(* Title: HOL/Tools/Sledgehammer/sledgehammer_filter.ML
Author: Jia Meng, Cambridge University Computer Laboratory and NICTA
Author: Jasmin Blanchette, TU Muenchen
*)
signature SLEDGEHAMMER_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 theory_const_rel_weight : real Unsynchronized.ref
val theory_const_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_Filter : SLEDGEHAMMER_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
val abs_name = "Sledgehammer.abs"
val skolem_prefix = "Sledgehammer.sko"
val theory_const_suffix = Long_Name.separator ^ " 1"
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) ^ "}"
(* 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 ^ theory_const_suffix, @{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
val theory_const_rel_weight = Unsynchronized.ref 0.5
val theory_const_irrel_weight = Unsynchronized.ref 0.25
(* Computes a constant's weight, as determined by its frequency. *)
fun generic_pconst_weight abs_weight skolem_weight theory_const_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 if String.isSuffix theory_const_suffix s then theory_const_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 (!theory_const_rel_weight)
rel_weight_for I const_tab
fun irrel_pconst_weight const_tab =
generic_pconst_weight (!abs_irrel_weight) (!skolem_irrel_weight)
(!theory_const_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;