ct_weight const_tab) rel 0.0
in
rel_weight / (rel_weight + real (length consts_typs - length rel))
end;
(*Multiplies out to a list of pairs: 'a * 'b list -> ('a * 'b) list -> ('a * 'b) list*)
fun add_expand_pairs (x,ys) xys = List.foldl (fn (y,acc) => (x,y)::acc) xys ys;
fun consts_typs_of_term thy t =
Symtab.fold add_expand_pairs (get_consts_typs thy (SOME false) [t]) []
fun pair_consts_typs_axiom theory_relevant thy axiom =
(axiom, axiom |> snd |> theory_const_prop_of theory_relevant
|> consts_typs_of_term thy)
exception CONST_OR_FREE of unit
fun dest_Const_or_Free (Const x) = x
| dest_Const_or_Free (Free x) = x
| dest_Const_or_Free _ = raise CONST_OR_FREE ()
(*Look for definitions of the form f ?x1 ... ?xn = t, but not reversed.*)
fun defines thy thm gctypes =
let val tm = prop_of thm
fun defs lhs rhs =
let val (rator,args) = strip_comb lhs
val ct = const_with_typ thy (dest_Const_or_Free rator)
in
forall is_Var args andalso uni_mem gctypes ct andalso
subset (op =) (Term.add_vars rhs [], Term.add_vars lhs [])
end
handle CONST_OR_FREE () => false
in
case tm of
@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ lhs $ rhs) =>
defs lhs rhs
| _ => false
end;
type annotated_cnf_thm = (string * thm) * (string * const_typ list) list
(*For a reverse sort, putting the largest values first.*)
fun compare_pairs ((_, w1), (_, w2)) = Real.compare (w2, w1)
(*Limit the number of new clauses, to prevent runaway acceptance.*)
fun take_best max_new (newpairs : (annotated_cnf_thm * real) list) =
let val nnew = length newpairs
in
if nnew <= max_new then (map #1 newpairs, [])
else
let val cls = sort compare_pairs newpairs
val accepted = List.take (cls, max_new)
in
trace_msg (fn () => ("Number of candidates, " ^ Int.toString nnew ^
", exceeds the limit of " ^ Int.toString (max_new)));
trace_msg (fn () => ("Effective pass mark: " ^ Real.toString (#2 (List.last accepted))));
trace_msg (fn () => "Actually passed: " ^
space_implode ", " (map (fst o fst o fst) accepted));
(map #1 accepted, map #1 (List.drop (cls, max_new)))
end
end;
fun relevant_clauses ctxt relevance_convergence defs_relevant max_new
({add, del, ...} : relevance_override) const_tab =
let
val thy = ProofContext.theory_of ctxt
val add_thms = maps (ProofContext.get_fact ctxt) add
val del_thms = maps (ProofContext.get_fact ctxt) del
fun iter threshold rel_const_tab =
let
fun relevant ([], _) [] = [] (* Nothing added this iteration *)
| relevant (newpairs, rejects) [] =
let
val (newrels, more_rejects) = take_best max_new newpairs
val new_consts = maps #2 newrels
val rel_const_tab =
rel_const_tab |> fold add_const_type_to_table new_consts
val threshold =
threshold + (1.0 - threshold) / relevance_convergence
in
trace_msg (fn () => "relevant this iteration: " ^
Int.toString (length newrels));
map #1 newrels @ iter threshold rel_const_tab
(more_rejects @ rejects)
end
| relevant (newrels, rejects)
((ax as (clsthm as (name, th), consts_typs)) :: axs) =
let
val weight =
if member Thm.eq_thm add_thms th then 1.0
else if member Thm.eq_thm del_thms th then 0.0
else clause_weight const_tab rel_const_tab consts_typs
in
if weight >= threshold orelse
(defs_relevant andalso defines thy th rel_const_tab) then
(trace_msg (fn () =>
name ^ " passes: " ^ Real.toString weight
(* ^ " consts: " ^ commas (map fst consts_typs) *));
relevant ((ax, weight) :: newrels, rejects) axs)
else
relevant (newrels, ax :: rejects) axs
end
in
trace_msg (fn () => "relevant_clauses, current threshold: " ^
Real.toString threshold);
relevant ([], [])
end
in iter end
fun relevance_filter ctxt relevance_threshold relevance_convergence
defs_relevant max_new theory_relevant relevance_override
thy axioms goal_ts =
if relevance_threshold > 1.0 then
[]
else if relevance_threshold < 0.0 then
axioms
else
let
val const_tab = fold (count_axiom_consts theory_relevant thy) axioms
Symtab.empty
val goal_const_tab = get_consts_typs thy (SOME true) goal_ts
val relevance_threshold = 0.9 * relevance_threshold (* FIXME *)
val _ =
trace_msg (fn () => "Initial constants: " ^
commas (goal_const_tab
|> Symtab.dest
|> filter (curry (op <>) [] o snd)
|> map fst))
val relevant =
relevant_clauses ctxt relevance_convergence defs_relevant max_new
relevance_override const_tab relevance_threshold
goal_const_tab
(map (pair_consts_typs_axiom theory_relevant thy)
axioms)
in
trace_msg (fn () => "Total relevant: " ^ Int.toString (length relevant));
relevant
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_clause_table xs =
fold (Termtab.update o `(prop_of o snd)) xs Termtab.empty
fun make_unique xs =
Termtab.fold (cons o snd) (make_clause_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"]
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
fun is_formula_type T = (T = HOLogic.boolT orelse T = propT)
(* 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 31-10-2007)
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 Meson.too_many_clauses NONE t orelse
formula_has_too_many_lambdas [] t
val exists_sledgehammer_const =
exists_Const (fn (s, _) => String.isPrefix sledgehammer_prefix s)
fun is_strange_thm 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)
fun is_theorem_bad_for_atps thm =
let val t = prop_of thm in
is_formula_too_complex t orelse exists_type type_has_top_sort t orelse
exists_sledgehammer_const t orelse is_strange_thm thm
end
fun all_name_thms_pairs ctxt chained_ths =
let
val global_facts = PureThy.facts_of (ProofContext.theory_of ctxt);
val local_facts = ProofContext.facts_of ctxt;
val full_space =
Name_Space.merge (Facts.space_of global_facts, Facts.space_of local_facts);
fun valid_facts facts =
(facts, []) |-> Facts.fold_static (fn (name, ths0) =>
if Facts.is_concealed facts name orelse
(respect_no_atp andalso is_package_def name) orelse
member (op =) multi_base_blacklist (Long_Name.base_name name) then
I
else
let
fun check_thms a =
(case try (ProofContext.get_thms ctxt) a of
NONE => false
| SOME ths1 => Thm.eq_thms (ths0, ths1));
val name1 = Facts.extern facts name;
val name2 = Name_Space.extern full_space name;
val ths = filter_out is_theorem_bad_for_atps ths0
in
case find_first check_thms [name1, name2, name] of
NONE => I
| SOME name' =>
cons (name' |> forall (member Thm.eq_thm chained_ths) ths
? prefix chained_prefix, ths)
end)
in valid_facts global_facts @ valid_facts local_facts end;
fun multi_name a th (n, pairs) =
(n + 1, (a ^ "(" ^ Int.toString n ^ ")", th) :: pairs);
fun add_names (_, []) pairs = pairs
| add_names (a, [th]) pairs = (a, th) :: pairs
| add_names (a, ths) pairs = #2 (fold (multi_name a) ths (1, pairs))
fun is_multi (a, ths) = length ths > 1 orelse String.isSuffix ".axioms" a;
(* 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 name_thms_pairs =
let
val (mults, singles) = List.partition is_multi name_thms_pairs
val ps = [] |> fold add_names singles |> fold add_names mults
in ps |> respect_no_atp ? filter_out (No_ATPs.member ctxt o snd) end;
fun is_named ("", th) =
(warning ("No name for theorem " ^
Display.string_of_thm_without_context th); false)
| is_named _ = true
fun checked_name_thm_pairs respect_no_atp ctxt =
name_thm_pairs ctxt respect_no_atp
#> tap (fn ps => trace_msg
(fn () => ("Considering " ^ Int.toString (length ps) ^
" theorems")))
#> filter is_named
(***************************************************************)
(* ATP invocation methods setup *)
(***************************************************************)
(**** Predicates to detect unwanted clauses (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 clauses such as V=a|V=b, though it by no means guarantees soundness. **)
fun var_occurs_in_term ix =
let
fun aux (Var (jx, _)) = (ix = jx)
| aux (t1 $ t2) = aux t1 orelse aux t2
| aux (Abs (_, _, t)) = aux t
| aux _ = false
in aux end
fun is_record_type T = not (null (Record.dest_recTs T))
(*Unwanted equalities include
(1) those between a variable that does not properly occur in the second operand,
(2) those between a variable and a record, since these seem to be prolific "cases" thms
*)
fun too_general_eqterms (Var (ix,T), t) =
not (var_occurs_in_term ix t) orelse is_record_type T
| too_general_eqterms _ = false;
fun too_general_equality (Const (@{const_name "op ="}, _) $ x $ y) =
too_general_eqterms (x,y) orelse too_general_eqterms(y,x)
| too_general_equality _ = false;
fun has_typed_var tycons = exists_subterm
(fn Var (_, Type (a, _)) => member (op =) tycons a | _ => false);
(* Clauses 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 clause 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}];
(* Clauses containing variables of type "unit" or "bool" or of the form
"?x = A | ?x = B | ?x = C" are likely to lead to unsound proofs if types are
omitted. *)
fun is_dangerous_term _ @{prop True} = true
| is_dangerous_term full_types t =
not full_types andalso
(has_typed_var dangerous_types t orelse
forall too_general_equality (HOLogic.disjuncts (strip_Trueprop t)))
fun relevant_facts full_types relevance_threshold relevance_convergence
defs_relevant max_new theory_relevant
(relevance_override as {add, del, only})
(ctxt, (chained_ths, _)) hyp_ts concl_t =
let
val thy = ProofContext.theory_of ctxt
val add_thms = maps (ProofContext.get_fact ctxt) add
val has_override = not (null add) orelse not (null del)
(*###
val is_FO = forall Meson.is_fol_term thy (concl_t :: hyp_ts)
*)
val axioms =
checked_name_thm_pairs (respect_no_atp andalso not only) ctxt
(map (name_thms_pair_from_ref ctxt chained_ths) add @
(if only then [] else all_name_thms_pairs ctxt chained_ths))
|> not has_override ? make_unique
|> filter (fn (_, th) =>
member Thm.eq_thm add_thms th orelse
((* ### FIXME: keep? (not is_FO orelse is_quasi_fol_theorem thy th) andalso*)
not (is_dangerous_term full_types (prop_of th))))
in
relevance_filter ctxt relevance_threshold relevance_convergence
defs_relevant max_new theory_relevant relevance_override
thy axioms (concl_t :: hyp_ts)
|> has_override ? make_unique
|> sort_wrt fst
end
end;