(* Title: HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
Author: Fabian Immler, TU Muenchen
Author: Makarius
Author: Jasmin Blanchette, TU Muenchen
Translation of HOL to FOL for Sledgehammer.
*)
signature SLEDGEHAMMER_ATP_TRANSLATE =
sig
type 'a fo_term = 'a ATP_Problem.fo_term
type format = ATP_Problem.format
type formula_kind = ATP_Problem.formula_kind
type 'a problem = 'a ATP_Problem.problem
type locality = Sledgehammer_Filter.locality
datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
datatype type_level =
All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
datatype type_heaviness = Heavy | Light
datatype type_system =
Simple_Types of type_level |
Preds of polymorphism * type_level * type_heaviness |
Tags of polymorphism * type_level * type_heaviness
type translated_formula
val readable_names : bool Config.T
val fact_prefix : string
val conjecture_prefix : string
val helper_prefix : string
val typed_helper_suffix : string
val predicator_name : string
val app_op_name : string
val type_pred_name : string
val simple_type_prefix : string
val type_sys_from_string : string -> type_system
val polymorphism_of_type_sys : type_system -> polymorphism
val level_of_type_sys : type_system -> type_level
val is_type_sys_virtually_sound : type_system -> bool
val is_type_sys_fairly_sound : type_system -> bool
val unmangled_const : string -> string * string fo_term list
val translate_atp_fact :
Proof.context -> format -> type_system -> bool -> (string * locality) * thm
-> translated_formula option * ((string * locality) * thm)
val prepare_atp_problem :
Proof.context -> format -> formula_kind -> formula_kind -> type_system
-> bool -> term list -> term
-> (translated_formula option * ((string * 'a) * thm)) list
-> string problem * string Symtab.table * int * int
* (string * 'a) list vector * int list * int Symtab.table
val atp_problem_weights : string problem -> (string * real) list
end;
structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
struct
open ATP_Problem
open Metis_Translate
open Sledgehammer_Util
open Sledgehammer_Filter
(* experimental *)
val generate_useful_info = false
fun useful_isabelle_info s =
if generate_useful_info then
SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
else
NONE
val intro_info = useful_isabelle_info "intro"
val elim_info = useful_isabelle_info "elim"
val simp_info = useful_isabelle_info "simp"
(* Readable names are often much shorter, especially if types are mangled in
names. Also, the logic for generating legal SNARK sort names is only
implemented for readable names. Finally, readable names are, well, more
readable. For these reason, they are enabled by default. *)
val readable_names =
Attrib.setup_config_bool @{binding sledgehammer_atp_readable_names} (K true)
val type_decl_prefix = "ty_"
val sym_decl_prefix = "sy_"
val sym_formula_prefix = "sym_"
val fact_prefix = "fact_"
val conjecture_prefix = "conj_"
val helper_prefix = "help_"
val class_rel_clause_prefix = "crel_";
val arity_clause_prefix = "arity_"
val tfree_prefix = "tfree_"
val typed_helper_suffix = "_T"
val untyped_helper_suffix = "_U"
val predicator_name = "hBOOL"
val app_op_name = "hAPP"
val type_pred_name = "is"
val simple_type_prefix = "ty_"
fun make_simple_type s =
if s = tptp_bool_type orelse s = tptp_fun_type orelse
s = tptp_individual_type then
s
else
simple_type_prefix ^ ascii_of s
(* Freshness almost guaranteed! *)
val sledgehammer_weak_prefix = "Sledgehammer:"
datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
datatype type_level =
All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
datatype type_heaviness = Heavy | Light
datatype type_system =
Simple_Types of type_level |
Preds of polymorphism * type_level * type_heaviness |
Tags of polymorphism * type_level * type_heaviness
fun try_unsuffixes ss s =
fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
fun type_sys_from_string s =
(case try (unprefix "poly_") s of
SOME s => (SOME Polymorphic, s)
| NONE =>
case try (unprefix "mono_") s of
SOME s => (SOME Monomorphic, s)
| NONE =>
case try (unprefix "mangled_") s of
SOME s => (SOME Mangled_Monomorphic, s)
| NONE => (NONE, s))
||> (fn s =>
(* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
case try_unsuffixes ["?", "_query"] s of
SOME s => (Nonmonotonic_Types, s)
| NONE =>
case try_unsuffixes ["!", "_bang"] s of
SOME s => (Finite_Types, s)
| NONE => (All_Types, s))
||> apsnd (fn s =>
case try (unsuffix "_heavy") s of
SOME s => (Heavy, s)
| NONE => (Light, s))
|> (fn (poly, (level, (heaviness, core))) =>
case (core, (poly, level, heaviness)) of
("simple", (NONE, _, Light)) => Simple_Types level
| ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
| ("tags", (SOME Polymorphic, All_Types, _)) =>
Tags (Polymorphic, All_Types, heaviness)
| ("tags", (SOME Polymorphic, _, _)) =>
(* The actual light encoding is very unsound. *)
Tags (Polymorphic, level, Heavy)
| ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
| ("args", (SOME poly, All_Types (* naja *), Light)) =>
Preds (poly, Const_Arg_Types, Light)
| ("erased", (NONE, All_Types (* naja *), Light)) =>
Preds (Polymorphic, No_Types, Light)
| _ => raise Same.SAME)
handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
| polymorphism_of_type_sys (Preds (poly, _, _)) = poly
| polymorphism_of_type_sys (Tags (poly, _, _)) = poly
fun level_of_type_sys (Simple_Types level) = level
| level_of_type_sys (Preds (_, level, _)) = level
| level_of_type_sys (Tags (_, level, _)) = level
fun heaviness_of_type_sys (Simple_Types _) = Heavy
| heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
| heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
fun is_type_level_virtually_sound level =
level = All_Types orelse level = Nonmonotonic_Types
val is_type_sys_virtually_sound =
is_type_level_virtually_sound o level_of_type_sys
fun is_type_level_fairly_sound level =
is_type_level_virtually_sound level orelse level = Finite_Types
val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
fun is_setting_higher_order THF (Simple_Types _) = true
| is_setting_higher_order _ _ = false
type translated_formula =
{name: string,
locality: locality,
kind: formula_kind,
combformula: (name, typ, combterm) formula,
atomic_types: typ list}
fun update_combformula f ({name, locality, kind, combformula, atomic_types}
: translated_formula) =
{name = name, locality = locality, kind = kind, combformula = f combformula,
atomic_types = atomic_types} : translated_formula
fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
(* The Booleans indicate whether all type arguments should be kept. *)
datatype type_arg_policy =
Explicit_Type_Args of bool |
Mangled_Type_Args of bool |
No_Type_Args
fun should_drop_arg_type_args (Simple_Types _) =
false (* since TFF doesn't support overloading *)
| should_drop_arg_type_args type_sys =
level_of_type_sys type_sys = All_Types andalso
heaviness_of_type_sys type_sys = Heavy
fun general_type_arg_policy type_sys =
if level_of_type_sys type_sys = No_Types then
No_Type_Args
else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
Mangled_Type_Args (should_drop_arg_type_args type_sys)
else
Explicit_Type_Args (should_drop_arg_type_args type_sys)
fun type_arg_policy type_sys s =
if s = @{const_name HOL.eq} orelse
(s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
No_Type_Args
else
general_type_arg_policy type_sys
fun atp_type_literals_for_types format type_sys kind Ts =
if level_of_type_sys type_sys = No_Types orelse format = CNF_UEQ then
[]
else
Ts |> type_literals_for_types
|> filter (fn TyLitVar _ => kind <> Conjecture
| TyLitFree _ => kind = Conjecture)
fun mk_aconns c phis =
let val (phis', phi') = split_last phis in
fold_rev (mk_aconn c) phis' phi'
end
fun mk_ahorn [] phi = phi
| mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
fun mk_aquant _ [] phi = phi
| mk_aquant q xs (phi as AQuant (q', xs', phi')) =
if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
| mk_aquant q xs phi = AQuant (q, xs, phi)
fun close_universally atom_vars phi =
let
fun formula_vars bounds (AQuant (_, xs, phi)) =
formula_vars (map fst xs @ bounds) phi
| formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
| formula_vars bounds (AAtom tm) =
union (op =) (atom_vars tm []
|> filter_out (member (op =) bounds o fst))
in mk_aquant AForall (formula_vars [] phi []) phi end
fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
| combterm_vars (CombConst _) = I
| combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
fun close_combformula_universally phi = close_universally combterm_vars phi
fun term_vars (ATerm (name as (s, _), tms)) =
is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
fun close_formula_universally phi = close_universally term_vars phi
val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
val homo_infinite_type = Type (homo_infinite_type_name, [])
fun fo_term_from_typ higher_order =
let
fun term (Type (s, Ts)) =
ATerm (case (higher_order, s) of
(true, @{type_name bool}) => `I tptp_bool_type
| (true, @{type_name fun}) => `I tptp_fun_type
| _ => if s = homo_infinite_type_name then `I tptp_individual_type
else `make_fixed_type_const s,
map term Ts)
| term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
| term (TVar ((x as (s, _)), _)) =
ATerm ((make_schematic_type_var x, s), [])
in term end
(* This shouldn't clash with anything else. *)
val mangled_type_sep = "\000"
fun generic_mangled_type_name f (ATerm (name, [])) = f name
| generic_mangled_type_name f (ATerm (name, tys)) =
f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
^ ")"
val bool_atype = AType (`I tptp_bool_type)
fun ho_type_from_fo_term higher_order pred_sym ary =
let
fun to_atype ty =
AType ((make_simple_type (generic_mangled_type_name fst ty),
generic_mangled_type_name snd ty))
fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
| to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
fun to_ho (ty as ATerm ((s, _), tys)) =
if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
in if higher_order then to_ho else to_fo ary end
fun mangled_type higher_order pred_sym ary =
ho_type_from_fo_term higher_order pred_sym ary o fo_term_from_typ higher_order
fun mangled_const_name T_args (s, s') =
let
val ty_args = map (fo_term_from_typ false) T_args
fun type_suffix f g =
fold_rev (curry (op ^) o g o prefix mangled_type_sep
o generic_mangled_type_name f) ty_args ""
in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
val parse_mangled_ident =
Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
fun parse_mangled_type x =
(parse_mangled_ident
-- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
[] >> ATerm) x
and parse_mangled_types x =
(parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
fun unmangled_type s =
s |> suffix ")" |> raw_explode
|> Scan.finite Symbol.stopper
(Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
quote s)) parse_mangled_type))
|> fst
val unmangled_const_name = space_explode mangled_type_sep #> hd
fun unmangled_const s =
let val ss = space_explode mangled_type_sep s in
(hd ss, map unmangled_type (tl ss))
end
fun introduce_proxies format type_sys tm =
let
fun aux ary top_level (CombApp (tm1, tm2)) =
CombApp (aux (ary + 1) top_level tm1, aux 0 false tm2)
| aux ary top_level (CombConst (name as (s, s'), T, T_args)) =
(case proxify_const s of
SOME proxy_base =>
(* Proxies are not needed in THF, except for partially applied
equality since THF does not provide any syntax for it. *)
if top_level orelse
(is_setting_higher_order format type_sys andalso
(s <> "equal" orelse ary = 2)) then
(case s of
"c_False" => (tptp_false, s')
| "c_True" => (tptp_true, s')
| _ => name, [])
else
(proxy_base |>> prefix const_prefix, T_args)
| NONE => (name, T_args))
|> (fn (name, T_args) => CombConst (name, T, T_args))
| aux _ _ tm = tm
in aux 0 true tm end
fun combformula_from_prop thy format type_sys eq_as_iff =
let
fun do_term bs t atomic_types =
combterm_from_term thy bs (Envir.eta_contract t)
|>> (introduce_proxies format type_sys #> AAtom)
||> union (op =) atomic_types
fun do_quant bs q s T t' =
let val s = Name.variant (map fst bs) s in
do_formula ((s, T) :: bs) t'
#>> mk_aquant q [(`make_bound_var s, SOME T)]
end
and do_conn bs c t1 t2 =
do_formula bs t1 ##>> do_formula bs t2
#>> uncurry (mk_aconn c)
and do_formula bs t =
case t of
@{const Not} $ t1 => do_formula bs t1 #>> mk_anot
| Const (@{const_name All}, _) $ Abs (s, T, t') =>
do_quant bs AForall s T t'
| Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
do_quant bs AExists s T t'
| @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
| @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
| @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
| Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
| _ => do_term bs t
in do_formula [] end
fun presimplify_term ctxt =
Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
#> Meson.presimplify ctxt
#> prop_of
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
fun conceal_bounds Ts t =
subst_bounds (map (Free o apfst concealed_bound_name)
(0 upto length Ts - 1 ~~ Ts), t)
fun reveal_bounds Ts =
subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
(0 upto length Ts - 1 ~~ Ts))
fun extensionalize_term ctxt t =
let val thy = Proof_Context.theory_of ctxt in
t |> cterm_of thy |> Meson.extensionalize_conv ctxt
|> prop_of |> Logic.dest_equals |> snd
end
fun introduce_combinators_in_term ctxt kind t =
let val thy = Proof_Context.theory_of ctxt in
if Meson.is_fol_term thy t then
t
else
let
fun aux Ts t =
case t of
@{const Not} $ t1 => @{const Not} $ aux Ts t1
| (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
t0 $ Abs (s, T, aux (T :: Ts) t')
| (t0 as Const (@{const_name All}, _)) $ t1 =>
aux Ts (t0 $ eta_expand Ts t1 1)
| (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
t0 $ Abs (s, T, aux (T :: Ts) t')
| (t0 as Const (@{const_name Ex}, _)) $ t1 =>
aux Ts (t0 $ eta_expand Ts t1 1)
| (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
| (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
| (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
| (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
$ t1 $ t2 =>
t0 $ aux Ts t1 $ aux Ts t2
| _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
t
else
t |> conceal_bounds Ts
|> Envir.eta_contract
|> cterm_of thy
|> Meson_Clausify.introduce_combinators_in_cterm
|> prop_of |> Logic.dest_equals |> snd
|> reveal_bounds Ts
val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
handle THM _ =>
(* A type variable of sort "{}" will make abstraction fail. *)
if kind = Conjecture then HOLogic.false_const
else HOLogic.true_const
end
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
fun freeze_term t =
let
fun aux (t $ u) = aux t $ aux u
| aux (Abs (s, T, t)) = Abs (s, T, aux t)
| aux (Var ((s, i), T)) =
Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
| aux t = t
in t |> exists_subterm is_Var t ? aux end
(* making fact and conjecture formulas *)
fun make_formula ctxt format type_sys eq_as_iff presimp name loc kind t =
let
val thy = Proof_Context.theory_of ctxt
val t = t |> Envir.beta_eta_contract
|> transform_elim_prop
|> Object_Logic.atomize_term thy
val need_trueprop = (fastype_of t = @{typ bool})
val t = t |> need_trueprop ? HOLogic.mk_Trueprop
|> Raw_Simplifier.rewrite_term thy
(Meson.unfold_set_const_simps ctxt) []
|> extensionalize_term ctxt
|> presimp ? presimplify_term ctxt
|> perhaps (try (HOLogic.dest_Trueprop))
|> introduce_combinators_in_term ctxt kind
|> kind <> Axiom ? freeze_term
val (combformula, atomic_types) =
combformula_from_prop thy format type_sys eq_as_iff t []
in
{name = name, locality = loc, kind = kind, combformula = combformula,
atomic_types = atomic_types}
end
fun make_fact ctxt format type_sys keep_trivial eq_as_iff presimp
((name, loc), t) =
case (keep_trivial,
make_formula ctxt format type_sys eq_as_iff presimp name loc Axiom t) of
(false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
NONE
| (_, formula) => SOME formula
fun make_conjecture ctxt format prem_kind type_sys ts =
let val last = length ts - 1 in
map2 (fn j => fn t =>
let
val (kind, maybe_negate) =
if j = last then
(Conjecture, I)
else
(prem_kind,
if prem_kind = Conjecture then update_combformula mk_anot
else I)
in
t |> make_formula ctxt format type_sys true true
(string_of_int j) General kind
|> maybe_negate
end)
(0 upto last) ts
end
(** Finite and infinite type inference **)
fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
| deep_freeze_atyp T = T
val deep_freeze_type = map_atyps deep_freeze_atyp
val type_instance = Sign.typ_instance o Proof_Context.theory_of
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
dangerous because their "exhaust" properties can easily lead to unsound ATP
proofs. On the other hand, all HOL infinite types can be given the same
models in first-order logic (via Löwenheim-Skolem). *)
fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
| should_encode_type _ _ All_Types _ = true
| should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
| should_encode_type _ _ _ _ = false
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
should_predicate_on_var T =
(heaviness = Heavy orelse should_predicate_on_var ()) andalso
should_encode_type ctxt nonmono_Ts level T
| should_predicate_on_type _ _ _ _ _ = false
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
String.isPrefix bound_var_prefix s
| is_var_or_bound_var (CombVar _) = true
| is_var_or_bound_var _ = false
datatype tag_site = Top_Level | Eq_Arg | Elsewhere
fun should_tag_with_type _ _ _ Top_Level _ _ = false
| should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
(case heaviness of
Heavy => should_encode_type ctxt nonmono_Ts level T
| Light =>
case (site, is_var_or_bound_var u) of
(Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
| _ => false)
| should_tag_with_type _ _ _ _ _ _ = false
fun homogenized_type ctxt nonmono_Ts level =
let
val should_encode = should_encode_type ctxt nonmono_Ts level
fun homo 0 T = if should_encode T then T else homo_infinite_type
| homo ary (Type (@{type_name fun}, [T1, T2])) =
homo 0 T1 --> homo (ary - 1) T2
| homo _ _ = raise Fail "expected function type"
in homo end
(** "hBOOL" and "hAPP" **)
type sym_info =
{pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
fun add_combterm_syms_to_table explicit_apply =
let
fun aux top_level tm =
let val (head, args) = strip_combterm_comb tm in
(case head of
CombConst ((s, _), T, _) =>
if String.isPrefix bound_var_prefix s then
I
else
let val ary = length args in
Symtab.map_default
(s, {pred_sym = true,
min_ary = if explicit_apply then 0 else ary,
max_ary = 0, typ = SOME T})
(fn {pred_sym, min_ary, max_ary, typ} =>
{pred_sym = pred_sym andalso top_level,
min_ary = Int.min (ary, min_ary),
max_ary = Int.max (ary, max_ary),
typ = if typ = SOME T then typ else NONE})
end
| _ => I)
#> fold (aux false) args
end
in aux true end
fun add_fact_syms_to_table explicit_apply =
fact_lift (formula_fold NONE (K (add_combterm_syms_to_table explicit_apply)))
val default_sym_table_entries : (string * sym_info) list =
[("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
(make_fixed_const predicator_name,
{pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
([tptp_false, tptp_true]
|> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
fun sym_table_for_facts explicit_apply facts =
Symtab.empty |> fold Symtab.default default_sym_table_entries
|> fold (add_fact_syms_to_table explicit_apply) facts
fun min_arity_of sym_tab s =
case Symtab.lookup sym_tab s of
SOME ({min_ary, ...} : sym_info) => min_ary
| NONE =>
case strip_prefix_and_unascii const_prefix s of
SOME s =>
let val s = s |> unmangled_const_name |> invert_const in
if s = predicator_name then 1
else if s = app_op_name then 2
else if s = type_pred_name then 1
else 0
end
| NONE => 0
(* True if the constant ever appears outside of the top-level position in
literals, or if it appears with different arities (e.g., because of different
type instantiations). If false, the constant always receives all of its
arguments and is used as a predicate. *)
fun is_pred_sym sym_tab s =
case Symtab.lookup sym_tab s of
SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
pred_sym andalso min_ary = max_ary
| NONE => false
val predicator_combconst =
CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
fun predicator tm = CombApp (predicator_combconst, tm)
fun introduce_predicators_in_combterm sym_tab tm =
case strip_combterm_comb tm of
(CombConst ((s, _), _, _), _) =>
if is_pred_sym sym_tab s then tm else predicator tm
| _ => predicator tm
fun list_app head args = fold (curry (CombApp o swap)) args head
fun explicit_app arg head =
let
val head_T = combtyp_of head
val (arg_T, res_T) = dest_funT head_T
val explicit_app =
CombConst (`make_fixed_const app_op_name, head_T --> head_T,
[arg_T, res_T])
in list_app explicit_app [head, arg] end
fun list_explicit_app head args = fold explicit_app args head
fun introduce_explicit_apps_in_combterm sym_tab =
let
fun aux tm =
case strip_combterm_comb tm of
(head as CombConst ((s, _), _, _), args) =>
args |> map aux
|> chop (min_arity_of sym_tab s)
|>> list_app head
|-> list_explicit_app
| (head, args) => list_explicit_app head (map aux args)
in aux end
fun chop_fun 0 T = ([], T)
| chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
chop_fun (n - 1) ran_T |>> cons dom_T
| chop_fun _ _ = raise Fail "unexpected non-function"
fun filter_type_args _ _ _ [] = []
| filter_type_args thy s arity T_args =
let
(* will throw "TYPE" for pseudo-constants *)
val U = if s = app_op_name then
@{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
else
s |> Sign.the_const_type thy
in
case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
[] => []
| res_U_vars =>
let val U_args = (s, U) |> Sign.const_typargs thy in
U_args ~~ T_args
|> map_filter (fn (U, T) =>
if member (op =) res_U_vars (dest_TVar U) then
SOME T
else
NONE)
end
end
handle TYPE _ => T_args
fun enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
let
val thy = Proof_Context.theory_of ctxt
fun aux arity (CombApp (tm1, tm2)) =
CombApp (aux (arity + 1) tm1, aux 0 tm2)
| aux arity (CombConst (name as (s, _), T, T_args)) =
let
val level = level_of_type_sys type_sys
val (T, T_args) =
(* Aggressively merge most "hAPPs" if the type system is unsound
anyway, by distinguishing overloads only on the homogenized
result type. Don't do it for lightweight type systems, though,
since it leads to too many unsound proofs. *)
if s = const_prefix ^ app_op_name andalso
length T_args = 2 andalso
not (is_type_sys_virtually_sound type_sys) andalso
heaviness_of_type_sys type_sys = Heavy then
T_args |> map (homogenized_type ctxt nonmono_Ts level 0)
|> (fn Ts => let val T = hd Ts --> nth Ts 1 in
(T --> T, tl Ts)
end)
else
(T, T_args)
in
(case strip_prefix_and_unascii const_prefix s of
NONE => (name, T_args)
| SOME s'' =>
let
val s'' = invert_const s''
fun filtered_T_args false = T_args
| filtered_T_args true = filter_type_args thy s'' arity T_args
in
case type_arg_policy type_sys s'' of
Explicit_Type_Args drop_args =>
(name, filtered_T_args drop_args)
| Mangled_Type_Args drop_args =>
(mangled_const_name (filtered_T_args drop_args) name, [])
| No_Type_Args => (name, [])
end)
|> (fn (name, T_args) => CombConst (name, T, T_args))
end
| aux _ tm = tm
in aux 0 end
fun repair_combterm ctxt format nonmono_Ts type_sys sym_tab =
not (is_setting_higher_order format type_sys)
? (introduce_explicit_apps_in_combterm sym_tab
#> introduce_predicators_in_combterm sym_tab)
#> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
fun repair_fact ctxt format nonmono_Ts type_sys sym_tab =
update_combformula (formula_map
(repair_combterm ctxt format nonmono_Ts type_sys sym_tab))
(** Helper facts **)
fun ti_ti_helper_fact () =
let
fun var s = ATerm (`I s, [])
fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
in
Formula (helper_prefix ^ "ti_ti", Axiom,
AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
|> close_formula_universally, simp_info, NONE)
end
fun helper_facts_for_sym ctxt format type_sys (s, {typ, ...} : sym_info) =
case strip_prefix_and_unascii const_prefix s of
SOME mangled_s =>
let
val thy = Proof_Context.theory_of ctxt
val unmangled_s = mangled_s |> unmangled_const_name
fun dub_and_inst c needs_fairly_sound (th, j) =
((c ^ "_" ^ string_of_int j ^
(if needs_fairly_sound then typed_helper_suffix
else untyped_helper_suffix),
General),
let val t = th |> prop_of in
t |> ((case general_type_arg_policy type_sys of
Mangled_Type_Args _ => true
| _ => false) andalso
not (null (Term.hidden_polymorphism t)))
? (case typ of
SOME T => specialize_type thy (invert_const unmangled_s, T)
| NONE => I)
end)
fun make_facts eq_as_iff =
map_filter (make_fact ctxt format type_sys false eq_as_iff false)
val fairly_sound = is_type_sys_fairly_sound type_sys
in
metis_helpers
|> maps (fn (metis_s, (needs_fairly_sound, ths)) =>
if metis_s <> unmangled_s orelse
(needs_fairly_sound andalso not fairly_sound) then
[]
else
ths ~~ (1 upto length ths)
|> map (dub_and_inst mangled_s needs_fairly_sound)
|> make_facts (not needs_fairly_sound))
end
| NONE => []
fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
[]
fun translate_atp_fact ctxt format type_sys keep_trivial =
`(make_fact ctxt format type_sys keep_trivial true true o apsnd prop_of)
fun translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t
rich_facts =
let
val thy = Proof_Context.theory_of ctxt
val fact_ts = map (prop_of o snd o snd) rich_facts
val (facts, fact_names) =
rich_facts
|> map_filter (fn (NONE, _) => NONE
| (SOME fact, (name, _)) => SOME (fact, name))
|> ListPair.unzip
(* Remove existing facts from the conjecture, as this can dramatically
boost an ATP's performance (for some reason). *)
val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
val goal_t = Logic.list_implies (hyp_ts, concl_t)
val all_ts = goal_t :: fact_ts
val subs = tfree_classes_of_terms all_ts
val supers = tvar_classes_of_terms all_ts
val tycons = type_consts_of_terms thy all_ts
val conjs =
hyp_ts @ [concl_t] |> make_conjecture ctxt format prem_kind type_sys
val (supers', arity_clauses) =
if level_of_type_sys type_sys = No_Types then ([], [])
else make_arity_clauses thy tycons supers
val class_rel_clauses = make_class_rel_clauses thy subs supers'
in
(fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
end
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
(true, ATerm (class, [ATerm (name, [])]))
| fo_literal_from_type_literal (TyLitFree (class, name)) =
(true, ATerm (class, [ATerm (name, [])]))
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
fun type_pred_combterm ctxt nonmono_Ts type_sys T tm =
CombApp (CombConst (`make_fixed_const type_pred_name, T --> @{typ bool}, [T])
|> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys,
tm)
fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
| var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
accum orelse (s = "equal" andalso member (op =) tms (ATerm (name, [])))
fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
| is_var_nonmonotonic_in_formula pos phi _ name =
formula_fold pos (var_occurs_positively_naked_in_term name) phi false
fun mk_const_aterm x T_args args =
ATerm (x, map (fo_term_from_typ false) T_args @ args)
fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
CombConst (`make_fixed_const type_tag_name, T --> T, [T])
|> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
|> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
|> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
and term_from_combterm ctxt format nonmono_Ts type_sys =
let
fun aux site u =
let
val (head, args) = strip_combterm_comb u
val (x as (s, _), T_args) =
case head of
CombConst (name, _, T_args) => (name, T_args)
| CombVar (name, _) => (name, [])
| CombApp _ => raise Fail "impossible \"CombApp\""
val arg_site = if site = Top_Level andalso s = "equal" then Eq_Arg
else Elsewhere
val t = mk_const_aterm x T_args (map (aux arg_site) args)
val T = combtyp_of u
in
t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
tag_with_type ctxt format nonmono_Ts type_sys T
else
I)
end
in aux end
and formula_from_combformula ctxt format nonmono_Ts type_sys
should_predicate_on_var =
let
val higher_order = is_setting_higher_order format type_sys
val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
val do_bound_type =
case type_sys of
Simple_Types level =>
homogenized_type ctxt nonmono_Ts level 0
#> mangled_type higher_order false 0 #> SOME
| _ => K NONE
fun do_out_of_bound_type pos phi universal (name, T) =
if should_predicate_on_type ctxt nonmono_Ts type_sys
(fn () => should_predicate_on_var pos phi universal name) T then
CombVar (name, T)
|> type_pred_combterm ctxt nonmono_Ts type_sys T
|> do_term |> AAtom |> SOME
else
NONE
fun do_formula pos (AQuant (q, xs, phi)) =
let
val phi = phi |> do_formula pos
val universal = Option.map (q = AExists ? not) pos
in
AQuant (q, xs |> map (apsnd (fn NONE => NONE
| SOME T => do_bound_type T)),
(if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
(map_filter
(fn (_, NONE) => NONE
| (s, SOME T) =>
do_out_of_bound_type pos phi universal (s, T))
xs)
phi)
end
| do_formula pos (AConn conn) = aconn_map pos do_formula conn
| do_formula _ (AAtom tm) = AAtom (do_term tm)
in do_formula o SOME end
fun bound_atomic_types format type_sys Ts =
mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
(atp_type_literals_for_types format type_sys Axiom Ts))
fun formula_for_fact ctxt format nonmono_Ts type_sys
({combformula, atomic_types, ...} : translated_formula) =
combformula
|> close_combformula_universally
|> formula_from_combformula ctxt format nonmono_Ts type_sys
is_var_nonmonotonic_in_formula true
|> bound_atomic_types format type_sys atomic_types
|> close_formula_universally
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
of monomorphization). The TPTP explicitly forbids name clashes, and some of
the remote provers might care. *)
fun formula_line_for_fact ctxt format prefix nonmono_Ts type_sys
(j, formula as {name, locality, kind, ...}) =
Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
else string_of_int j ^ "_") ^
ascii_of name,
kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
case locality of
Intro => intro_info
| Elim => elim_info
| Simp => simp_info
| _ => NONE)
fun formula_line_for_class_rel_clause
(ClassRelClause {name, subclass, superclass, ...}) =
let val ty_arg = ATerm (`I "T", []) in
Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
AAtom (ATerm (superclass, [ty_arg]))])
|> close_formula_universally, intro_info, NONE)
end
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
(true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
| fo_literal_from_arity_literal (TVarLit (c, sort)) =
(false, ATerm (c, [ATerm (sort, [])]))
fun formula_line_for_arity_clause
(ArityClause {name, prem_lits, concl_lits, ...}) =
Formula (arity_clause_prefix ^ ascii_of name, Axiom,
mk_ahorn (map (formula_from_fo_literal o apfst not
o fo_literal_from_arity_literal) prem_lits)
(formula_from_fo_literal
(fo_literal_from_arity_literal concl_lits))
|> close_formula_universally, intro_info, NONE)
fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
({name, kind, combformula, ...} : translated_formula) =
Formula (conjecture_prefix ^ name, kind,
formula_from_combformula ctxt format nonmono_Ts type_sys
is_var_nonmonotonic_in_formula false
(close_combformula_universally combformula)
|> close_formula_universally, NONE, NONE)
fun free_type_literals format type_sys
({atomic_types, ...} : translated_formula) =
atomic_types |> atp_type_literals_for_types format type_sys Conjecture
|> map fo_literal_from_type_literal
fun formula_line_for_free_type j lit =
Formula (tfree_prefix ^ string_of_int j, Hypothesis,
formula_from_fo_literal lit, NONE, NONE)
fun formula_lines_for_free_types format type_sys facts =
let
val litss = map (free_type_literals format type_sys) facts
val lits = fold (union (op =)) litss []
in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
(** Symbol declarations **)
fun insert_type ctxt get_T x xs =
let val T = get_T x in
if exists (curry (type_instance ctxt) T o get_T) xs then xs
else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
end
fun should_declare_sym type_sys pred_sym s =
is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
(case type_sys of
Simple_Types _ => true
| Tags (_, _, Light) => true
| _ => not pred_sym)
fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
let
fun add_combterm in_conj tm =
let val (head, args) = strip_combterm_comb tm in
(case head of
CombConst ((s, s'), T, T_args) =>
let val pred_sym = is_pred_sym repaired_sym_tab s in
if should_declare_sym type_sys pred_sym s then
Symtab.map_default (s, [])
(insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
in_conj))
else
I
end
| _ => I)
#> fold (add_combterm in_conj) args
end
fun add_fact in_conj =
fact_lift (formula_fold NONE (K (add_combterm in_conj)))
in
Symtab.empty
|> is_type_sys_fairly_sound type_sys
? (fold (add_fact true) conjs #> fold (add_fact false) facts)
end
(* These types witness that the type classes they belong to allow infinite
models and hence that any types with these type classes is monotonic. *)
val known_infinite_types = [@{typ nat}, @{typ int}, @{typ "nat => bool"}]
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
out with monotonicity" paper presented at CADE 2011. *)
fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
| add_combterm_nonmonotonic_types ctxt level _
(CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
tm2)) =
(exists is_var_or_bound_var [tm1, tm2] andalso
(case level of
Nonmonotonic_Types =>
not (is_type_surely_infinite ctxt known_infinite_types T)
| Finite_Types => is_type_surely_finite ctxt T
| _ => true)) ? insert_type ctxt I (deep_freeze_type T)
| add_combterm_nonmonotonic_types _ _ _ _ = I
fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
: translated_formula) =
formula_fold (SOME (kind <> Conjecture))
(add_combterm_nonmonotonic_types ctxt level) combformula
fun nonmonotonic_types_for_facts ctxt type_sys facts =
let val level = level_of_type_sys type_sys in
if level = Nonmonotonic_Types orelse level = Finite_Types then
[] |> fold (add_fact_nonmonotonic_types ctxt level) facts
(* We must add "bool" in case the helper "True_or_False" is added
later. In addition, several places in the code rely on the list of
nonmonotonic types not being empty. *)
|> insert_type ctxt I @{typ bool}
else
[]
end
fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
(s', T_args, T, pred_sym, ary, _) =
let
val (higher_order, T_arg_Ts, level) =
case type_sys of
Simple_Types level => (format = THF, [], level)
| _ => (false, replicate (length T_args) homo_infinite_type, No_Types)
in
Decl (sym_decl_prefix ^ s, (s, s'),
(T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
|> mangled_type higher_order pred_sym (length T_arg_Ts + ary))
end
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
fun formula_line_for_pred_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
n s j (s', T_args, T, _, ary, in_conj) =
let
val (kind, maybe_negate) =
if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
else (Axiom, I)
val (arg_Ts, res_T) = chop_fun ary T
val bound_names =
1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
val bounds =
bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
val bound_Ts =
arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
else NONE)
in
Formula (sym_formula_prefix ^ s ^
(if n > 1 then "_" ^ string_of_int j else ""), kind,
CombConst ((s, s'), T, T_args)
|> fold (curry (CombApp o swap)) bounds
|> type_pred_combterm ctxt nonmono_Ts type_sys res_T
|> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
|> formula_from_combformula ctxt format nonmono_Ts type_sys
(K (K (K (K true)))) true
|> n > 1 ? bound_atomic_types format type_sys (atyps_of T)
|> close_formula_universally
|> maybe_negate,
intro_info, NONE)
end
fun formula_lines_for_tag_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
let
val ident_base =
sym_formula_prefix ^ s ^ (if n > 1 then "_" ^ string_of_int j else "")
val (kind, maybe_negate) =
if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
else (Axiom, I)
val (arg_Ts, res_T) = chop_fun ary T
val bound_names =
1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
val bounds = bound_names |> map (fn name => ATerm (name, []))
val cst = mk_const_aterm (s, s') T_args
val atomic_Ts = atyps_of T
fun eq tms =
(if pred_sym then AConn (AIff, map AAtom tms)
else AAtom (ATerm (`I "equal", tms)))
|> bound_atomic_types format type_sys atomic_Ts
|> close_formula_universally
|> maybe_negate
val should_encode = should_encode_type ctxt nonmono_Ts All_Types
val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
val add_formula_for_res =
if should_encode res_T then
cons (Formula (ident_base ^ "_res", kind,
eq [tag_with res_T (cst bounds), cst bounds],
simp_info, NONE))
else
I
fun add_formula_for_arg k =
let val arg_T = nth arg_Ts k in
if should_encode arg_T then
case chop k bounds of
(bounds1, bound :: bounds2) =>
cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
cst bounds],
simp_info, NONE))
| _ => raise Fail "expected nonempty tail"
else
I
end
in
[] |> not pred_sym ? add_formula_for_res
|> fold add_formula_for_arg (ary - 1 downto 0)
end
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
(s, decls) =
case type_sys of
Simple_Types _ =>
decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
| Preds _ =>
let
val decls =
case decls of
decl :: (decls' as _ :: _) =>
let val T = result_type_of_decl decl in
if forall (curry (type_instance ctxt o swap) T
o result_type_of_decl) decls' then
[decl]
else
decls
end
| _ => decls
val n = length decls
val decls =
decls
|> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
o result_type_of_decl)
in
(0 upto length decls - 1, decls)
|-> map2 (formula_line_for_pred_sym_decl ctxt format conj_sym_kind
nonmono_Ts type_sys n s)
end
| Tags (_, _, heaviness) =>
(case heaviness of
Heavy => []
| Light =>
let val n = length decls in
(0 upto n - 1 ~~ decls)
|> maps (formula_lines_for_tag_sym_decl ctxt format conj_sym_kind
nonmono_Ts type_sys n s)
end)
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
type_sys sym_decl_tab =
sym_decl_tab
|> Symtab.dest
|> sort_wrt fst
|> rpair []
|-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
nonmono_Ts type_sys)
fun should_add_ti_ti_helper (Tags (Polymorphic, level, Heavy)) =
level = Nonmonotonic_Types orelse level = Finite_Types
| should_add_ti_ti_helper _ = false
fun offset_of_heading_in_problem _ [] j = j
| offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
if heading = needle then j
else offset_of_heading_in_problem needle problem (j + length lines)
val implicit_declsN = "Should-be-implicit typings"
val explicit_declsN = "Explicit typings"
val factsN = "Relevant facts"
val class_relsN = "Class relationships"
val aritiesN = "Arities"
val helpersN = "Helper facts"
val conjsN = "Conjectures"
val free_typesN = "Type variables"
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
explicit_apply hyp_ts concl_t facts =
let
val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t facts
val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
val repair = repair_fact ctxt format nonmono_Ts type_sys sym_tab
val (conjs, facts) = (conjs, facts) |> pairself (map repair)
val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
val helpers =
repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
|> map repair
val lavish_nonmono_Ts =
if null nonmono_Ts orelse
polymorphism_of_type_sys type_sys <> Polymorphic then
nonmono_Ts
else
[TVar (("'a", 0), HOLogic.typeS)]
val sym_decl_lines =
(conjs, helpers @ facts)
|> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
|> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
lavish_nonmono_Ts type_sys
val helper_lines =
0 upto length helpers - 1 ~~ helpers
|> map (formula_line_for_fact ctxt format helper_prefix lavish_nonmono_Ts
type_sys)
|> (if should_add_ti_ti_helper type_sys then cons (ti_ti_helper_fact ())
else I)
(* Reordering these might confuse the proof reconstruction code or the SPASS
Flotter hack. *)
val problem =
[(explicit_declsN, sym_decl_lines),
(factsN,
map (formula_line_for_fact ctxt format fact_prefix nonmono_Ts type_sys)
(0 upto length facts - 1 ~~ facts)),
(class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
(aritiesN, map formula_line_for_arity_clause arity_clauses),
(helpersN, helper_lines),
(conjsN,
map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
conjs),
(free_typesN,
formula_lines_for_free_types format type_sys (facts @ conjs))]
val problem =
problem
|> (if format = CNF_UEQ then filter_cnf_ueq_problem else I)
|> (if is_format_typed format then
declare_undeclared_syms_in_atp_problem type_decl_prefix
implicit_declsN
else
I)
val (problem, pool) =
problem |> nice_atp_problem (Config.get ctxt readable_names)
val helpers_offset = offset_of_heading_in_problem helpersN problem 0
val typed_helpers =
map_filter (fn (j, {name, ...}) =>
if String.isSuffix typed_helper_suffix name then SOME j
else NONE)
((helpers_offset + 1 upto helpers_offset + length helpers)
~~ helpers)
fun add_sym_arity (s, {min_ary, ...} : sym_info) =
if min_ary > 0 then
case strip_prefix_and_unascii const_prefix s of
SOME s => Symtab.insert (op =) (s, min_ary)
| NONE => I
else
I
in
(problem,
case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
offset_of_heading_in_problem conjsN problem 0,
offset_of_heading_in_problem factsN problem 0,
fact_names |> Vector.fromList,
typed_helpers,
Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
end
(* FUDGE *)
val conj_weight = 0.0
val hyp_weight = 0.1
val fact_min_weight = 0.2
val fact_max_weight = 1.0
val type_info_default_weight = 0.8
fun add_term_weights weight (ATerm (s, tms)) =
is_tptp_user_symbol s ? Symtab.default (s, weight)
#> fold (add_term_weights weight) tms
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
formula_fold NONE (K (add_term_weights weight)) phi
| add_problem_line_weights _ _ = I
fun add_conjectures_weights [] = I
| add_conjectures_weights conjs =
let val (hyps, conj) = split_last conjs in
add_problem_line_weights conj_weight conj
#> fold (add_problem_line_weights hyp_weight) hyps
end
fun add_facts_weights facts =
let
val num_facts = length facts
fun weight_of j =
fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
/ Real.fromInt num_facts
in
map weight_of (0 upto num_facts - 1) ~~ facts
|> fold (uncurry add_problem_line_weights)
end
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
fun atp_problem_weights problem =
let val get = these o AList.lookup (op =) problem in
Symtab.empty
|> add_conjectures_weights (get free_typesN @ get conjsN)
|> add_facts_weights (get factsN)
|> fold (fold (add_problem_line_weights type_info_default_weight) o get)
[explicit_declsN, class_relsN, aritiesN]
|> Symtab.dest
|> sort (prod_ord Real.compare string_ord o pairself swap)
end
end;