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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 format = ATP_Problem.format
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type formula_kind = ATP_Problem.formula_kind
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type 'a problem = 'a ATP_Problem.problem
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type locality = Sledgehammer_Filter.locality
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datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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datatype type_level =
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All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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datatype type_heaviness = Heavy | Light
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datatype type_system =
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Simple_Types of type_level |
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Preds of polymorphism * type_level * type_heaviness |
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Tags of polymorphism * type_level * type_heaviness
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type translated_formula
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val readable_names : bool Config.T
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val fact_prefix : string
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val conjecture_prefix : string
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val helper_prefix : string
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val typed_helper_suffix : 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 simple_type_prefix : string
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val type_sys_from_string : string -> type_system
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val polymorphism_of_type_sys : type_system -> polymorphism
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val level_of_type_sys : type_system -> type_level
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val is_type_sys_virtually_sound : type_system -> bool
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val is_type_sys_fairly_sound : type_system -> bool
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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 -> format -> bool -> (string * locality) * thm
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-> translated_formula option * ((string * locality) * thm)
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val prepare_atp_problem :
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Proof.context -> format -> formula_kind -> formula_kind -> type_system
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-> 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 * int list * int Symtab.table
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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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open Sledgehammer_Filter
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(* experimental *)
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val generate_useful_info = false
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fun useful_isabelle_info s =
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if generate_useful_info then
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SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
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else
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NONE
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val intro_info = useful_isabelle_info "intro"
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val elim_info = useful_isabelle_info "elim"
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val simp_info = useful_isabelle_info "simp"
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(* Readable names are often much shorter, especially if types are mangled in
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names. Also, the logic for generating legal SNARK sort names is only
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implemented for readable names. Finally, readable names are, well, more
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readable. For these reason, they are enabled by default. *)
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val readable_names =
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Attrib.setup_config_bool @{binding sledgehammer_atp_readable_names} (K 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 typed_helper_suffix = "_T"
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val untyped_helper_suffix = "_U"
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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 simple_type_prefix = "ty_"
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fun make_simple_type s =
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if s = tptp_bool_type orelse s = tptp_fun_type then s
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else simple_type_prefix ^ ascii_of s
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(* Freshness almost guaranteed! *)
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val sledgehammer_weak_prefix = "Sledgehammer:"
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datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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datatype type_level =
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All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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datatype type_heaviness = Heavy | Light
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datatype type_system =
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Simple_Types of type_level |
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Preds of polymorphism * type_level * type_heaviness |
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Tags of polymorphism * type_level * type_heaviness
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fun try_unsuffixes ss s =
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fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
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fun type_sys_from_string s =
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(case try (unprefix "poly_") s of
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SOME s => (SOME Polymorphic, s)
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| NONE =>
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case try (unprefix "mono_") s of
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SOME s => (SOME Monomorphic, s)
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| NONE =>
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case try (unprefix "mangled_") s of
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SOME s => (SOME Mangled_Monomorphic, s)
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| NONE => (NONE, s))
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||> (fn s =>
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(* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
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case try_unsuffixes ["?", "_query"] s of
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SOME s => (Nonmonotonic_Types, s)
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| NONE =>
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case try_unsuffixes ["!", "_bang"] s of
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SOME s => (Finite_Types, s)
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| NONE => (All_Types, s))
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||> apsnd (fn s =>
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case try (unsuffix "_heavy") s of
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SOME s => (Heavy, s)
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| NONE => (Light, s))
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|> (fn (poly, (level, (heaviness, core))) =>
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case (core, (poly, level, heaviness)) of
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("simple", (NONE, _, Light)) => Simple_Types level
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| ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
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| ("tags", (SOME Polymorphic, All_Types, _)) =>
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Tags (Polymorphic, All_Types, heaviness)
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| ("tags", (SOME Polymorphic, _, _)) =>
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(* The actual light encoding is very unsound. *)
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Tags (Polymorphic, level, Heavy)
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| ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
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| ("args", (SOME poly, All_Types (* naja *), Light)) =>
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Preds (poly, Const_Arg_Types, Light)
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| ("erased", (NONE, All_Types (* naja *), Light)) =>
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Preds (Polymorphic, No_Types, Light)
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| _ => raise Same.SAME)
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handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
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fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
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| polymorphism_of_type_sys (Preds (poly, _, _)) = poly
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| polymorphism_of_type_sys (Tags (poly, _, _)) = poly
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fun level_of_type_sys (Simple_Types level) = level
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| level_of_type_sys (Preds (_, level, _)) = level
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| level_of_type_sys (Tags (_, level, _)) = level
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fun heaviness_of_type_sys (Simple_Types _) = Heavy
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| heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
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| heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
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fun is_type_level_virtually_sound level =
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level = All_Types orelse level = Nonmonotonic_Types
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val is_type_sys_virtually_sound =
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is_type_level_virtually_sound o level_of_type_sys
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fun is_type_level_fairly_sound level =
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is_type_level_virtually_sound level orelse level = Finite_Types
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val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
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fun aconn_fold pos f (ANot, [phi]) = f (Option.map not pos) phi
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| aconn_fold pos f (AImplies, [phi1, phi2]) =
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f (Option.map not pos) phi1 #> f pos phi2
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| aconn_fold pos f (AAnd, phis) = fold (f pos) phis
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| aconn_fold pos f (AOr, phis) = fold (f pos) phis
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| aconn_fold _ f (_, phis) = fold (f NONE) phis
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fun aconn_map pos f (ANot, [phi]) = AConn (ANot, [f (Option.map not pos) phi])
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| aconn_map pos f (AImplies, [phi1, phi2]) =
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AConn (AImplies, [f (Option.map not pos) phi1, f pos phi2])
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| aconn_map pos f (AAnd, phis) = AConn (AAnd, map (f pos) phis)
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| aconn_map pos f (AOr, phis) = AConn (AOr, map (f pos) phis)
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| aconn_map _ f (c, phis) = AConn (c, map (f NONE) phis)
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fun formula_fold pos f =
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let
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fun aux pos (AQuant (_, _, phi)) = aux pos phi
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| aux pos (AConn conn) = aconn_fold pos aux conn
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| aux pos (AAtom tm) = f pos tm
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in aux pos end
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type translated_formula =
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{name: string,
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locality: locality,
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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 ({name, locality, kind, combformula, atomic_types}
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: translated_formula) =
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{name = name, locality = locality, kind = kind, combformula = f combformula,
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atomic_types = atomic_types} : translated_formula
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blanchet@43429
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fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
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blanchet@43547
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(* The Booleans indicate whether all type arguments should be kept. *)
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datatype type_arg_policy =
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Explicit_Type_Args of bool |
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Mangled_Type_Args of bool |
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No_Type_Args
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blanchet@41384
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blanchet@43707
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fun should_drop_arg_type_args (Simple_Types _) =
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blanchet@43707
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false (* since TFF doesn't support overloading *)
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blanchet@43707
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| should_drop_arg_type_args type_sys =
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blanchet@43707
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level_of_type_sys type_sys = All_Types andalso
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heaviness_of_type_sys type_sys = Heavy
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blanchet@43702
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blanchet@43460
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fun general_type_arg_policy type_sys =
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blanchet@43460
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if level_of_type_sys type_sys = No_Types then
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blanchet@43460
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No_Type_Args
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blanchet@43460
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else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
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blanchet@43702
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Mangled_Type_Args (should_drop_arg_type_args type_sys)
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else
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blanchet@43702
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Explicit_Type_Args (should_drop_arg_type_args type_sys)
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blanchet@43434
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blanchet@43792
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fun type_arg_policy type_sys s =
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blanchet@43792
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if s = @{const_name HOL.eq} orelse
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blanchet@43792
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(s = explicit_app_base andalso
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blanchet@43792
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level_of_type_sys type_sys = Const_Arg_Types) then
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blanchet@43792
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No_Type_Args
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blanchet@43792
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else
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blanchet@43792
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general_type_arg_policy type_sys
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blanchet@43088
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blanchet@43797
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fun atp_type_literals_for_types format type_sys kind Ts =
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blanchet@43797
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if level_of_type_sys type_sys = No_Types orelse format = CNF_UEQ then
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blanchet@43224
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[]
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else
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Ts |> type_literals_for_types
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blanchet@43224
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|> filter (fn TyLitVar _ => kind <> Conjecture
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blanchet@43224
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| TyLitFree _ => kind = Conjecture)
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blanchet@41385
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blanchet@43405
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fun mk_aconns c phis =
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blanchet@43405
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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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blanchet@43405
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| mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
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blanchet@43393
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fun mk_aquant _ [] phi = phi
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blanchet@43393
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| mk_aquant q xs (phi as AQuant (q', xs', phi')) =
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blanchet@43393
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if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
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blanchet@43393
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| mk_aquant q xs phi = AQuant (q, xs, phi)
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blanchet@38506
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blanchet@43393
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fun close_universally atom_vars phi =
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blanchet@41393
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let
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blanchet@41393
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fun formula_vars bounds (AQuant (_, xs, phi)) =
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blanchet@43397
|
267 |
formula_vars (map fst xs @ bounds) phi
|
blanchet@41393
|
268 |
| formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
|
blanchet@43393
|
269 |
| formula_vars bounds (AAtom tm) =
|
blanchet@43397
|
270 |
union (op =) (atom_vars tm []
|
blanchet@43397
|
271 |
|> filter_out (member (op =) bounds o fst))
|
blanchet@43393
|
272 |
in mk_aquant AForall (formula_vars [] phi []) phi end
|
blanchet@43393
|
273 |
|
blanchet@43402
|
274 |
fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
|
blanchet@43393
|
275 |
| combterm_vars (CombConst _) = I
|
blanchet@43445
|
276 |
| combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
|
blanchet@43545
|
277 |
fun close_combformula_universally phi = close_universally combterm_vars phi
|
blanchet@43393
|
278 |
|
blanchet@43393
|
279 |
fun term_vars (ATerm (name as (s, _), tms)) =
|
blanchet@43402
|
280 |
is_atp_variable s ? insert (op =) (name, NONE)
|
blanchet@43397
|
281 |
#> fold term_vars tms
|
blanchet@43545
|
282 |
fun close_formula_universally phi = close_universally term_vars phi
|
blanchet@41393
|
283 |
|
blanchet@43803
|
284 |
fun fo_term_from_typ format (Type (s, Ts)) =
|
blanchet@43804
|
285 |
ATerm (case (format, s) of
|
blanchet@43804
|
286 |
(THF, @{type_name bool}) => `I tptp_bool_type
|
blanchet@43804
|
287 |
| (THF, @{type_name fun}) => `I tptp_fun_type
|
blanchet@43804
|
288 |
| _ => `make_fixed_type_const s,
|
blanchet@43803
|
289 |
map (fo_term_from_typ format) Ts)
|
blanchet@43803
|
290 |
| fo_term_from_typ _ (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
|
blanchet@43803
|
291 |
| fo_term_from_typ _ (TVar ((x as (s, _)), _)) =
|
blanchet@43433
|
292 |
ATerm ((make_schematic_type_var x, s), [])
|
blanchet@43433
|
293 |
|
blanchet@43433
|
294 |
(* This shouldn't clash with anything else. *)
|
blanchet@43413
|
295 |
val mangled_type_sep = "\000"
|
blanchet@43413
|
296 |
|
blanchet@43433
|
297 |
fun generic_mangled_type_name f (ATerm (name, [])) = f name
|
blanchet@43433
|
298 |
| generic_mangled_type_name f (ATerm (name, tys)) =
|
blanchet@43626
|
299 |
f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
|
blanchet@43626
|
300 |
^ ")"
|
blanchet@43413
|
301 |
|
blanchet@43804
|
302 |
fun ho_type_from_fo_term format pred_sym ary =
|
blanchet@43804
|
303 |
let
|
blanchet@43804
|
304 |
fun to_atype ty =
|
blanchet@43804
|
305 |
AType ((make_simple_type (generic_mangled_type_name fst ty),
|
blanchet@43804
|
306 |
generic_mangled_type_name snd ty))
|
blanchet@43804
|
307 |
fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
|
blanchet@43804
|
308 |
fun to_tff 0 ty =
|
blanchet@43804
|
309 |
if pred_sym then AType (`I tptp_bool_type) else to_atype ty
|
blanchet@43804
|
310 |
| to_tff ary (ATerm (_, tys)) = to_afun to_atype (to_tff (ary - 1)) tys
|
blanchet@43804
|
311 |
fun to_thf (ty as ATerm ((s, _), tys)) =
|
blanchet@43804
|
312 |
if s = tptp_fun_type then to_afun to_thf to_thf tys else to_atype ty
|
blanchet@43804
|
313 |
in if format = THF then to_thf else to_tff ary end
|
blanchet@43804
|
314 |
|
blanchet@43804
|
315 |
fun mangled_type format pred_sym ary =
|
blanchet@43804
|
316 |
ho_type_from_fo_term format pred_sym ary o fo_term_from_typ format
|
blanchet@43804
|
317 |
|
blanchet@43803
|
318 |
fun mangled_const_name format T_args (s, s') =
|
blanchet@43804
|
319 |
let
|
blanchet@43804
|
320 |
val ty_args = map (fo_term_from_typ format) T_args
|
blanchet@43804
|
321 |
fun type_suffix f g =
|
blanchet@43804
|
322 |
fold_rev (curry (op ^) o g o prefix mangled_type_sep
|
blanchet@43804
|
323 |
o generic_mangled_type_name f) ty_args ""
|
blanchet@43804
|
324 |
in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
|
blanchet@43413
|
325 |
|
blanchet@43413
|
326 |
val parse_mangled_ident =
|
blanchet@43413
|
327 |
Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
|
blanchet@43413
|
328 |
|
blanchet@43413
|
329 |
fun parse_mangled_type x =
|
blanchet@43413
|
330 |
(parse_mangled_ident
|
blanchet@43413
|
331 |
-- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
|
blanchet@43413
|
332 |
[] >> ATerm) x
|
blanchet@43413
|
333 |
and parse_mangled_types x =
|
blanchet@43413
|
334 |
(parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
|
blanchet@43413
|
335 |
|
blanchet@43413
|
336 |
fun unmangled_type s =
|
blanchet@43413
|
337 |
s |> suffix ")" |> raw_explode
|
blanchet@43413
|
338 |
|> Scan.finite Symbol.stopper
|
blanchet@43413
|
339 |
(Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
|
blanchet@43413
|
340 |
quote s)) parse_mangled_type))
|
blanchet@43413
|
341 |
|> fst
|
blanchet@43413
|
342 |
|
blanchet@43432
|
343 |
val unmangled_const_name = space_explode mangled_type_sep #> hd
|
blanchet@43413
|
344 |
fun unmangled_const s =
|
blanchet@43413
|
345 |
let val ss = space_explode mangled_type_sep s in
|
blanchet@43413
|
346 |
(hd ss, map unmangled_type (tl ss))
|
blanchet@43413
|
347 |
end
|
blanchet@43413
|
348 |
|
blanchet@43803
|
349 |
fun introduce_proxies format tm =
|
blanchet@43439
|
350 |
let
|
blanchet@43804
|
351 |
fun aux ary top_level (CombApp (tm1, tm2)) =
|
blanchet@43804
|
352 |
CombApp (aux (ary + 1) top_level tm1, aux 0 false tm2)
|
blanchet@43804
|
353 |
| aux ary top_level (CombConst (name as (s, s'), T, T_args)) =
|
blanchet@43441
|
354 |
(case proxify_const s of
|
blanchet@43439
|
355 |
SOME proxy_base =>
|
blanchet@43804
|
356 |
(* Proxies are not needed in THF, except for partially applied
|
blanchet@43804
|
357 |
equality since THF does not provide any syntax for it. *)
|
blanchet@43804
|
358 |
if top_level orelse
|
blanchet@43804
|
359 |
(format = THF andalso (s <> "equal" orelse ary = 2)) then
|
blanchet@43439
|
360 |
(case s of
|
blanchet@43439
|
361 |
"c_False" => (tptp_false, s')
|
blanchet@43439
|
362 |
| "c_True" => (tptp_true, s')
|
blanchet@43439
|
363 |
| _ => name, [])
|
blanchet@43440
|
364 |
else
|
blanchet@43445
|
365 |
(proxy_base |>> prefix const_prefix, T_args)
|
blanchet@43445
|
366 |
| NONE => (name, T_args))
|
blanchet@43445
|
367 |
|> (fn (name, T_args) => CombConst (name, T, T_args))
|
blanchet@43804
|
368 |
| aux _ _ tm = tm
|
blanchet@43804
|
369 |
in aux 0 true tm end
|
blanchet@43439
|
370 |
|
blanchet@43803
|
371 |
fun combformula_from_prop thy format eq_as_iff =
|
blanchet@38506
|
372 |
let
|
blanchet@43439
|
373 |
fun do_term bs t atomic_types =
|
blanchet@41388
|
374 |
combterm_from_term thy bs (Envir.eta_contract t)
|
blanchet@43803
|
375 |
|>> (introduce_proxies format #> AAtom)
|
blanchet@43439
|
376 |
||> union (op =) atomic_types
|
blanchet@38506
|
377 |
fun do_quant bs q s T t' =
|
blanchet@38743
|
378 |
let val s = Name.variant (map fst bs) s in
|
blanchet@38743
|
379 |
do_formula ((s, T) :: bs) t'
|
blanchet@43433
|
380 |
#>> mk_aquant q [(`make_bound_var s, SOME T)]
|
blanchet@38743
|
381 |
end
|
blanchet@38506
|
382 |
and do_conn bs c t1 t2 =
|
blanchet@38506
|
383 |
do_formula bs t1 ##>> do_formula bs t2
|
blanchet@43402
|
384 |
#>> uncurry (mk_aconn c)
|
blanchet@38506
|
385 |
and do_formula bs t =
|
blanchet@38506
|
386 |
case t of
|
blanchet@43402
|
387 |
@{const Not} $ t1 => do_formula bs t1 #>> mk_anot
|
blanchet@38506
|
388 |
| Const (@{const_name All}, _) $ Abs (s, T, t') =>
|
blanchet@38506
|
389 |
do_quant bs AForall s T t'
|
blanchet@38506
|
390 |
| Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
|
blanchet@38506
|
391 |
do_quant bs AExists s T t'
|
haftmann@39028
|
392 |
| @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
|
haftmann@39028
|
393 |
| @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
|
haftmann@39019
|
394 |
| @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
|
haftmann@39093
|
395 |
| Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
|
blanchet@41388
|
396 |
if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
|
blanchet@41388
|
397 |
| _ => do_term bs t
|
blanchet@38506
|
398 |
in do_formula [] end
|
blanchet@38506
|
399 |
|
blanchet@43615
|
400 |
fun presimplify_term ctxt =
|
blanchet@43615
|
401 |
Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
|
blanchet@43615
|
402 |
#> Meson.presimplify ctxt
|
blanchet@43615
|
403 |
#> prop_of
|
blanchet@38506
|
404 |
|
wenzelm@41739
|
405 |
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
|
blanchet@38506
|
406 |
fun conceal_bounds Ts t =
|
blanchet@38506
|
407 |
subst_bounds (map (Free o apfst concealed_bound_name)
|
blanchet@38506
|
408 |
(0 upto length Ts - 1 ~~ Ts), t)
|
blanchet@38506
|
409 |
fun reveal_bounds Ts =
|
blanchet@38506
|
410 |
subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
|
blanchet@38506
|
411 |
(0 upto length Ts - 1 ~~ Ts))
|
blanchet@38506
|
412 |
|
blanchet@43612
|
413 |
fun extensionalize_term ctxt t =
|
blanchet@43612
|
414 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@43612
|
415 |
t |> cterm_of thy |> Meson.extensionalize_conv ctxt
|
blanchet@43612
|
416 |
|> prop_of |> Logic.dest_equals |> snd
|
blanchet@43612
|
417 |
end
|
blanchet@38831
|
418 |
|
blanchet@38506
|
419 |
fun introduce_combinators_in_term ctxt kind t =
|
wenzelm@43232
|
420 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@38716
|
421 |
if Meson.is_fol_term thy t then
|
blanchet@38716
|
422 |
t
|
blanchet@38716
|
423 |
else
|
blanchet@38716
|
424 |
let
|
blanchet@38716
|
425 |
fun aux Ts t =
|
blanchet@38716
|
426 |
case t of
|
blanchet@38716
|
427 |
@{const Not} $ t1 => @{const Not} $ aux Ts t1
|
blanchet@38716
|
428 |
| (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
|
blanchet@38716
|
429 |
t0 $ Abs (s, T, aux (T :: Ts) t')
|
blanchet@38890
|
430 |
| (t0 as Const (@{const_name All}, _)) $ t1 =>
|
blanchet@38890
|
431 |
aux Ts (t0 $ eta_expand Ts t1 1)
|
blanchet@38716
|
432 |
| (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
|
blanchet@38716
|
433 |
t0 $ Abs (s, T, aux (T :: Ts) t')
|
blanchet@38890
|
434 |
| (t0 as Const (@{const_name Ex}, _)) $ t1 =>
|
blanchet@38890
|
435 |
aux Ts (t0 $ eta_expand Ts t1 1)
|
haftmann@39028
|
436 |
| (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39028
|
437 |
| (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39019
|
438 |
| (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39093
|
439 |
| (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
|
blanchet@38716
|
440 |
$ t1 $ t2 =>
|
blanchet@38716
|
441 |
t0 $ aux Ts t1 $ aux Ts t2
|
blanchet@38716
|
442 |
| _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
|
blanchet@38716
|
443 |
t
|
blanchet@38716
|
444 |
else
|
blanchet@38716
|
445 |
t |> conceal_bounds Ts
|
blanchet@38716
|
446 |
|> Envir.eta_contract
|
blanchet@38716
|
447 |
|> cterm_of thy
|
blanchet@40071
|
448 |
|> Meson_Clausify.introduce_combinators_in_cterm
|
blanchet@38716
|
449 |
|> prop_of |> Logic.dest_equals |> snd
|
blanchet@38716
|
450 |
|> reveal_bounds Ts
|
blanchet@39616
|
451 |
val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
|
blanchet@38716
|
452 |
in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
|
blanchet@38716
|
453 |
handle THM _ =>
|
blanchet@38716
|
454 |
(* A type variable of sort "{}" will make abstraction fail. *)
|
blanchet@38836
|
455 |
if kind = Conjecture then HOLogic.false_const
|
blanchet@38836
|
456 |
else HOLogic.true_const
|
blanchet@38716
|
457 |
end
|
blanchet@38506
|
458 |
|
blanchet@38506
|
459 |
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
|
blanchet@43224
|
460 |
same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
|
blanchet@38506
|
461 |
fun freeze_term t =
|
blanchet@38506
|
462 |
let
|
blanchet@38506
|
463 |
fun aux (t $ u) = aux t $ aux u
|
blanchet@38506
|
464 |
| aux (Abs (s, T, t)) = Abs (s, T, aux t)
|
blanchet@38506
|
465 |
| aux (Var ((s, i), T)) =
|
blanchet@38506
|
466 |
Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
|
blanchet@38506
|
467 |
| aux t = t
|
blanchet@38506
|
468 |
in t |> exists_subterm is_Var t ? aux end
|
blanchet@38506
|
469 |
|
blanchet@40445
|
470 |
(* making fact and conjecture formulas *)
|
blanchet@43803
|
471 |
fun make_formula ctxt format eq_as_iff presimp name loc kind t =
|
blanchet@38506
|
472 |
let
|
wenzelm@43232
|
473 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@38831
|
474 |
val t = t |> Envir.beta_eta_contract
|
blanchet@43785
|
475 |
|> transform_elim_prop
|
blanchet@41459
|
476 |
|> Object_Logic.atomize_term thy
|
blanchet@43434
|
477 |
val need_trueprop = (fastype_of t = @{typ bool})
|
blanchet@38890
|
478 |
val t = t |> need_trueprop ? HOLogic.mk_Trueprop
|
blanchet@43607
|
479 |
|> Raw_Simplifier.rewrite_term thy
|
blanchet@43607
|
480 |
(Meson.unfold_set_const_simps ctxt) []
|
blanchet@43612
|
481 |
|> extensionalize_term ctxt
|
blanchet@43615
|
482 |
|> presimp ? presimplify_term ctxt
|
blanchet@38506
|
483 |
|> perhaps (try (HOLogic.dest_Trueprop))
|
blanchet@38506
|
484 |
|> introduce_combinators_in_term ctxt kind
|
blanchet@38836
|
485 |
|> kind <> Axiom ? freeze_term
|
blanchet@43803
|
486 |
val (combformula, atomic_types) =
|
blanchet@43803
|
487 |
combformula_from_prop thy format eq_as_iff t []
|
blanchet@38506
|
488 |
in
|
blanchet@43511
|
489 |
{name = name, locality = loc, kind = kind, combformula = combformula,
|
blanchet@43433
|
490 |
atomic_types = atomic_types}
|
blanchet@38506
|
491 |
end
|
blanchet@38506
|
492 |
|
blanchet@43803
|
493 |
fun make_fact ctxt format keep_trivial eq_as_iff presimp ((name, loc), t) =
|
blanchet@43803
|
494 |
case (keep_trivial,
|
blanchet@43803
|
495 |
make_formula ctxt format eq_as_iff presimp name loc Axiom t) of
|
blanchet@42861
|
496 |
(false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
|
blanchet@42861
|
497 |
NONE
|
blanchet@42861
|
498 |
| (_, formula) => SOME formula
|
blanchet@43432
|
499 |
|
blanchet@43803
|
500 |
fun make_conjecture ctxt format prem_kind ts =
|
blanchet@38836
|
501 |
let val last = length ts - 1 in
|
blanchet@43580
|
502 |
map2 (fn j => fn t =>
|
blanchet@43580
|
503 |
let
|
blanchet@43580
|
504 |
val (kind, maybe_negate) =
|
blanchet@43580
|
505 |
if j = last then
|
blanchet@43580
|
506 |
(Conjecture, I)
|
blanchet@43580
|
507 |
else
|
blanchet@43580
|
508 |
(prem_kind,
|
blanchet@43580
|
509 |
if prem_kind = Conjecture then update_combformula mk_anot
|
blanchet@43580
|
510 |
else I)
|
blanchet@43580
|
511 |
in
|
blanchet@43803
|
512 |
t |> make_formula ctxt format true true (string_of_int j)
|
blanchet@43803
|
513 |
General kind
|
blanchet@43803
|
514 |
|> maybe_negate
|
blanchet@43580
|
515 |
end)
|
blanchet@38836
|
516 |
(0 upto last) ts
|
blanchet@38836
|
517 |
end
|
blanchet@38506
|
518 |
|
blanchet@43552
|
519 |
(** Finite and infinite type inference **)
|
blanchet@43552
|
520 |
|
blanchet@43755
|
521 |
fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
|
blanchet@43755
|
522 |
| deep_freeze_atyp T = T
|
blanchet@43755
|
523 |
val deep_freeze_type = map_atyps deep_freeze_atyp
|
blanchet@43755
|
524 |
|
blanchet@43755
|
525 |
val type_instance = Sign.typ_instance o Proof_Context.theory_of
|
blanchet@43755
|
526 |
|
blanchet@43552
|
527 |
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
|
blanchet@43552
|
528 |
dangerous because their "exhaust" properties can easily lead to unsound ATP
|
blanchet@43552
|
529 |
proofs. On the other hand, all HOL infinite types can be given the same
|
blanchet@43552
|
530 |
models in first-order logic (via Löwenheim-Skolem). *)
|
blanchet@43552
|
531 |
|
blanchet@43755
|
532 |
fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
|
blanchet@43755
|
533 |
exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
|
blanchet@43707
|
534 |
| should_encode_type _ _ All_Types _ = true
|
blanchet@43552
|
535 |
| should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
|
blanchet@43552
|
536 |
| should_encode_type _ _ _ _ = false
|
blanchet@43552
|
537 |
|
blanchet@43708
|
538 |
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
|
blanchet@43705
|
539 |
should_predicate_on_var T =
|
blanchet@43747
|
540 |
(heaviness = Heavy orelse should_predicate_on_var ()) andalso
|
blanchet@43747
|
541 |
should_encode_type ctxt nonmono_Ts level T
|
blanchet@43705
|
542 |
| should_predicate_on_type _ _ _ _ _ = false
|
blanchet@43552
|
543 |
|
blanchet@43707
|
544 |
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
|
blanchet@43707
|
545 |
String.isPrefix bound_var_prefix s
|
blanchet@43707
|
546 |
| is_var_or_bound_var (CombVar _) = true
|
blanchet@43707
|
547 |
| is_var_or_bound_var _ = false
|
blanchet@43707
|
548 |
|
blanchet@43700
|
549 |
datatype tag_site = Top_Level | Eq_Arg | Elsewhere
|
blanchet@43700
|
550 |
|
blanchet@43700
|
551 |
fun should_tag_with_type _ _ _ Top_Level _ _ = false
|
blanchet@43708
|
552 |
| should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
|
blanchet@43708
|
553 |
(case heaviness of
|
blanchet@43708
|
554 |
Heavy => should_encode_type ctxt nonmono_Ts level T
|
blanchet@43708
|
555 |
| Light =>
|
blanchet@43707
|
556 |
case (site, is_var_or_bound_var u) of
|
blanchet@43707
|
557 |
(Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
|
blanchet@43700
|
558 |
| _ => false)
|
blanchet@43700
|
559 |
| should_tag_with_type _ _ _ _ _ _ = false
|
blanchet@43552
|
560 |
|
blanchet@43552
|
561 |
val homo_infinite_T = @{typ ind} (* any infinite type *)
|
blanchet@43552
|
562 |
|
blanchet@43552
|
563 |
fun homogenized_type ctxt nonmono_Ts level T =
|
blanchet@43552
|
564 |
if should_encode_type ctxt nonmono_Ts level T then T else homo_infinite_T
|
blanchet@43552
|
565 |
|
blanchet@43444
|
566 |
(** "hBOOL" and "hAPP" **)
|
blanchet@41561
|
567 |
|
blanchet@43445
|
568 |
type sym_info =
|
blanchet@43434
|
569 |
{pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
|
blanchet@43434
|
570 |
|
blanchet@43445
|
571 |
fun add_combterm_syms_to_table explicit_apply =
|
blanchet@43429
|
572 |
let
|
blanchet@43429
|
573 |
fun aux top_level tm =
|
blanchet@43429
|
574 |
let val (head, args) = strip_combterm_comb tm in
|
blanchet@43429
|
575 |
(case head of
|
blanchet@43434
|
576 |
CombConst ((s, _), T, _) =>
|
blanchet@43429
|
577 |
if String.isPrefix bound_var_prefix s then
|
blanchet@43429
|
578 |
I
|
blanchet@43429
|
579 |
else
|
blanchet@43434
|
580 |
let val ary = length args in
|
blanchet@43429
|
581 |
Symtab.map_default
|
blanchet@43429
|
582 |
(s, {pred_sym = true,
|
blanchet@43434
|
583 |
min_ary = if explicit_apply then 0 else ary,
|
blanchet@43434
|
584 |
max_ary = 0, typ = SOME T})
|
blanchet@43434
|
585 |
(fn {pred_sym, min_ary, max_ary, typ} =>
|
blanchet@43429
|
586 |
{pred_sym = pred_sym andalso top_level,
|
blanchet@43434
|
587 |
min_ary = Int.min (ary, min_ary),
|
blanchet@43434
|
588 |
max_ary = Int.max (ary, max_ary),
|
blanchet@43434
|
589 |
typ = if typ = SOME T then typ else NONE})
|
blanchet@43429
|
590 |
end
|
blanchet@43429
|
591 |
| _ => I)
|
blanchet@43429
|
592 |
#> fold (aux false) args
|
blanchet@43429
|
593 |
end
|
blanchet@43429
|
594 |
in aux true end
|
blanchet@43545
|
595 |
fun add_fact_syms_to_table explicit_apply =
|
blanchet@43705
|
596 |
fact_lift (formula_fold NONE (K (add_combterm_syms_to_table explicit_apply)))
|
blanchet@38506
|
597 |
|
blanchet@43546
|
598 |
val default_sym_table_entries : (string * sym_info) list =
|
blanchet@43434
|
599 |
[("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
|
blanchet@43439
|
600 |
(make_fixed_const predicator_base,
|
blanchet@43434
|
601 |
{pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
|
blanchet@43439
|
602 |
([tptp_false, tptp_true]
|
blanchet@43434
|
603 |
|> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
|
blanchet@41388
|
604 |
|
blanchet@43415
|
605 |
fun sym_table_for_facts explicit_apply facts =
|
blanchet@43439
|
606 |
Symtab.empty |> fold Symtab.default default_sym_table_entries
|
blanchet@43445
|
607 |
|> fold (add_fact_syms_to_table explicit_apply) facts
|
blanchet@38506
|
608 |
|
blanchet@43429
|
609 |
fun min_arity_of sym_tab s =
|
blanchet@43429
|
610 |
case Symtab.lookup sym_tab s of
|
blanchet@43445
|
611 |
SOME ({min_ary, ...} : sym_info) => min_ary
|
blanchet@43429
|
612 |
| NONE =>
|
blanchet@43429
|
613 |
case strip_prefix_and_unascii const_prefix s of
|
blanchet@43418
|
614 |
SOME s =>
|
blanchet@43441
|
615 |
let val s = s |> unmangled_const_name |> invert_const in
|
blanchet@43439
|
616 |
if s = predicator_base then 1
|
blanchet@43418
|
617 |
else if s = explicit_app_base then 2
|
blanchet@43418
|
618 |
else if s = type_pred_base then 1
|
blanchet@43428
|
619 |
else 0
|
blanchet@43418
|
620 |
end
|
blanchet@38506
|
621 |
| NONE => 0
|
blanchet@38506
|
622 |
|
blanchet@38506
|
623 |
(* True if the constant ever appears outside of the top-level position in
|
blanchet@38506
|
624 |
literals, or if it appears with different arities (e.g., because of different
|
blanchet@38506
|
625 |
type instantiations). If false, the constant always receives all of its
|
blanchet@38506
|
626 |
arguments and is used as a predicate. *)
|
blanchet@43429
|
627 |
fun is_pred_sym sym_tab s =
|
blanchet@43429
|
628 |
case Symtab.lookup sym_tab s of
|
blanchet@43445
|
629 |
SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
|
blanchet@43445
|
630 |
pred_sym andalso min_ary = max_ary
|
blanchet@43429
|
631 |
| NONE => false
|
blanchet@38506
|
632 |
|
blanchet@43439
|
633 |
val predicator_combconst =
|
blanchet@43439
|
634 |
CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
|
blanchet@43439
|
635 |
fun predicator tm = CombApp (predicator_combconst, tm)
|
blanchet@38506
|
636 |
|
blanchet@43439
|
637 |
fun introduce_predicators_in_combterm sym_tab tm =
|
blanchet@43413
|
638 |
case strip_combterm_comb tm of
|
blanchet@43413
|
639 |
(CombConst ((s, _), _, _), _) =>
|
blanchet@43439
|
640 |
if is_pred_sym sym_tab s then tm else predicator tm
|
blanchet@43439
|
641 |
| _ => predicator tm
|
blanchet@38506
|
642 |
|
blanchet@43415
|
643 |
fun list_app head args = fold (curry (CombApp o swap)) args head
|
blanchet@38506
|
644 |
|
blanchet@43415
|
645 |
fun explicit_app arg head =
|
blanchet@43415
|
646 |
let
|
blanchet@43433
|
647 |
val head_T = combtyp_of head
|
blanchet@43563
|
648 |
val (arg_T, res_T) = dest_funT head_T
|
blanchet@43415
|
649 |
val explicit_app =
|
blanchet@43433
|
650 |
CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
|
blanchet@43563
|
651 |
[arg_T, res_T])
|
blanchet@43415
|
652 |
in list_app explicit_app [head, arg] end
|
blanchet@43415
|
653 |
fun list_explicit_app head args = fold explicit_app args head
|
blanchet@43415
|
654 |
|
blanchet@43436
|
655 |
fun introduce_explicit_apps_in_combterm sym_tab =
|
blanchet@43415
|
656 |
let
|
blanchet@43415
|
657 |
fun aux tm =
|
blanchet@43415
|
658 |
case strip_combterm_comb tm of
|
blanchet@43415
|
659 |
(head as CombConst ((s, _), _, _), args) =>
|
blanchet@43415
|
660 |
args |> map aux
|
blanchet@43428
|
661 |
|> chop (min_arity_of sym_tab s)
|
blanchet@43415
|
662 |
|>> list_app head
|
blanchet@43415
|
663 |
|-> list_explicit_app
|
blanchet@43415
|
664 |
| (head, args) => list_explicit_app head (map aux args)
|
blanchet@43415
|
665 |
in aux end
|
blanchet@43415
|
666 |
|
blanchet@43618
|
667 |
fun chop_fun 0 T = ([], T)
|
blanchet@43618
|
668 |
| chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
|
blanchet@43618
|
669 |
chop_fun (n - 1) ran_T |>> cons dom_T
|
blanchet@43618
|
670 |
| chop_fun _ _ = raise Fail "unexpected non-function"
|
blanchet@43618
|
671 |
|
blanchet@43651
|
672 |
fun filter_type_args _ _ _ [] = []
|
blanchet@43651
|
673 |
| filter_type_args thy s arity T_args =
|
blanchet@43705
|
674 |
let
|
blanchet@43705
|
675 |
(* will throw "TYPE" for pseudo-constants *)
|
blanchet@43705
|
676 |
val U = if s = explicit_app_base then
|
blanchet@43705
|
677 |
@{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
|
blanchet@43705
|
678 |
else
|
blanchet@43705
|
679 |
s |> Sign.the_const_type thy
|
blanchet@43705
|
680 |
in
|
blanchet@43652
|
681 |
case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
|
blanchet@43652
|
682 |
[] => []
|
blanchet@43652
|
683 |
| res_U_vars =>
|
blanchet@43652
|
684 |
let val U_args = (s, U) |> Sign.const_typargs thy in
|
blanchet@43652
|
685 |
U_args ~~ T_args
|
blanchet@43652
|
686 |
|> map_filter (fn (U, T) =>
|
blanchet@43652
|
687 |
if member (op =) res_U_vars (dest_TVar U) then
|
blanchet@43652
|
688 |
SOME T
|
blanchet@43652
|
689 |
else
|
blanchet@43652
|
690 |
NONE)
|
blanchet@43652
|
691 |
end
|
blanchet@43651
|
692 |
end
|
blanchet@43651
|
693 |
handle TYPE _ => T_args
|
blanchet@43618
|
694 |
|
blanchet@43803
|
695 |
fun enforce_type_arg_policy_in_combterm ctxt format nonmono_Ts type_sys =
|
blanchet@43618
|
696 |
let
|
blanchet@43618
|
697 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@43618
|
698 |
fun aux arity (CombApp (tm1, tm2)) =
|
blanchet@43618
|
699 |
CombApp (aux (arity + 1) tm1, aux 0 tm2)
|
blanchet@43618
|
700 |
| aux arity (CombConst (name as (s, _), T, T_args)) =
|
blanchet@43571
|
701 |
let
|
blanchet@43571
|
702 |
val level = level_of_type_sys type_sys
|
blanchet@43571
|
703 |
val (T, T_args) =
|
blanchet@43571
|
704 |
(* Aggressively merge most "hAPPs" if the type system is unsound
|
blanchet@43571
|
705 |
anyway, by distinguishing overloads only on the homogenized
|
blanchet@43708
|
706 |
result type. Don't do it for lightweight type systems, though,
|
blanchet@43708
|
707 |
since it leads to too many unsound proofs. *)
|
blanchet@43571
|
708 |
if s = const_prefix ^ explicit_app_base andalso
|
blanchet@43591
|
709 |
length T_args = 2 andalso
|
blanchet@43707
|
710 |
not (is_type_sys_virtually_sound type_sys) andalso
|
blanchet@43708
|
711 |
heaviness_of_type_sys type_sys = Heavy then
|
blanchet@43571
|
712 |
T_args |> map (homogenized_type ctxt nonmono_Ts level)
|
blanchet@43571
|
713 |
|> (fn Ts => let val T = hd Ts --> nth Ts 1 in
|
blanchet@43702
|
714 |
(T --> T, tl Ts)
|
blanchet@43571
|
715 |
end)
|
blanchet@43571
|
716 |
else
|
blanchet@43571
|
717 |
(T, T_args)
|
blanchet@43571
|
718 |
in
|
blanchet@43571
|
719 |
(case strip_prefix_and_unascii const_prefix s of
|
blanchet@43571
|
720 |
NONE => (name, T_args)
|
blanchet@43571
|
721 |
| SOME s'' =>
|
blanchet@43618
|
722 |
let
|
blanchet@43618
|
723 |
val s'' = invert_const s''
|
blanchet@43702
|
724 |
fun filtered_T_args false = T_args
|
blanchet@43702
|
725 |
| filtered_T_args true = filter_type_args thy s'' arity T_args
|
blanchet@43618
|
726 |
in
|
blanchet@43571
|
727 |
case type_arg_policy type_sys s'' of
|
blanchet@43702
|
728 |
Explicit_Type_Args drop_args =>
|
blanchet@43702
|
729 |
(name, filtered_T_args drop_args)
|
blanchet@43702
|
730 |
| Mangled_Type_Args drop_args =>
|
blanchet@43803
|
731 |
(mangled_const_name format (filtered_T_args drop_args) name,
|
blanchet@43803
|
732 |
[])
|
blanchet@43618
|
733 |
| No_Type_Args => (name, [])
|
blanchet@43571
|
734 |
end)
|
blanchet@43571
|
735 |
|> (fn (name, T_args) => CombConst (name, T, T_args))
|
blanchet@43571
|
736 |
end
|
blanchet@43618
|
737 |
| aux _ tm = tm
|
blanchet@43618
|
738 |
in aux 0 end
|
blanchet@43444
|
739 |
|
blanchet@43803
|
740 |
fun repair_combterm ctxt format nonmono_Ts type_sys sym_tab =
|
blanchet@43803
|
741 |
format <> THF ? (introduce_explicit_apps_in_combterm sym_tab
|
blanchet@43803
|
742 |
#> introduce_predicators_in_combterm sym_tab)
|
blanchet@43803
|
743 |
#> enforce_type_arg_policy_in_combterm ctxt format nonmono_Ts type_sys
|
blanchet@43803
|
744 |
fun repair_fact ctxt format nonmono_Ts type_sys sym_tab =
|
blanchet@43571
|
745 |
update_combformula (formula_map
|
blanchet@43803
|
746 |
(repair_combterm ctxt format nonmono_Ts type_sys sym_tab))
|
blanchet@43444
|
747 |
|
blanchet@43444
|
748 |
(** Helper facts **)
|
blanchet@43444
|
749 |
|
blanchet@43444
|
750 |
fun ti_ti_helper_fact () =
|
blanchet@43444
|
751 |
let
|
blanchet@43444
|
752 |
fun var s = ATerm (`I s, [])
|
blanchet@43460
|
753 |
fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
|
blanchet@43444
|
754 |
in
|
blanchet@43483
|
755 |
Formula (helper_prefix ^ "ti_ti", Axiom,
|
blanchet@43444
|
756 |
AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
|
blanchet@43748
|
757 |
|> close_formula_universally, simp_info, NONE)
|
blanchet@43444
|
758 |
end
|
blanchet@43444
|
759 |
|
blanchet@43803
|
760 |
fun helper_facts_for_sym ctxt format type_sys (s, {typ, ...} : sym_info) =
|
blanchet@43444
|
761 |
case strip_prefix_and_unascii const_prefix s of
|
blanchet@43444
|
762 |
SOME mangled_s =>
|
blanchet@43444
|
763 |
let
|
blanchet@43444
|
764 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@43444
|
765 |
val unmangled_s = mangled_s |> unmangled_const_name
|
blanchet@43764
|
766 |
fun dub_and_inst c needs_fairly_sound (th, j) =
|
blanchet@43750
|
767 |
((c ^ "_" ^ string_of_int j ^
|
blanchet@43764
|
768 |
(if needs_fairly_sound then typed_helper_suffix
|
blanchet@43750
|
769 |
else untyped_helper_suffix),
|
blanchet@43750
|
770 |
General),
|
blanchet@43444
|
771 |
let val t = th |> prop_of in
|
blanchet@43618
|
772 |
t |> ((case general_type_arg_policy type_sys of
|
blanchet@43618
|
773 |
Mangled_Type_Args _ => true
|
blanchet@43618
|
774 |
| _ => false) andalso
|
blanchet@43444
|
775 |
not (null (Term.hidden_polymorphism t)))
|
blanchet@43444
|
776 |
? (case typ of
|
blanchet@43444
|
777 |
SOME T => specialize_type thy (invert_const unmangled_s, T)
|
blanchet@43444
|
778 |
| NONE => I)
|
blanchet@43444
|
779 |
end)
|
blanchet@43444
|
780 |
fun make_facts eq_as_iff =
|
blanchet@43803
|
781 |
map_filter (make_fact ctxt format false eq_as_iff false)
|
blanchet@43764
|
782 |
val fairly_sound = is_type_sys_fairly_sound type_sys
|
blanchet@43444
|
783 |
in
|
blanchet@43444
|
784 |
metis_helpers
|
blanchet@43765
|
785 |
|> maps (fn (metis_s, (needs_fairly_sound, ths)) =>
|
blanchet@43444
|
786 |
if metis_s <> unmangled_s orelse
|
blanchet@43765
|
787 |
(needs_fairly_sound andalso not fairly_sound) then
|
blanchet@43444
|
788 |
[]
|
blanchet@43444
|
789 |
else
|
blanchet@43444
|
790 |
ths ~~ (1 upto length ths)
|
blanchet@43764
|
791 |
|> map (dub_and_inst mangled_s needs_fairly_sound)
|
blanchet@43764
|
792 |
|> make_facts (not needs_fairly_sound))
|
blanchet@43444
|
793 |
end
|
blanchet@43444
|
794 |
| NONE => []
|
blanchet@43803
|
795 |
fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
|
blanchet@43803
|
796 |
Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
|
blanchet@43803
|
797 |
[]
|
blanchet@43444
|
798 |
|
blanchet@43803
|
799 |
fun translate_atp_fact ctxt format keep_trivial =
|
blanchet@43803
|
800 |
`(make_fact ctxt format keep_trivial true true o apsnd prop_of)
|
blanchet@43444
|
801 |
|
blanchet@43803
|
802 |
fun translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t
|
blanchet@43803
|
803 |
rich_facts =
|
blanchet@43444
|
804 |
let
|
blanchet@43444
|
805 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@43444
|
806 |
val fact_ts = map (prop_of o snd o snd) rich_facts
|
blanchet@43444
|
807 |
val (facts, fact_names) =
|
blanchet@43444
|
808 |
rich_facts
|
blanchet@43444
|
809 |
|> map_filter (fn (NONE, _) => NONE
|
blanchet@43444
|
810 |
| (SOME fact, (name, _)) => SOME (fact, name))
|
blanchet@43444
|
811 |
|> ListPair.unzip
|
blanchet@43444
|
812 |
(* Remove existing facts from the conjecture, as this can dramatically
|
blanchet@43444
|
813 |
boost an ATP's performance (for some reason). *)
|
blanchet@43444
|
814 |
val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
|
blanchet@43444
|
815 |
val goal_t = Logic.list_implies (hyp_ts, concl_t)
|
blanchet@43444
|
816 |
val all_ts = goal_t :: fact_ts
|
blanchet@43444
|
817 |
val subs = tfree_classes_of_terms all_ts
|
blanchet@43444
|
818 |
val supers = tvar_classes_of_terms all_ts
|
blanchet@43444
|
819 |
val tycons = type_consts_of_terms thy all_ts
|
blanchet@43803
|
820 |
val conjs = make_conjecture ctxt format prem_kind (hyp_ts @ [concl_t])
|
blanchet@43444
|
821 |
val (supers', arity_clauses) =
|
blanchet@43460
|
822 |
if level_of_type_sys type_sys = No_Types then ([], [])
|
blanchet@43444
|
823 |
else make_arity_clauses thy tycons supers
|
blanchet@43444
|
824 |
val class_rel_clauses = make_class_rel_clauses thy subs supers'
|
blanchet@43444
|
825 |
in
|
blanchet@43444
|
826 |
(fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
|
blanchet@43444
|
827 |
end
|
blanchet@43444
|
828 |
|
blanchet@43444
|
829 |
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
|
blanchet@43444
|
830 |
(true, ATerm (class, [ATerm (name, [])]))
|
blanchet@43444
|
831 |
| fo_literal_from_type_literal (TyLitFree (class, name)) =
|
blanchet@43444
|
832 |
(true, ATerm (class, [ATerm (name, [])]))
|
blanchet@43444
|
833 |
|
blanchet@43444
|
834 |
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
|
blanchet@43444
|
835 |
|
blanchet@43803
|
836 |
fun type_pred_combterm ctxt format nonmono_Ts type_sys T tm =
|
blanchet@43705
|
837 |
CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T])
|
blanchet@43803
|
838 |
|> enforce_type_arg_policy_in_combterm ctxt format nonmono_Ts
|
blanchet@43803
|
839 |
type_sys,
|
blanchet@43444
|
840 |
tm)
|
blanchet@43444
|
841 |
|
blanchet@43747
|
842 |
fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
|
blanchet@43747
|
843 |
| var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
|
blanchet@43747
|
844 |
accum orelse (s = "equal" andalso member (op =) tms (ATerm (name, [])))
|
blanchet@43747
|
845 |
fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
|
blanchet@43747
|
846 |
| is_var_nonmonotonic_in_formula pos phi _ name =
|
blanchet@43747
|
847 |
formula_fold pos (var_occurs_positively_naked_in_term name) phi false
|
blanchet@43705
|
848 |
|
blanchet@43803
|
849 |
fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
|
blanchet@43700
|
850 |
CombConst (`make_fixed_const type_tag_name, T --> T, [T])
|
blanchet@43803
|
851 |
|> enforce_type_arg_policy_in_combterm ctxt format nonmono_Ts type_sys
|
blanchet@43803
|
852 |
|> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
|
blanchet@43700
|
853 |
|> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
|
blanchet@43803
|
854 |
and term_from_combterm ctxt format nonmono_Ts type_sys =
|
blanchet@43444
|
855 |
let
|
blanchet@43803
|
856 |
fun aux site u =
|
blanchet@43803
|
857 |
let
|
blanchet@43803
|
858 |
val (head, args) = strip_combterm_comb u
|
blanchet@43803
|
859 |
val (x as (s, _), T_args) =
|
blanchet@43803
|
860 |
case head of
|
blanchet@43803
|
861 |
CombConst (name, _, T_args) => (name, T_args)
|
blanchet@43803
|
862 |
| CombVar (name, _) => (name, [])
|
blanchet@43803
|
863 |
| CombApp _ => raise Fail "impossible \"CombApp\""
|
blanchet@43803
|
864 |
val arg_site = if site = Top_Level andalso s = "equal" then Eq_Arg
|
blanchet@43803
|
865 |
else Elsewhere
|
blanchet@43803
|
866 |
val t = ATerm (x, map (fo_term_from_typ format) T_args @
|
blanchet@43803
|
867 |
map (aux arg_site) args)
|
blanchet@43803
|
868 |
val T = combtyp_of u
|
blanchet@43803
|
869 |
in
|
blanchet@43803
|
870 |
t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
|
blanchet@43803
|
871 |
tag_with_type ctxt format nonmono_Ts type_sys T
|
blanchet@43803
|
872 |
else
|
blanchet@43803
|
873 |
I)
|
blanchet@43803
|
874 |
end
|
blanchet@43803
|
875 |
in aux end
|
blanchet@43803
|
876 |
and formula_from_combformula ctxt format nonmono_Ts type_sys
|
blanchet@43803
|
877 |
should_predicate_on_var =
|
blanchet@43700
|
878 |
let
|
blanchet@43803
|
879 |
val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
|
blanchet@43444
|
880 |
val do_bound_type =
|
blanchet@43552
|
881 |
case type_sys of
|
blanchet@43587
|
882 |
Simple_Types level =>
|
blanchet@43804
|
883 |
homogenized_type ctxt nonmono_Ts level
|
blanchet@43804
|
884 |
#> mangled_type format false 0 #> SOME
|
blanchet@43552
|
885 |
| _ => K NONE
|
blanchet@43747
|
886 |
fun do_out_of_bound_type pos phi universal (name, T) =
|
blanchet@43705
|
887 |
if should_predicate_on_type ctxt nonmono_Ts type_sys
|
blanchet@43747
|
888 |
(fn () => should_predicate_on_var pos phi universal name) T then
|
blanchet@43705
|
889 |
CombVar (name, T)
|
blanchet@43803
|
890 |
|> type_pred_combterm ctxt format nonmono_Ts type_sys T
|
blanchet@43747
|
891 |
|> do_term |> AAtom |> SOME
|
blanchet@43444
|
892 |
else
|
blanchet@43444
|
893 |
NONE
|
blanchet@43747
|
894 |
fun do_formula pos (AQuant (q, xs, phi)) =
|
blanchet@43747
|
895 |
let
|
blanchet@43747
|
896 |
val phi = phi |> do_formula pos
|
blanchet@43747
|
897 |
val universal = Option.map (q = AExists ? not) pos
|
blanchet@43747
|
898 |
in
|
blanchet@43705
|
899 |
AQuant (q, xs |> map (apsnd (fn NONE => NONE
|
blanchet@43705
|
900 |
| SOME T => do_bound_type T)),
|
blanchet@43705
|
901 |
(if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
|
blanchet@43705
|
902 |
(map_filter
|
blanchet@43705
|
903 |
(fn (_, NONE) => NONE
|
blanchet@43705
|
904 |
| (s, SOME T) =>
|
blanchet@43747
|
905 |
do_out_of_bound_type pos phi universal (s, T))
|
blanchet@43747
|
906 |
xs)
|
blanchet@43705
|
907 |
phi)
|
blanchet@43705
|
908 |
end
|
blanchet@43747
|
909 |
| do_formula pos (AConn conn) = aconn_map pos do_formula conn
|
blanchet@43747
|
910 |
| do_formula _ (AAtom tm) = AAtom (do_term tm)
|
blanchet@43747
|
911 |
in do_formula o SOME end
|
blanchet@43444
|
912 |
|
blanchet@43797
|
913 |
fun bound_atomic_types format type_sys Ts =
|
blanchet@43592
|
914 |
mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
|
blanchet@43797
|
915 |
(atp_type_literals_for_types format type_sys Axiom Ts))
|
blanchet@43592
|
916 |
|
blanchet@43797
|
917 |
fun formula_for_fact ctxt format nonmono_Ts type_sys
|
blanchet@43444
|
918 |
({combformula, atomic_types, ...} : translated_formula) =
|
blanchet@43592
|
919 |
combformula
|
blanchet@43592
|
920 |
|> close_combformula_universally
|
blanchet@43803
|
921 |
|> formula_from_combformula ctxt format nonmono_Ts type_sys
|
blanchet@43747
|
922 |
is_var_nonmonotonic_in_formula true
|
blanchet@43797
|
923 |
|> bound_atomic_types format type_sys atomic_types
|
blanchet@43444
|
924 |
|> close_formula_universally
|
blanchet@43444
|
925 |
|
blanchet@43444
|
926 |
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
|
blanchet@43444
|
927 |
of monomorphization). The TPTP explicitly forbids name clashes, and some of
|
blanchet@43444
|
928 |
the remote provers might care. *)
|
blanchet@43797
|
929 |
fun formula_line_for_fact ctxt format prefix nonmono_Ts type_sys
|
blanchet@43511
|
930 |
(j, formula as {name, locality, kind, ...}) =
|
blanchet@43550
|
931 |
Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
|
blanchet@43550
|
932 |
else string_of_int j ^ "_") ^
|
blanchet@43518
|
933 |
ascii_of name,
|
blanchet@43797
|
934 |
kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
|
blanchet@43748
|
935 |
case locality of
|
blanchet@43748
|
936 |
Intro => intro_info
|
blanchet@43748
|
937 |
| Elim => elim_info
|
blanchet@43748
|
938 |
| Simp => simp_info
|
blanchet@43748
|
939 |
| _ => NONE)
|
blanchet@43444
|
940 |
|
blanchet@43780
|
941 |
fun formula_line_for_class_rel_clause
|
blanchet@43780
|
942 |
(ClassRelClause {name, subclass, superclass, ...}) =
|
blanchet@43444
|
943 |
let val ty_arg = ATerm (`I "T", []) in
|
blanchet@43448
|
944 |
Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
|
blanchet@43444
|
945 |
AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
|
blanchet@43444
|
946 |
AAtom (ATerm (superclass, [ty_arg]))])
|
blanchet@43748
|
947 |
|> close_formula_universally, intro_info, NONE)
|
blanchet@43444
|
948 |
end
|
blanchet@43444
|
949 |
|
blanchet@43444
|
950 |
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
|
blanchet@43444
|
951 |
(true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
|
blanchet@43444
|
952 |
| fo_literal_from_arity_literal (TVarLit (c, sort)) =
|
blanchet@43444
|
953 |
(false, ATerm (c, [ATerm (sort, [])]))
|
blanchet@43444
|
954 |
|
blanchet@43780
|
955 |
fun formula_line_for_arity_clause
|
blanchet@43780
|
956 |
(ArityClause {name, prem_lits, concl_lits, ...}) =
|
blanchet@43448
|
957 |
Formula (arity_clause_prefix ^ ascii_of name, Axiom,
|
blanchet@43444
|
958 |
mk_ahorn (map (formula_from_fo_literal o apfst not
|
blanchet@43766
|
959 |
o fo_literal_from_arity_literal) prem_lits)
|
blanchet@43444
|
960 |
(formula_from_fo_literal
|
blanchet@43766
|
961 |
(fo_literal_from_arity_literal concl_lits))
|
blanchet@43748
|
962 |
|> close_formula_universally, intro_info, NONE)
|
blanchet@43444
|
963 |
|
blanchet@43803
|
964 |
fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
|
blanchet@43444
|
965 |
({name, kind, combformula, ...} : translated_formula) =
|
blanchet@43448
|
966 |
Formula (conjecture_prefix ^ name, kind,
|
blanchet@43803
|
967 |
formula_from_combformula ctxt format nonmono_Ts type_sys
|
blanchet@43780
|
968 |
is_var_nonmonotonic_in_formula false
|
blanchet@43780
|
969 |
(close_combformula_universally combformula)
|
blanchet@43444
|
970 |
|> close_formula_universally, NONE, NONE)
|
blanchet@43444
|
971 |
|
blanchet@43797
|
972 |
fun free_type_literals format type_sys
|
blanchet@43797
|
973 |
({atomic_types, ...} : translated_formula) =
|
blanchet@43797
|
974 |
atomic_types |> atp_type_literals_for_types format type_sys Conjecture
|
blanchet@43444
|
975 |
|> map fo_literal_from_type_literal
|
blanchet@43444
|
976 |
|
blanchet@43444
|
977 |
fun formula_line_for_free_type j lit =
|
blanchet@43448
|
978 |
Formula (tfree_prefix ^ string_of_int j, Hypothesis,
|
blanchet@43444
|
979 |
formula_from_fo_literal lit, NONE, NONE)
|
blanchet@43797
|
980 |
fun formula_lines_for_free_types format type_sys facts =
|
blanchet@43444
|
981 |
let
|
blanchet@43797
|
982 |
val litss = map (free_type_literals format type_sys) facts
|
blanchet@43444
|
983 |
val lits = fold (union (op =)) litss []
|
blanchet@43444
|
984 |
in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
|
blanchet@43444
|
985 |
|
blanchet@43444
|
986 |
(** Symbol declarations **)
|
blanchet@43415
|
987 |
|
blanchet@43755
|
988 |
fun insert_type ctxt get_T x xs =
|
blanchet@43547
|
989 |
let val T = get_T x in
|
blanchet@43755
|
990 |
if exists (curry (type_instance ctxt) T o get_T) xs then xs
|
blanchet@43755
|
991 |
else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
|
blanchet@43547
|
992 |
end
|
blanchet@43547
|
993 |
|
blanchet@43445
|
994 |
fun should_declare_sym type_sys pred_sym s =
|
blanchet@43413
|
995 |
not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
|
blanchet@43618
|
996 |
not (String.isPrefix tptp_special_prefix s) andalso
|
blanchet@43765
|
997 |
(case type_sys of
|
blanchet@43765
|
998 |
Simple_Types _ => true
|
blanchet@43765
|
999 |
| Tags (_, _, Light) => true
|
blanchet@43765
|
1000 |
| _ => not pred_sym)
|
blanchet@43413
|
1001 |
|
blanchet@43755
|
1002 |
fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
|
blanchet@43445
|
1003 |
let
|
blanchet@43568
|
1004 |
fun add_combterm in_conj tm =
|
blanchet@43445
|
1005 |
let val (head, args) = strip_combterm_comb tm in
|
blanchet@43445
|
1006 |
(case head of
|
blanchet@43445
|
1007 |
CombConst ((s, s'), T, T_args) =>
|
blanchet@43445
|
1008 |
let val pred_sym = is_pred_sym repaired_sym_tab s in
|
blanchet@43445
|
1009 |
if should_declare_sym type_sys pred_sym s then
|
blanchet@43447
|
1010 |
Symtab.map_default (s, [])
|
blanchet@43755
|
1011 |
(insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
|
blanchet@43755
|
1012 |
in_conj))
|
blanchet@43445
|
1013 |
else
|
blanchet@43445
|
1014 |
I
|
blanchet@43445
|
1015 |
end
|
blanchet@43445
|
1016 |
| _ => I)
|
blanchet@43568
|
1017 |
#> fold (add_combterm in_conj) args
|
blanchet@43445
|
1018 |
end
|
blanchet@43568
|
1019 |
fun add_fact in_conj =
|
blanchet@43705
|
1020 |
fact_lift (formula_fold NONE (K (add_combterm in_conj)))
|
blanchet@43568
|
1021 |
in
|
blanchet@43568
|
1022 |
Symtab.empty
|
blanchet@43568
|
1023 |
|> is_type_sys_fairly_sound type_sys
|
blanchet@43568
|
1024 |
? (fold (add_fact true) conjs #> fold (add_fact false) facts)
|
blanchet@43568
|
1025 |
end
|
blanchet@43445
|
1026 |
|
blanchet@43755
|
1027 |
(* These types witness that the type classes they belong to allow infinite
|
blanchet@43755
|
1028 |
models and hence that any types with these type classes is monotonic. *)
|
blanchet@43755
|
1029 |
val known_infinite_types = [@{typ nat}, @{typ int}, @{typ "nat => bool"}]
|
blanchet@43755
|
1030 |
|
blanchet@43555
|
1031 |
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
|
blanchet@43555
|
1032 |
out with monotonicity" paper presented at CADE 2011. *)
|
blanchet@43755
|
1033 |
fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
|
blanchet@43700
|
1034 |
| add_combterm_nonmonotonic_types ctxt level _
|
blanchet@43550
|
1035 |
(CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
|
blanchet@43550
|
1036 |
tm2)) =
|
blanchet@43550
|
1037 |
(exists is_var_or_bound_var [tm1, tm2] andalso
|
blanchet@43700
|
1038 |
(case level of
|
blanchet@43755
|
1039 |
Nonmonotonic_Types =>
|
blanchet@43755
|
1040 |
not (is_type_surely_infinite ctxt known_infinite_types T)
|
blanchet@43700
|
1041 |
| Finite_Types => is_type_surely_finite ctxt T
|
blanchet@43755
|
1042 |
| _ => true)) ? insert_type ctxt I (deep_freeze_type T)
|
blanchet@43700
|
1043 |
| add_combterm_nonmonotonic_types _ _ _ _ = I
|
blanchet@43700
|
1044 |
fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
|
blanchet@43700
|
1045 |
: translated_formula) =
|
blanchet@43705
|
1046 |
formula_fold (SOME (kind <> Conjecture))
|
blanchet@43700
|
1047 |
(add_combterm_nonmonotonic_types ctxt level) combformula
|
blanchet@43755
|
1048 |
fun nonmonotonic_types_for_facts ctxt type_sys facts =
|
blanchet@43700
|
1049 |
let val level = level_of_type_sys type_sys in
|
blanchet@43755
|
1050 |
if level = Nonmonotonic_Types orelse level = Finite_Types then
|
blanchet@43755
|
1051 |
[] |> fold (add_fact_nonmonotonic_types ctxt level) facts
|
blanchet@43755
|
1052 |
(* We must add "bool" in case the helper "True_or_False" is added
|
blanchet@43755
|
1053 |
later. In addition, several places in the code rely on the list of
|
blanchet@43755
|
1054 |
nonmonotonic types not being empty. *)
|
blanchet@43755
|
1055 |
|> insert_type ctxt I @{typ bool}
|
blanchet@43755
|
1056 |
else
|
blanchet@43755
|
1057 |
[]
|
blanchet@43700
|
1058 |
end
|
blanchet@43547
|
1059 |
|
blanchet@43803
|
1060 |
fun decl_line_for_sym ctxt format nonmono_Ts level s
|
blanchet@43803
|
1061 |
(s', _, T, pred_sym, ary, _) =
|
blanchet@43804
|
1062 |
Decl (sym_decl_prefix ^ s, (s, s'),
|
blanchet@43804
|
1063 |
T |> homogenized_type ctxt nonmono_Ts level
|
blanchet@43804
|
1064 |
|> mangled_type format pred_sym ary)
|
blanchet@43450
|
1065 |
|
blanchet@43463
|
1066 |
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
|
blanchet@43463
|
1067 |
|
blanchet@43797
|
1068 |
fun formula_line_for_pred_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
|
blanchet@43797
|
1069 |
n s j (s', T_args, T, _, ary, in_conj) =
|
blanchet@43450
|
1070 |
let
|
blanchet@43580
|
1071 |
val (kind, maybe_negate) =
|
blanchet@43580
|
1072 |
if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
|
blanchet@43580
|
1073 |
else (Axiom, I)
|
blanchet@43618
|
1074 |
val (arg_Ts, res_T) = chop_fun ary T
|
blanchet@43450
|
1075 |
val bound_names =
|
blanchet@43450
|
1076 |
1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
|
blanchet@43700
|
1077 |
val bounds =
|
blanchet@43450
|
1078 |
bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
|
blanchet@43450
|
1079 |
val bound_Ts =
|
blanchet@43463
|
1080 |
arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
|
blanchet@43463
|
1081 |
else NONE)
|
blanchet@43450
|
1082 |
in
|
blanchet@43483
|
1083 |
Formula (sym_decl_prefix ^ s ^
|
blanchet@43580
|
1084 |
(if n > 1 then "_" ^ string_of_int j else ""), kind,
|
blanchet@43450
|
1085 |
CombConst ((s, s'), T, T_args)
|
blanchet@43700
|
1086 |
|> fold (curry (CombApp o swap)) bounds
|
blanchet@43803
|
1087 |
|> type_pred_combterm ctxt format nonmono_Ts type_sys res_T
|
blanchet@43804
|
1088 |
|> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
|
blanchet@43803
|
1089 |
|> formula_from_combformula ctxt format nonmono_Ts type_sys
|
blanchet@43747
|
1090 |
(K (K (K (K true)))) true
|
blanchet@43797
|
1091 |
|> n > 1 ? bound_atomic_types format type_sys (atyps_of T)
|
blanchet@43580
|
1092 |
|> close_formula_universally
|
blanchet@43580
|
1093 |
|> maybe_negate,
|
blanchet@43748
|
1094 |
intro_info, NONE)
|
blanchet@43450
|
1095 |
end
|
blanchet@43450
|
1096 |
|
blanchet@43797
|
1097 |
fun formula_lines_for_tag_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
|
blanchet@43797
|
1098 |
n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
|
blanchet@43700
|
1099 |
let
|
blanchet@43700
|
1100 |
val ident_base =
|
blanchet@43700
|
1101 |
sym_decl_prefix ^ s ^ (if n > 1 then "_" ^ string_of_int j else "")
|
blanchet@43721
|
1102 |
val (kind, maybe_negate) =
|
blanchet@43721
|
1103 |
if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
|
blanchet@43721
|
1104 |
else (Axiom, I)
|
blanchet@43700
|
1105 |
val (arg_Ts, res_T) = chop_fun ary T
|
blanchet@43700
|
1106 |
val bound_names =
|
blanchet@43700
|
1107 |
1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
|
blanchet@43700
|
1108 |
val bounds = bound_names |> map (fn name => ATerm (name, []))
|
blanchet@43803
|
1109 |
fun const args =
|
blanchet@43803
|
1110 |
ATerm ((s, s'), map (fo_term_from_typ format) T_args @ args)
|
blanchet@43701
|
1111 |
val atomic_Ts = atyps_of T
|
blanchet@43705
|
1112 |
fun eq tms =
|
blanchet@43705
|
1113 |
(if pred_sym then AConn (AIff, map AAtom tms)
|
blanchet@43705
|
1114 |
else AAtom (ATerm (`I "equal", tms)))
|
blanchet@43797
|
1115 |
|> bound_atomic_types format type_sys atomic_Ts
|
blanchet@43701
|
1116 |
|> close_formula_universally
|
blanchet@43721
|
1117 |
|> maybe_negate
|
blanchet@43707
|
1118 |
val should_encode = should_encode_type ctxt nonmono_Ts All_Types
|
blanchet@43803
|
1119 |
val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
|
blanchet@43700
|
1120 |
val add_formula_for_res =
|
blanchet@43700
|
1121 |
if should_encode res_T then
|
blanchet@43721
|
1122 |
cons (Formula (ident_base ^ "_res", kind,
|
blanchet@43705
|
1123 |
eq [tag_with res_T (const bounds), const bounds],
|
blanchet@43748
|
1124 |
simp_info, NONE))
|
blanchet@43700
|
1125 |
else
|
blanchet@43700
|
1126 |
I
|
blanchet@43700
|
1127 |
fun add_formula_for_arg k =
|
blanchet@43700
|
1128 |
let val arg_T = nth arg_Ts k in
|
blanchet@43700
|
1129 |
if should_encode arg_T then
|
blanchet@43700
|
1130 |
case chop k bounds of
|
blanchet@43700
|
1131 |
(bounds1, bound :: bounds2) =>
|
blanchet@43721
|
1132 |
cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
|
blanchet@43705
|
1133 |
eq [const (bounds1 @ tag_with arg_T bound ::
|
blanchet@43705
|
1134 |
bounds2),
|
blanchet@43705
|
1135 |
const bounds],
|
blanchet@43748
|
1136 |
simp_info, NONE))
|
blanchet@43700
|
1137 |
| _ => raise Fail "expected nonempty tail"
|
blanchet@43700
|
1138 |
else
|
blanchet@43700
|
1139 |
I
|
blanchet@43700
|
1140 |
end
|
blanchet@43700
|
1141 |
in
|
blanchet@43705
|
1142 |
[] |> not pred_sym ? add_formula_for_res
|
blanchet@43700
|
1143 |
|> fold add_formula_for_arg (ary - 1 downto 0)
|
blanchet@43700
|
1144 |
end
|
blanchet@43700
|
1145 |
|
blanchet@43707
|
1146 |
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
|
blanchet@43707
|
1147 |
|
blanchet@43797
|
1148 |
fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
|
blanchet@43580
|
1149 |
(s, decls) =
|
blanchet@43552
|
1150 |
case type_sys of
|
blanchet@43803
|
1151 |
Simple_Types level =>
|
blanchet@43803
|
1152 |
map (decl_line_for_sym ctxt format nonmono_Ts level s) decls
|
blanchet@43700
|
1153 |
| Preds _ =>
|
blanchet@43445
|
1154 |
let
|
blanchet@43450
|
1155 |
val decls =
|
blanchet@43450
|
1156 |
case decls of
|
blanchet@43450
|
1157 |
decl :: (decls' as _ :: _) =>
|
blanchet@43463
|
1158 |
let val T = result_type_of_decl decl in
|
blanchet@43755
|
1159 |
if forall (curry (type_instance ctxt o swap) T
|
blanchet@43463
|
1160 |
o result_type_of_decl) decls' then
|
blanchet@43463
|
1161 |
[decl]
|
blanchet@43463
|
1162 |
else
|
blanchet@43463
|
1163 |
decls
|
blanchet@43463
|
1164 |
end
|
blanchet@43450
|
1165 |
| _ => decls
|
blanchet@43450
|
1166 |
val n = length decls
|
blanchet@43450
|
1167 |
val decls =
|
blanchet@43705
|
1168 |
decls
|
blanchet@43705
|
1169 |
|> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
|
blanchet@43705
|
1170 |
o result_type_of_decl)
|
blanchet@43445
|
1171 |
in
|
blanchet@43580
|
1172 |
(0 upto length decls - 1, decls)
|
blanchet@43797
|
1173 |
|-> map2 (formula_line_for_pred_sym_decl ctxt format conj_sym_kind
|
blanchet@43797
|
1174 |
nonmono_Ts type_sys n s)
|
blanchet@43445
|
1175 |
end
|
blanchet@43708
|
1176 |
| Tags (_, _, heaviness) =>
|
blanchet@43708
|
1177 |
(case heaviness of
|
blanchet@43708
|
1178 |
Heavy => []
|
blanchet@43708
|
1179 |
| Light =>
|
blanchet@43700
|
1180 |
let val n = length decls in
|
blanchet@43700
|
1181 |
(0 upto n - 1 ~~ decls)
|
blanchet@43797
|
1182 |
|> maps (formula_lines_for_tag_sym_decl ctxt format conj_sym_kind
|
blanchet@43797
|
1183 |
nonmono_Ts type_sys n s)
|
blanchet@43700
|
1184 |
end)
|
blanchet@43450
|
1185 |
|
blanchet@43797
|
1186 |
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
|
blanchet@43797
|
1187 |
type_sys sym_decl_tab =
|
blanchet@43797
|
1188 |
Symtab.fold_rev
|
blanchet@43797
|
1189 |
(append o problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
|
blanchet@43797
|
1190 |
type_sys)
|
blanchet@43797
|
1191 |
sym_decl_tab []
|
blanchet@43410
|
1192 |
|
blanchet@43804
|
1193 |
fun add_simple_types_in_type (AFun (ty1, ty2)) =
|
blanchet@43804
|
1194 |
fold add_simple_types_in_type [ty1, ty2]
|
blanchet@43804
|
1195 |
| add_simple_types_in_type (AType name) = insert (op =) name
|
blanchet@43804
|
1196 |
|
blanchet@43803
|
1197 |
fun add_simple_types_in_formula (AQuant (_, xs, phi)) =
|
blanchet@43804
|
1198 |
fold add_simple_types_in_type (map_filter snd xs)
|
blanchet@43804
|
1199 |
#> add_simple_types_in_formula phi
|
blanchet@43803
|
1200 |
| add_simple_types_in_formula (AConn (_, phis)) =
|
blanchet@43803
|
1201 |
fold add_simple_types_in_formula phis
|
blanchet@43803
|
1202 |
| add_simple_types_in_formula (AAtom _) = I
|
blanchet@43414
|
1203 |
|
blanchet@43804
|
1204 |
fun add_simple_types_in_problem_line (Decl (_, _, ty)) =
|
blanchet@43804
|
1205 |
add_simple_types_in_type ty
|
blanchet@43803
|
1206 |
| add_simple_types_in_problem_line (Formula (_, _, phi, _, _)) =
|
blanchet@43803
|
1207 |
add_simple_types_in_formula phi
|
blanchet@43414
|
1208 |
|
blanchet@43803
|
1209 |
fun simple_types_in_problem problem =
|
blanchet@43803
|
1210 |
fold (fold add_simple_types_in_problem_line o snd) problem []
|
blanchet@43803
|
1211 |
|> filter_out (String.isPrefix tptp_special_prefix o fst)
|
blanchet@43414
|
1212 |
|
blanchet@43803
|
1213 |
fun decl_line_for_simple_type (s, s') =
|
blanchet@43804
|
1214 |
Decl (type_decl_prefix ^ s, (s, s'), AType (`I tptp_type_of_types))
|
blanchet@43414
|
1215 |
|
blanchet@43708
|
1216 |
fun should_add_ti_ti_helper (Tags (Polymorphic, level, Heavy)) =
|
blanchet@43702
|
1217 |
level = Nonmonotonic_Types orelse level = Finite_Types
|
blanchet@43702
|
1218 |
| should_add_ti_ti_helper _ = false
|
blanchet@43702
|
1219 |
|
blanchet@43780
|
1220 |
fun offset_of_heading_in_problem _ [] j = j
|
blanchet@43780
|
1221 |
| offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
|
blanchet@43780
|
1222 |
if heading = needle then j
|
blanchet@43780
|
1223 |
else offset_of_heading_in_problem needle problem (j + length lines)
|
blanchet@43780
|
1224 |
|
blanchet@43414
|
1225 |
val type_declsN = "Types"
|
blanchet@43415
|
1226 |
val sym_declsN = "Symbol types"
|
blanchet@41405
|
1227 |
val factsN = "Relevant facts"
|
blanchet@41405
|
1228 |
val class_relsN = "Class relationships"
|
blanchet@43414
|
1229 |
val aritiesN = "Arities"
|
blanchet@41405
|
1230 |
val helpersN = "Helper facts"
|
blanchet@41405
|
1231 |
val conjsN = "Conjectures"
|
blanchet@41561
|
1232 |
val free_typesN = "Type variables"
|
blanchet@41405
|
1233 |
|
blanchet@43780
|
1234 |
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
|
blanchet@43780
|
1235 |
explicit_apply hyp_ts concl_t facts =
|
blanchet@38506
|
1236 |
let
|
blanchet@41561
|
1237 |
val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
|
blanchet@43803
|
1238 |
translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t facts
|
blanchet@43434
|
1239 |
val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
|
blanchet@43755
|
1240 |
val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
|
blanchet@43803
|
1241 |
val repair = repair_fact ctxt format nonmono_Ts type_sys sym_tab
|
blanchet@43552
|
1242 |
val (conjs, facts) = (conjs, facts) |> pairself (map repair)
|
blanchet@43550
|
1243 |
val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
|
blanchet@43444
|
1244 |
val helpers =
|
blanchet@43803
|
1245 |
repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
|
blanchet@43803
|
1246 |
|> map repair
|
blanchet@43765
|
1247 |
val lavish_nonmono_Ts =
|
blanchet@43765
|
1248 |
if null nonmono_Ts orelse
|
blanchet@43765
|
1249 |
polymorphism_of_type_sys type_sys <> Polymorphic then
|
blanchet@43765
|
1250 |
nonmono_Ts
|
blanchet@43765
|
1251 |
else
|
blanchet@43765
|
1252 |
[TVar (("'a", 0), HOLogic.typeS)]
|
blanchet@43550
|
1253 |
val sym_decl_lines =
|
blanchet@43596
|
1254 |
(conjs, helpers @ facts)
|
blanchet@43755
|
1255 |
|> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
|
blanchet@43797
|
1256 |
|> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
|
blanchet@43797
|
1257 |
lavish_nonmono_Ts type_sys
|
blanchet@43750
|
1258 |
val helper_lines =
|
blanchet@43797
|
1259 |
0 upto length helpers - 1 ~~ helpers
|
blanchet@43797
|
1260 |
|> map (formula_line_for_fact ctxt format helper_prefix lavish_nonmono_Ts
|
blanchet@43797
|
1261 |
type_sys)
|
blanchet@43797
|
1262 |
|> (if should_add_ti_ti_helper type_sys then cons (ti_ti_helper_fact ())
|
blanchet@43797
|
1263 |
else I)
|
blanchet@43393
|
1264 |
(* Reordering these might confuse the proof reconstruction code or the SPASS
|
blanchet@43393
|
1265 |
Flotter hack. *)
|
blanchet@38506
|
1266 |
val problem =
|
blanchet@43432
|
1267 |
[(sym_declsN, sym_decl_lines),
|
blanchet@43797
|
1268 |
(factsN,
|
blanchet@43797
|
1269 |
map (formula_line_for_fact ctxt format fact_prefix nonmono_Ts type_sys)
|
blanchet@43797
|
1270 |
(0 upto length facts - 1 ~~ facts)),
|
blanchet@43416
|
1271 |
(class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
|
blanchet@43416
|
1272 |
(aritiesN, map formula_line_for_arity_clause arity_clauses),
|
blanchet@43750
|
1273 |
(helpersN, helper_lines),
|
blanchet@43803
|
1274 |
(conjsN,
|
blanchet@43803
|
1275 |
map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
|
blanchet@43803
|
1276 |
conjs),
|
blanchet@43797
|
1277 |
(free_typesN,
|
blanchet@43797
|
1278 |
formula_lines_for_free_types format type_sys (facts @ conjs))]
|
blanchet@43414
|
1279 |
val problem =
|
blanchet@43432
|
1280 |
problem
|
blanchet@43552
|
1281 |
|> (case type_sys of
|
blanchet@43587
|
1282 |
Simple_Types _ =>
|
blanchet@43803
|
1283 |
cons (type_declsN, problem |> simple_types_in_problem
|
blanchet@43803
|
1284 |
|> map decl_line_for_simple_type)
|
blanchet@43552
|
1285 |
| _ => I)
|
blanchet@43780
|
1286 |
val problem =
|
blanchet@43780
|
1287 |
problem |> (if format = CNF_UEQ then filter_cnf_ueq_problem else I)
|
blanchet@43517
|
1288 |
val (problem, pool) =
|
blanchet@43517
|
1289 |
problem |> nice_atp_problem (Config.get ctxt readable_names)
|
blanchet@43750
|
1290 |
val helpers_offset = offset_of_heading_in_problem helpersN problem 0
|
blanchet@43750
|
1291 |
val typed_helpers =
|
blanchet@43750
|
1292 |
map_filter (fn (j, {name, ...}) =>
|
blanchet@43750
|
1293 |
if String.isSuffix typed_helper_suffix name then SOME j
|
blanchet@43750
|
1294 |
else NONE)
|
blanchet@43750
|
1295 |
((helpers_offset + 1 upto helpers_offset + length helpers)
|
blanchet@43750
|
1296 |
~~ helpers)
|
blanchet@43649
|
1297 |
fun add_sym_arity (s, {min_ary, ...} : sym_info) =
|
blanchet@43620
|
1298 |
if min_ary > 0 then
|
blanchet@43620
|
1299 |
case strip_prefix_and_unascii const_prefix s of
|
blanchet@43620
|
1300 |
SOME s => Symtab.insert (op =) (s, min_ary)
|
blanchet@43620
|
1301 |
| NONE => I
|
blanchet@43620
|
1302 |
else
|
blanchet@43620
|
1303 |
I
|
blanchet@38506
|
1304 |
in
|
blanchet@38506
|
1305 |
(problem,
|
blanchet@38506
|
1306 |
case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
|
blanchet@43456
|
1307 |
offset_of_heading_in_problem conjsN problem 0,
|
blanchet@43412
|
1308 |
offset_of_heading_in_problem factsN problem 0,
|
blanchet@43620
|
1309 |
fact_names |> Vector.fromList,
|
blanchet@43750
|
1310 |
typed_helpers,
|
blanchet@43620
|
1311 |
Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
|
blanchet@38506
|
1312 |
end
|
blanchet@38506
|
1313 |
|
blanchet@41561
|
1314 |
(* FUDGE *)
|
blanchet@41561
|
1315 |
val conj_weight = 0.0
|
blanchet@42641
|
1316 |
val hyp_weight = 0.1
|
blanchet@42641
|
1317 |
val fact_min_weight = 0.2
|
blanchet@41561
|
1318 |
val fact_max_weight = 1.0
|
blanchet@43479
|
1319 |
val type_info_default_weight = 0.8
|
blanchet@41561
|
1320 |
|
blanchet@41561
|
1321 |
fun add_term_weights weight (ATerm (s, tms)) =
|
blanchet@43599
|
1322 |
(not (is_atp_variable s) andalso s <> "equal" andalso
|
blanchet@43618
|
1323 |
not (String.isPrefix tptp_special_prefix s)) ? Symtab.default (s, weight)
|
blanchet@41561
|
1324 |
#> fold (add_term_weights weight) tms
|
blanchet@43448
|
1325 |
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
|
blanchet@43705
|
1326 |
formula_fold NONE (K (add_term_weights weight)) phi
|
blanchet@43399
|
1327 |
| add_problem_line_weights _ _ = I
|
blanchet@41561
|
1328 |
|
blanchet@41561
|
1329 |
fun add_conjectures_weights [] = I
|
blanchet@41561
|
1330 |
| add_conjectures_weights conjs =
|
blanchet@41561
|
1331 |
let val (hyps, conj) = split_last conjs in
|
blanchet@41561
|
1332 |
add_problem_line_weights conj_weight conj
|
blanchet@41561
|
1333 |
#> fold (add_problem_line_weights hyp_weight) hyps
|
blanchet@41561
|
1334 |
end
|
blanchet@41561
|
1335 |
|
blanchet@41561
|
1336 |
fun add_facts_weights facts =
|
blanchet@41561
|
1337 |
let
|
blanchet@41561
|
1338 |
val num_facts = length facts
|
blanchet@41561
|
1339 |
fun weight_of j =
|
blanchet@41561
|
1340 |
fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
|
blanchet@41561
|
1341 |
/ Real.fromInt num_facts
|
blanchet@41561
|
1342 |
in
|
blanchet@41561
|
1343 |
map weight_of (0 upto num_facts - 1) ~~ facts
|
blanchet@41561
|
1344 |
|> fold (uncurry add_problem_line_weights)
|
blanchet@41561
|
1345 |
end
|
blanchet@41561
|
1346 |
|
blanchet@41561
|
1347 |
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
|
blanchet@41561
|
1348 |
fun atp_problem_weights problem =
|
blanchet@43479
|
1349 |
let val get = these o AList.lookup (op =) problem in
|
blanchet@43479
|
1350 |
Symtab.empty
|
blanchet@43479
|
1351 |
|> add_conjectures_weights (get free_typesN @ get conjsN)
|
blanchet@43479
|
1352 |
|> add_facts_weights (get factsN)
|
blanchet@43479
|
1353 |
|> fold (fold (add_problem_line_weights type_info_default_weight) o get)
|
blanchet@43479
|
1354 |
[sym_declsN, class_relsN, aritiesN]
|
blanchet@43479
|
1355 |
|> Symtab.dest
|
blanchet@43479
|
1356 |
|> sort (prod_ord Real.compare string_ord o pairself swap)
|
blanchet@43479
|
1357 |
end
|
blanchet@41561
|
1358 |
|
blanchet@38506
|
1359 |
end;
|