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(* Title: HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
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Author: Fabian Immler, TU Muenchen
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Author: Makarius
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Author: Jasmin Blanchette, TU Muenchen
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Translation of HOL to FOL for Sledgehammer.
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*)
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signature SLEDGEHAMMER_ATP_TRANSLATE =
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sig
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type 'a fo_term = 'a ATP_Problem.fo_term
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type 'a problem = 'a ATP_Problem.problem
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type translated_formula
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datatype type_system =
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Many_Typed |
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Mangled of bool |
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Args of bool |
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Tags of bool |
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No_Types
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val readable_names : bool Unsynchronized.ref
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val fact_prefix : string
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val conjecture_prefix : string
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val predicator_base : string
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val explicit_app_base : string
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val type_pred_base : string
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val tff_type_prefix : string
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val is_type_system_sound : type_system -> bool
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val type_system_types_dangerous_types : type_system -> bool
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val num_atp_type_args : theory -> type_system -> string -> int
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val unmangled_const : string -> string * string fo_term list
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val translate_atp_fact :
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Proof.context -> bool -> (string * 'a) * thm
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-> translated_formula option * ((string * 'a) * thm)
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val prepare_atp_problem :
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Proof.context -> type_system -> bool -> term list -> term
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-> (translated_formula option * ((string * 'a) * thm)) list
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-> string problem * string Symtab.table * int * int
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* (string * 'a) list vector
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val atp_problem_weights : string problem -> (string * real) list
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end;
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structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
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struct
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open ATP_Problem
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open Metis_Translate
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open Sledgehammer_Util
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(* Readable names are often much shorter, especially if types are mangled in
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names. For that reason, they are on by default. *)
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val readable_names = Unsynchronized.ref true
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val type_decl_prefix = "type_"
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val sym_decl_prefix = "sym_"
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val fact_prefix = "fact_"
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val conjecture_prefix = "conj_"
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val helper_prefix = "help_"
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val class_rel_clause_prefix = "crel_";
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val arity_clause_prefix = "arity_"
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val tfree_prefix = "tfree_"
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val predicator_base = "hBOOL"
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val explicit_app_base = "hAPP"
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val type_pred_base = "is"
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val tff_type_prefix = "ty_"
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fun make_tff_type s = tff_type_prefix ^ ascii_of s
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(* official TPTP syntax *)
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val tptp_tff_type_of_types = "$tType"
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val tptp_tff_bool_type = "$o"
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val tptp_false = "$false"
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val tptp_true = "$true"
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(* Freshness almost guaranteed! *)
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val sledgehammer_weak_prefix = "Sledgehammer:"
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type translated_formula =
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{name: string,
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kind: formula_kind,
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combformula: (name, typ, combterm) formula,
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atomic_types: typ list}
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fun update_combformula f
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({name, kind, combformula, atomic_types} : translated_formula) =
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{name = name, kind = kind, combformula = f combformula,
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atomic_types = atomic_types} : translated_formula
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fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
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datatype type_system =
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Many_Typed |
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Mangled of bool |
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Args of bool |
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Tags of bool |
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No_Types
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fun is_type_system_sound Many_Typed = true
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| is_type_system_sound (Mangled full_types) = full_types
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| is_type_system_sound (Args full_types) = full_types
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| is_type_system_sound (Tags full_types) = full_types
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| is_type_system_sound No_Types = false
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fun type_system_types_dangerous_types (Tags _) = true
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| type_system_types_dangerous_types type_sys = is_type_system_sound type_sys
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fun dont_need_type_args type_sys s =
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s <> type_pred_base andalso
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(member (op =) [@{const_name HOL.eq}] s orelse
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case type_sys of
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Many_Typed => false
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| Mangled _ => false
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| Args _ => s = explicit_app_base
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| Tags full_types => full_types orelse s = explicit_app_base
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| No_Types => true)
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datatype type_arg_policy = No_Type_Args | Mangled_Types | Explicit_Type_Args
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fun general_type_arg_policy Many_Typed = Mangled_Types
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| general_type_arg_policy (Mangled _) = Mangled_Types
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| general_type_arg_policy _ = Explicit_Type_Args
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fun type_arg_policy type_sys s =
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if dont_need_type_args type_sys s then No_Type_Args
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else general_type_arg_policy type_sys
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fun num_atp_type_args thy type_sys s =
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if type_arg_policy type_sys s = Explicit_Type_Args then num_type_args thy s
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else 0
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fun atp_type_literals_for_types type_sys kind Ts =
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if type_sys = No_Types then
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[]
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else
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Ts |> type_literals_for_types
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|> filter (fn TyLitVar _ => kind <> Conjecture
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| TyLitFree _ => kind = Conjecture)
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fun mk_anot phi = AConn (ANot, [phi])
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fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
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fun mk_aconns c phis =
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let val (phis', phi') = split_last phis in
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fold_rev (mk_aconn c) phis' phi'
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end
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fun mk_ahorn [] phi = phi
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| mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
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fun mk_aquant _ [] phi = phi
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| mk_aquant q xs (phi as AQuant (q', xs', phi')) =
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if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
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| mk_aquant q xs phi = AQuant (q, xs, phi)
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fun close_universally atom_vars phi =
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let
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fun formula_vars bounds (AQuant (_, xs, phi)) =
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formula_vars (map fst xs @ bounds) phi
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| formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
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| formula_vars bounds (AAtom tm) =
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union (op =) (atom_vars tm []
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|> filter_out (member (op =) bounds o fst))
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in mk_aquant AForall (formula_vars [] phi []) phi end
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fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
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| combterm_vars (CombConst _) = I
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| combterm_vars (CombVar (name, ty)) = insert (op =) (name, SOME ty)
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val close_combformula_universally = close_universally combterm_vars
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fun term_vars (ATerm (name as (s, _), tms)) =
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is_atp_variable s ? insert (op =) (name, NONE)
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#> fold term_vars tms
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val close_formula_universally = close_universally term_vars
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fun fo_term_from_typ (Type (s, Ts)) =
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ATerm (`make_fixed_type_const s, map fo_term_from_typ Ts)
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| fo_term_from_typ (TFree (s, _)) =
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ATerm (`make_fixed_type_var s, [])
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| fo_term_from_typ (TVar ((x as (s, _)), _)) =
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ATerm ((make_schematic_type_var x, s), [])
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(* This shouldn't clash with anything else. *)
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val mangled_type_sep = "\000"
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fun generic_mangled_type_name f (ATerm (name, [])) = f name
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| generic_mangled_type_name f (ATerm (name, tys)) =
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f name ^ "(" ^ commas (map (generic_mangled_type_name f) tys) ^ ")"
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val mangled_type_name =
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fo_term_from_typ
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#> (fn ty => (make_tff_type (generic_mangled_type_name fst ty),
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generic_mangled_type_name snd ty))
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fun generic_mangled_type_suffix f g tys =
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fold_rev (curry (op ^) o g o prefix mangled_type_sep
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o generic_mangled_type_name f) tys ""
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fun mangled_const_name T_args (s, s') =
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let val ty_args = map fo_term_from_typ T_args in
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(s ^ generic_mangled_type_suffix fst ascii_of ty_args,
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s' ^ generic_mangled_type_suffix snd I ty_args)
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end
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val parse_mangled_ident =
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Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
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fun parse_mangled_type x =
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(parse_mangled_ident
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-- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
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[] >> ATerm) x
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and parse_mangled_types x =
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(parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
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fun unmangled_type s =
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s |> suffix ")" |> raw_explode
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|> Scan.finite Symbol.stopper
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(Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
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quote s)) parse_mangled_type))
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|> fst
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val unmangled_const_name = space_explode mangled_type_sep #> hd
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fun unmangled_const s =
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let val ss = space_explode mangled_type_sep s in
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(hd ss, map unmangled_type (tl ss))
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end
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val introduce_proxies =
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let
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fun aux top_level (CombApp (tm1, tm2)) =
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CombApp (aux top_level tm1, aux false tm2)
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| aux top_level (CombConst (name as (s, s'), ty, ty_args)) =
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(case AList.lookup (op =) metis_proxies s of
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SOME proxy_base =>
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if top_level then
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(case s of
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"c_False" => (tptp_false, s')
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| "c_True" => (tptp_true, s')
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| _ => name, [])
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else
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(proxy_base |>> prefix const_prefix, ty_args)
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| NONE => (name, ty_args))
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|> (fn (name, ty_args) => CombConst (name, ty, ty_args))
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| aux _ tm = tm
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in aux true end
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fun combformula_from_prop thy eq_as_iff =
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let
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fun do_term bs t atomic_types =
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combterm_from_term thy bs (Envir.eta_contract t)
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|>> (introduce_proxies #> AAtom)
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||> union (op =) atomic_types
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fun do_quant bs q s T t' =
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let val s = Name.variant (map fst bs) s in
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do_formula ((s, T) :: bs) t'
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#>> mk_aquant q [(`make_bound_var s, SOME T)]
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end
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and do_conn bs c t1 t2 =
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do_formula bs t1 ##>> do_formula bs t2
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#>> uncurry (mk_aconn c)
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and do_formula bs t =
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case t of
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@{const Not} $ t1 => do_formula bs t1 #>> mk_anot
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| Const (@{const_name All}, _) $ Abs (s, T, t') =>
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do_quant bs AForall s T t'
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| Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
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blanchet@38506
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do_quant bs AExists s T t'
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haftmann@39028
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| @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
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haftmann@39028
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| @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
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haftmann@39019
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| @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
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haftmann@39093
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| Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
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blanchet@41388
|
268 |
if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
|
blanchet@41388
|
269 |
| _ => do_term bs t
|
blanchet@38506
|
270 |
in do_formula [] end
|
blanchet@38506
|
271 |
|
blanchet@38841
|
272 |
val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
|
blanchet@38506
|
273 |
|
wenzelm@41739
|
274 |
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
|
blanchet@38506
|
275 |
fun conceal_bounds Ts t =
|
blanchet@38506
|
276 |
subst_bounds (map (Free o apfst concealed_bound_name)
|
blanchet@38506
|
277 |
(0 upto length Ts - 1 ~~ Ts), t)
|
blanchet@38506
|
278 |
fun reveal_bounds Ts =
|
blanchet@38506
|
279 |
subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
|
blanchet@38506
|
280 |
(0 upto length Ts - 1 ~~ Ts))
|
blanchet@38506
|
281 |
|
blanchet@38831
|
282 |
(* Removes the lambdas from an equation of the form "t = (%x. u)".
|
blanchet@40071
|
283 |
(Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
|
blanchet@38831
|
284 |
fun extensionalize_term t =
|
blanchet@38831
|
285 |
let
|
blanchet@38831
|
286 |
fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
|
blanchet@38831
|
287 |
| aux j (t as Const (s, Type (_, [Type (_, [_, T']),
|
blanchet@38831
|
288 |
Type (_, [_, res_T])]))
|
blanchet@38831
|
289 |
$ t2 $ Abs (var_s, var_T, t')) =
|
haftmann@39093
|
290 |
if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
|
blanchet@38831
|
291 |
let val var_t = Var ((var_s, j), var_T) in
|
blanchet@38831
|
292 |
Const (s, T' --> T' --> res_T)
|
blanchet@38831
|
293 |
$ betapply (t2, var_t) $ subst_bound (var_t, t')
|
blanchet@38831
|
294 |
|> aux (j + 1)
|
blanchet@38831
|
295 |
end
|
blanchet@38831
|
296 |
else
|
blanchet@38831
|
297 |
t
|
blanchet@38831
|
298 |
| aux _ t = t
|
blanchet@38831
|
299 |
in aux (maxidx_of_term t + 1) t end
|
blanchet@38831
|
300 |
|
blanchet@38506
|
301 |
fun introduce_combinators_in_term ctxt kind t =
|
wenzelm@43232
|
302 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@38716
|
303 |
if Meson.is_fol_term thy t then
|
blanchet@38716
|
304 |
t
|
blanchet@38716
|
305 |
else
|
blanchet@38716
|
306 |
let
|
blanchet@38716
|
307 |
fun aux Ts t =
|
blanchet@38716
|
308 |
case t of
|
blanchet@38716
|
309 |
@{const Not} $ t1 => @{const Not} $ aux Ts t1
|
blanchet@38716
|
310 |
| (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
|
blanchet@38716
|
311 |
t0 $ Abs (s, T, aux (T :: Ts) t')
|
blanchet@38890
|
312 |
| (t0 as Const (@{const_name All}, _)) $ t1 =>
|
blanchet@38890
|
313 |
aux Ts (t0 $ eta_expand Ts t1 1)
|
blanchet@38716
|
314 |
| (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
|
blanchet@38716
|
315 |
t0 $ Abs (s, T, aux (T :: Ts) t')
|
blanchet@38890
|
316 |
| (t0 as Const (@{const_name Ex}, _)) $ t1 =>
|
blanchet@38890
|
317 |
aux Ts (t0 $ eta_expand Ts t1 1)
|
haftmann@39028
|
318 |
| (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39028
|
319 |
| (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39019
|
320 |
| (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39093
|
321 |
| (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
|
blanchet@38716
|
322 |
$ t1 $ t2 =>
|
blanchet@38716
|
323 |
t0 $ aux Ts t1 $ aux Ts t2
|
blanchet@38716
|
324 |
| _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
|
blanchet@38716
|
325 |
t
|
blanchet@38716
|
326 |
else
|
blanchet@38716
|
327 |
t |> conceal_bounds Ts
|
blanchet@38716
|
328 |
|> Envir.eta_contract
|
blanchet@38716
|
329 |
|> cterm_of thy
|
blanchet@40071
|
330 |
|> Meson_Clausify.introduce_combinators_in_cterm
|
blanchet@38716
|
331 |
|> prop_of |> Logic.dest_equals |> snd
|
blanchet@38716
|
332 |
|> reveal_bounds Ts
|
blanchet@39616
|
333 |
val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
|
blanchet@38716
|
334 |
in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
|
blanchet@38716
|
335 |
handle THM _ =>
|
blanchet@38716
|
336 |
(* A type variable of sort "{}" will make abstraction fail. *)
|
blanchet@38836
|
337 |
if kind = Conjecture then HOLogic.false_const
|
blanchet@38836
|
338 |
else HOLogic.true_const
|
blanchet@38716
|
339 |
end
|
blanchet@38506
|
340 |
|
blanchet@38506
|
341 |
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
|
blanchet@43224
|
342 |
same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
|
blanchet@38506
|
343 |
fun freeze_term t =
|
blanchet@38506
|
344 |
let
|
blanchet@38506
|
345 |
fun aux (t $ u) = aux t $ aux u
|
blanchet@38506
|
346 |
| aux (Abs (s, T, t)) = Abs (s, T, aux t)
|
blanchet@38506
|
347 |
| aux (Var ((s, i), T)) =
|
blanchet@38506
|
348 |
Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
|
blanchet@38506
|
349 |
| aux t = t
|
blanchet@38506
|
350 |
in t |> exists_subterm is_Var t ? aux end
|
blanchet@38506
|
351 |
|
blanchet@40445
|
352 |
(* making fact and conjecture formulas *)
|
blanchet@43415
|
353 |
fun make_formula ctxt eq_as_iff presimp name kind t =
|
blanchet@38506
|
354 |
let
|
wenzelm@43232
|
355 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@38831
|
356 |
val t = t |> Envir.beta_eta_contract
|
blanchet@38890
|
357 |
|> transform_elim_term
|
blanchet@41459
|
358 |
|> Object_Logic.atomize_term thy
|
blanchet@43434
|
359 |
val need_trueprop = (fastype_of t = @{typ bool})
|
blanchet@38890
|
360 |
val t = t |> need_trueprop ? HOLogic.mk_Trueprop
|
blanchet@38506
|
361 |
|> extensionalize_term
|
blanchet@38506
|
362 |
|> presimp ? presimplify_term thy
|
blanchet@38506
|
363 |
|> perhaps (try (HOLogic.dest_Trueprop))
|
blanchet@38506
|
364 |
|> introduce_combinators_in_term ctxt kind
|
blanchet@38836
|
365 |
|> kind <> Axiom ? freeze_term
|
blanchet@43433
|
366 |
val (combformula, atomic_types) =
|
blanchet@43433
|
367 |
combformula_from_prop thy eq_as_iff t []
|
blanchet@38506
|
368 |
in
|
blanchet@38991
|
369 |
{name = name, combformula = combformula, kind = kind,
|
blanchet@43433
|
370 |
atomic_types = atomic_types}
|
blanchet@38506
|
371 |
end
|
blanchet@38506
|
372 |
|
blanchet@43432
|
373 |
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, _), t) =
|
blanchet@43432
|
374 |
case (keep_trivial, make_formula ctxt eq_as_iff presimp name Axiom t) of
|
blanchet@42861
|
375 |
(false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
|
blanchet@42861
|
376 |
NONE
|
blanchet@42861
|
377 |
| (_, formula) => SOME formula
|
blanchet@43432
|
378 |
|
blanchet@43415
|
379 |
fun make_conjecture ctxt ts =
|
blanchet@38836
|
380 |
let val last = length ts - 1 in
|
blanchet@43415
|
381 |
map2 (fn j => make_formula ctxt true true (string_of_int j)
|
blanchet@38836
|
382 |
(if j = last then Conjecture else Hypothesis))
|
blanchet@38836
|
383 |
(0 upto last) ts
|
blanchet@38836
|
384 |
end
|
blanchet@38506
|
385 |
|
blanchet@38506
|
386 |
(** Helper facts **)
|
blanchet@38506
|
387 |
|
blanchet@43413
|
388 |
fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
|
blanchet@43413
|
389 |
| formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
|
blanchet@43413
|
390 |
| formula_map f (AAtom tm) = AAtom (f tm)
|
blanchet@43413
|
391 |
|
blanchet@43413
|
392 |
fun formula_fold f (AQuant (_, _, phi)) = formula_fold f phi
|
blanchet@43413
|
393 |
| formula_fold f (AConn (_, phis)) = fold (formula_fold f) phis
|
blanchet@43413
|
394 |
| formula_fold f (AAtom tm) = f tm
|
blanchet@41561
|
395 |
|
blanchet@43434
|
396 |
type sym_table_info =
|
blanchet@43434
|
397 |
{pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
|
blanchet@43434
|
398 |
|
blanchet@43432
|
399 |
fun ti_ti_helper_fact () =
|
blanchet@38506
|
400 |
let
|
blanchet@43432
|
401 |
fun var s = ATerm (`I s, [])
|
blanchet@43432
|
402 |
fun tag tm = ATerm (`I type_tag_name, [var "X", tm])
|
blanchet@38506
|
403 |
in
|
blanchet@43432
|
404 |
Formula (Fof, helper_prefix ^ ascii_of "ti_ti", Axiom,
|
blanchet@43432
|
405 |
AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
|
blanchet@43432
|
406 |
|> close_formula_universally, NONE, NONE)
|
blanchet@38506
|
407 |
end
|
blanchet@38506
|
408 |
|
blanchet@43434
|
409 |
fun helper_facts_for_sym ctxt type_sys (s, {typ, ...} : sym_table_info) =
|
blanchet@43432
|
410 |
case strip_prefix_and_unascii const_prefix s of
|
blanchet@43434
|
411 |
SOME mangled_s =>
|
blanchet@43432
|
412 |
let
|
blanchet@43432
|
413 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@43434
|
414 |
val unmangled_s = mangled_s |> unmangled_const_name
|
blanchet@43432
|
415 |
fun dub_and_inst c needs_full_types (th, j) =
|
blanchet@43432
|
416 |
((c ^ "_" ^ string_of_int j ^ (if needs_full_types then "ft" else ""),
|
blanchet@43432
|
417 |
false),
|
blanchet@43437
|
418 |
let val t = th |> prop_of in
|
blanchet@43437
|
419 |
t |> (general_type_arg_policy type_sys = Mangled_Types andalso
|
blanchet@43437
|
420 |
not (null (Term.hidden_polymorphism t)))
|
blanchet@43437
|
421 |
? (case typ of
|
blanchet@43437
|
422 |
SOME T =>
|
blanchet@43437
|
423 |
specialize_type thy (safe_invert_const unmangled_s, T)
|
blanchet@43437
|
424 |
| NONE => I)
|
blanchet@43437
|
425 |
end)
|
blanchet@43432
|
426 |
fun make_facts eq_as_iff =
|
blanchet@43432
|
427 |
map_filter (make_fact ctxt false eq_as_iff false)
|
blanchet@43432
|
428 |
in
|
blanchet@43432
|
429 |
metis_helpers
|
blanchet@43432
|
430 |
|> maps (fn (metis_s, (needs_full_types, ths)) =>
|
blanchet@43432
|
431 |
if metis_s <> unmangled_s orelse
|
blanchet@43432
|
432 |
(needs_full_types andalso
|
blanchet@43432
|
433 |
not (type_system_types_dangerous_types type_sys)) then
|
blanchet@43432
|
434 |
[]
|
blanchet@43432
|
435 |
else
|
blanchet@43432
|
436 |
ths ~~ (1 upto length ths)
|
blanchet@43434
|
437 |
|> map (dub_and_inst mangled_s needs_full_types)
|
blanchet@43432
|
438 |
|> make_facts (not needs_full_types))
|
blanchet@43432
|
439 |
end
|
blanchet@43432
|
440 |
| NONE => []
|
blanchet@43434
|
441 |
fun helper_facts_for_sym_table ctxt type_sys sym_tab =
|
blanchet@43434
|
442 |
Symtab.fold_rev (append o helper_facts_for_sym ctxt type_sys) sym_tab []
|
blanchet@43432
|
443 |
|
blanchet@43415
|
444 |
fun translate_atp_fact ctxt keep_trivial =
|
blanchet@43432
|
445 |
`(make_fact ctxt keep_trivial true true o apsnd prop_of)
|
blanchet@39248
|
446 |
|
blanchet@41382
|
447 |
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
|
blanchet@38506
|
448 |
let
|
wenzelm@43232
|
449 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@41339
|
450 |
val fact_ts = map (prop_of o snd o snd) rich_facts
|
blanchet@41339
|
451 |
val (facts, fact_names) =
|
blanchet@41339
|
452 |
rich_facts
|
blanchet@41339
|
453 |
|> map_filter (fn (NONE, _) => NONE
|
blanchet@41339
|
454 |
| (SOME fact, (name, _)) => SOME (fact, name))
|
blanchet@41339
|
455 |
|> ListPair.unzip
|
blanchet@40445
|
456 |
(* Remove existing facts from the conjecture, as this can dramatically
|
blanchet@39249
|
457 |
boost an ATP's performance (for some reason). *)
|
blanchet@40445
|
458 |
val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
|
blanchet@38506
|
459 |
val goal_t = Logic.list_implies (hyp_ts, concl_t)
|
blanchet@43224
|
460 |
val all_ts = goal_t :: fact_ts
|
blanchet@43224
|
461 |
val subs = tfree_classes_of_terms all_ts
|
blanchet@43224
|
462 |
val supers = tvar_classes_of_terms all_ts
|
blanchet@43224
|
463 |
val tycons = type_consts_of_terms thy all_ts
|
blanchet@43415
|
464 |
val conjs = make_conjecture ctxt (hyp_ts @ [concl_t])
|
blanchet@41385
|
465 |
val (supers', arity_clauses) =
|
blanchet@41385
|
466 |
if type_sys = No_Types then ([], [])
|
blanchet@41385
|
467 |
else make_arity_clauses thy tycons supers
|
blanchet@38506
|
468 |
val class_rel_clauses = make_class_rel_clauses thy subs supers'
|
blanchet@38506
|
469 |
in
|
blanchet@41561
|
470 |
(fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
|
blanchet@38506
|
471 |
end
|
blanchet@38506
|
472 |
|
blanchet@43436
|
473 |
fun impose_type_arg_policy type_sys =
|
blanchet@43436
|
474 |
let
|
blanchet@43436
|
475 |
fun aux (CombApp tmp) = CombApp (pairself aux tmp)
|
blanchet@43436
|
476 |
| aux (CombConst (name as (s, _), ty, ty_args)) =
|
blanchet@43432
|
477 |
(case strip_prefix_and_unascii const_prefix s of
|
blanchet@43432
|
478 |
NONE => (name, ty_args)
|
blanchet@43432
|
479 |
| SOME s'' =>
|
blanchet@43440
|
480 |
let val s'' = safe_invert_const s'' in
|
blanchet@43432
|
481 |
case type_arg_policy type_sys s'' of
|
blanchet@43432
|
482 |
No_Type_Args => (name, [])
|
blanchet@43432
|
483 |
| Mangled_Types => (mangled_const_name ty_args name, [])
|
blanchet@43432
|
484 |
| Explicit_Type_Args => (name, ty_args)
|
blanchet@43432
|
485 |
end)
|
blanchet@43432
|
486 |
|> (fn (name, ty_args) => CombConst (name, ty, ty_args))
|
blanchet@43436
|
487 |
| aux tm = tm
|
blanchet@43436
|
488 |
in aux end
|
blanchet@43436
|
489 |
val impose_type_arg_policy_on_fact =
|
blanchet@43436
|
490 |
update_combformula o formula_map o impose_type_arg_policy
|
blanchet@43432
|
491 |
|
blanchet@41386
|
492 |
fun tag_with_type ty t = ATerm (`I type_tag_name, [ty, t])
|
blanchet@38506
|
493 |
|
blanchet@43433
|
494 |
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
|
blanchet@38506
|
495 |
(true, ATerm (class, [ATerm (name, [])]))
|
blanchet@43433
|
496 |
| fo_literal_from_type_literal (TyLitFree (class, name)) =
|
blanchet@38506
|
497 |
(true, ATerm (class, [ATerm (name, [])]))
|
blanchet@38506
|
498 |
|
blanchet@43433
|
499 |
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
|
blanchet@38506
|
500 |
|
blanchet@41386
|
501 |
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
|
blanchet@41386
|
502 |
considered dangerous because their "exhaust" properties can easily lead to
|
blanchet@41386
|
503 |
unsound ATP proofs. The checks below are an (unsound) approximation of
|
blanchet@41386
|
504 |
finiteness. *)
|
blanchet@41386
|
505 |
|
blanchet@41386
|
506 |
fun is_dtyp_dangerous _ (Datatype_Aux.DtTFree _) = true
|
blanchet@41386
|
507 |
| is_dtyp_dangerous ctxt (Datatype_Aux.DtType (s, Us)) =
|
blanchet@41386
|
508 |
is_type_constr_dangerous ctxt s andalso forall (is_dtyp_dangerous ctxt) Us
|
blanchet@41386
|
509 |
| is_dtyp_dangerous _ (Datatype_Aux.DtRec _) = false
|
blanchet@41386
|
510 |
and is_type_dangerous ctxt (Type (s, Ts)) =
|
blanchet@41386
|
511 |
is_type_constr_dangerous ctxt s andalso forall (is_type_dangerous ctxt) Ts
|
blanchet@41388
|
512 |
| is_type_dangerous _ _ = false
|
blanchet@41386
|
513 |
and is_type_constr_dangerous ctxt s =
|
wenzelm@43232
|
514 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@41386
|
515 |
case Datatype_Data.get_info thy s of
|
blanchet@41386
|
516 |
SOME {descr, ...} =>
|
blanchet@41386
|
517 |
forall (fn (_, (_, _, constrs)) =>
|
blanchet@41386
|
518 |
forall (forall (is_dtyp_dangerous ctxt) o snd) constrs) descr
|
blanchet@41386
|
519 |
| NONE =>
|
blanchet@41386
|
520 |
case Typedef.get_info ctxt s of
|
blanchet@41386
|
521 |
({rep_type, ...}, _) :: _ => is_type_dangerous ctxt rep_type
|
blanchet@41386
|
522 |
| [] => true
|
blanchet@41386
|
523 |
end
|
blanchet@41386
|
524 |
|
blanchet@43433
|
525 |
fun should_tag_with_type ctxt (Tags full_types) T =
|
blanchet@43433
|
526 |
full_types orelse is_type_dangerous ctxt T
|
blanchet@41386
|
527 |
| should_tag_with_type _ _ _ = false
|
blanchet@41386
|
528 |
|
blanchet@43433
|
529 |
fun type_pred_combatom type_sys T tm =
|
blanchet@43434
|
530 |
CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T]),
|
blanchet@43434
|
531 |
tm)
|
blanchet@43436
|
532 |
|> impose_type_arg_policy type_sys
|
blanchet@43405
|
533 |
|> AAtom
|
blanchet@43405
|
534 |
|
blanchet@43433
|
535 |
fun formula_from_combformula ctxt type_sys =
|
blanchet@38506
|
536 |
let
|
blanchet@43427
|
537 |
fun do_term top_level u =
|
blanchet@38506
|
538 |
let
|
blanchet@38506
|
539 |
val (head, args) = strip_combterm_comb u
|
blanchet@38506
|
540 |
val (x, ty_args) =
|
blanchet@38506
|
541 |
case head of
|
blanchet@43424
|
542 |
CombConst (name, _, ty_args) => (name, ty_args)
|
blanchet@38506
|
543 |
| CombVar (name, _) => (name, [])
|
blanchet@38506
|
544 |
| CombApp _ => raise Fail "impossible \"CombApp\""
|
blanchet@43433
|
545 |
val t = ATerm (x, map fo_term_from_typ ty_args @
|
blanchet@43427
|
546 |
map (do_term false) args)
|
blanchet@41386
|
547 |
val ty = combtyp_of u
|
blanchet@43401
|
548 |
in
|
blanchet@43427
|
549 |
t |> (if not top_level andalso
|
blanchet@43427
|
550 |
should_tag_with_type ctxt type_sys ty then
|
blanchet@43433
|
551 |
tag_with_type (fo_term_from_typ ty)
|
blanchet@43401
|
552 |
else
|
blanchet@43401
|
553 |
I)
|
blanchet@43401
|
554 |
end
|
blanchet@43402
|
555 |
val do_bound_type =
|
blanchet@43433
|
556 |
if type_sys = Many_Typed then SOME o mangled_type_name else K NONE
|
blanchet@43402
|
557 |
val do_out_of_bound_type =
|
blanchet@43419
|
558 |
if member (op =) [Mangled true, Args true] type_sys then
|
blanchet@43402
|
559 |
(fn (s, ty) =>
|
blanchet@43413
|
560 |
type_pred_combatom type_sys ty (CombVar (s, ty))
|
blanchet@43433
|
561 |
|> formula_from_combformula ctxt type_sys |> SOME)
|
blanchet@43402
|
562 |
else
|
blanchet@43402
|
563 |
K NONE
|
blanchet@43401
|
564 |
fun do_formula (AQuant (q, xs, phi)) =
|
blanchet@43402
|
565 |
AQuant (q, xs |> map (apsnd (fn NONE => NONE
|
blanchet@43402
|
566 |
| SOME ty => do_bound_type ty)),
|
blanchet@43405
|
567 |
(if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
|
blanchet@43402
|
568 |
(map_filter
|
blanchet@43402
|
569 |
(fn (_, NONE) => NONE
|
blanchet@43402
|
570 |
| (s, SOME ty) => do_out_of_bound_type (s, ty)) xs)
|
blanchet@43402
|
571 |
(do_formula phi))
|
blanchet@43401
|
572 |
| do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
|
blanchet@43427
|
573 |
| do_formula (AAtom tm) = AAtom (do_term true tm)
|
blanchet@43401
|
574 |
in do_formula end
|
blanchet@38506
|
575 |
|
blanchet@41386
|
576 |
fun formula_for_fact ctxt type_sys
|
blanchet@43433
|
577 |
({combformula, atomic_types, ...} : translated_formula) =
|
blanchet@43433
|
578 |
mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
|
blanchet@43433
|
579 |
(atp_type_literals_for_types type_sys Axiom atomic_types))
|
blanchet@43433
|
580 |
(formula_from_combformula ctxt type_sys
|
blanchet@43433
|
581 |
(close_combformula_universally combformula))
|
blanchet@43413
|
582 |
|> close_formula_universally
|
blanchet@38506
|
583 |
|
blanchet@43409
|
584 |
fun logic_for_type_sys Many_Typed = Tff
|
blanchet@43409
|
585 |
| logic_for_type_sys _ = Fof
|
blanchet@43409
|
586 |
|
blanchet@43051
|
587 |
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
|
blanchet@43051
|
588 |
of monomorphization). The TPTP explicitly forbids name clashes, and some of
|
blanchet@43051
|
589 |
the remote provers might care. *)
|
blanchet@43416
|
590 |
fun formula_line_for_fact ctxt prefix type_sys
|
blanchet@43051
|
591 |
(j, formula as {name, kind, ...}) =
|
blanchet@43409
|
592 |
Formula (logic_for_type_sys type_sys,
|
blanchet@43409
|
593 |
prefix ^ string_of_int j ^ "_" ^ ascii_of name, kind,
|
blanchet@43409
|
594 |
formula_for_fact ctxt type_sys formula, NONE, NONE)
|
blanchet@38506
|
595 |
|
blanchet@43416
|
596 |
fun formula_line_for_class_rel_clause (ClassRelClause {name, subclass,
|
blanchet@38506
|
597 |
superclass, ...}) =
|
blanchet@43413
|
598 |
let val ty_arg = ATerm (`I "T", []) in
|
blanchet@43409
|
599 |
Formula (Fof, class_rel_clause_prefix ^ ascii_of name, Axiom,
|
blanchet@43398
|
600 |
AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
|
blanchet@43413
|
601 |
AAtom (ATerm (superclass, [ty_arg]))])
|
blanchet@43413
|
602 |
|> close_formula_universally, NONE, NONE)
|
blanchet@38506
|
603 |
end
|
blanchet@38506
|
604 |
|
blanchet@43433
|
605 |
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
|
blanchet@38506
|
606 |
(true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
|
blanchet@43433
|
607 |
| fo_literal_from_arity_literal (TVarLit (c, sort)) =
|
blanchet@38506
|
608 |
(false, ATerm (c, [ATerm (sort, [])]))
|
blanchet@38506
|
609 |
|
blanchet@43416
|
610 |
fun formula_line_for_arity_clause (ArityClause {name, conclLit, premLits,
|
blanchet@38506
|
611 |
...}) =
|
blanchet@43409
|
612 |
Formula (Fof, arity_clause_prefix ^ ascii_of name, Axiom,
|
blanchet@43433
|
613 |
mk_ahorn (map (formula_from_fo_literal o apfst not
|
blanchet@43433
|
614 |
o fo_literal_from_arity_literal) premLits)
|
blanchet@43433
|
615 |
(formula_from_fo_literal
|
blanchet@43433
|
616 |
(fo_literal_from_arity_literal conclLit))
|
blanchet@43413
|
617 |
|> close_formula_universally, NONE, NONE)
|
blanchet@38506
|
618 |
|
blanchet@43416
|
619 |
fun formula_line_for_conjecture ctxt type_sys
|
blanchet@40358
|
620 |
({name, kind, combformula, ...} : translated_formula) =
|
blanchet@43409
|
621 |
Formula (logic_for_type_sys type_sys, conjecture_prefix ^ name, kind,
|
blanchet@43433
|
622 |
formula_from_combformula ctxt type_sys
|
blanchet@43433
|
623 |
(close_combformula_universally combformula)
|
blanchet@43413
|
624 |
|> close_formula_universally, NONE, NONE)
|
blanchet@38506
|
625 |
|
blanchet@43433
|
626 |
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
|
blanchet@43433
|
627 |
atomic_types |> atp_type_literals_for_types type_sys Conjecture
|
blanchet@43433
|
628 |
|> map fo_literal_from_type_literal
|
blanchet@38506
|
629 |
|
blanchet@43416
|
630 |
fun formula_line_for_free_type j lit =
|
blanchet@43409
|
631 |
Formula (Fof, tfree_prefix ^ string_of_int j, Hypothesis,
|
blanchet@43433
|
632 |
formula_from_fo_literal lit, NONE, NONE)
|
blanchet@43416
|
633 |
fun formula_lines_for_free_types type_sys facts =
|
blanchet@38506
|
634 |
let
|
blanchet@43224
|
635 |
val litss = map (free_type_literals type_sys) facts
|
blanchet@38506
|
636 |
val lits = fold (union (op =)) litss []
|
blanchet@43416
|
637 |
in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
|
blanchet@38506
|
638 |
|
blanchet@38506
|
639 |
(** "hBOOL" and "hAPP" **)
|
blanchet@38506
|
640 |
|
blanchet@43431
|
641 |
fun add_combterm_to_sym_table explicit_apply =
|
blanchet@43429
|
642 |
let
|
blanchet@43429
|
643 |
fun aux top_level tm =
|
blanchet@43429
|
644 |
let val (head, args) = strip_combterm_comb tm in
|
blanchet@43429
|
645 |
(case head of
|
blanchet@43434
|
646 |
CombConst ((s, _), T, _) =>
|
blanchet@43429
|
647 |
if String.isPrefix bound_var_prefix s then
|
blanchet@43429
|
648 |
I
|
blanchet@43429
|
649 |
else
|
blanchet@43434
|
650 |
let val ary = length args in
|
blanchet@43429
|
651 |
Symtab.map_default
|
blanchet@43429
|
652 |
(s, {pred_sym = true,
|
blanchet@43434
|
653 |
min_ary = if explicit_apply then 0 else ary,
|
blanchet@43434
|
654 |
max_ary = 0, typ = SOME T})
|
blanchet@43434
|
655 |
(fn {pred_sym, min_ary, max_ary, typ} =>
|
blanchet@43429
|
656 |
{pred_sym = pred_sym andalso top_level,
|
blanchet@43434
|
657 |
min_ary = Int.min (ary, min_ary),
|
blanchet@43434
|
658 |
max_ary = Int.max (ary, max_ary),
|
blanchet@43434
|
659 |
typ = if typ = SOME T then typ else NONE})
|
blanchet@43429
|
660 |
end
|
blanchet@43429
|
661 |
| _ => I)
|
blanchet@43429
|
662 |
#> fold (aux false) args
|
blanchet@43429
|
663 |
end
|
blanchet@43429
|
664 |
in aux true end
|
blanchet@38506
|
665 |
|
blanchet@43431
|
666 |
val add_fact_to_sym_table = fact_lift o formula_fold o add_combterm_to_sym_table
|
blanchet@38506
|
667 |
|
blanchet@43428
|
668 |
val default_sym_table_entries =
|
blanchet@43434
|
669 |
[("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
|
blanchet@43439
|
670 |
(make_fixed_const predicator_base,
|
blanchet@43434
|
671 |
{pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
|
blanchet@43439
|
672 |
([tptp_false, tptp_true]
|
blanchet@43434
|
673 |
|> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
|
blanchet@41388
|
674 |
|
blanchet@43415
|
675 |
fun sym_table_for_facts explicit_apply facts =
|
blanchet@43439
|
676 |
Symtab.empty |> fold Symtab.default default_sym_table_entries
|
blanchet@43439
|
677 |
|> fold (add_fact_to_sym_table explicit_apply) facts
|
blanchet@38506
|
678 |
|
blanchet@43429
|
679 |
fun min_arity_of sym_tab s =
|
blanchet@43429
|
680 |
case Symtab.lookup sym_tab s of
|
blanchet@43434
|
681 |
SOME ({min_ary, ...} : sym_table_info) => min_ary
|
blanchet@43429
|
682 |
| NONE =>
|
blanchet@43429
|
683 |
case strip_prefix_and_unascii const_prefix s of
|
blanchet@43418
|
684 |
SOME s =>
|
blanchet@43440
|
685 |
let val s = s |> unmangled_const_name |> safe_invert_const in
|
blanchet@43439
|
686 |
if s = predicator_base then 1
|
blanchet@43418
|
687 |
else if s = explicit_app_base then 2
|
blanchet@43418
|
688 |
else if s = type_pred_base then 1
|
blanchet@43428
|
689 |
else 0
|
blanchet@43418
|
690 |
end
|
blanchet@38506
|
691 |
| NONE => 0
|
blanchet@38506
|
692 |
|
blanchet@38506
|
693 |
(* True if the constant ever appears outside of the top-level position in
|
blanchet@38506
|
694 |
literals, or if it appears with different arities (e.g., because of different
|
blanchet@38506
|
695 |
type instantiations). If false, the constant always receives all of its
|
blanchet@38506
|
696 |
arguments and is used as a predicate. *)
|
blanchet@43429
|
697 |
fun is_pred_sym sym_tab s =
|
blanchet@43429
|
698 |
case Symtab.lookup sym_tab s of
|
blanchet@43434
|
699 |
SOME {pred_sym, min_ary, max_ary, ...} => pred_sym andalso min_ary = max_ary
|
blanchet@43429
|
700 |
| NONE => false
|
blanchet@38506
|
701 |
|
blanchet@43439
|
702 |
val predicator_combconst =
|
blanchet@43439
|
703 |
CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
|
blanchet@43439
|
704 |
fun predicator tm = CombApp (predicator_combconst, tm)
|
blanchet@38506
|
705 |
|
blanchet@43439
|
706 |
fun introduce_predicators_in_combterm sym_tab tm =
|
blanchet@43413
|
707 |
case strip_combterm_comb tm of
|
blanchet@43413
|
708 |
(CombConst ((s, _), _, _), _) =>
|
blanchet@43439
|
709 |
if is_pred_sym sym_tab s then tm else predicator tm
|
blanchet@43439
|
710 |
| _ => predicator tm
|
blanchet@38506
|
711 |
|
blanchet@43415
|
712 |
fun list_app head args = fold (curry (CombApp o swap)) args head
|
blanchet@38506
|
713 |
|
blanchet@43415
|
714 |
fun explicit_app arg head =
|
blanchet@43415
|
715 |
let
|
blanchet@43433
|
716 |
val head_T = combtyp_of head
|
blanchet@43433
|
717 |
val (arg_T, res_T) = dest_funT head_T
|
blanchet@43415
|
718 |
val explicit_app =
|
blanchet@43433
|
719 |
CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
|
blanchet@43433
|
720 |
[arg_T, res_T])
|
blanchet@43415
|
721 |
in list_app explicit_app [head, arg] end
|
blanchet@43415
|
722 |
fun list_explicit_app head args = fold explicit_app args head
|
blanchet@43415
|
723 |
|
blanchet@43436
|
724 |
fun introduce_explicit_apps_in_combterm sym_tab =
|
blanchet@43415
|
725 |
let
|
blanchet@43415
|
726 |
fun aux tm =
|
blanchet@43415
|
727 |
case strip_combterm_comb tm of
|
blanchet@43415
|
728 |
(head as CombConst ((s, _), _, _), args) =>
|
blanchet@43415
|
729 |
args |> map aux
|
blanchet@43428
|
730 |
|> chop (min_arity_of sym_tab s)
|
blanchet@43415
|
731 |
|>> list_app head
|
blanchet@43415
|
732 |
|-> list_explicit_app
|
blanchet@43415
|
733 |
| (head, args) => list_explicit_app head (map aux args)
|
blanchet@43415
|
734 |
in aux end
|
blanchet@43415
|
735 |
|
blanchet@43436
|
736 |
fun firstorderize_combterm sym_tab =
|
blanchet@43436
|
737 |
introduce_explicit_apps_in_combterm sym_tab
|
blanchet@43439
|
738 |
#> introduce_predicators_in_combterm sym_tab
|
blanchet@43436
|
739 |
val firstorderize_fact =
|
blanchet@43436
|
740 |
update_combformula o formula_map o firstorderize_combterm
|
blanchet@43415
|
741 |
|
blanchet@43415
|
742 |
fun is_const_relevant type_sys sym_tab s =
|
blanchet@43413
|
743 |
not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
|
blanchet@43415
|
744 |
(type_sys = Many_Typed orelse not (is_pred_sym sym_tab s))
|
blanchet@43413
|
745 |
|
blanchet@43415
|
746 |
fun consider_combterm_consts type_sys sym_tab tm =
|
blanchet@43404
|
747 |
let val (head, args) = strip_combterm_comb tm in
|
blanchet@43404
|
748 |
(case head of
|
blanchet@43404
|
749 |
CombConst ((s, s'), ty, ty_args) =>
|
blanchet@43404
|
750 |
(* FIXME: exploit type subsumption *)
|
blanchet@43415
|
751 |
is_const_relevant type_sys sym_tab s
|
blanchet@43405
|
752 |
? Symtab.insert_list (op =) (s, (s', ty_args, ty))
|
blanchet@43415
|
753 |
| _ => I)
|
blanchet@43415
|
754 |
#> fold (consider_combterm_consts type_sys sym_tab) args
|
blanchet@43404
|
755 |
end
|
blanchet@43404
|
756 |
|
blanchet@43429
|
757 |
fun consider_fact_consts type_sys sym_tab =
|
blanchet@43429
|
758 |
fact_lift (formula_fold (consider_combterm_consts type_sys sym_tab))
|
blanchet@43404
|
759 |
|
blanchet@43416
|
760 |
(* FIXME: needed? *)
|
blanchet@43432
|
761 |
fun typed_const_table_for_facts type_sys sym_tab facts =
|
blanchet@43419
|
762 |
Symtab.empty |> member (op =) [Many_Typed, Mangled true, Args true] type_sys
|
blanchet@43415
|
763 |
? fold (consider_fact_consts type_sys sym_tab) facts
|
blanchet@43404
|
764 |
|
blanchet@43433
|
765 |
fun strip_and_map_type 0 f T = ([], f T)
|
blanchet@43433
|
766 |
| strip_and_map_type n f (Type (@{type_name fun}, [dom_T, ran_T])) =
|
blanchet@43433
|
767 |
strip_and_map_type (n - 1) f ran_T |>> cons (f dom_T)
|
blanchet@43433
|
768 |
| strip_and_map_type _ _ _ = raise Fail "unexpected non-function"
|
blanchet@43404
|
769 |
|
blanchet@43436
|
770 |
fun problem_line_for_typed_const ctxt type_sys sym_tab s n j (s', ty_args, T) =
|
blanchet@43434
|
771 |
let val ary = min_arity_of sym_tab s in
|
blanchet@43415
|
772 |
if type_sys = Many_Typed then
|
blanchet@43435
|
773 |
let val (arg_Ts, res_T) = strip_and_map_type ary mangled_type_name T in
|
blanchet@43433
|
774 |
Decl (sym_decl_prefix ^ ascii_of s, (s, s'), arg_Ts,
|
blanchet@43432
|
775 |
(* ### FIXME: put that in typed_const_tab *)
|
blanchet@43439
|
776 |
if is_pred_sym sym_tab s then `I tptp_tff_bool_type else res_T)
|
blanchet@43415
|
777 |
end
|
blanchet@43415
|
778 |
else
|
blanchet@43415
|
779 |
let
|
blanchet@43434
|
780 |
val (arg_Ts, res_T) = strip_and_map_type ary I T
|
blanchet@43435
|
781 |
val bound_names =
|
blanchet@43435
|
782 |
1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
|
blanchet@43415
|
783 |
val bound_tms =
|
blanchet@43435
|
784 |
bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
|
blanchet@43436
|
785 |
val bound_Ts = arg_Ts |> map (if n > 1 then SOME else K NONE)
|
blanchet@43417
|
786 |
val freshener =
|
blanchet@43417
|
787 |
case type_sys of Args _ => string_of_int j ^ "_" | _ => ""
|
blanchet@43415
|
788 |
in
|
blanchet@43417
|
789 |
Formula (Fof, sym_decl_prefix ^ freshener ^ "_" ^ ascii_of s, Axiom,
|
blanchet@43433
|
790 |
CombConst ((s, s'), T, ty_args)
|
blanchet@43415
|
791 |
|> fold (curry (CombApp o swap)) bound_tms
|
blanchet@43433
|
792 |
|> type_pred_combatom type_sys res_T
|
blanchet@43435
|
793 |
|> mk_aquant AForall (bound_names ~~ bound_Ts)
|
blanchet@43433
|
794 |
|> formula_from_combformula ctxt type_sys,
|
blanchet@43415
|
795 |
NONE, NONE)
|
blanchet@43415
|
796 |
end
|
blanchet@43415
|
797 |
end
|
blanchet@43432
|
798 |
fun problem_lines_for_sym_decl ctxt type_sys sym_tab (s, xs) =
|
blanchet@43436
|
799 |
let val n = length xs in
|
blanchet@43436
|
800 |
map2 (problem_line_for_typed_const ctxt type_sys sym_tab s n)
|
blanchet@43436
|
801 |
(0 upto n - 1) xs
|
blanchet@43436
|
802 |
end
|
blanchet@43434
|
803 |
fun problem_lines_for_sym_decls ctxt type_sys sym_tab typed_const_tab =
|
blanchet@43434
|
804 |
Symtab.fold_rev (append o problem_lines_for_sym_decl ctxt type_sys sym_tab)
|
blanchet@43434
|
805 |
typed_const_tab []
|
blanchet@43410
|
806 |
|
blanchet@43414
|
807 |
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
|
blanchet@43414
|
808 |
union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
|
blanchet@43414
|
809 |
| add_tff_types_in_formula (AConn (_, phis)) =
|
blanchet@43414
|
810 |
fold add_tff_types_in_formula phis
|
blanchet@43414
|
811 |
| add_tff_types_in_formula (AAtom _) = I
|
blanchet@43414
|
812 |
|
blanchet@43433
|
813 |
fun add_tff_types_in_problem_line (Decl (_, _, arg_Ts, res_T)) =
|
blanchet@43433
|
814 |
union (op =) (res_T :: arg_Ts)
|
blanchet@43414
|
815 |
| add_tff_types_in_problem_line (Formula (_, _, _, phi, _, _)) =
|
blanchet@43414
|
816 |
add_tff_types_in_formula phi
|
blanchet@43414
|
817 |
|
blanchet@43414
|
818 |
fun tff_types_in_problem problem =
|
blanchet@43414
|
819 |
fold (fold add_tff_types_in_problem_line o snd) problem []
|
blanchet@43414
|
820 |
|
blanchet@43416
|
821 |
fun decl_line_for_tff_type (s, s') =
|
blanchet@43439
|
822 |
Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tptp_tff_type_of_types)
|
blanchet@43414
|
823 |
|
blanchet@43414
|
824 |
val type_declsN = "Types"
|
blanchet@43415
|
825 |
val sym_declsN = "Symbol types"
|
blanchet@41405
|
826 |
val factsN = "Relevant facts"
|
blanchet@41405
|
827 |
val class_relsN = "Class relationships"
|
blanchet@43414
|
828 |
val aritiesN = "Arities"
|
blanchet@41405
|
829 |
val helpersN = "Helper facts"
|
blanchet@41405
|
830 |
val conjsN = "Conjectures"
|
blanchet@41561
|
831 |
val free_typesN = "Type variables"
|
blanchet@41405
|
832 |
|
blanchet@41405
|
833 |
fun offset_of_heading_in_problem _ [] j = j
|
blanchet@41405
|
834 |
| offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
|
blanchet@41405
|
835 |
if heading = needle then j
|
blanchet@41405
|
836 |
else offset_of_heading_in_problem needle problem (j + length lines)
|
blanchet@41405
|
837 |
|
blanchet@43439
|
838 |
fun prepare_atp_problem ctxt type_sys explicit_apply hyp_ts concl_t facts =
|
blanchet@38506
|
839 |
let
|
blanchet@41561
|
840 |
val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
|
blanchet@41382
|
841 |
translate_formulas ctxt type_sys hyp_ts concl_t facts
|
blanchet@43434
|
842 |
val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
|
blanchet@43436
|
843 |
val (conjs, facts) =
|
blanchet@43436
|
844 |
(conjs, facts) |> pairself (map (firstorderize_fact sym_tab))
|
blanchet@43436
|
845 |
val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
|
blanchet@43436
|
846 |
val (conjs, facts) =
|
blanchet@43436
|
847 |
(conjs, facts) |> pairself (map (impose_type_arg_policy_on_fact type_sys))
|
blanchet@43434
|
848 |
val sym_tab' = conjs @ facts |> sym_table_for_facts false
|
blanchet@43432
|
849 |
val typed_const_tab =
|
blanchet@43434
|
850 |
conjs @ facts |> typed_const_table_for_facts type_sys sym_tab'
|
blanchet@43432
|
851 |
val sym_decl_lines =
|
blanchet@43434
|
852 |
typed_const_tab |> problem_lines_for_sym_decls ctxt type_sys sym_tab'
|
blanchet@43434
|
853 |
val helpers = helper_facts_for_sym_table ctxt type_sys sym_tab'
|
blanchet@43436
|
854 |
|> map (firstorderize_fact sym_tab
|
blanchet@43436
|
855 |
#> impose_type_arg_policy_on_fact type_sys)
|
blanchet@43393
|
856 |
(* Reordering these might confuse the proof reconstruction code or the SPASS
|
blanchet@43393
|
857 |
Flotter hack. *)
|
blanchet@38506
|
858 |
val problem =
|
blanchet@43432
|
859 |
[(sym_declsN, sym_decl_lines),
|
blanchet@43416
|
860 |
(factsN, map (formula_line_for_fact ctxt fact_prefix type_sys)
|
blanchet@43051
|
861 |
(0 upto length facts - 1 ~~ facts)),
|
blanchet@43416
|
862 |
(class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
|
blanchet@43416
|
863 |
(aritiesN, map formula_line_for_arity_clause arity_clauses),
|
blanchet@43432
|
864 |
(helpersN, map (formula_line_for_fact ctxt helper_prefix type_sys)
|
blanchet@43434
|
865 |
(0 upto length helpers - 1 ~~ helpers)
|
blanchet@43434
|
866 |
|> (if type_sys = Tags false then cons (ti_ti_helper_fact ())
|
blanchet@43434
|
867 |
else I)),
|
blanchet@43416
|
868 |
(conjsN, map (formula_line_for_conjecture ctxt type_sys) conjs),
|
blanchet@43416
|
869 |
(free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
|
blanchet@43414
|
870 |
val problem =
|
blanchet@43432
|
871 |
problem
|
blanchet@43432
|
872 |
|> (if type_sys = Many_Typed then
|
blanchet@43432
|
873 |
cons (type_declsN,
|
blanchet@43432
|
874 |
map decl_line_for_tff_type (tff_types_in_problem problem))
|
blanchet@43432
|
875 |
else
|
blanchet@43432
|
876 |
I)
|
blanchet@43439
|
877 |
val (problem, pool) = problem |> nice_atp_problem (!readable_names)
|
blanchet@38506
|
878 |
in
|
blanchet@38506
|
879 |
(problem,
|
blanchet@38506
|
880 |
case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
|
blanchet@43412
|
881 |
offset_of_heading_in_problem factsN problem 0,
|
blanchet@41405
|
882 |
offset_of_heading_in_problem conjsN problem 0,
|
blanchet@41405
|
883 |
fact_names |> Vector.fromList)
|
blanchet@38506
|
884 |
end
|
blanchet@38506
|
885 |
|
blanchet@41561
|
886 |
(* FUDGE *)
|
blanchet@41561
|
887 |
val conj_weight = 0.0
|
blanchet@42641
|
888 |
val hyp_weight = 0.1
|
blanchet@42641
|
889 |
val fact_min_weight = 0.2
|
blanchet@41561
|
890 |
val fact_max_weight = 1.0
|
blanchet@41561
|
891 |
|
blanchet@41561
|
892 |
fun add_term_weights weight (ATerm (s, tms)) =
|
blanchet@41561
|
893 |
(not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
|
blanchet@41561
|
894 |
#> fold (add_term_weights weight) tms
|
blanchet@43409
|
895 |
fun add_problem_line_weights weight (Formula (_, _, _, phi, _, _)) =
|
blanchet@43413
|
896 |
formula_fold (add_term_weights weight) phi
|
blanchet@43399
|
897 |
| add_problem_line_weights _ _ = I
|
blanchet@41561
|
898 |
|
blanchet@41561
|
899 |
fun add_conjectures_weights [] = I
|
blanchet@41561
|
900 |
| add_conjectures_weights conjs =
|
blanchet@41561
|
901 |
let val (hyps, conj) = split_last conjs in
|
blanchet@41561
|
902 |
add_problem_line_weights conj_weight conj
|
blanchet@41561
|
903 |
#> fold (add_problem_line_weights hyp_weight) hyps
|
blanchet@41561
|
904 |
end
|
blanchet@41561
|
905 |
|
blanchet@41561
|
906 |
fun add_facts_weights facts =
|
blanchet@41561
|
907 |
let
|
blanchet@41561
|
908 |
val num_facts = length facts
|
blanchet@41561
|
909 |
fun weight_of j =
|
blanchet@41561
|
910 |
fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
|
blanchet@41561
|
911 |
/ Real.fromInt num_facts
|
blanchet@41561
|
912 |
in
|
blanchet@41561
|
913 |
map weight_of (0 upto num_facts - 1) ~~ facts
|
blanchet@41561
|
914 |
|> fold (uncurry add_problem_line_weights)
|
blanchet@41561
|
915 |
end
|
blanchet@41561
|
916 |
|
blanchet@41561
|
917 |
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
|
blanchet@41561
|
918 |
fun atp_problem_weights problem =
|
blanchet@41561
|
919 |
Symtab.empty
|
blanchet@41561
|
920 |
|> add_conjectures_weights (these (AList.lookup (op =) problem conjsN))
|
blanchet@41561
|
921 |
|> add_facts_weights (these (AList.lookup (op =) problem factsN))
|
blanchet@41561
|
922 |
|> Symtab.dest
|
blanchet@42590
|
923 |
|> sort (prod_ord Real.compare string_ord o pairself swap)
|
blanchet@41561
|
924 |
|
blanchet@38506
|
925 |
end;
|