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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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Tags of bool |
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Args of bool |
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Mangled of bool |
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No_Types
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val fact_prefix : string
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val conjecture_prefix : string
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val boolify_base : string
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val explicit_app_base : 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 -> bool -> 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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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 boolify_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 type_prefix = "ty_"
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fun make_type ty = type_prefix ^ ascii_of ty
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(* official TPTP TFF syntax *)
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val tff_type_of_types = "$tType"
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val tff_bool_type = "$o"
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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, combtyp, combterm) formula,
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ctypes_sorts: typ list}
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fun map_combformula f
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({name, kind, combformula, ctypes_sorts} : translated_formula) =
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{name = name, kind = kind, combformula = f combformula,
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ctypes_sorts = ctypes_sorts} : translated_formula
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datatype type_system =
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Many_Typed |
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Tags of bool |
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Args of bool |
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Mangled 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 (Tags 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 (Mangled 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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| Tags full_types => full_types orelse s = explicit_app_base
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| Args _ => s = explicit_app_base
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| Mangled _ => s = explicit_app_base
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| No_Types => true)
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datatype type_arg_policy = No_Type_Args | Explicit_Type_Args | Mangled_Types
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fun type_arg_policy type_sys s =
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if dont_need_type_args type_sys s then
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No_Type_Args
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else
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case type_sys of
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Many_Typed => Mangled_Types
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| Mangled _ => Mangled_Types
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| _ => Explicit_Type_Args
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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
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if s = type_pred_base then 1 else num_type_args thy s
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else
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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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(* We are crossing our fingers that it doesn't clash with anything else. *)
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val mangled_type_sep = "\000"
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fun mangled_combtyp_component f (CombTFree name) = f name
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| mangled_combtyp_component f (CombTVar name) =
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f name (* FIXME: shouldn't happen *)
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(* raise Fail "impossible schematic type variable" *)
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| mangled_combtyp_component f (CombType (name, tys)) =
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f name ^ "(" ^ commas (map (mangled_combtyp_component f) tys) ^ ")"
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fun mangled_combtyp ty =
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(make_type (mangled_combtyp_component fst ty),
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mangled_combtyp_component snd ty)
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fun 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 mangled_combtyp_component f) tys ""
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fun mangled_const_name_fst ty_args s =
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s ^ mangled_type_suffix fst ascii_of ty_args
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fun mangled_const_name_snd ty_args s' = s' ^ mangled_type_suffix snd I ty_args
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fun mangled_const_name ty_args (s, s') =
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(mangled_const_name_fst ty_args s, mangled_const_name_snd ty_args s')
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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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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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fun combformula_for_prop thy eq_as_iff =
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let
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fun do_term bs t ts =
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combterm_from_term thy bs (Envir.eta_contract t)
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|>> AAtom ||> union (op =) ts
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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 (combtyp_from_typ 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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blanchet@38506
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| Const (@{const_name All}, _) $ Abs (s, T, t') =>
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blanchet@38506
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do_quant bs AForall s T t'
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blanchet@38506
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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
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if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
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blanchet@41388
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| _ => do_term bs t
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blanchet@38506
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in do_formula [] end
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blanchet@38841
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val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
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wenzelm@41739
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fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
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blanchet@38506
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fun conceal_bounds Ts t =
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blanchet@38506
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subst_bounds (map (Free o apfst concealed_bound_name)
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blanchet@38506
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(0 upto length Ts - 1 ~~ Ts), t)
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blanchet@38506
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fun reveal_bounds Ts =
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blanchet@38506
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subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
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blanchet@38506
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(0 upto length Ts - 1 ~~ Ts))
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blanchet@38506
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blanchet@38831
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(* Removes the lambdas from an equation of the form "t = (%x. u)".
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blanchet@40071
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(Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
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blanchet@38831
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fun extensionalize_term t =
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blanchet@38831
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let
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blanchet@38831
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fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
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blanchet@38831
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| aux j (t as Const (s, Type (_, [Type (_, [_, T']),
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blanchet@38831
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Type (_, [_, res_T])]))
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blanchet@38831
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$ t2 $ Abs (var_s, var_T, t')) =
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haftmann@39093
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if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
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blanchet@38831
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let val var_t = Var ((var_s, j), var_T) in
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blanchet@38831
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Const (s, T' --> T' --> res_T)
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blanchet@38831
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$ betapply (t2, var_t) $ subst_bound (var_t, t')
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blanchet@38831
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|> aux (j + 1)
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blanchet@38831
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end
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blanchet@38831
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else
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blanchet@38831
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t
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blanchet@38831
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| aux _ t = t
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blanchet@38831
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in aux (maxidx_of_term t + 1) t end
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blanchet@38831
|
268 |
|
blanchet@38506
|
269 |
fun introduce_combinators_in_term ctxt kind t =
|
wenzelm@43232
|
270 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@38716
|
271 |
if Meson.is_fol_term thy t then
|
blanchet@38716
|
272 |
t
|
blanchet@38716
|
273 |
else
|
blanchet@38716
|
274 |
let
|
blanchet@38716
|
275 |
fun aux Ts t =
|
blanchet@38716
|
276 |
case t of
|
blanchet@38716
|
277 |
@{const Not} $ t1 => @{const Not} $ aux Ts t1
|
blanchet@38716
|
278 |
| (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
|
blanchet@38716
|
279 |
t0 $ Abs (s, T, aux (T :: Ts) t')
|
blanchet@38890
|
280 |
| (t0 as Const (@{const_name All}, _)) $ t1 =>
|
blanchet@38890
|
281 |
aux Ts (t0 $ eta_expand Ts t1 1)
|
blanchet@38716
|
282 |
| (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
|
blanchet@38716
|
283 |
t0 $ Abs (s, T, aux (T :: Ts) t')
|
blanchet@38890
|
284 |
| (t0 as Const (@{const_name Ex}, _)) $ t1 =>
|
blanchet@38890
|
285 |
aux Ts (t0 $ eta_expand Ts t1 1)
|
haftmann@39028
|
286 |
| (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39028
|
287 |
| (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39019
|
288 |
| (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39093
|
289 |
| (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
|
blanchet@38716
|
290 |
$ t1 $ t2 =>
|
blanchet@38716
|
291 |
t0 $ aux Ts t1 $ aux Ts t2
|
blanchet@38716
|
292 |
| _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
|
blanchet@38716
|
293 |
t
|
blanchet@38716
|
294 |
else
|
blanchet@38716
|
295 |
t |> conceal_bounds Ts
|
blanchet@38716
|
296 |
|> Envir.eta_contract
|
blanchet@38716
|
297 |
|> cterm_of thy
|
blanchet@40071
|
298 |
|> Meson_Clausify.introduce_combinators_in_cterm
|
blanchet@38716
|
299 |
|> prop_of |> Logic.dest_equals |> snd
|
blanchet@38716
|
300 |
|> reveal_bounds Ts
|
blanchet@39616
|
301 |
val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
|
blanchet@38716
|
302 |
in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
|
blanchet@38716
|
303 |
handle THM _ =>
|
blanchet@38716
|
304 |
(* A type variable of sort "{}" will make abstraction fail. *)
|
blanchet@38836
|
305 |
if kind = Conjecture then HOLogic.false_const
|
blanchet@38836
|
306 |
else HOLogic.true_const
|
blanchet@38716
|
307 |
end
|
blanchet@38506
|
308 |
|
blanchet@38506
|
309 |
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
|
blanchet@43224
|
310 |
same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
|
blanchet@38506
|
311 |
fun freeze_term t =
|
blanchet@38506
|
312 |
let
|
blanchet@38506
|
313 |
fun aux (t $ u) = aux t $ aux u
|
blanchet@38506
|
314 |
| aux (Abs (s, T, t)) = Abs (s, T, aux t)
|
blanchet@38506
|
315 |
| aux (Var ((s, i), T)) =
|
blanchet@38506
|
316 |
Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
|
blanchet@38506
|
317 |
| aux t = t
|
blanchet@38506
|
318 |
in t |> exists_subterm is_Var t ? aux end
|
blanchet@38506
|
319 |
|
blanchet@40445
|
320 |
(* making fact and conjecture formulas *)
|
blanchet@43415
|
321 |
fun make_formula ctxt eq_as_iff presimp name kind t =
|
blanchet@38506
|
322 |
let
|
wenzelm@43232
|
323 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@38831
|
324 |
val t = t |> Envir.beta_eta_contract
|
blanchet@38890
|
325 |
|> transform_elim_term
|
blanchet@41459
|
326 |
|> Object_Logic.atomize_term thy
|
blanchet@38890
|
327 |
val need_trueprop = (fastype_of t = HOLogic.boolT)
|
blanchet@38890
|
328 |
val t = t |> need_trueprop ? HOLogic.mk_Trueprop
|
blanchet@38506
|
329 |
|> extensionalize_term
|
blanchet@38506
|
330 |
|> presimp ? presimplify_term thy
|
blanchet@38506
|
331 |
|> perhaps (try (HOLogic.dest_Trueprop))
|
blanchet@38506
|
332 |
|> introduce_combinators_in_term ctxt kind
|
blanchet@38836
|
333 |
|> kind <> Axiom ? freeze_term
|
blanchet@43413
|
334 |
val (combformula, ctypes_sorts) =
|
blanchet@43415
|
335 |
combformula_for_prop thy eq_as_iff t []
|
blanchet@38506
|
336 |
in
|
blanchet@38991
|
337 |
{name = name, combformula = combformula, kind = kind,
|
blanchet@38991
|
338 |
ctypes_sorts = ctypes_sorts}
|
blanchet@38506
|
339 |
end
|
blanchet@38506
|
340 |
|
blanchet@43415
|
341 |
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, _), th) =
|
blanchet@42861
|
342 |
case (keep_trivial,
|
blanchet@43415
|
343 |
make_formula ctxt eq_as_iff presimp name Axiom (prop_of th)) of
|
blanchet@42861
|
344 |
(false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
|
blanchet@42861
|
345 |
NONE
|
blanchet@42861
|
346 |
| (_, formula) => SOME formula
|
blanchet@43415
|
347 |
fun make_conjecture ctxt ts =
|
blanchet@38836
|
348 |
let val last = length ts - 1 in
|
blanchet@43415
|
349 |
map2 (fn j => make_formula ctxt true true (string_of_int j)
|
blanchet@38836
|
350 |
(if j = last then Conjecture else Hypothesis))
|
blanchet@38836
|
351 |
(0 upto last) ts
|
blanchet@38836
|
352 |
end
|
blanchet@38506
|
353 |
|
blanchet@38506
|
354 |
(** Helper facts **)
|
blanchet@38506
|
355 |
|
blanchet@43413
|
356 |
fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
|
blanchet@43413
|
357 |
| formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
|
blanchet@43413
|
358 |
| formula_map f (AAtom tm) = AAtom (f tm)
|
blanchet@43413
|
359 |
|
blanchet@43413
|
360 |
fun formula_fold f (AQuant (_, _, phi)) = formula_fold f phi
|
blanchet@43413
|
361 |
| formula_fold f (AConn (_, phis)) = fold (formula_fold f) phis
|
blanchet@43413
|
362 |
| formula_fold f (AAtom tm) = f tm
|
blanchet@41561
|
363 |
|
blanchet@41388
|
364 |
fun count_term (ATerm ((s, _), tms)) =
|
blanchet@43413
|
365 |
(if is_atp_variable s then I else Symtab.map_entry s (Integer.add 1))
|
blanchet@41388
|
366 |
#> fold count_term tms
|
blanchet@43413
|
367 |
fun count_formula x = formula_fold count_term x
|
blanchet@38506
|
368 |
|
blanchet@38506
|
369 |
val init_counters =
|
blanchet@41388
|
370 |
metis_helpers |> map fst |> sort_distinct string_ord |> map (rpair 0)
|
blanchet@41388
|
371 |
|> Symtab.make
|
blanchet@38506
|
372 |
|
blanchet@43413
|
373 |
(* ### FIXME: do this on repaired combterms *)
|
blanchet@43392
|
374 |
fun get_helper_facts ctxt type_sys formulas =
|
blanchet@38506
|
375 |
let
|
blanchet@43320
|
376 |
val no_dangerous_types = type_system_types_dangerous_types type_sys
|
blanchet@41388
|
377 |
val ct = init_counters |> fold count_formula formulas
|
blanchet@41388
|
378 |
fun is_used s = the (Symtab.lookup ct s) > 0
|
blanchet@41388
|
379 |
fun dub c needs_full_types (th, j) =
|
blanchet@41388
|
380 |
((c ^ "_" ^ string_of_int j ^ (if needs_full_types then "ft" else ""),
|
blanchet@41388
|
381 |
false), th)
|
blanchet@43415
|
382 |
fun make_facts eq_as_iff = map_filter (make_fact ctxt false eq_as_iff false)
|
blanchet@38506
|
383 |
in
|
blanchet@41393
|
384 |
(metis_helpers
|
blanchet@41393
|
385 |
|> filter (is_used o fst)
|
blanchet@41393
|
386 |
|> maps (fn (c, (needs_full_types, ths)) =>
|
blanchet@41393
|
387 |
if needs_full_types andalso not no_dangerous_types then
|
blanchet@41393
|
388 |
[]
|
blanchet@41393
|
389 |
else
|
blanchet@41393
|
390 |
ths ~~ (1 upto length ths)
|
blanchet@41393
|
391 |
|> map (dub c needs_full_types)
|
blanchet@41393
|
392 |
|> make_facts (not needs_full_types)),
|
blanchet@41393
|
393 |
if type_sys = Tags false then
|
blanchet@41393
|
394 |
let
|
blanchet@41393
|
395 |
fun var s = ATerm (`I s, [])
|
blanchet@41393
|
396 |
fun tag tm = ATerm (`I type_tag_name, [var "X", tm])
|
blanchet@41393
|
397 |
in
|
blanchet@43409
|
398 |
[Formula (Fof, helper_prefix ^ ascii_of "ti_ti", Axiom,
|
blanchet@43398
|
399 |
AAtom (ATerm (`I "equal",
|
blanchet@43398
|
400 |
[tag (tag (var "Y")), tag (var "Y")]))
|
blanchet@43400
|
401 |
|> close_formula_universally, NONE, NONE)]
|
blanchet@41393
|
402 |
end
|
blanchet@41393
|
403 |
else
|
blanchet@41393
|
404 |
[])
|
blanchet@38506
|
405 |
end
|
blanchet@38506
|
406 |
|
blanchet@43415
|
407 |
fun translate_atp_fact ctxt keep_trivial =
|
blanchet@43415
|
408 |
`(make_fact ctxt keep_trivial true true)
|
blanchet@39248
|
409 |
|
blanchet@41382
|
410 |
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
|
blanchet@38506
|
411 |
let
|
wenzelm@43232
|
412 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@41339
|
413 |
val fact_ts = map (prop_of o snd o snd) rich_facts
|
blanchet@41339
|
414 |
val (facts, fact_names) =
|
blanchet@41339
|
415 |
rich_facts
|
blanchet@41339
|
416 |
|> map_filter (fn (NONE, _) => NONE
|
blanchet@41339
|
417 |
| (SOME fact, (name, _)) => SOME (fact, name))
|
blanchet@41339
|
418 |
|> ListPair.unzip
|
blanchet@40445
|
419 |
(* Remove existing facts from the conjecture, as this can dramatically
|
blanchet@39249
|
420 |
boost an ATP's performance (for some reason). *)
|
blanchet@40445
|
421 |
val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
|
blanchet@38506
|
422 |
val goal_t = Logic.list_implies (hyp_ts, concl_t)
|
blanchet@43224
|
423 |
val all_ts = goal_t :: fact_ts
|
blanchet@43224
|
424 |
val subs = tfree_classes_of_terms all_ts
|
blanchet@43224
|
425 |
val supers = tvar_classes_of_terms all_ts
|
blanchet@43224
|
426 |
val tycons = type_consts_of_terms thy all_ts
|
blanchet@43415
|
427 |
val conjs = make_conjecture ctxt (hyp_ts @ [concl_t])
|
blanchet@41385
|
428 |
val (supers', arity_clauses) =
|
blanchet@41385
|
429 |
if type_sys = No_Types then ([], [])
|
blanchet@41385
|
430 |
else make_arity_clauses thy tycons supers
|
blanchet@38506
|
431 |
val class_rel_clauses = make_class_rel_clauses thy subs supers'
|
blanchet@38506
|
432 |
in
|
blanchet@41561
|
433 |
(fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
|
blanchet@38506
|
434 |
end
|
blanchet@38506
|
435 |
|
blanchet@41386
|
436 |
fun tag_with_type ty t = ATerm (`I type_tag_name, [ty, t])
|
blanchet@38506
|
437 |
|
blanchet@38506
|
438 |
fun fo_term_for_combtyp (CombTVar name) = ATerm (name, [])
|
blanchet@38506
|
439 |
| fo_term_for_combtyp (CombTFree name) = ATerm (name, [])
|
blanchet@38506
|
440 |
| fo_term_for_combtyp (CombType (name, tys)) =
|
blanchet@38506
|
441 |
ATerm (name, map fo_term_for_combtyp tys)
|
blanchet@38506
|
442 |
|
blanchet@38506
|
443 |
fun fo_literal_for_type_literal (TyLitVar (class, name)) =
|
blanchet@38506
|
444 |
(true, ATerm (class, [ATerm (name, [])]))
|
blanchet@38506
|
445 |
| fo_literal_for_type_literal (TyLitFree (class, name)) =
|
blanchet@38506
|
446 |
(true, ATerm (class, [ATerm (name, [])]))
|
blanchet@38506
|
447 |
|
blanchet@38506
|
448 |
fun formula_for_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
|
blanchet@38506
|
449 |
|
blanchet@41386
|
450 |
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
|
blanchet@41386
|
451 |
considered dangerous because their "exhaust" properties can easily lead to
|
blanchet@41386
|
452 |
unsound ATP proofs. The checks below are an (unsound) approximation of
|
blanchet@41386
|
453 |
finiteness. *)
|
blanchet@41386
|
454 |
|
blanchet@41386
|
455 |
fun is_dtyp_dangerous _ (Datatype_Aux.DtTFree _) = true
|
blanchet@41386
|
456 |
| is_dtyp_dangerous ctxt (Datatype_Aux.DtType (s, Us)) =
|
blanchet@41386
|
457 |
is_type_constr_dangerous ctxt s andalso forall (is_dtyp_dangerous ctxt) Us
|
blanchet@41386
|
458 |
| is_dtyp_dangerous _ (Datatype_Aux.DtRec _) = false
|
blanchet@41386
|
459 |
and is_type_dangerous ctxt (Type (s, Ts)) =
|
blanchet@41386
|
460 |
is_type_constr_dangerous ctxt s andalso forall (is_type_dangerous ctxt) Ts
|
blanchet@41388
|
461 |
| is_type_dangerous _ _ = false
|
blanchet@41386
|
462 |
and is_type_constr_dangerous ctxt s =
|
wenzelm@43232
|
463 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@41386
|
464 |
case Datatype_Data.get_info thy s of
|
blanchet@41386
|
465 |
SOME {descr, ...} =>
|
blanchet@41386
|
466 |
forall (fn (_, (_, _, constrs)) =>
|
blanchet@41386
|
467 |
forall (forall (is_dtyp_dangerous ctxt) o snd) constrs) descr
|
blanchet@41386
|
468 |
| NONE =>
|
blanchet@41386
|
469 |
case Typedef.get_info ctxt s of
|
blanchet@41386
|
470 |
({rep_type, ...}, _) :: _ => is_type_dangerous ctxt rep_type
|
blanchet@41386
|
471 |
| [] => true
|
blanchet@41386
|
472 |
end
|
blanchet@41386
|
473 |
|
blanchet@41386
|
474 |
fun is_combtyp_dangerous ctxt (CombType ((s, _), tys)) =
|
blanchet@41386
|
475 |
(case strip_prefix_and_unascii type_const_prefix s of
|
blanchet@41386
|
476 |
SOME s' => forall (is_combtyp_dangerous ctxt) tys andalso
|
blanchet@41386
|
477 |
is_type_constr_dangerous ctxt (invert_const s')
|
blanchet@41386
|
478 |
| NONE => false)
|
blanchet@41386
|
479 |
| is_combtyp_dangerous _ _ = false
|
blanchet@41386
|
480 |
|
blanchet@41386
|
481 |
fun should_tag_with_type ctxt (Tags full_types) ty =
|
blanchet@41386
|
482 |
full_types orelse is_combtyp_dangerous ctxt ty
|
blanchet@41386
|
483 |
| should_tag_with_type _ _ _ = false
|
blanchet@41386
|
484 |
|
blanchet@41388
|
485 |
val fname_table =
|
blanchet@41388
|
486 |
[("c_False", (0, ("c_fFalse", @{const_name Metis.fFalse}))),
|
blanchet@41388
|
487 |
("c_True", (0, ("c_fTrue", @{const_name Metis.fTrue}))),
|
blanchet@41388
|
488 |
("c_Not", (1, ("c_fNot", @{const_name Metis.fNot}))),
|
blanchet@41388
|
489 |
("c_conj", (2, ("c_fconj", @{const_name Metis.fconj}))),
|
blanchet@41388
|
490 |
("c_disj", (2, ("c_fdisj", @{const_name Metis.fdisj}))),
|
blanchet@41388
|
491 |
("c_implies", (2, ("c_fimplies", @{const_name Metis.fimplies}))),
|
blanchet@41388
|
492 |
("equal", (2, ("c_fequal", @{const_name Metis.fequal})))]
|
blanchet@41388
|
493 |
|
blanchet@43415
|
494 |
fun repair_combterm_consts type_sys =
|
blanchet@43415
|
495 |
let
|
blanchet@43415
|
496 |
fun aux (CombApp tmp) = CombApp (pairself aux tmp)
|
blanchet@43415
|
497 |
| aux (CombConst (name as (s, _), ty, ty_args)) =
|
blanchet@43415
|
498 |
(case strip_prefix_and_unascii const_prefix s of
|
blanchet@43415
|
499 |
NONE => (name, ty_args)
|
blanchet@43415
|
500 |
| SOME s'' =>
|
blanchet@43415
|
501 |
let val s'' = invert_const s'' in
|
blanchet@43415
|
502 |
case type_arg_policy type_sys s'' of
|
blanchet@43415
|
503 |
No_Type_Args => (name, [])
|
blanchet@43415
|
504 |
| Explicit_Type_Args => (name, ty_args)
|
blanchet@43415
|
505 |
| Mangled_Types => (mangled_const_name ty_args name, [])
|
blanchet@43415
|
506 |
end)
|
blanchet@43415
|
507 |
|> (fn (name, ty_args) => CombConst (name, ty, ty_args))
|
blanchet@43415
|
508 |
| aux tm = tm
|
blanchet@43415
|
509 |
in aux end
|
blanchet@43415
|
510 |
|
blanchet@43402
|
511 |
fun pred_combtyp ty =
|
blanchet@43402
|
512 |
case combtyp_from_typ @{typ "unit => bool"} of
|
blanchet@43402
|
513 |
CombType (name, [_, bool_ty]) => CombType (name, [ty, bool_ty])
|
blanchet@43402
|
514 |
| _ => raise Fail "expected two-argument type constructor"
|
blanchet@43402
|
515 |
|
blanchet@43413
|
516 |
fun type_pred_combatom type_sys ty tm =
|
blanchet@43413
|
517 |
CombApp (CombConst ((const_prefix ^ type_pred_base, type_pred_base),
|
blanchet@43413
|
518 |
pred_combtyp ty, [ty]), tm)
|
blanchet@43413
|
519 |
|> repair_combterm_consts type_sys
|
blanchet@43405
|
520 |
|> AAtom
|
blanchet@43405
|
521 |
|
blanchet@43401
|
522 |
fun formula_for_combformula ctxt type_sys =
|
blanchet@38506
|
523 |
let
|
blanchet@43401
|
524 |
fun do_term top_level u =
|
blanchet@38506
|
525 |
let
|
blanchet@38506
|
526 |
val (head, args) = strip_combterm_comb u
|
blanchet@38506
|
527 |
val (x, ty_args) =
|
blanchet@38506
|
528 |
case head of
|
blanchet@38506
|
529 |
CombConst (name as (s, s'), _, ty_args) =>
|
blanchet@41388
|
530 |
(case AList.lookup (op =) fname_table s of
|
blanchet@41388
|
531 |
SOME (n, fname) =>
|
blanchet@43413
|
532 |
(*### FIXME: do earlier? *)
|
blanchet@41398
|
533 |
(if top_level andalso length args = n then
|
blanchet@41398
|
534 |
case s of
|
blanchet@41398
|
535 |
"c_False" => ("$false", s')
|
blanchet@41398
|
536 |
| "c_True" => ("$true", s')
|
blanchet@41398
|
537 |
| _ => name
|
blanchet@41398
|
538 |
else
|
blanchet@41398
|
539 |
fname, [])
|
blanchet@43413
|
540 |
| NONE => (name, ty_args))
|
blanchet@38506
|
541 |
| CombVar (name, _) => (name, [])
|
blanchet@38506
|
542 |
| CombApp _ => raise Fail "impossible \"CombApp\""
|
blanchet@43401
|
543 |
val t = ATerm (x, map fo_term_for_combtyp ty_args @
|
blanchet@43401
|
544 |
map (do_term false) args)
|
blanchet@41386
|
545 |
val ty = combtyp_of u
|
blanchet@43401
|
546 |
in
|
blanchet@43401
|
547 |
t |> (if should_tag_with_type ctxt type_sys ty then
|
blanchet@43401
|
548 |
tag_with_type (fo_term_for_combtyp ty)
|
blanchet@43401
|
549 |
else
|
blanchet@43401
|
550 |
I)
|
blanchet@43401
|
551 |
end
|
blanchet@43402
|
552 |
val do_bound_type =
|
blanchet@43402
|
553 |
if type_sys = Many_Typed then SOME o mangled_combtyp else K NONE
|
blanchet@43402
|
554 |
val do_out_of_bound_type =
|
blanchet@43402
|
555 |
if member (op =) [Args true, Mangled true] type_sys then
|
blanchet@43402
|
556 |
(fn (s, ty) =>
|
blanchet@43413
|
557 |
type_pred_combatom type_sys ty (CombVar (s, ty))
|
blanchet@43405
|
558 |
|> formula_for_combformula ctxt type_sys |> SOME)
|
blanchet@43402
|
559 |
else
|
blanchet@43402
|
560 |
K NONE
|
blanchet@43401
|
561 |
fun do_formula (AQuant (q, xs, phi)) =
|
blanchet@43402
|
562 |
AQuant (q, xs |> map (apsnd (fn NONE => NONE
|
blanchet@43402
|
563 |
| SOME ty => do_bound_type ty)),
|
blanchet@43405
|
564 |
(if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
|
blanchet@43402
|
565 |
(map_filter
|
blanchet@43402
|
566 |
(fn (_, NONE) => NONE
|
blanchet@43402
|
567 |
| (s, SOME ty) => do_out_of_bound_type (s, ty)) xs)
|
blanchet@43402
|
568 |
(do_formula phi))
|
blanchet@43401
|
569 |
| do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
|
blanchet@43401
|
570 |
| do_formula (AAtom tm) = AAtom (do_term true tm)
|
blanchet@43401
|
571 |
in do_formula end
|
blanchet@38506
|
572 |
|
blanchet@41386
|
573 |
fun formula_for_fact ctxt type_sys
|
blanchet@40445
|
574 |
({combformula, ctypes_sorts, ...} : translated_formula) =
|
blanchet@38506
|
575 |
mk_ahorn (map (formula_for_fo_literal o fo_literal_for_type_literal)
|
blanchet@43224
|
576 |
(atp_type_literals_for_types type_sys Axiom ctypes_sorts))
|
blanchet@43393
|
577 |
(formula_for_combformula ctxt type_sys
|
blanchet@43393
|
578 |
(close_combformula_universally combformula))
|
blanchet@43413
|
579 |
|> close_formula_universally
|
blanchet@38506
|
580 |
|
blanchet@43409
|
581 |
fun logic_for_type_sys Many_Typed = Tff
|
blanchet@43409
|
582 |
| logic_for_type_sys _ = Fof
|
blanchet@43409
|
583 |
|
blanchet@43051
|
584 |
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
|
blanchet@43051
|
585 |
of monomorphization). The TPTP explicitly forbids name clashes, and some of
|
blanchet@43051
|
586 |
the remote provers might care. *)
|
blanchet@43051
|
587 |
fun problem_line_for_fact ctxt prefix type_sys
|
blanchet@43051
|
588 |
(j, formula as {name, kind, ...}) =
|
blanchet@43409
|
589 |
Formula (logic_for_type_sys type_sys,
|
blanchet@43409
|
590 |
prefix ^ string_of_int j ^ "_" ^ ascii_of name, kind,
|
blanchet@43409
|
591 |
formula_for_fact ctxt type_sys formula, NONE, NONE)
|
blanchet@38506
|
592 |
|
blanchet@38506
|
593 |
fun problem_line_for_class_rel_clause (ClassRelClause {name, subclass,
|
blanchet@38506
|
594 |
superclass, ...}) =
|
blanchet@43413
|
595 |
let val ty_arg = ATerm (`I "T", []) in
|
blanchet@43409
|
596 |
Formula (Fof, class_rel_clause_prefix ^ ascii_of name, Axiom,
|
blanchet@43398
|
597 |
AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
|
blanchet@43413
|
598 |
AAtom (ATerm (superclass, [ty_arg]))])
|
blanchet@43413
|
599 |
|> close_formula_universally, NONE, NONE)
|
blanchet@38506
|
600 |
end
|
blanchet@38506
|
601 |
|
blanchet@38506
|
602 |
fun fo_literal_for_arity_literal (TConsLit (c, t, args)) =
|
blanchet@38506
|
603 |
(true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
|
blanchet@38506
|
604 |
| fo_literal_for_arity_literal (TVarLit (c, sort)) =
|
blanchet@38506
|
605 |
(false, ATerm (c, [ATerm (sort, [])]))
|
blanchet@38506
|
606 |
|
blanchet@38506
|
607 |
fun problem_line_for_arity_clause (ArityClause {name, conclLit, premLits,
|
blanchet@38506
|
608 |
...}) =
|
blanchet@43409
|
609 |
Formula (Fof, arity_clause_prefix ^ ascii_of name, Axiom,
|
blanchet@43398
|
610 |
mk_ahorn (map (formula_for_fo_literal o apfst not
|
blanchet@43398
|
611 |
o fo_literal_for_arity_literal) premLits)
|
blanchet@43398
|
612 |
(formula_for_fo_literal
|
blanchet@43413
|
613 |
(fo_literal_for_arity_literal conclLit))
|
blanchet@43413
|
614 |
|> close_formula_universally, NONE, NONE)
|
blanchet@38506
|
615 |
|
blanchet@41386
|
616 |
fun problem_line_for_conjecture ctxt type_sys
|
blanchet@40358
|
617 |
({name, kind, combformula, ...} : translated_formula) =
|
blanchet@43409
|
618 |
Formula (logic_for_type_sys type_sys, conjecture_prefix ^ name, kind,
|
blanchet@43398
|
619 |
formula_for_combformula ctxt type_sys
|
blanchet@43413
|
620 |
(close_combformula_universally combformula)
|
blanchet@43413
|
621 |
|> close_formula_universally, NONE, NONE)
|
blanchet@38506
|
622 |
|
blanchet@43224
|
623 |
fun free_type_literals type_sys ({ctypes_sorts, ...} : translated_formula) =
|
blanchet@43224
|
624 |
ctypes_sorts |> atp_type_literals_for_types type_sys Conjecture
|
blanchet@41385
|
625 |
|> map fo_literal_for_type_literal
|
blanchet@38506
|
626 |
|
blanchet@40156
|
627 |
fun problem_line_for_free_type j lit =
|
blanchet@43409
|
628 |
Formula (Fof, tfree_prefix ^ string_of_int j, Hypothesis,
|
blanchet@43400
|
629 |
formula_for_fo_literal lit, NONE, NONE)
|
blanchet@43224
|
630 |
fun problem_lines_for_free_types type_sys facts =
|
blanchet@38506
|
631 |
let
|
blanchet@43224
|
632 |
val litss = map (free_type_literals type_sys) facts
|
blanchet@38506
|
633 |
val lits = fold (union (op =)) litss []
|
blanchet@40156
|
634 |
in map2 problem_line_for_free_type (0 upto length lits - 1) lits end
|
blanchet@38506
|
635 |
|
blanchet@38506
|
636 |
(** "hBOOL" and "hAPP" **)
|
blanchet@38506
|
637 |
|
blanchet@43415
|
638 |
type repair_info = {pred_sym: bool, min_arity: int, max_arity: int}
|
blanchet@38506
|
639 |
|
blanchet@43415
|
640 |
fun consider_combterm_for_repair top_level tm =
|
blanchet@43413
|
641 |
let val (head, args) = strip_combterm_comb tm in
|
blanchet@43413
|
642 |
(case head of
|
blanchet@43413
|
643 |
CombConst ((s, _), _, _) =>
|
blanchet@43413
|
644 |
if String.isPrefix bound_var_prefix s then
|
blanchet@43413
|
645 |
I
|
blanchet@43413
|
646 |
else
|
blanchet@43413
|
647 |
let val n = length args in
|
blanchet@43413
|
648 |
Symtab.map_default
|
blanchet@43415
|
649 |
(s, {pred_sym = true, min_arity = n, max_arity = 0})
|
blanchet@43415
|
650 |
(fn {pred_sym, min_arity, max_arity} =>
|
blanchet@43415
|
651 |
{pred_sym = pred_sym andalso top_level,
|
blanchet@43415
|
652 |
min_arity = Int.min (n, min_arity),
|
blanchet@43415
|
653 |
max_arity = Int.max (n, max_arity)})
|
blanchet@43413
|
654 |
end
|
blanchet@43413
|
655 |
| _ => I)
|
blanchet@43415
|
656 |
#> fold (consider_combterm_for_repair false) args
|
blanchet@43413
|
657 |
end
|
blanchet@38506
|
658 |
|
blanchet@43415
|
659 |
fun consider_fact_for_repair ({combformula, ...} : translated_formula) =
|
blanchet@43415
|
660 |
formula_fold (consider_combterm_for_repair true) combformula
|
blanchet@38506
|
661 |
|
blanchet@43410
|
662 |
(* The "equal" entry is needed for helper facts if the problem otherwise does
|
blanchet@43415
|
663 |
not involve equality. The "hBOOL" and "hAPP" entries are needed for symbol
|
blanchet@43415
|
664 |
declarations. *)
|
blanchet@43410
|
665 |
val default_entries =
|
blanchet@43415
|
666 |
[("equal", {pred_sym = true, min_arity = 2, max_arity = 2}),
|
blanchet@43415
|
667 |
(make_fixed_const boolify_base,
|
blanchet@43415
|
668 |
{pred_sym = true, min_arity = 1, max_arity = 1}),
|
blanchet@43415
|
669 |
(make_fixed_const explicit_app_base,
|
blanchet@43415
|
670 |
{pred_sym = false, min_arity = 2, max_arity = 2})]
|
blanchet@43415
|
671 |
(* FIXME: last two entries needed? ### *)
|
blanchet@41388
|
672 |
|
blanchet@43415
|
673 |
fun sym_table_for_facts explicit_apply facts =
|
blanchet@41388
|
674 |
if explicit_apply then
|
blanchet@41388
|
675 |
NONE
|
blanchet@41388
|
676 |
else
|
blanchet@43410
|
677 |
SOME (Symtab.empty |> fold Symtab.default default_entries
|
blanchet@43415
|
678 |
|> fold consider_fact_for_repair facts)
|
blanchet@38506
|
679 |
|
blanchet@43415
|
680 |
fun min_arity_of _ _ (SOME sym_tab) s =
|
blanchet@43415
|
681 |
(case Symtab.lookup sym_tab s of
|
blanchet@43415
|
682 |
SOME ({min_arity, ...} : repair_info) => min_arity
|
blanchet@38506
|
683 |
| NONE => 0)
|
blanchet@43415
|
684 |
| min_arity_of thy type_sys NONE s =
|
blanchet@43415
|
685 |
if s = "equal" orelse s = type_tag_name orelse
|
blanchet@43415
|
686 |
String.isPrefix type_const_prefix s orelse
|
blanchet@43415
|
687 |
String.isPrefix class_prefix s then
|
blanchet@43415
|
688 |
16383 (* large number *)
|
blanchet@43415
|
689 |
else case strip_prefix_and_unascii const_prefix s of
|
blanchet@43415
|
690 |
SOME s' => s' |> unmangled_const |> fst |> invert_const
|
blanchet@43415
|
691 |
|> num_atp_type_args thy type_sys
|
blanchet@38506
|
692 |
| NONE => 0
|
blanchet@38506
|
693 |
|
blanchet@38506
|
694 |
(* True if the constant ever appears outside of the top-level position in
|
blanchet@38506
|
695 |
literals, or if it appears with different arities (e.g., because of different
|
blanchet@38506
|
696 |
type instantiations). If false, the constant always receives all of its
|
blanchet@38506
|
697 |
arguments and is used as a predicate. *)
|
blanchet@43391
|
698 |
fun is_pred_sym NONE s =
|
blanchet@38812
|
699 |
s = "equal" orelse s = "$false" orelse s = "$true" orelse
|
blanchet@38812
|
700 |
String.isPrefix type_const_prefix s orelse String.isPrefix class_prefix s
|
blanchet@43415
|
701 |
| is_pred_sym (SOME sym_tab) s =
|
blanchet@43415
|
702 |
case Symtab.lookup sym_tab s of
|
blanchet@43415
|
703 |
SOME {pred_sym, min_arity, max_arity} =>
|
blanchet@43413
|
704 |
pred_sym andalso min_arity = max_arity
|
blanchet@38506
|
705 |
| NONE => false
|
blanchet@38506
|
706 |
|
blanchet@43413
|
707 |
val boolify_combconst =
|
blanchet@43415
|
708 |
CombConst (`make_fixed_const boolify_base,
|
blanchet@43415
|
709 |
combtyp_from_typ @{typ "bool => bool"}, [])
|
blanchet@43413
|
710 |
fun boolify tm = CombApp (boolify_combconst, tm)
|
blanchet@38506
|
711 |
|
blanchet@43415
|
712 |
fun repair_pred_syms_in_combterm sym_tab tm =
|
blanchet@43413
|
713 |
case strip_combterm_comb tm of
|
blanchet@43413
|
714 |
(CombConst ((s, _), _, _), _) =>
|
blanchet@43415
|
715 |
if is_pred_sym sym_tab s then tm else boolify tm
|
blanchet@43413
|
716 |
| _ => boolify tm
|
blanchet@38506
|
717 |
|
blanchet@43415
|
718 |
fun list_app head args = fold (curry (CombApp o swap)) args head
|
blanchet@38506
|
719 |
|
blanchet@43415
|
720 |
val fun_name = `make_fixed_type_const @{type_name fun}
|
blanchet@43404
|
721 |
|
blanchet@43415
|
722 |
fun explicit_app arg head =
|
blanchet@43415
|
723 |
let
|
blanchet@43415
|
724 |
val head_ty = combtyp_of head
|
blanchet@43415
|
725 |
val (arg_ty, res_ty) = dest_combfun head_ty
|
blanchet@43415
|
726 |
val explicit_app =
|
blanchet@43415
|
727 |
CombConst (`make_fixed_const explicit_app_base,
|
blanchet@43415
|
728 |
CombType (fun_name, [head_ty, head_ty]), [arg_ty, res_ty])
|
blanchet@43415
|
729 |
in list_app explicit_app [head, arg] end
|
blanchet@43415
|
730 |
fun list_explicit_app head args = fold explicit_app args head
|
blanchet@43415
|
731 |
|
blanchet@43415
|
732 |
fun repair_apps_in_combterm thy type_sys sym_tab =
|
blanchet@43415
|
733 |
let
|
blanchet@43415
|
734 |
fun aux tm =
|
blanchet@43415
|
735 |
case strip_combterm_comb tm of
|
blanchet@43415
|
736 |
(head as CombConst ((s, _), _, _), args) =>
|
blanchet@43415
|
737 |
args |> map aux
|
blanchet@43415
|
738 |
|> chop (min_arity_of thy type_sys sym_tab s)
|
blanchet@43415
|
739 |
|>> list_app head
|
blanchet@43415
|
740 |
|-> list_explicit_app
|
blanchet@43415
|
741 |
| (head, args) => list_explicit_app head (map aux args)
|
blanchet@43415
|
742 |
in aux end
|
blanchet@43415
|
743 |
|
blanchet@43415
|
744 |
fun repair_combterm thy type_sys sym_tab =
|
blanchet@43415
|
745 |
(case type_sys of Tags _ => I | _ => repair_pred_syms_in_combterm sym_tab)
|
blanchet@43415
|
746 |
#> repair_apps_in_combterm thy type_sys sym_tab
|
blanchet@43415
|
747 |
#> repair_combterm_consts type_sys
|
blanchet@43415
|
748 |
val repair_combformula = formula_map ooo repair_combterm
|
blanchet@43415
|
749 |
val repair_fact = map_combformula ooo repair_combformula
|
blanchet@43415
|
750 |
|
blanchet@43415
|
751 |
fun is_const_relevant type_sys sym_tab s =
|
blanchet@43413
|
752 |
not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
|
blanchet@43415
|
753 |
(type_sys = Many_Typed orelse not (is_pred_sym sym_tab s))
|
blanchet@43413
|
754 |
|
blanchet@43415
|
755 |
fun consider_combterm_consts type_sys sym_tab tm =
|
blanchet@43404
|
756 |
let val (head, args) = strip_combterm_comb tm in
|
blanchet@43404
|
757 |
(case head of
|
blanchet@43404
|
758 |
CombConst ((s, s'), ty, ty_args) =>
|
blanchet@43404
|
759 |
(* FIXME: exploit type subsumption *)
|
blanchet@43415
|
760 |
is_const_relevant type_sys sym_tab s
|
blanchet@43405
|
761 |
? Symtab.insert_list (op =) (s, (s', ty_args, ty))
|
blanchet@43415
|
762 |
| _ => I)
|
blanchet@43415
|
763 |
#> fold (consider_combterm_consts type_sys sym_tab) args
|
blanchet@43404
|
764 |
end
|
blanchet@43404
|
765 |
|
blanchet@43415
|
766 |
fun consider_fact_consts type_sys sym_tab
|
blanchet@43405
|
767 |
({combformula, ...} : translated_formula) =
|
blanchet@43415
|
768 |
formula_fold (consider_combterm_consts type_sys sym_tab) combformula
|
blanchet@43404
|
769 |
|
blanchet@43415
|
770 |
fun const_table_for_facts type_sys sym_tab facts =
|
blanchet@43404
|
771 |
Symtab.empty |> member (op =) [Many_Typed, Args true, Mangled true] type_sys
|
blanchet@43415
|
772 |
? fold (consider_fact_consts type_sys sym_tab) facts
|
blanchet@43404
|
773 |
|
blanchet@43415
|
774 |
fun strip_and_map_combtyp 0 f ty = ([], f ty)
|
blanchet@43415
|
775 |
| strip_and_map_combtyp n f (ty as CombType ((s, _), tys)) =
|
blanchet@43404
|
776 |
(case (strip_prefix_and_unascii type_const_prefix s, tys) of
|
blanchet@43404
|
777 |
(SOME @{type_name fun}, [dom_ty, ran_ty]) =>
|
blanchet@43415
|
778 |
strip_and_map_combtyp (n - 1) f ran_ty |>> cons (f dom_ty)
|
blanchet@43405
|
779 |
| _ => ([], f ty))
|
blanchet@43415
|
780 |
| strip_and_map_combtyp _ _ _ = raise Fail "unexpected non-function"
|
blanchet@43404
|
781 |
|
blanchet@43415
|
782 |
fun sym_decl_line_for_const_entry ctxt type_sys sym_tab s (s', ty_args, ty) =
|
blanchet@43415
|
783 |
let
|
blanchet@43415
|
784 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@43415
|
785 |
val arity = min_arity_of thy type_sys sym_tab s
|
blanchet@43415
|
786 |
in
|
blanchet@43415
|
787 |
if type_sys = Many_Typed then
|
blanchet@43415
|
788 |
let
|
blanchet@43415
|
789 |
val (arg_tys, res_ty) = strip_and_map_combtyp arity mangled_combtyp ty
|
blanchet@43415
|
790 |
val (s, s') = (s, s') |> mangled_const_name ty_args
|
blanchet@43415
|
791 |
in
|
blanchet@43415
|
792 |
Decl (sym_decl_prefix ^ ascii_of s, (s, s'), arg_tys,
|
blanchet@43415
|
793 |
if is_pred_sym sym_tab s then `I tff_bool_type else res_ty)
|
blanchet@43415
|
794 |
end
|
blanchet@43415
|
795 |
else
|
blanchet@43415
|
796 |
let
|
blanchet@43415
|
797 |
val (arg_tys, res_ty) = strip_and_map_combtyp arity I ty
|
blanchet@43415
|
798 |
val bounds =
|
blanchet@43415
|
799 |
map (`I o make_bound_var o string_of_int) (1 upto length arg_tys)
|
blanchet@43415
|
800 |
~~ map SOME arg_tys
|
blanchet@43415
|
801 |
val bound_tms =
|
blanchet@43415
|
802 |
map (fn (name, ty) => CombConst (name, the ty, [])) bounds
|
blanchet@43415
|
803 |
in
|
blanchet@43415
|
804 |
Formula (Fof, sym_decl_prefix ^ ascii_of s, Axiom,
|
blanchet@43415
|
805 |
CombConst ((s, s'), ty, ty_args)
|
blanchet@43415
|
806 |
|> fold (curry (CombApp o swap)) bound_tms
|
blanchet@43415
|
807 |
|> type_pred_combatom type_sys res_ty
|
blanchet@43415
|
808 |
|> mk_aquant AForall bounds
|
blanchet@43415
|
809 |
|> formula_for_combformula ctxt type_sys,
|
blanchet@43415
|
810 |
NONE, NONE)
|
blanchet@43415
|
811 |
end
|
blanchet@43415
|
812 |
end
|
blanchet@43415
|
813 |
fun sym_decl_lines_for_const ctxt type_sys sym_tab (s, xs) =
|
blanchet@43415
|
814 |
map (sym_decl_line_for_const_entry ctxt type_sys sym_tab s) xs
|
blanchet@43410
|
815 |
|
blanchet@43414
|
816 |
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
|
blanchet@43414
|
817 |
union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
|
blanchet@43414
|
818 |
| add_tff_types_in_formula (AConn (_, phis)) =
|
blanchet@43414
|
819 |
fold add_tff_types_in_formula phis
|
blanchet@43414
|
820 |
| add_tff_types_in_formula (AAtom _) = I
|
blanchet@43414
|
821 |
|
blanchet@43414
|
822 |
fun add_tff_types_in_problem_line (Decl (_, _, arg_tys, res_ty)) =
|
blanchet@43414
|
823 |
union (op =) (res_ty :: arg_tys)
|
blanchet@43414
|
824 |
| add_tff_types_in_problem_line (Formula (_, _, _, phi, _, _)) =
|
blanchet@43414
|
825 |
add_tff_types_in_formula phi
|
blanchet@43414
|
826 |
|
blanchet@43414
|
827 |
fun tff_types_in_problem problem =
|
blanchet@43414
|
828 |
fold (fold add_tff_types_in_problem_line o snd) problem []
|
blanchet@43414
|
829 |
|
blanchet@43414
|
830 |
fun problem_line_for_tff_type (s, s') =
|
blanchet@43414
|
831 |
Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tff_type_of_types)
|
blanchet@43414
|
832 |
|
blanchet@43414
|
833 |
val type_declsN = "Types"
|
blanchet@43415
|
834 |
val sym_declsN = "Symbol types"
|
blanchet@41405
|
835 |
val factsN = "Relevant facts"
|
blanchet@41405
|
836 |
val class_relsN = "Class relationships"
|
blanchet@43414
|
837 |
val aritiesN = "Arities"
|
blanchet@41405
|
838 |
val helpersN = "Helper facts"
|
blanchet@41405
|
839 |
val conjsN = "Conjectures"
|
blanchet@41561
|
840 |
val free_typesN = "Type variables"
|
blanchet@41405
|
841 |
|
blanchet@41405
|
842 |
fun offset_of_heading_in_problem _ [] j = j
|
blanchet@41405
|
843 |
| offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
|
blanchet@41405
|
844 |
if heading = needle then j
|
blanchet@41405
|
845 |
else offset_of_heading_in_problem needle problem (j + length lines)
|
blanchet@41405
|
846 |
|
blanchet@43392
|
847 |
fun prepare_atp_problem ctxt readable_names type_sys explicit_apply hyp_ts
|
blanchet@43392
|
848 |
concl_t facts =
|
blanchet@38506
|
849 |
let
|
blanchet@43415
|
850 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@41561
|
851 |
val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
|
blanchet@41382
|
852 |
translate_formulas ctxt type_sys hyp_ts concl_t facts
|
blanchet@43415
|
853 |
val sym_tab = sym_table_for_facts explicit_apply (conjs @ facts)
|
blanchet@43415
|
854 |
val conjs = map (repair_fact thy type_sys sym_tab) conjs
|
blanchet@43415
|
855 |
val facts = map (repair_fact thy type_sys sym_tab) facts
|
blanchet@43415
|
856 |
val sym_tab = sym_table_for_facts explicit_apply (conjs @ facts)
|
blanchet@43393
|
857 |
(* Reordering these might confuse the proof reconstruction code or the SPASS
|
blanchet@43393
|
858 |
Flotter hack. *)
|
blanchet@38506
|
859 |
val problem =
|
blanchet@43412
|
860 |
[(type_declsN, []),
|
blanchet@43414
|
861 |
(sym_declsN, []),
|
blanchet@43412
|
862 |
(factsN, map (problem_line_for_fact ctxt fact_prefix type_sys)
|
blanchet@43051
|
863 |
(0 upto length facts - 1 ~~ facts)),
|
blanchet@41405
|
864 |
(class_relsN, map problem_line_for_class_rel_clause class_rel_clauses),
|
blanchet@41405
|
865 |
(aritiesN, map problem_line_for_arity_clause arity_clauses),
|
blanchet@41405
|
866 |
(helpersN, []),
|
blanchet@41561
|
867 |
(conjsN, map (problem_line_for_conjecture ctxt type_sys) conjs),
|
blanchet@43224
|
868 |
(free_typesN, problem_lines_for_free_types type_sys (facts @ conjs))]
|
blanchet@43392
|
869 |
val helper_facts =
|
blanchet@43409
|
870 |
problem |> maps (map_filter (fn Formula (_, _, _, phi, _, _) => SOME phi
|
blanchet@43399
|
871 |
| _ => NONE) o snd)
|
blanchet@43398
|
872 |
|> get_helper_facts ctxt type_sys
|
blanchet@43415
|
873 |
|>> map (repair_fact thy type_sys sym_tab)
|
blanchet@43415
|
874 |
val const_tab = const_table_for_facts type_sys sym_tab (conjs @ facts)
|
blanchet@43414
|
875 |
val sym_decl_lines =
|
blanchet@43415
|
876 |
Symtab.fold_rev (append o sym_decl_lines_for_const ctxt type_sys sym_tab)
|
blanchet@43405
|
877 |
const_tab []
|
blanchet@41405
|
878 |
val helper_lines =
|
blanchet@43392
|
879 |
helper_facts
|
blanchet@43413
|
880 |
|>> map (pair 0 #> problem_line_for_fact ctxt helper_prefix type_sys)
|
blanchet@41405
|
881 |
|> op @
|
blanchet@43414
|
882 |
val problem =
|
blanchet@43414
|
883 |
problem |> fold (AList.update (op =))
|
blanchet@43414
|
884 |
[(sym_declsN, sym_decl_lines),
|
blanchet@43414
|
885 |
(helpersN, helper_lines)]
|
blanchet@43414
|
886 |
val type_decl_lines =
|
blanchet@43414
|
887 |
if type_sys = Many_Typed then
|
blanchet@43414
|
888 |
problem |> tff_types_in_problem |> map problem_line_for_tff_type
|
blanchet@43414
|
889 |
else
|
blanchet@43414
|
890 |
[]
|
blanchet@41388
|
891 |
val (problem, pool) =
|
blanchet@43414
|
892 |
problem |> AList.update (op =) (type_declsN, type_decl_lines)
|
blanchet@41388
|
893 |
|> nice_atp_problem readable_names
|
blanchet@38506
|
894 |
in
|
blanchet@38506
|
895 |
(problem,
|
blanchet@38506
|
896 |
case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
|
blanchet@43412
|
897 |
offset_of_heading_in_problem factsN problem 0,
|
blanchet@41405
|
898 |
offset_of_heading_in_problem conjsN problem 0,
|
blanchet@41405
|
899 |
fact_names |> Vector.fromList)
|
blanchet@38506
|
900 |
end
|
blanchet@38506
|
901 |
|
blanchet@41561
|
902 |
(* FUDGE *)
|
blanchet@41561
|
903 |
val conj_weight = 0.0
|
blanchet@42641
|
904 |
val hyp_weight = 0.1
|
blanchet@42641
|
905 |
val fact_min_weight = 0.2
|
blanchet@41561
|
906 |
val fact_max_weight = 1.0
|
blanchet@41561
|
907 |
|
blanchet@41561
|
908 |
fun add_term_weights weight (ATerm (s, tms)) =
|
blanchet@41561
|
909 |
(not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
|
blanchet@41561
|
910 |
#> fold (add_term_weights weight) tms
|
blanchet@43409
|
911 |
fun add_problem_line_weights weight (Formula (_, _, _, phi, _, _)) =
|
blanchet@43413
|
912 |
formula_fold (add_term_weights weight) phi
|
blanchet@43399
|
913 |
| add_problem_line_weights _ _ = I
|
blanchet@41561
|
914 |
|
blanchet@41561
|
915 |
fun add_conjectures_weights [] = I
|
blanchet@41561
|
916 |
| add_conjectures_weights conjs =
|
blanchet@41561
|
917 |
let val (hyps, conj) = split_last conjs in
|
blanchet@41561
|
918 |
add_problem_line_weights conj_weight conj
|
blanchet@41561
|
919 |
#> fold (add_problem_line_weights hyp_weight) hyps
|
blanchet@41561
|
920 |
end
|
blanchet@41561
|
921 |
|
blanchet@41561
|
922 |
fun add_facts_weights facts =
|
blanchet@41561
|
923 |
let
|
blanchet@41561
|
924 |
val num_facts = length facts
|
blanchet@41561
|
925 |
fun weight_of j =
|
blanchet@41561
|
926 |
fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
|
blanchet@41561
|
927 |
/ Real.fromInt num_facts
|
blanchet@41561
|
928 |
in
|
blanchet@41561
|
929 |
map weight_of (0 upto num_facts - 1) ~~ facts
|
blanchet@41561
|
930 |
|> fold (uncurry add_problem_line_weights)
|
blanchet@41561
|
931 |
end
|
blanchet@41561
|
932 |
|
blanchet@41561
|
933 |
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
|
blanchet@41561
|
934 |
fun atp_problem_weights problem =
|
blanchet@41561
|
935 |
Symtab.empty
|
blanchet@41561
|
936 |
|> add_conjectures_weights (these (AList.lookup (op =) problem conjsN))
|
blanchet@41561
|
937 |
|> add_facts_weights (these (AList.lookup (op =) problem factsN))
|
blanchet@41561
|
938 |
|> Symtab.dest
|
blanchet@42590
|
939 |
|> sort (prod_ord Real.compare string_ord o pairself swap)
|
blanchet@41561
|
940 |
|
blanchet@38506
|
941 |
end;
|