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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 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 connective = ATP_Problem.connective
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type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
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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 name = string * string
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datatype type_literal =
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TyLitVar of name * name |
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TyLitFree of name * name
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datatype arity_literal =
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TConsLit of name * name * name list |
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TVarLit of name * name
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type arity_clause =
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{name: string,
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prem_lits: arity_literal list,
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concl_lits: arity_literal}
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type class_rel_clause =
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{name: string,
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subclass: name,
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superclass: name}
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datatype combterm =
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CombConst of name * typ * typ list |
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CombVar of name * typ |
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CombApp of combterm * combterm
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datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
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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 = Heavyweight | Lightweight
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datatype type_sys =
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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 bound_var_prefix : string
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val schematic_var_prefix: string
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val fixed_var_prefix: string
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val tvar_prefix: string
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val tfree_prefix: string
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val const_prefix: string
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val type_const_prefix: string
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val class_prefix: string
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val skolem_const_prefix : string
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val old_skolem_const_prefix : string
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val new_skolem_const_prefix : string
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val type_decl_prefix : string
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val sym_decl_prefix : string
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val preds_sym_formula_prefix : string
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val lightweight_tags_sym_formula_prefix : string
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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 class_rel_clause_prefix : string
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val arity_clause_prefix : string
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val tfree_clause_prefix : string
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val typed_helper_suffix : string
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val untyped_helper_suffix : string
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val type_tag_idempotence_helper_name : string
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val predicator_name : string
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val app_op_name : string
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val type_tag_name : string
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val type_pred_name : string
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val simple_type_prefix : string
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val prefixed_predicator_name : string
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val prefixed_app_op_name : string
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val prefixed_type_tag_name : string
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val ascii_of: string -> string
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val unascii_of: string -> string
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val strip_prefix_and_unascii : string -> string -> string option
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val proxy_table : (string * (string * (thm * (string * string)))) list
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val proxify_const : string -> (string * string) option
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val invert_const: string -> string
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val unproxify_const: string -> string
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val make_bound_var : string -> string
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val make_schematic_var : string * int -> string
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val make_fixed_var : string -> string
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val make_schematic_type_var : string * int -> string
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val make_fixed_type_var : string -> string
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val make_fixed_const : string -> string
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val make_fixed_type_const : string -> string
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val make_type_class : string -> string
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val new_skolem_var_name_from_const : string -> string
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val num_type_args : theory -> string -> int
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val make_arity_clauses :
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theory -> string list -> class list -> class list * arity_clause list
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val make_class_rel_clauses :
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theory -> class list -> class list -> class_rel_clause list
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val combtyp_of : combterm -> typ
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val strip_combterm_comb : combterm -> combterm * combterm list
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val atyps_of : typ -> typ list
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val combterm_from_term :
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theory -> (string * typ) list -> term -> combterm * typ list
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val is_locality_global : locality -> bool
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val type_sys_from_string : string -> type_sys
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val polymorphism_of_type_sys : type_sys -> polymorphism
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val level_of_type_sys : type_sys -> type_level
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val is_type_sys_virtually_sound : type_sys -> bool
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val is_type_sys_fairly_sound : type_sys -> bool
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val choose_format : format list -> type_sys -> format * type_sys
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val raw_type_literals_for_types : typ list -> type_literal list
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val mk_aconns :
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connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
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val unmangled_const_name : string -> string
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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 -> type_sys -> bool -> (string * locality) * thm
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-> translated_formula option * ((string * locality) * thm)
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val helper_table : ((string * bool) * thm list) list
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val should_specialize_helper : type_sys -> term -> bool
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val tfree_classes_of_terms : term list -> string list
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val tvar_classes_of_terms : term list -> string list
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val type_constrs_of_terms : theory -> term list -> string list
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val prepare_atp_problem :
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Proof.context -> format -> formula_kind -> formula_kind -> type_sys
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-> bool option -> bool -> 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 ATP_Translate : ATP_TRANSLATE =
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struct
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open ATP_Util
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open ATP_Problem
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type name = string * string
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(* FIXME: avoid *)
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fun union_all xss = fold (union (op =)) xss []
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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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val bound_var_prefix = "B_"
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val schematic_var_prefix = "V_"
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val fixed_var_prefix = "v_"
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val tvar_prefix = "T_"
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val tfree_prefix = "t_"
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val const_prefix = "c_"
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val type_const_prefix = "tc_"
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val class_prefix = "cl_"
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val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
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val old_skolem_const_prefix = skolem_const_prefix ^ "o"
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val new_skolem_const_prefix = skolem_const_prefix ^ "n"
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val type_decl_prefix = "ty_"
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val sym_decl_prefix = "sy_"
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val preds_sym_formula_prefix = "psy_"
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val lightweight_tags_sym_formula_prefix = "tsy_"
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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 = "clar_"
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val arity_clause_prefix = "arity_"
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val tfree_clause_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 type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
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val predicator_name = "hBOOL"
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val app_op_name = "hAPP"
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val type_tag_name = "ti"
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val type_pred_name = "is"
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val simple_type_prefix = "ty_"
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val prefixed_predicator_name = const_prefix ^ predicator_name
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val prefixed_app_op_name = const_prefix ^ app_op_name
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val prefixed_type_tag_name = const_prefix ^ type_tag_name
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(* Freshness almost guaranteed! *)
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val sledgehammer_weak_prefix = "Sledgehammer:"
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(*Escaping of special characters.
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Alphanumeric characters are left unchanged.
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The character _ goes to __
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Characters in the range ASCII space to / go to _A to _P, respectively.
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Other characters go to _nnn where nnn is the decimal ASCII code.*)
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val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
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fun stringN_of_int 0 _ = ""
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| stringN_of_int k n =
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stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
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fun ascii_of_char c =
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if Char.isAlphaNum c then
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String.str c
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else if c = #"_" then
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"__"
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else if #" " <= c andalso c <= #"/" then
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"_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
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else
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(* fixed width, in case more digits follow *)
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"_" ^ stringN_of_int 3 (Char.ord c)
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val ascii_of = String.translate ascii_of_char
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(** Remove ASCII armoring from names in proof files **)
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(* We don't raise error exceptions because this code can run inside a worker
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thread. Also, the errors are impossible. *)
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val unascii_of =
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let
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fun un rcs [] = String.implode(rev rcs)
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| un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
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(* Three types of _ escapes: __, _A to _P, _nnn *)
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| un rcs (#"_" :: #"_" :: cs) = un (#"_"::rcs) cs
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| un rcs (#"_" :: c :: cs) =
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if #"A" <= c andalso c<= #"P" then
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(* translation of #" " to #"/" *)
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un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
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else
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let val digits = List.take (c::cs, 3) handle Subscript => [] in
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case Int.fromString (String.implode digits) of
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blanchet@43926
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SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
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| NONE => un (c:: #"_"::rcs) cs (* ERROR *)
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end
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| un rcs (c :: cs) = un (c :: rcs) cs
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in un [] o String.explode end
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(* If string s has the prefix s1, return the result of deleting it,
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un-ASCII'd. *)
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blanchet@43926
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fun strip_prefix_and_unascii s1 s =
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blanchet@43926
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if String.isPrefix s1 s then
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blanchet@43926
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SOME (unascii_of (String.extract (s, size s1, NONE)))
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else
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blanchet@43926
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NONE
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blanchet@44000
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val proxy_table =
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[("c_False", (@{const_name False}, (@{thm fFalse_def},
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blanchet@44000
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("fFalse", @{const_name ATP.fFalse})))),
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("c_True", (@{const_name True}, (@{thm fTrue_def},
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("fTrue", @{const_name ATP.fTrue})))),
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("c_Not", (@{const_name Not}, (@{thm fNot_def},
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blanchet@44000
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("fNot", @{const_name ATP.fNot})))),
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("c_conj", (@{const_name conj}, (@{thm fconj_def},
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("fconj", @{const_name ATP.fconj})))),
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blanchet@44000
|
275 |
("c_disj", (@{const_name disj}, (@{thm fdisj_def},
|
blanchet@44000
|
276 |
("fdisj", @{const_name ATP.fdisj})))),
|
blanchet@44000
|
277 |
("c_implies", (@{const_name implies}, (@{thm fimplies_def},
|
blanchet@44000
|
278 |
("fimplies", @{const_name ATP.fimplies})))),
|
blanchet@44000
|
279 |
("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
|
blanchet@44000
|
280 |
("fequal", @{const_name ATP.fequal}))))]
|
blanchet@43926
|
281 |
|
blanchet@44000
|
282 |
val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
|
blanchet@43926
|
283 |
|
blanchet@43926
|
284 |
(* Readable names for the more common symbolic functions. Do not mess with the
|
blanchet@43926
|
285 |
table unless you know what you are doing. *)
|
blanchet@43926
|
286 |
val const_trans_table =
|
blanchet@43926
|
287 |
[(@{type_name Product_Type.prod}, "prod"),
|
blanchet@43926
|
288 |
(@{type_name Sum_Type.sum}, "sum"),
|
blanchet@43926
|
289 |
(@{const_name False}, "False"),
|
blanchet@43926
|
290 |
(@{const_name True}, "True"),
|
blanchet@43926
|
291 |
(@{const_name Not}, "Not"),
|
blanchet@43926
|
292 |
(@{const_name conj}, "conj"),
|
blanchet@43926
|
293 |
(@{const_name disj}, "disj"),
|
blanchet@43926
|
294 |
(@{const_name implies}, "implies"),
|
blanchet@43926
|
295 |
(@{const_name HOL.eq}, "equal"),
|
blanchet@43926
|
296 |
(@{const_name If}, "If"),
|
blanchet@43926
|
297 |
(@{const_name Set.member}, "member"),
|
blanchet@43926
|
298 |
(@{const_name Meson.COMBI}, "COMBI"),
|
blanchet@43926
|
299 |
(@{const_name Meson.COMBK}, "COMBK"),
|
blanchet@43926
|
300 |
(@{const_name Meson.COMBB}, "COMBB"),
|
blanchet@43926
|
301 |
(@{const_name Meson.COMBC}, "COMBC"),
|
blanchet@43926
|
302 |
(@{const_name Meson.COMBS}, "COMBS")]
|
blanchet@43926
|
303 |
|> Symtab.make
|
blanchet@44000
|
304 |
|> fold (Symtab.update o swap o snd o snd o snd) proxy_table
|
blanchet@43926
|
305 |
|
blanchet@43926
|
306 |
(* Invert the table of translations between Isabelle and ATPs. *)
|
blanchet@43926
|
307 |
val const_trans_table_inv =
|
blanchet@43926
|
308 |
const_trans_table |> Symtab.dest |> map swap |> Symtab.make
|
blanchet@43926
|
309 |
val const_trans_table_unprox =
|
blanchet@43926
|
310 |
Symtab.empty
|
blanchet@44000
|
311 |
|> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
|
blanchet@43926
|
312 |
|
blanchet@43926
|
313 |
val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
|
blanchet@43926
|
314 |
val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
|
blanchet@43926
|
315 |
|
blanchet@43926
|
316 |
fun lookup_const c =
|
blanchet@43926
|
317 |
case Symtab.lookup const_trans_table c of
|
blanchet@43926
|
318 |
SOME c' => c'
|
blanchet@43926
|
319 |
| NONE => ascii_of c
|
blanchet@43926
|
320 |
|
blanchet@43926
|
321 |
(*Remove the initial ' character from a type variable, if it is present*)
|
blanchet@43926
|
322 |
fun trim_type_var s =
|
blanchet@43926
|
323 |
if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
|
blanchet@43926
|
324 |
else raise Fail ("trim_type: Malformed type variable encountered: " ^ s)
|
blanchet@43926
|
325 |
|
blanchet@43926
|
326 |
fun ascii_of_indexname (v,0) = ascii_of v
|
blanchet@43926
|
327 |
| ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ string_of_int i
|
blanchet@43926
|
328 |
|
blanchet@43926
|
329 |
fun make_bound_var x = bound_var_prefix ^ ascii_of x
|
blanchet@43926
|
330 |
fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
|
blanchet@43926
|
331 |
fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
|
blanchet@43926
|
332 |
|
blanchet@43926
|
333 |
fun make_schematic_type_var (x,i) =
|
blanchet@43926
|
334 |
tvar_prefix ^ (ascii_of_indexname (trim_type_var x, i))
|
blanchet@43926
|
335 |
fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x))
|
blanchet@43926
|
336 |
|
blanchet@43926
|
337 |
(* HOL.eq MUST BE "equal" because it's built into ATPs. *)
|
blanchet@43926
|
338 |
fun make_fixed_const @{const_name HOL.eq} = "equal"
|
blanchet@43926
|
339 |
| make_fixed_const c = const_prefix ^ lookup_const c
|
blanchet@43926
|
340 |
|
blanchet@43926
|
341 |
fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
|
blanchet@43926
|
342 |
|
blanchet@43926
|
343 |
fun make_type_class clas = class_prefix ^ ascii_of clas
|
blanchet@43926
|
344 |
|
blanchet@43934
|
345 |
fun new_skolem_var_name_from_const s =
|
blanchet@43934
|
346 |
let val ss = s |> space_explode Long_Name.separator in
|
blanchet@43934
|
347 |
nth ss (length ss - 2)
|
blanchet@43934
|
348 |
end
|
blanchet@43934
|
349 |
|
blanchet@43934
|
350 |
(* The number of type arguments of a constant, zero if it's monomorphic. For
|
blanchet@43934
|
351 |
(instances of) Skolem pseudoconstants, this information is encoded in the
|
blanchet@43934
|
352 |
constant name. *)
|
blanchet@43934
|
353 |
fun num_type_args thy s =
|
blanchet@43934
|
354 |
if String.isPrefix skolem_const_prefix s then
|
blanchet@43934
|
355 |
s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
|
blanchet@43934
|
356 |
else
|
blanchet@43934
|
357 |
(s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
|
blanchet@43934
|
358 |
|
blanchet@43926
|
359 |
(** Definitions and functions for FOL clauses and formulas for TPTP **)
|
blanchet@43926
|
360 |
|
blanchet@43926
|
361 |
(* The first component is the type class; the second is a "TVar" or "TFree". *)
|
blanchet@43926
|
362 |
datatype type_literal =
|
blanchet@43926
|
363 |
TyLitVar of name * name |
|
blanchet@43926
|
364 |
TyLitFree of name * name
|
blanchet@43926
|
365 |
|
blanchet@43926
|
366 |
|
blanchet@43926
|
367 |
(** Isabelle arities **)
|
blanchet@43926
|
368 |
|
blanchet@43926
|
369 |
datatype arity_literal =
|
blanchet@43926
|
370 |
TConsLit of name * name * name list |
|
blanchet@43926
|
371 |
TVarLit of name * name
|
blanchet@43926
|
372 |
|
blanchet@43926
|
373 |
fun gen_TVars 0 = []
|
blanchet@43934
|
374 |
| gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
|
blanchet@43926
|
375 |
|
blanchet@43926
|
376 |
fun pack_sort (_,[]) = []
|
blanchet@43926
|
377 |
| pack_sort (tvar, "HOL.type" :: srt) =
|
blanchet@43926
|
378 |
pack_sort (tvar, srt) (* IGNORE sort "type" *)
|
blanchet@43926
|
379 |
| pack_sort (tvar, cls :: srt) =
|
blanchet@43926
|
380 |
(`make_type_class cls, `I tvar) :: pack_sort (tvar, srt)
|
blanchet@43926
|
381 |
|
blanchet@43927
|
382 |
type arity_clause =
|
blanchet@43927
|
383 |
{name: string,
|
blanchet@43927
|
384 |
prem_lits: arity_literal list,
|
blanchet@43927
|
385 |
concl_lits: arity_literal}
|
blanchet@43926
|
386 |
|
blanchet@43926
|
387 |
(* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
|
blanchet@43926
|
388 |
fun make_axiom_arity_clause (tcons, name, (cls, args)) =
|
blanchet@43926
|
389 |
let
|
blanchet@43926
|
390 |
val tvars = gen_TVars (length args)
|
blanchet@43926
|
391 |
val tvars_srts = ListPair.zip (tvars, args)
|
blanchet@43926
|
392 |
in
|
blanchet@43927
|
393 |
{name = name,
|
blanchet@43927
|
394 |
prem_lits = map TVarLit (union_all (map pack_sort tvars_srts)),
|
blanchet@43927
|
395 |
concl_lits = TConsLit (`make_type_class cls,
|
blanchet@43927
|
396 |
`make_fixed_type_const tcons,
|
blanchet@43927
|
397 |
tvars ~~ tvars)}
|
blanchet@43926
|
398 |
end
|
blanchet@43926
|
399 |
|
blanchet@43926
|
400 |
fun arity_clause _ _ (_, []) = []
|
blanchet@43926
|
401 |
| arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*)
|
blanchet@43926
|
402 |
arity_clause seen n (tcons,ars)
|
blanchet@43926
|
403 |
| arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
|
blanchet@43926
|
404 |
if member (op =) seen class then (*multiple arities for the same tycon, class pair*)
|
blanchet@43926
|
405 |
make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ string_of_int n, ar) ::
|
blanchet@43926
|
406 |
arity_clause seen (n+1) (tcons,ars)
|
blanchet@43926
|
407 |
else
|
blanchet@43926
|
408 |
make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) ::
|
blanchet@43926
|
409 |
arity_clause (class::seen) n (tcons,ars)
|
blanchet@43926
|
410 |
|
blanchet@43926
|
411 |
fun multi_arity_clause [] = []
|
blanchet@43926
|
412 |
| multi_arity_clause ((tcons, ars) :: tc_arlists) =
|
blanchet@43926
|
413 |
arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
|
blanchet@43926
|
414 |
|
blanchet@43926
|
415 |
(*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
|
blanchet@43926
|
416 |
provided its arguments have the corresponding sorts.*)
|
blanchet@43926
|
417 |
fun type_class_pairs thy tycons classes =
|
blanchet@43934
|
418 |
let
|
blanchet@43934
|
419 |
val alg = Sign.classes_of thy
|
blanchet@43934
|
420 |
fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
|
blanchet@43934
|
421 |
fun add_class tycon class =
|
blanchet@43934
|
422 |
cons (class, domain_sorts tycon class)
|
blanchet@43934
|
423 |
handle Sorts.CLASS_ERROR _ => I
|
blanchet@43934
|
424 |
fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
|
blanchet@43934
|
425 |
in map try_classes tycons end
|
blanchet@43926
|
426 |
|
blanchet@43926
|
427 |
(*Proving one (tycon, class) membership may require proving others, so iterate.*)
|
blanchet@43926
|
428 |
fun iter_type_class_pairs _ _ [] = ([], [])
|
blanchet@43926
|
429 |
| iter_type_class_pairs thy tycons classes =
|
blanchet@43926
|
430 |
let val cpairs = type_class_pairs thy tycons classes
|
blanchet@43926
|
431 |
val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs)))
|
blanchet@43926
|
432 |
|> subtract (op =) classes |> subtract (op =) HOLogic.typeS
|
blanchet@43926
|
433 |
val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
|
blanchet@43934
|
434 |
in (union (op =) classes' classes, union (op =) cpairs' cpairs) end
|
blanchet@43926
|
435 |
|
blanchet@43926
|
436 |
fun make_arity_clauses thy tycons =
|
blanchet@43926
|
437 |
iter_type_class_pairs thy tycons ##> multi_arity_clause
|
blanchet@43926
|
438 |
|
blanchet@43926
|
439 |
|
blanchet@43926
|
440 |
(** Isabelle class relations **)
|
blanchet@43926
|
441 |
|
blanchet@43927
|
442 |
type class_rel_clause =
|
blanchet@43927
|
443 |
{name: string,
|
blanchet@43927
|
444 |
subclass: name,
|
blanchet@43927
|
445 |
superclass: name}
|
blanchet@43926
|
446 |
|
blanchet@43926
|
447 |
(*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
|
blanchet@43926
|
448 |
fun class_pairs _ [] _ = []
|
blanchet@43926
|
449 |
| class_pairs thy subs supers =
|
blanchet@43926
|
450 |
let
|
blanchet@43926
|
451 |
val class_less = Sorts.class_less (Sign.classes_of thy)
|
blanchet@43926
|
452 |
fun add_super sub super = class_less (sub, super) ? cons (sub, super)
|
blanchet@43926
|
453 |
fun add_supers sub = fold (add_super sub) supers
|
blanchet@43926
|
454 |
in fold add_supers subs [] end
|
blanchet@43926
|
455 |
|
blanchet@43926
|
456 |
fun make_class_rel_clause (sub,super) =
|
blanchet@43927
|
457 |
{name = sub ^ "_" ^ super,
|
blanchet@43927
|
458 |
subclass = `make_type_class sub,
|
blanchet@43927
|
459 |
superclass = `make_type_class super}
|
blanchet@43926
|
460 |
|
blanchet@43926
|
461 |
fun make_class_rel_clauses thy subs supers =
|
blanchet@43934
|
462 |
map make_class_rel_clause (class_pairs thy subs supers)
|
blanchet@43926
|
463 |
|
blanchet@43926
|
464 |
datatype combterm =
|
blanchet@43926
|
465 |
CombConst of name * typ * typ list |
|
blanchet@43926
|
466 |
CombVar of name * typ |
|
blanchet@43926
|
467 |
CombApp of combterm * combterm
|
blanchet@43926
|
468 |
|
blanchet@43926
|
469 |
fun combtyp_of (CombConst (_, T, _)) = T
|
blanchet@43926
|
470 |
| combtyp_of (CombVar (_, T)) = T
|
blanchet@43926
|
471 |
| combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
|
blanchet@43926
|
472 |
|
blanchet@43926
|
473 |
(*gets the head of a combinator application, along with the list of arguments*)
|
blanchet@43926
|
474 |
fun strip_combterm_comb u =
|
blanchet@43926
|
475 |
let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
|
blanchet@43926
|
476 |
| stripc x = x
|
blanchet@43926
|
477 |
in stripc(u,[]) end
|
blanchet@43926
|
478 |
|
blanchet@43926
|
479 |
fun atyps_of T = fold_atyps (insert (op =)) T []
|
blanchet@43926
|
480 |
|
blanchet@43926
|
481 |
fun new_skolem_const_name s num_T_args =
|
blanchet@43926
|
482 |
[new_skolem_const_prefix, s, string_of_int num_T_args]
|
blanchet@43926
|
483 |
|> space_implode Long_Name.separator
|
blanchet@43926
|
484 |
|
blanchet@43926
|
485 |
(* Converts a term (with combinators) into a combterm. Also accumulates sort
|
blanchet@43926
|
486 |
infomation. *)
|
blanchet@43926
|
487 |
fun combterm_from_term thy bs (P $ Q) =
|
blanchet@43926
|
488 |
let
|
blanchet@43926
|
489 |
val (P', P_atomics_Ts) = combterm_from_term thy bs P
|
blanchet@43926
|
490 |
val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
|
blanchet@43926
|
491 |
in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
|
blanchet@43926
|
492 |
| combterm_from_term thy _ (Const (c, T)) =
|
blanchet@43926
|
493 |
let
|
blanchet@43926
|
494 |
val tvar_list =
|
blanchet@43926
|
495 |
(if String.isPrefix old_skolem_const_prefix c then
|
blanchet@43926
|
496 |
[] |> Term.add_tvarsT T |> map TVar
|
blanchet@43926
|
497 |
else
|
blanchet@43926
|
498 |
(c, T) |> Sign.const_typargs thy)
|
blanchet@43926
|
499 |
val c' = CombConst (`make_fixed_const c, T, tvar_list)
|
blanchet@43926
|
500 |
in (c', atyps_of T) end
|
blanchet@43926
|
501 |
| combterm_from_term _ _ (Free (v, T)) =
|
blanchet@43926
|
502 |
(CombConst (`make_fixed_var v, T, []), atyps_of T)
|
blanchet@43926
|
503 |
| combterm_from_term _ _ (Var (v as (s, _), T)) =
|
blanchet@43926
|
504 |
(if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
|
blanchet@43926
|
505 |
let
|
blanchet@43926
|
506 |
val Ts = T |> strip_type |> swap |> op ::
|
blanchet@43926
|
507 |
val s' = new_skolem_const_name s (length Ts)
|
blanchet@43926
|
508 |
in CombConst (`make_fixed_const s', T, Ts) end
|
blanchet@43926
|
509 |
else
|
blanchet@43926
|
510 |
CombVar ((make_schematic_var v, s), T), atyps_of T)
|
blanchet@43926
|
511 |
| combterm_from_term _ bs (Bound j) =
|
blanchet@43926
|
512 |
nth bs j
|
blanchet@43926
|
513 |
|> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
|
blanchet@43926
|
514 |
| combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
|
blanchet@43926
|
515 |
|
blanchet@43926
|
516 |
datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
|
blanchet@43926
|
517 |
|
blanchet@43926
|
518 |
(* (quasi-)underapproximation of the truth *)
|
blanchet@43926
|
519 |
fun is_locality_global Local = false
|
blanchet@43926
|
520 |
| is_locality_global Assum = false
|
blanchet@43926
|
521 |
| is_locality_global Chained = false
|
blanchet@43926
|
522 |
| is_locality_global _ = true
|
blanchet@43926
|
523 |
|
blanchet@43484
|
524 |
datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
|
blanchet@43484
|
525 |
datatype type_level =
|
blanchet@43484
|
526 |
All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
|
blanchet@43969
|
527 |
datatype type_heaviness = Heavyweight | Lightweight
|
blanchet@43484
|
528 |
|
blanchet@43943
|
529 |
datatype type_sys =
|
blanchet@43587
|
530 |
Simple_Types of type_level |
|
blanchet@43708
|
531 |
Preds of polymorphism * type_level * type_heaviness |
|
blanchet@43708
|
532 |
Tags of polymorphism * type_level * type_heaviness
|
blanchet@43484
|
533 |
|
blanchet@43559
|
534 |
fun try_unsuffixes ss s =
|
blanchet@43559
|
535 |
fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
|
blanchet@43559
|
536 |
|
blanchet@43484
|
537 |
fun type_sys_from_string s =
|
blanchet@43587
|
538 |
(case try (unprefix "poly_") s of
|
blanchet@43587
|
539 |
SOME s => (SOME Polymorphic, s)
|
blanchet@43484
|
540 |
| NONE =>
|
blanchet@43484
|
541 |
case try (unprefix "mono_") s of
|
blanchet@43587
|
542 |
SOME s => (SOME Monomorphic, s)
|
blanchet@43587
|
543 |
| NONE =>
|
blanchet@43587
|
544 |
case try (unprefix "mangled_") s of
|
blanchet@43587
|
545 |
SOME s => (SOME Mangled_Monomorphic, s)
|
blanchet@43587
|
546 |
| NONE => (NONE, s))
|
blanchet@43484
|
547 |
||> (fn s =>
|
blanchet@43559
|
548 |
(* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
|
blanchet@43559
|
549 |
case try_unsuffixes ["?", "_query"] s of
|
blanchet@43484
|
550 |
SOME s => (Nonmonotonic_Types, s)
|
blanchet@43484
|
551 |
| NONE =>
|
blanchet@43559
|
552 |
case try_unsuffixes ["!", "_bang"] s of
|
blanchet@43484
|
553 |
SOME s => (Finite_Types, s)
|
blanchet@43484
|
554 |
| NONE => (All_Types, s))
|
blanchet@43699
|
555 |
||> apsnd (fn s =>
|
blanchet@43708
|
556 |
case try (unsuffix "_heavy") s of
|
blanchet@43969
|
557 |
SOME s => (Heavyweight, s)
|
blanchet@43969
|
558 |
| NONE => (Lightweight, s))
|
blanchet@43708
|
559 |
|> (fn (poly, (level, (heaviness, core))) =>
|
blanchet@43708
|
560 |
case (core, (poly, level, heaviness)) of
|
blanchet@43969
|
561 |
("simple", (NONE, _, Lightweight)) => Simple_Types level
|
blanchet@43723
|
562 |
| ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
|
blanchet@43720
|
563 |
| ("tags", (SOME Polymorphic, All_Types, _)) =>
|
blanchet@43723
|
564 |
Tags (Polymorphic, All_Types, heaviness)
|
blanchet@43755
|
565 |
| ("tags", (SOME Polymorphic, _, _)) =>
|
blanchet@43755
|
566 |
(* The actual light encoding is very unsound. *)
|
blanchet@43969
|
567 |
Tags (Polymorphic, level, Heavyweight)
|
blanchet@43723
|
568 |
| ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
|
blanchet@43969
|
569 |
| ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
|
blanchet@43969
|
570 |
Preds (poly, Const_Arg_Types, Lightweight)
|
blanchet@43969
|
571 |
| ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
|
blanchet@43969
|
572 |
Preds (Polymorphic, No_Types, Lightweight)
|
blanchet@43618
|
573 |
| _ => raise Same.SAME)
|
blanchet@43618
|
574 |
handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
|
blanchet@43484
|
575 |
|
blanchet@43587
|
576 |
fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
|
blanchet@43699
|
577 |
| polymorphism_of_type_sys (Preds (poly, _, _)) = poly
|
blanchet@43699
|
578 |
| polymorphism_of_type_sys (Tags (poly, _, _)) = poly
|
blanchet@43484
|
579 |
|
blanchet@43587
|
580 |
fun level_of_type_sys (Simple_Types level) = level
|
blanchet@43699
|
581 |
| level_of_type_sys (Preds (_, level, _)) = level
|
blanchet@43699
|
582 |
| level_of_type_sys (Tags (_, level, _)) = level
|
blanchet@43699
|
583 |
|
blanchet@43969
|
584 |
fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
|
blanchet@43708
|
585 |
| heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
|
blanchet@43708
|
586 |
| heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
|
blanchet@43702
|
587 |
|
blanchet@43557
|
588 |
fun is_type_level_virtually_sound level =
|
blanchet@43557
|
589 |
level = All_Types orelse level = Nonmonotonic_Types
|
blanchet@43484
|
590 |
val is_type_sys_virtually_sound =
|
blanchet@43484
|
591 |
is_type_level_virtually_sound o level_of_type_sys
|
blanchet@43484
|
592 |
|
blanchet@43484
|
593 |
fun is_type_level_fairly_sound level =
|
blanchet@43484
|
594 |
is_type_level_virtually_sound level orelse level = Finite_Types
|
blanchet@43484
|
595 |
val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
|
blanchet@43484
|
596 |
|
blanchet@43835
|
597 |
fun is_setting_higher_order THF (Simple_Types _) = true
|
blanchet@43835
|
598 |
| is_setting_higher_order _ _ = false
|
blanchet@43835
|
599 |
|
blanchet@43942
|
600 |
fun choose_format formats (Simple_Types level) =
|
blanchet@43942
|
601 |
if member (op =) formats THF then (THF, Simple_Types level)
|
blanchet@43942
|
602 |
else if member (op =) formats TFF then (TFF, Simple_Types level)
|
blanchet@43969
|
603 |
else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
|
blanchet@43942
|
604 |
| choose_format formats type_sys =
|
blanchet@43942
|
605 |
(case hd formats of
|
blanchet@43942
|
606 |
CNF_UEQ =>
|
blanchet@43942
|
607 |
(CNF_UEQ, case type_sys of
|
blanchet@43942
|
608 |
Preds stuff =>
|
blanchet@43942
|
609 |
(if is_type_sys_fairly_sound type_sys then Preds else Tags)
|
blanchet@43942
|
610 |
stuff
|
blanchet@43942
|
611 |
| _ => type_sys)
|
blanchet@43942
|
612 |
| format => (format, type_sys))
|
blanchet@43942
|
613 |
|
blanchet@40358
|
614 |
type translated_formula =
|
blanchet@38991
|
615 |
{name: string,
|
blanchet@43511
|
616 |
locality: locality,
|
blanchet@43396
|
617 |
kind: formula_kind,
|
blanchet@43433
|
618 |
combformula: (name, typ, combterm) formula,
|
blanchet@43433
|
619 |
atomic_types: typ list}
|
blanchet@38506
|
620 |
|
blanchet@43511
|
621 |
fun update_combformula f ({name, locality, kind, combformula, atomic_types}
|
blanchet@43511
|
622 |
: translated_formula) =
|
blanchet@43511
|
623 |
{name = name, locality = locality, kind = kind, combformula = f combformula,
|
blanchet@43433
|
624 |
atomic_types = atomic_types} : translated_formula
|
blanchet@43413
|
625 |
|
blanchet@43429
|
626 |
fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
|
blanchet@43429
|
627 |
|
blanchet@43905
|
628 |
val type_instance = Sign.typ_instance o Proof_Context.theory_of
|
blanchet@43905
|
629 |
|
blanchet@43905
|
630 |
fun insert_type ctxt get_T x xs =
|
blanchet@43905
|
631 |
let val T = get_T x in
|
blanchet@43905
|
632 |
if exists (curry (type_instance ctxt) T o get_T) xs then xs
|
blanchet@43905
|
633 |
else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
|
blanchet@43905
|
634 |
end
|
blanchet@43547
|
635 |
|
blanchet@43618
|
636 |
(* The Booleans indicate whether all type arguments should be kept. *)
|
blanchet@43618
|
637 |
datatype type_arg_policy =
|
blanchet@43618
|
638 |
Explicit_Type_Args of bool |
|
blanchet@43618
|
639 |
Mangled_Type_Args of bool |
|
blanchet@43618
|
640 |
No_Type_Args
|
blanchet@41384
|
641 |
|
blanchet@43707
|
642 |
fun should_drop_arg_type_args (Simple_Types _) =
|
blanchet@43707
|
643 |
false (* since TFF doesn't support overloading *)
|
blanchet@43707
|
644 |
| should_drop_arg_type_args type_sys =
|
blanchet@43707
|
645 |
level_of_type_sys type_sys = All_Types andalso
|
blanchet@43969
|
646 |
heaviness_of_type_sys type_sys = Heavyweight
|
blanchet@43702
|
647 |
|
blanchet@43969
|
648 |
fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
|
blanchet@43946
|
649 |
| general_type_arg_policy type_sys =
|
blanchet@43946
|
650 |
if level_of_type_sys type_sys = No_Types then
|
blanchet@43946
|
651 |
No_Type_Args
|
blanchet@43946
|
652 |
else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
|
blanchet@43946
|
653 |
Mangled_Type_Args (should_drop_arg_type_args type_sys)
|
blanchet@43946
|
654 |
else
|
blanchet@43946
|
655 |
Explicit_Type_Args (should_drop_arg_type_args type_sys)
|
blanchet@43434
|
656 |
|
blanchet@43792
|
657 |
fun type_arg_policy type_sys s =
|
blanchet@43792
|
658 |
if s = @{const_name HOL.eq} orelse
|
blanchet@43807
|
659 |
(s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
|
blanchet@43792
|
660 |
No_Type_Args
|
blanchet@43946
|
661 |
else if s = type_tag_name then
|
blanchet@43946
|
662 |
Explicit_Type_Args false
|
blanchet@43792
|
663 |
else
|
blanchet@43792
|
664 |
general_type_arg_policy type_sys
|
blanchet@43088
|
665 |
|
blanchet@43926
|
666 |
(*Make literals for sorted type variables*)
|
blanchet@43939
|
667 |
fun generic_sorts_on_type (_, []) = []
|
blanchet@43939
|
668 |
| generic_sorts_on_type ((x, i), s :: ss) =
|
blanchet@43939
|
669 |
generic_sorts_on_type ((x, i), ss)
|
blanchet@43934
|
670 |
|> (if s = the_single @{sort HOL.type} then
|
blanchet@43934
|
671 |
I
|
blanchet@43934
|
672 |
else if i = ~1 then
|
blanchet@43934
|
673 |
cons (TyLitFree (`make_type_class s, `make_fixed_type_var x))
|
blanchet@43934
|
674 |
else
|
blanchet@43934
|
675 |
cons (TyLitVar (`make_type_class s,
|
blanchet@43934
|
676 |
(make_schematic_type_var (x, i), x))))
|
blanchet@43939
|
677 |
fun sorts_on_tfree (TFree (s, S)) = generic_sorts_on_type ((s, ~1), S)
|
blanchet@43939
|
678 |
| sorts_on_tfree _ = []
|
blanchet@43939
|
679 |
fun sorts_on_tvar (TVar z) = generic_sorts_on_type z
|
blanchet@43939
|
680 |
| sorts_on_tvar _ = []
|
blanchet@43926
|
681 |
|
blanchet@43939
|
682 |
(* Given a list of sorted type variables, return a list of type literals. *)
|
blanchet@43939
|
683 |
fun raw_type_literals_for_types Ts =
|
blanchet@43939
|
684 |
union_all (map sorts_on_tfree Ts @ map sorts_on_tvar Ts)
|
blanchet@43926
|
685 |
|
blanchet@43939
|
686 |
fun type_literals_for_types type_sys sorts_on_typ Ts =
|
blanchet@43939
|
687 |
if level_of_type_sys type_sys = No_Types then []
|
blanchet@43939
|
688 |
else union_all (map sorts_on_typ Ts)
|
blanchet@41385
|
689 |
|
blanchet@43405
|
690 |
fun mk_aconns c phis =
|
blanchet@43405
|
691 |
let val (phis', phi') = split_last phis in
|
blanchet@43405
|
692 |
fold_rev (mk_aconn c) phis' phi'
|
blanchet@43405
|
693 |
end
|
blanchet@38506
|
694 |
fun mk_ahorn [] phi = phi
|
blanchet@43405
|
695 |
| mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
|
blanchet@43393
|
696 |
fun mk_aquant _ [] phi = phi
|
blanchet@43393
|
697 |
| mk_aquant q xs (phi as AQuant (q', xs', phi')) =
|
blanchet@43393
|
698 |
if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
|
blanchet@43393
|
699 |
| mk_aquant q xs phi = AQuant (q, xs, phi)
|
blanchet@38506
|
700 |
|
blanchet@43393
|
701 |
fun close_universally atom_vars phi =
|
blanchet@41393
|
702 |
let
|
blanchet@41393
|
703 |
fun formula_vars bounds (AQuant (_, xs, phi)) =
|
blanchet@43397
|
704 |
formula_vars (map fst xs @ bounds) phi
|
blanchet@41393
|
705 |
| formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
|
blanchet@43393
|
706 |
| formula_vars bounds (AAtom tm) =
|
blanchet@43397
|
707 |
union (op =) (atom_vars tm []
|
blanchet@43397
|
708 |
|> filter_out (member (op =) bounds o fst))
|
blanchet@43393
|
709 |
in mk_aquant AForall (formula_vars [] phi []) phi end
|
blanchet@43393
|
710 |
|
blanchet@43402
|
711 |
fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
|
blanchet@43393
|
712 |
| combterm_vars (CombConst _) = I
|
blanchet@43445
|
713 |
| combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
|
blanchet@43545
|
714 |
fun close_combformula_universally phi = close_universally combterm_vars phi
|
blanchet@43393
|
715 |
|
blanchet@43393
|
716 |
fun term_vars (ATerm (name as (s, _), tms)) =
|
blanchet@43839
|
717 |
is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
|
blanchet@43545
|
718 |
fun close_formula_universally phi = close_universally term_vars phi
|
blanchet@41393
|
719 |
|
blanchet@43835
|
720 |
val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
|
blanchet@43835
|
721 |
val homo_infinite_type = Type (homo_infinite_type_name, [])
|
blanchet@43835
|
722 |
|
blanchet@44019
|
723 |
fun fo_term_from_typ format type_sys =
|
blanchet@43835
|
724 |
let
|
blanchet@43835
|
725 |
fun term (Type (s, Ts)) =
|
blanchet@44019
|
726 |
ATerm (case (is_setting_higher_order format type_sys, s) of
|
blanchet@43835
|
727 |
(true, @{type_name bool}) => `I tptp_bool_type
|
blanchet@43835
|
728 |
| (true, @{type_name fun}) => `I tptp_fun_type
|
blanchet@44019
|
729 |
| _ => if s = homo_infinite_type_name andalso
|
blanchet@44019
|
730 |
(format = TFF orelse format = THF) then
|
blanchet@44019
|
731 |
`I tptp_individual_type
|
blanchet@44019
|
732 |
else
|
blanchet@44019
|
733 |
`make_fixed_type_const s,
|
blanchet@43835
|
734 |
map term Ts)
|
blanchet@43835
|
735 |
| term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
|
blanchet@43835
|
736 |
| term (TVar ((x as (s, _)), _)) =
|
blanchet@43835
|
737 |
ATerm ((make_schematic_type_var x, s), [])
|
blanchet@43835
|
738 |
in term end
|
blanchet@43433
|
739 |
|
blanchet@43433
|
740 |
(* This shouldn't clash with anything else. *)
|
blanchet@43413
|
741 |
val mangled_type_sep = "\000"
|
blanchet@43413
|
742 |
|
blanchet@43433
|
743 |
fun generic_mangled_type_name f (ATerm (name, [])) = f name
|
blanchet@43433
|
744 |
| generic_mangled_type_name f (ATerm (name, tys)) =
|
blanchet@43626
|
745 |
f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
|
blanchet@43626
|
746 |
^ ")"
|
blanchet@43413
|
747 |
|
blanchet@43839
|
748 |
val bool_atype = AType (`I tptp_bool_type)
|
blanchet@43839
|
749 |
|
blanchet@43926
|
750 |
fun make_simple_type s =
|
blanchet@43926
|
751 |
if s = tptp_bool_type orelse s = tptp_fun_type orelse
|
blanchet@43926
|
752 |
s = tptp_individual_type then
|
blanchet@43926
|
753 |
s
|
blanchet@43926
|
754 |
else
|
blanchet@43926
|
755 |
simple_type_prefix ^ ascii_of s
|
blanchet@43926
|
756 |
|
blanchet@44019
|
757 |
fun ho_type_from_fo_term format type_sys pred_sym ary =
|
blanchet@43804
|
758 |
let
|
blanchet@43804
|
759 |
fun to_atype ty =
|
blanchet@43804
|
760 |
AType ((make_simple_type (generic_mangled_type_name fst ty),
|
blanchet@43804
|
761 |
generic_mangled_type_name snd ty))
|
blanchet@43804
|
762 |
fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
|
blanchet@43839
|
763 |
fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
|
blanchet@43835
|
764 |
| to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
|
blanchet@43835
|
765 |
fun to_ho (ty as ATerm ((s, _), tys)) =
|
blanchet@43835
|
766 |
if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
|
blanchet@44019
|
767 |
in if is_setting_higher_order format type_sys then to_ho else to_fo ary end
|
blanchet@43804
|
768 |
|
blanchet@44019
|
769 |
fun mangled_type format type_sys pred_sym ary =
|
blanchet@44019
|
770 |
ho_type_from_fo_term format type_sys pred_sym ary
|
blanchet@44019
|
771 |
o fo_term_from_typ format type_sys
|
blanchet@43804
|
772 |
|
blanchet@44019
|
773 |
fun mangled_const_name format type_sys T_args (s, s') =
|
blanchet@43804
|
774 |
let
|
blanchet@44019
|
775 |
val ty_args = map (fo_term_from_typ format type_sys) T_args
|
blanchet@43804
|
776 |
fun type_suffix f g =
|
blanchet@43804
|
777 |
fold_rev (curry (op ^) o g o prefix mangled_type_sep
|
blanchet@43804
|
778 |
o generic_mangled_type_name f) ty_args ""
|
blanchet@43804
|
779 |
in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
|
blanchet@43413
|
780 |
|
blanchet@43413
|
781 |
val parse_mangled_ident =
|
blanchet@43413
|
782 |
Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
|
blanchet@43413
|
783 |
|
blanchet@43413
|
784 |
fun parse_mangled_type x =
|
blanchet@43413
|
785 |
(parse_mangled_ident
|
blanchet@43413
|
786 |
-- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
|
blanchet@43413
|
787 |
[] >> ATerm) x
|
blanchet@43413
|
788 |
and parse_mangled_types x =
|
blanchet@43413
|
789 |
(parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
|
blanchet@43413
|
790 |
|
blanchet@43413
|
791 |
fun unmangled_type s =
|
blanchet@43413
|
792 |
s |> suffix ")" |> raw_explode
|
blanchet@43413
|
793 |
|> Scan.finite Symbol.stopper
|
blanchet@43413
|
794 |
(Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
|
blanchet@43413
|
795 |
quote s)) parse_mangled_type))
|
blanchet@43413
|
796 |
|> fst
|
blanchet@43413
|
797 |
|
blanchet@43432
|
798 |
val unmangled_const_name = space_explode mangled_type_sep #> hd
|
blanchet@43413
|
799 |
fun unmangled_const s =
|
blanchet@43413
|
800 |
let val ss = space_explode mangled_type_sep s in
|
blanchet@43413
|
801 |
(hd ss, map unmangled_type (tl ss))
|
blanchet@43413
|
802 |
end
|
blanchet@43413
|
803 |
|
blanchet@43858
|
804 |
fun introduce_proxies format type_sys =
|
blanchet@43439
|
805 |
let
|
blanchet@43858
|
806 |
fun intro top_level (CombApp (tm1, tm2)) =
|
blanchet@43858
|
807 |
CombApp (intro top_level tm1, intro false tm2)
|
blanchet@43858
|
808 |
| intro top_level (CombConst (name as (s, _), T, T_args)) =
|
blanchet@43441
|
809 |
(case proxify_const s of
|
blanchet@44000
|
810 |
SOME proxy_base =>
|
blanchet@43841
|
811 |
if top_level orelse is_setting_higher_order format type_sys then
|
blanchet@43841
|
812 |
case (top_level, s) of
|
blanchet@43841
|
813 |
(_, "c_False") => (`I tptp_false, [])
|
blanchet@43841
|
814 |
| (_, "c_True") => (`I tptp_true, [])
|
blanchet@43841
|
815 |
| (false, "c_Not") => (`I tptp_not, [])
|
blanchet@43841
|
816 |
| (false, "c_conj") => (`I tptp_and, [])
|
blanchet@43841
|
817 |
| (false, "c_disj") => (`I tptp_or, [])
|
blanchet@43841
|
818 |
| (false, "c_implies") => (`I tptp_implies, [])
|
blanchet@43841
|
819 |
| (false, s) =>
|
blanchet@43858
|
820 |
if is_tptp_equal s then (`I tptp_equal, [])
|
blanchet@43858
|
821 |
else (proxy_base |>> prefix const_prefix, T_args)
|
blanchet@43841
|
822 |
| _ => (name, [])
|
blanchet@43440
|
823 |
else
|
blanchet@43445
|
824 |
(proxy_base |>> prefix const_prefix, T_args)
|
blanchet@43445
|
825 |
| NONE => (name, T_args))
|
blanchet@43445
|
826 |
|> (fn (name, T_args) => CombConst (name, T, T_args))
|
blanchet@43858
|
827 |
| intro _ tm = tm
|
blanchet@43858
|
828 |
in intro true end
|
blanchet@43439
|
829 |
|
blanchet@43835
|
830 |
fun combformula_from_prop thy format type_sys eq_as_iff =
|
blanchet@38506
|
831 |
let
|
blanchet@43439
|
832 |
fun do_term bs t atomic_types =
|
blanchet@41388
|
833 |
combterm_from_term thy bs (Envir.eta_contract t)
|
blanchet@43835
|
834 |
|>> (introduce_proxies format type_sys #> AAtom)
|
blanchet@43439
|
835 |
||> union (op =) atomic_types
|
blanchet@38506
|
836 |
fun do_quant bs q s T t' =
|
blanchet@38743
|
837 |
let val s = Name.variant (map fst bs) s in
|
blanchet@38743
|
838 |
do_formula ((s, T) :: bs) t'
|
blanchet@43433
|
839 |
#>> mk_aquant q [(`make_bound_var s, SOME T)]
|
blanchet@38743
|
840 |
end
|
blanchet@38506
|
841 |
and do_conn bs c t1 t2 =
|
blanchet@44039
|
842 |
do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
|
blanchet@38506
|
843 |
and do_formula bs t =
|
blanchet@38506
|
844 |
case t of
|
blanchet@43937
|
845 |
@{const Trueprop} $ t1 => do_formula bs t1
|
blanchet@43937
|
846 |
| @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
|
blanchet@38506
|
847 |
| Const (@{const_name All}, _) $ Abs (s, T, t') =>
|
blanchet@38506
|
848 |
do_quant bs AForall s T t'
|
blanchet@38506
|
849 |
| Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
|
blanchet@38506
|
850 |
do_quant bs AExists s T t'
|
haftmann@39028
|
851 |
| @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
|
haftmann@39028
|
852 |
| @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
|
haftmann@39019
|
853 |
| @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
|
haftmann@39093
|
854 |
| Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
|
blanchet@41388
|
855 |
if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
|
blanchet@41388
|
856 |
| _ => do_term bs t
|
blanchet@38506
|
857 |
in do_formula [] end
|
blanchet@38506
|
858 |
|
blanchet@43615
|
859 |
fun presimplify_term ctxt =
|
blanchet@43615
|
860 |
Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
|
blanchet@43615
|
861 |
#> Meson.presimplify ctxt
|
blanchet@43615
|
862 |
#> prop_of
|
blanchet@38506
|
863 |
|
wenzelm@41739
|
864 |
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
|
blanchet@38506
|
865 |
fun conceal_bounds Ts t =
|
blanchet@38506
|
866 |
subst_bounds (map (Free o apfst concealed_bound_name)
|
blanchet@38506
|
867 |
(0 upto length Ts - 1 ~~ Ts), t)
|
blanchet@38506
|
868 |
fun reveal_bounds Ts =
|
blanchet@38506
|
869 |
subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
|
blanchet@38506
|
870 |
(0 upto length Ts - 1 ~~ Ts))
|
blanchet@38506
|
871 |
|
blanchet@43612
|
872 |
fun extensionalize_term ctxt t =
|
blanchet@43612
|
873 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@43612
|
874 |
t |> cterm_of thy |> Meson.extensionalize_conv ctxt
|
blanchet@43612
|
875 |
|> prop_of |> Logic.dest_equals |> snd
|
blanchet@43612
|
876 |
end
|
blanchet@38831
|
877 |
|
blanchet@38506
|
878 |
fun introduce_combinators_in_term ctxt kind t =
|
wenzelm@43232
|
879 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@38716
|
880 |
if Meson.is_fol_term thy t then
|
blanchet@38716
|
881 |
t
|
blanchet@38716
|
882 |
else
|
blanchet@38716
|
883 |
let
|
blanchet@38716
|
884 |
fun aux Ts t =
|
blanchet@38716
|
885 |
case t of
|
blanchet@38716
|
886 |
@{const Not} $ t1 => @{const Not} $ aux Ts t1
|
blanchet@38716
|
887 |
| (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
|
blanchet@38716
|
888 |
t0 $ Abs (s, T, aux (T :: Ts) t')
|
blanchet@38890
|
889 |
| (t0 as Const (@{const_name All}, _)) $ t1 =>
|
blanchet@38890
|
890 |
aux Ts (t0 $ eta_expand Ts t1 1)
|
blanchet@38716
|
891 |
| (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
|
blanchet@38716
|
892 |
t0 $ Abs (s, T, aux (T :: Ts) t')
|
blanchet@38890
|
893 |
| (t0 as Const (@{const_name Ex}, _)) $ t1 =>
|
blanchet@38890
|
894 |
aux Ts (t0 $ eta_expand Ts t1 1)
|
haftmann@39028
|
895 |
| (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39028
|
896 |
| (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39019
|
897 |
| (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39093
|
898 |
| (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
|
blanchet@38716
|
899 |
$ t1 $ t2 =>
|
blanchet@38716
|
900 |
t0 $ aux Ts t1 $ aux Ts t2
|
blanchet@38716
|
901 |
| _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
|
blanchet@38716
|
902 |
t
|
blanchet@38716
|
903 |
else
|
blanchet@38716
|
904 |
t |> conceal_bounds Ts
|
blanchet@38716
|
905 |
|> Envir.eta_contract
|
blanchet@38716
|
906 |
|> cterm_of thy
|
blanchet@40071
|
907 |
|> Meson_Clausify.introduce_combinators_in_cterm
|
blanchet@38716
|
908 |
|> prop_of |> Logic.dest_equals |> snd
|
blanchet@38716
|
909 |
|> reveal_bounds Ts
|
blanchet@39616
|
910 |
val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
|
blanchet@38716
|
911 |
in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
|
blanchet@38716
|
912 |
handle THM _ =>
|
blanchet@38716
|
913 |
(* A type variable of sort "{}" will make abstraction fail. *)
|
blanchet@38836
|
914 |
if kind = Conjecture then HOLogic.false_const
|
blanchet@38836
|
915 |
else HOLogic.true_const
|
blanchet@38716
|
916 |
end
|
blanchet@38506
|
917 |
|
blanchet@38506
|
918 |
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
|
blanchet@43224
|
919 |
same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
|
blanchet@38506
|
920 |
fun freeze_term t =
|
blanchet@38506
|
921 |
let
|
blanchet@38506
|
922 |
fun aux (t $ u) = aux t $ aux u
|
blanchet@38506
|
923 |
| aux (Abs (s, T, t)) = Abs (s, T, aux t)
|
blanchet@38506
|
924 |
| aux (Var ((s, i), T)) =
|
blanchet@38506
|
925 |
Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
|
blanchet@38506
|
926 |
| aux t = t
|
blanchet@38506
|
927 |
in t |> exists_subterm is_Var t ? aux end
|
blanchet@38506
|
928 |
|
blanchet@43937
|
929 |
fun preprocess_prop ctxt presimp kind t =
|
blanchet@38506
|
930 |
let
|
wenzelm@43232
|
931 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@38831
|
932 |
val t = t |> Envir.beta_eta_contract
|
blanchet@43785
|
933 |
|> transform_elim_prop
|
blanchet@41459
|
934 |
|> Object_Logic.atomize_term thy
|
blanchet@43434
|
935 |
val need_trueprop = (fastype_of t = @{typ bool})
|
blanchet@43937
|
936 |
in
|
blanchet@43937
|
937 |
t |> need_trueprop ? HOLogic.mk_Trueprop
|
blanchet@43937
|
938 |
|> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
|
blanchet@43937
|
939 |
|> extensionalize_term ctxt
|
blanchet@43937
|
940 |
|> presimp ? presimplify_term ctxt
|
blanchet@43961
|
941 |
|> perhaps (try (HOLogic.dest_Trueprop))
|
blanchet@43937
|
942 |
|> introduce_combinators_in_term ctxt kind
|
blanchet@43937
|
943 |
end
|
blanchet@43937
|
944 |
|
blanchet@43937
|
945 |
(* making fact and conjecture formulas *)
|
blanchet@43937
|
946 |
fun make_formula thy format type_sys eq_as_iff name loc kind t =
|
blanchet@43937
|
947 |
let
|
blanchet@43803
|
948 |
val (combformula, atomic_types) =
|
blanchet@43835
|
949 |
combformula_from_prop thy format type_sys eq_as_iff t []
|
blanchet@38506
|
950 |
in
|
blanchet@43511
|
951 |
{name = name, locality = loc, kind = kind, combformula = combformula,
|
blanchet@43433
|
952 |
atomic_types = atomic_types}
|
blanchet@38506
|
953 |
end
|
blanchet@38506
|
954 |
|
blanchet@43937
|
955 |
fun make_fact ctxt format type_sys keep_trivial eq_as_iff preproc presimp
|
blanchet@43835
|
956 |
((name, loc), t) =
|
blanchet@43937
|
957 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@43937
|
958 |
case (keep_trivial,
|
blanchet@43937
|
959 |
t |> preproc ? preprocess_prop ctxt presimp Axiom
|
blanchet@43937
|
960 |
|> make_formula thy format type_sys eq_as_iff name loc Axiom) of
|
blanchet@43937
|
961 |
(false,
|
blanchet@43937
|
962 |
formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...}) =>
|
blanchet@43937
|
963 |
if s = tptp_true then NONE else SOME formula
|
blanchet@43937
|
964 |
| (_, formula) => SOME formula
|
blanchet@43937
|
965 |
end
|
blanchet@43432
|
966 |
|
blanchet@43937
|
967 |
fun make_conjecture ctxt format prem_kind type_sys preproc ts =
|
blanchet@43937
|
968 |
let
|
blanchet@43937
|
969 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@43937
|
970 |
val last = length ts - 1
|
blanchet@43937
|
971 |
in
|
blanchet@43580
|
972 |
map2 (fn j => fn t =>
|
blanchet@43580
|
973 |
let
|
blanchet@43580
|
974 |
val (kind, maybe_negate) =
|
blanchet@43580
|
975 |
if j = last then
|
blanchet@43580
|
976 |
(Conjecture, I)
|
blanchet@43580
|
977 |
else
|
blanchet@43580
|
978 |
(prem_kind,
|
blanchet@43580
|
979 |
if prem_kind = Conjecture then update_combformula mk_anot
|
blanchet@43580
|
980 |
else I)
|
blanchet@43580
|
981 |
in
|
blanchet@43939
|
982 |
t |> preproc ? (preprocess_prop ctxt true kind #> freeze_term)
|
blanchet@44034
|
983 |
|> make_formula thy format type_sys (format <> CNF)
|
blanchet@44034
|
984 |
(string_of_int j) General kind
|
blanchet@43803
|
985 |
|> maybe_negate
|
blanchet@43580
|
986 |
end)
|
blanchet@38836
|
987 |
(0 upto last) ts
|
blanchet@38836
|
988 |
end
|
blanchet@38506
|
989 |
|
blanchet@43552
|
990 |
(** Finite and infinite type inference **)
|
blanchet@43552
|
991 |
|
blanchet@43755
|
992 |
fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
|
blanchet@43755
|
993 |
| deep_freeze_atyp T = T
|
blanchet@43755
|
994 |
val deep_freeze_type = map_atyps deep_freeze_atyp
|
blanchet@43755
|
995 |
|
blanchet@43552
|
996 |
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
|
blanchet@43552
|
997 |
dangerous because their "exhaust" properties can easily lead to unsound ATP
|
blanchet@43552
|
998 |
proofs. On the other hand, all HOL infinite types can be given the same
|
blanchet@43552
|
999 |
models in first-order logic (via Löwenheim-Skolem). *)
|
blanchet@43552
|
1000 |
|
blanchet@43755
|
1001 |
fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
|
blanchet@43755
|
1002 |
exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
|
blanchet@43707
|
1003 |
| should_encode_type _ _ All_Types _ = true
|
blanchet@43552
|
1004 |
| should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
|
blanchet@43552
|
1005 |
| should_encode_type _ _ _ _ = false
|
blanchet@43552
|
1006 |
|
blanchet@43708
|
1007 |
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
|
blanchet@43705
|
1008 |
should_predicate_on_var T =
|
blanchet@43969
|
1009 |
(heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
|
blanchet@43747
|
1010 |
should_encode_type ctxt nonmono_Ts level T
|
blanchet@43705
|
1011 |
| should_predicate_on_type _ _ _ _ _ = false
|
blanchet@43552
|
1012 |
|
blanchet@43707
|
1013 |
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
|
blanchet@43707
|
1014 |
String.isPrefix bound_var_prefix s
|
blanchet@43707
|
1015 |
| is_var_or_bound_var (CombVar _) = true
|
blanchet@43707
|
1016 |
| is_var_or_bound_var _ = false
|
blanchet@43707
|
1017 |
|
blanchet@43700
|
1018 |
datatype tag_site = Top_Level | Eq_Arg | Elsewhere
|
blanchet@43700
|
1019 |
|
blanchet@43700
|
1020 |
fun should_tag_with_type _ _ _ Top_Level _ _ = false
|
blanchet@43708
|
1021 |
| should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
|
blanchet@43708
|
1022 |
(case heaviness of
|
blanchet@43969
|
1023 |
Heavyweight => should_encode_type ctxt nonmono_Ts level T
|
blanchet@43969
|
1024 |
| Lightweight =>
|
blanchet@43707
|
1025 |
case (site, is_var_or_bound_var u) of
|
blanchet@43707
|
1026 |
(Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
|
blanchet@43700
|
1027 |
| _ => false)
|
blanchet@43700
|
1028 |
| should_tag_with_type _ _ _ _ _ _ = false
|
blanchet@43552
|
1029 |
|
blanchet@43835
|
1030 |
fun homogenized_type ctxt nonmono_Ts level =
|
blanchet@43835
|
1031 |
let
|
blanchet@43835
|
1032 |
val should_encode = should_encode_type ctxt nonmono_Ts level
|
blanchet@43835
|
1033 |
fun homo 0 T = if should_encode T then T else homo_infinite_type
|
blanchet@43835
|
1034 |
| homo ary (Type (@{type_name fun}, [T1, T2])) =
|
blanchet@43835
|
1035 |
homo 0 T1 --> homo (ary - 1) T2
|
blanchet@43835
|
1036 |
| homo _ _ = raise Fail "expected function type"
|
blanchet@43835
|
1037 |
in homo end
|
blanchet@43552
|
1038 |
|
blanchet@43444
|
1039 |
(** "hBOOL" and "hAPP" **)
|
blanchet@41561
|
1040 |
|
blanchet@43445
|
1041 |
type sym_info =
|
blanchet@43905
|
1042 |
{pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
|
blanchet@43434
|
1043 |
|
blanchet@43905
|
1044 |
fun add_combterm_syms_to_table ctxt explicit_apply =
|
blanchet@43429
|
1045 |
let
|
blanchet@43905
|
1046 |
fun consider_var_arity const_T var_T max_ary =
|
blanchet@43905
|
1047 |
let
|
blanchet@43905
|
1048 |
fun iter ary T =
|
blanchet@43905
|
1049 |
if ary = max_ary orelse type_instance ctxt (var_T, T) then ary
|
blanchet@43905
|
1050 |
else iter (ary + 1) (range_type T)
|
blanchet@43905
|
1051 |
in iter 0 const_T end
|
blanchet@44042
|
1052 |
fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
|
blanchet@44042
|
1053 |
if explicit_apply = NONE andalso
|
blanchet@44042
|
1054 |
(can dest_funT T orelse T = @{typ bool}) then
|
blanchet@44042
|
1055 |
let
|
blanchet@44042
|
1056 |
val bool_vars' = bool_vars orelse body_type T = @{typ bool}
|
blanchet@44042
|
1057 |
fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
|
blanchet@44042
|
1058 |
{pred_sym = pred_sym andalso not bool_vars',
|
blanchet@44042
|
1059 |
min_ary =
|
blanchet@44042
|
1060 |
fold (fn T' => consider_var_arity T' T) types min_ary,
|
blanchet@44042
|
1061 |
max_ary = max_ary, types = types}
|
blanchet@44042
|
1062 |
val fun_var_Ts' =
|
blanchet@44042
|
1063 |
fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
|
blanchet@44042
|
1064 |
in
|
blanchet@44042
|
1065 |
if bool_vars' = bool_vars andalso
|
blanchet@44042
|
1066 |
pointer_eq (fun_var_Ts', fun_var_Ts) then
|
blanchet@44042
|
1067 |
accum
|
blanchet@44008
|
1068 |
else
|
blanchet@44042
|
1069 |
((bool_vars', fun_var_Ts'),
|
blanchet@44042
|
1070 |
Symtab.map (K repair_min_arity) sym_tab)
|
blanchet@44042
|
1071 |
end
|
blanchet@44042
|
1072 |
else
|
blanchet@44042
|
1073 |
accum
|
blanchet@44042
|
1074 |
fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
|
blanchet@44042
|
1075 |
let val (head, args) = strip_combterm_comb tm in
|
blanchet@43429
|
1076 |
(case head of
|
blanchet@43434
|
1077 |
CombConst ((s, _), T, _) =>
|
blanchet@43429
|
1078 |
if String.isPrefix bound_var_prefix s then
|
blanchet@44042
|
1079 |
add_var_or_bound_var T accum
|
blanchet@43429
|
1080 |
else
|
blanchet@43980
|
1081 |
let val ary = length args in
|
blanchet@44042
|
1082 |
((bool_vars, fun_var_Ts),
|
blanchet@43905
|
1083 |
case Symtab.lookup sym_tab s of
|
blanchet@43905
|
1084 |
SOME {pred_sym, min_ary, max_ary, types} =>
|
blanchet@43905
|
1085 |
let
|
blanchet@44042
|
1086 |
val pred_sym =
|
blanchet@44042
|
1087 |
pred_sym andalso top_level andalso not bool_vars
|
blanchet@43905
|
1088 |
val types' = types |> insert_type ctxt I T
|
blanchet@43905
|
1089 |
val min_ary =
|
blanchet@43905
|
1090 |
if is_some explicit_apply orelse
|
blanchet@43905
|
1091 |
pointer_eq (types', types) then
|
blanchet@43905
|
1092 |
min_ary
|
blanchet@43905
|
1093 |
else
|
blanchet@44042
|
1094 |
fold (consider_var_arity T) fun_var_Ts min_ary
|
blanchet@43905
|
1095 |
in
|
blanchet@44042
|
1096 |
Symtab.update (s, {pred_sym = pred_sym,
|
blanchet@43905
|
1097 |
min_ary = Int.min (ary, min_ary),
|
blanchet@43905
|
1098 |
max_ary = Int.max (ary, max_ary),
|
blanchet@43905
|
1099 |
types = types'})
|
blanchet@43905
|
1100 |
sym_tab
|
blanchet@43905
|
1101 |
end
|
blanchet@43905
|
1102 |
| NONE =>
|
blanchet@43905
|
1103 |
let
|
blanchet@44042
|
1104 |
val pred_sym = top_level andalso not bool_vars
|
blanchet@43905
|
1105 |
val min_ary =
|
blanchet@43905
|
1106 |
case explicit_apply of
|
blanchet@43905
|
1107 |
SOME true => 0
|
blanchet@43905
|
1108 |
| SOME false => ary
|
blanchet@44042
|
1109 |
| NONE => fold (consider_var_arity T) fun_var_Ts ary
|
blanchet@43905
|
1110 |
in
|
blanchet@44042
|
1111 |
Symtab.update_new (s, {pred_sym = pred_sym,
|
blanchet@43905
|
1112 |
min_ary = min_ary, max_ary = ary,
|
blanchet@43905
|
1113 |
types = [T]})
|
blanchet@43905
|
1114 |
sym_tab
|
blanchet@43905
|
1115 |
end)
|
blanchet@43905
|
1116 |
end
|
blanchet@44042
|
1117 |
| CombVar (_, T) => add_var_or_bound_var T accum
|
blanchet@43905
|
1118 |
| _ => accum)
|
blanchet@43905
|
1119 |
|> fold (add false) args
|
blanchet@43429
|
1120 |
end
|
blanchet@43905
|
1121 |
in add true end
|
blanchet@43905
|
1122 |
fun add_fact_syms_to_table ctxt explicit_apply =
|
blanchet@43905
|
1123 |
fact_lift (formula_fold NONE
|
blanchet@43905
|
1124 |
(K (add_combterm_syms_to_table ctxt explicit_apply)))
|
blanchet@38506
|
1125 |
|
blanchet@43980
|
1126 |
val default_sym_tab_entries : (string * sym_info) list =
|
blanchet@44015
|
1127 |
(prefixed_predicator_name,
|
blanchet@43980
|
1128 |
{pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
|
blanchet@43439
|
1129 |
([tptp_false, tptp_true]
|
blanchet@43980
|
1130 |
|> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
|
blanchet@43980
|
1131 |
([tptp_equal, tptp_old_equal]
|
blanchet@43980
|
1132 |
|> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
|
blanchet@41388
|
1133 |
|
blanchet@43905
|
1134 |
fun sym_table_for_facts ctxt explicit_apply facts =
|
blanchet@44042
|
1135 |
((false, []), Symtab.empty)
|
blanchet@44042
|
1136 |
|> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
|
blanchet@43980
|
1137 |
|> fold Symtab.update default_sym_tab_entries
|
blanchet@38506
|
1138 |
|
blanchet@43429
|
1139 |
fun min_arity_of sym_tab s =
|
blanchet@43429
|
1140 |
case Symtab.lookup sym_tab s of
|
blanchet@43445
|
1141 |
SOME ({min_ary, ...} : sym_info) => min_ary
|
blanchet@43429
|
1142 |
| NONE =>
|
blanchet@43429
|
1143 |
case strip_prefix_and_unascii const_prefix s of
|
blanchet@43418
|
1144 |
SOME s =>
|
blanchet@43441
|
1145 |
let val s = s |> unmangled_const_name |> invert_const in
|
blanchet@43807
|
1146 |
if s = predicator_name then 1
|
blanchet@43807
|
1147 |
else if s = app_op_name then 2
|
blanchet@43807
|
1148 |
else if s = type_pred_name then 1
|
blanchet@43428
|
1149 |
else 0
|
blanchet@43418
|
1150 |
end
|
blanchet@38506
|
1151 |
| NONE => 0
|
blanchet@38506
|
1152 |
|
blanchet@38506
|
1153 |
(* True if the constant ever appears outside of the top-level position in
|
blanchet@38506
|
1154 |
literals, or if it appears with different arities (e.g., because of different
|
blanchet@38506
|
1155 |
type instantiations). If false, the constant always receives all of its
|
blanchet@38506
|
1156 |
arguments and is used as a predicate. *)
|
blanchet@43429
|
1157 |
fun is_pred_sym sym_tab s =
|
blanchet@43429
|
1158 |
case Symtab.lookup sym_tab s of
|
blanchet@43445
|
1159 |
SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
|
blanchet@43445
|
1160 |
pred_sym andalso min_ary = max_ary
|
blanchet@43429
|
1161 |
| NONE => false
|
blanchet@38506
|
1162 |
|
blanchet@43439
|
1163 |
val predicator_combconst =
|
blanchet@43807
|
1164 |
CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
|
blanchet@43439
|
1165 |
fun predicator tm = CombApp (predicator_combconst, tm)
|
blanchet@38506
|
1166 |
|
blanchet@43439
|
1167 |
fun introduce_predicators_in_combterm sym_tab tm =
|
blanchet@43413
|
1168 |
case strip_combterm_comb tm of
|
blanchet@43413
|
1169 |
(CombConst ((s, _), _, _), _) =>
|
blanchet@43439
|
1170 |
if is_pred_sym sym_tab s then tm else predicator tm
|
blanchet@43439
|
1171 |
| _ => predicator tm
|
blanchet@38506
|
1172 |
|
blanchet@43415
|
1173 |
fun list_app head args = fold (curry (CombApp o swap)) args head
|
blanchet@38506
|
1174 |
|
blanchet@43971
|
1175 |
val app_op = `make_fixed_const app_op_name
|
blanchet@43971
|
1176 |
|
blanchet@43415
|
1177 |
fun explicit_app arg head =
|
blanchet@43415
|
1178 |
let
|
blanchet@43433
|
1179 |
val head_T = combtyp_of head
|
blanchet@43563
|
1180 |
val (arg_T, res_T) = dest_funT head_T
|
blanchet@43415
|
1181 |
val explicit_app =
|
blanchet@43971
|
1182 |
CombConst (app_op, head_T --> head_T, [arg_T, res_T])
|
blanchet@43415
|
1183 |
in list_app explicit_app [head, arg] end
|
blanchet@43415
|
1184 |
fun list_explicit_app head args = fold explicit_app args head
|
blanchet@43415
|
1185 |
|
blanchet@43436
|
1186 |
fun introduce_explicit_apps_in_combterm sym_tab =
|
blanchet@43415
|
1187 |
let
|
blanchet@43415
|
1188 |
fun aux tm =
|
blanchet@43415
|
1189 |
case strip_combterm_comb tm of
|
blanchet@43415
|
1190 |
(head as CombConst ((s, _), _, _), args) =>
|
blanchet@43415
|
1191 |
args |> map aux
|
blanchet@43428
|
1192 |
|> chop (min_arity_of sym_tab s)
|
blanchet@43415
|
1193 |
|>> list_app head
|
blanchet@43415
|
1194 |
|-> list_explicit_app
|
blanchet@43415
|
1195 |
| (head, args) => list_explicit_app head (map aux args)
|
blanchet@43415
|
1196 |
in aux end
|
blanchet@43415
|
1197 |
|
blanchet@43618
|
1198 |
fun chop_fun 0 T = ([], T)
|
blanchet@43618
|
1199 |
| chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
|
blanchet@43618
|
1200 |
chop_fun (n - 1) ran_T |>> cons dom_T
|
blanchet@43618
|
1201 |
| chop_fun _ _ = raise Fail "unexpected non-function"
|
blanchet@43618
|
1202 |
|
blanchet@43651
|
1203 |
fun filter_type_args _ _ _ [] = []
|
blanchet@43651
|
1204 |
| filter_type_args thy s arity T_args =
|
blanchet@43705
|
1205 |
let
|
blanchet@43705
|
1206 |
(* will throw "TYPE" for pseudo-constants *)
|
blanchet@43807
|
1207 |
val U = if s = app_op_name then
|
blanchet@43705
|
1208 |
@{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
|
blanchet@43705
|
1209 |
else
|
blanchet@43705
|
1210 |
s |> Sign.the_const_type thy
|
blanchet@43705
|
1211 |
in
|
blanchet@43652
|
1212 |
case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
|
blanchet@43652
|
1213 |
[] => []
|
blanchet@43652
|
1214 |
| res_U_vars =>
|
blanchet@43652
|
1215 |
let val U_args = (s, U) |> Sign.const_typargs thy in
|
blanchet@43652
|
1216 |
U_args ~~ T_args
|
blanchet@43652
|
1217 |
|> map_filter (fn (U, T) =>
|
blanchet@43652
|
1218 |
if member (op =) res_U_vars (dest_TVar U) then
|
blanchet@43652
|
1219 |
SOME T
|
blanchet@43652
|
1220 |
else
|
blanchet@43652
|
1221 |
NONE)
|
blanchet@43652
|
1222 |
end
|
blanchet@43651
|
1223 |
end
|
blanchet@43651
|
1224 |
handle TYPE _ => T_args
|
blanchet@43618
|
1225 |
|
blanchet@44020
|
1226 |
fun enforce_type_arg_policy_in_combterm ctxt format type_sys =
|
blanchet@43618
|
1227 |
let
|
blanchet@43618
|
1228 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@43618
|
1229 |
fun aux arity (CombApp (tm1, tm2)) =
|
blanchet@43618
|
1230 |
CombApp (aux (arity + 1) tm1, aux 0 tm2)
|
blanchet@43618
|
1231 |
| aux arity (CombConst (name as (s, _), T, T_args)) =
|
blanchet@44020
|
1232 |
(case strip_prefix_and_unascii const_prefix s of
|
blanchet@44020
|
1233 |
NONE => (name, T_args)
|
blanchet@44020
|
1234 |
| SOME s'' =>
|
blanchet@44020
|
1235 |
let
|
blanchet@44020
|
1236 |
val s'' = invert_const s''
|
blanchet@44020
|
1237 |
fun filtered_T_args false = T_args
|
blanchet@44020
|
1238 |
| filtered_T_args true = filter_type_args thy s'' arity T_args
|
blanchet@44020
|
1239 |
in
|
blanchet@44020
|
1240 |
case type_arg_policy type_sys s'' of
|
blanchet@44020
|
1241 |
Explicit_Type_Args drop_args =>
|
blanchet@44020
|
1242 |
(name, filtered_T_args drop_args)
|
blanchet@44020
|
1243 |
| Mangled_Type_Args drop_args =>
|
blanchet@44020
|
1244 |
(mangled_const_name format type_sys (filtered_T_args drop_args)
|
blanchet@44020
|
1245 |
name, [])
|
blanchet@44020
|
1246 |
| No_Type_Args => (name, [])
|
blanchet@44020
|
1247 |
end)
|
blanchet@44020
|
1248 |
|> (fn (name, T_args) => CombConst (name, T, T_args))
|
blanchet@43618
|
1249 |
| aux _ tm = tm
|
blanchet@43618
|
1250 |
in aux 0 end
|
blanchet@43444
|
1251 |
|
blanchet@44020
|
1252 |
fun repair_combterm ctxt format type_sys sym_tab =
|
blanchet@43835
|
1253 |
not (is_setting_higher_order format type_sys)
|
blanchet@43835
|
1254 |
? (introduce_explicit_apps_in_combterm sym_tab
|
blanchet@43835
|
1255 |
#> introduce_predicators_in_combterm sym_tab)
|
blanchet@44020
|
1256 |
#> enforce_type_arg_policy_in_combterm ctxt format type_sys
|
blanchet@44020
|
1257 |
fun repair_fact ctxt format type_sys sym_tab =
|
blanchet@43571
|
1258 |
update_combformula (formula_map
|
blanchet@44020
|
1259 |
(repair_combterm ctxt format type_sys sym_tab))
|
blanchet@43444
|
1260 |
|
blanchet@43444
|
1261 |
(** Helper facts **)
|
blanchet@43444
|
1262 |
|
blanchet@44035
|
1263 |
(* The Boolean indicates that a fairly sound type encoding is needed. *)
|
blanchet@43926
|
1264 |
val helper_table =
|
blanchet@44035
|
1265 |
[(("COMBI", false), @{thms Meson.COMBI_def}),
|
blanchet@44035
|
1266 |
(("COMBK", false), @{thms Meson.COMBK_def}),
|
blanchet@44035
|
1267 |
(("COMBB", false), @{thms Meson.COMBB_def}),
|
blanchet@44035
|
1268 |
(("COMBC", false), @{thms Meson.COMBC_def}),
|
blanchet@44035
|
1269 |
(("COMBS", false), @{thms Meson.COMBS_def}),
|
blanchet@44035
|
1270 |
(("fequal", true),
|
blanchet@43926
|
1271 |
(* This is a lie: Higher-order equality doesn't need a sound type encoding.
|
blanchet@43926
|
1272 |
However, this is done so for backward compatibility: Including the
|
blanchet@43926
|
1273 |
equality helpers by default in Metis breaks a few existing proofs. *)
|
blanchet@44035
|
1274 |
@{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
|
blanchet@44035
|
1275 |
fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
|
blanchet@44035
|
1276 |
(("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
|
blanchet@44035
|
1277 |
(("fFalse", true), @{thms True_or_False}),
|
blanchet@44035
|
1278 |
(("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
|
blanchet@44035
|
1279 |
(("fTrue", true), @{thms True_or_False}),
|
blanchet@44035
|
1280 |
(("fNot", false),
|
blanchet@44035
|
1281 |
@{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
|
blanchet@44035
|
1282 |
fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
|
blanchet@44035
|
1283 |
(("fconj", false),
|
blanchet@44035
|
1284 |
@{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
|
blanchet@44035
|
1285 |
by (unfold fconj_def) fast+}),
|
blanchet@44035
|
1286 |
(("fdisj", false),
|
blanchet@44035
|
1287 |
@{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
|
blanchet@44035
|
1288 |
by (unfold fdisj_def) fast+}),
|
blanchet@44035
|
1289 |
(("fimplies", false),
|
blanchet@44035
|
1290 |
@{lemma "P | fimplies P Q" "~ Q | fimplies P Q"
|
blanchet@44035
|
1291 |
"~ fimplies P Q | ~ P | Q"
|
blanchet@44035
|
1292 |
by (unfold fimplies_def) fast+}),
|
blanchet@44035
|
1293 |
(("If", true), @{thms if_True if_False True_or_False})]
|
blanchet@44035
|
1294 |
|> map (apsnd (map zero_var_indexes))
|
blanchet@43926
|
1295 |
|
blanchet@43971
|
1296 |
val type_tag = `make_fixed_const type_tag_name
|
blanchet@43971
|
1297 |
|
blanchet@44000
|
1298 |
fun type_tag_idempotence_fact () =
|
blanchet@43444
|
1299 |
let
|
blanchet@43444
|
1300 |
fun var s = ATerm (`I s, [])
|
blanchet@44000
|
1301 |
fun tag tm = ATerm (type_tag, [var "T", tm])
|
blanchet@44000
|
1302 |
val tagged_x = tag (var "X")
|
blanchet@43444
|
1303 |
in
|
blanchet@44000
|
1304 |
Formula (type_tag_idempotence_helper_name, Axiom,
|
blanchet@44000
|
1305 |
AAtom (ATerm (`I tptp_equal, [tag tagged_x, tagged_x]))
|
blanchet@43748
|
1306 |
|> close_formula_universally, simp_info, NONE)
|
blanchet@43444
|
1307 |
end
|
blanchet@43444
|
1308 |
|
blanchet@44000
|
1309 |
fun should_specialize_helper type_sys t =
|
blanchet@44000
|
1310 |
case general_type_arg_policy type_sys of
|
blanchet@44000
|
1311 |
Mangled_Type_Args _ => not (null (Term.hidden_polymorphism t))
|
blanchet@44000
|
1312 |
| _ => false
|
blanchet@44000
|
1313 |
|
blanchet@43905
|
1314 |
fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
|
blanchet@43444
|
1315 |
case strip_prefix_and_unascii const_prefix s of
|
blanchet@43444
|
1316 |
SOME mangled_s =>
|
blanchet@43444
|
1317 |
let
|
blanchet@43444
|
1318 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@43444
|
1319 |
val unmangled_s = mangled_s |> unmangled_const_name
|
blanchet@44000
|
1320 |
fun dub_and_inst needs_fairly_sound (th, j) =
|
blanchet@44000
|
1321 |
((unmangled_s ^ "_" ^ string_of_int j ^
|
blanchet@44000
|
1322 |
(if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
|
blanchet@43764
|
1323 |
(if needs_fairly_sound then typed_helper_suffix
|
blanchet@43750
|
1324 |
else untyped_helper_suffix),
|
blanchet@43750
|
1325 |
General),
|
blanchet@43444
|
1326 |
let val t = th |> prop_of in
|
blanchet@44000
|
1327 |
t |> should_specialize_helper type_sys t
|
blanchet@43905
|
1328 |
? (case types of
|
blanchet@43905
|
1329 |
[T] => specialize_type thy (invert_const unmangled_s, T)
|
blanchet@43905
|
1330 |
| _ => I)
|
blanchet@43444
|
1331 |
end)
|
blanchet@44000
|
1332 |
val make_facts =
|
blanchet@44000
|
1333 |
map_filter (make_fact ctxt format type_sys false false false false)
|
blanchet@43764
|
1334 |
val fairly_sound = is_type_sys_fairly_sound type_sys
|
blanchet@43444
|
1335 |
in
|
blanchet@43926
|
1336 |
helper_table
|
blanchet@44035
|
1337 |
|> maps (fn ((helper_s, needs_fairly_sound), ths) =>
|
blanchet@44000
|
1338 |
if helper_s <> unmangled_s orelse
|
blanchet@43765
|
1339 |
(needs_fairly_sound andalso not fairly_sound) then
|
blanchet@43444
|
1340 |
[]
|
blanchet@43444
|
1341 |
else
|
blanchet@43444
|
1342 |
ths ~~ (1 upto length ths)
|
blanchet@44000
|
1343 |
|> map (dub_and_inst needs_fairly_sound)
|
blanchet@44000
|
1344 |
|> make_facts)
|
blanchet@43444
|
1345 |
end
|
blanchet@43444
|
1346 |
| NONE => []
|
blanchet@43803
|
1347 |
fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
|
blanchet@43803
|
1348 |
Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
|
blanchet@43803
|
1349 |
[]
|
blanchet@43444
|
1350 |
|
blanchet@43835
|
1351 |
fun translate_atp_fact ctxt format type_sys keep_trivial =
|
blanchet@43937
|
1352 |
`(make_fact ctxt format type_sys keep_trivial true true true o apsnd prop_of)
|
blanchet@43444
|
1353 |
|
blanchet@43926
|
1354 |
(***************************************************************)
|
blanchet@43926
|
1355 |
(* Type Classes Present in the Axiom or Conjecture Clauses *)
|
blanchet@43926
|
1356 |
(***************************************************************)
|
blanchet@43926
|
1357 |
|
blanchet@43926
|
1358 |
fun set_insert (x, s) = Symtab.update (x, ()) s
|
blanchet@43926
|
1359 |
|
blanchet@43926
|
1360 |
fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
|
blanchet@43926
|
1361 |
|
blanchet@43926
|
1362 |
(* Remove this trivial type class (FIXME: similar code elsewhere) *)
|
blanchet@43926
|
1363 |
fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
|
blanchet@43926
|
1364 |
|
blanchet@43934
|
1365 |
fun classes_of_terms get_Ts =
|
blanchet@43962
|
1366 |
map (map snd o get_Ts)
|
blanchet@43934
|
1367 |
#> List.foldl add_classes Symtab.empty
|
blanchet@43934
|
1368 |
#> delete_type #> Symtab.keys
|
blanchet@43926
|
1369 |
|
blanchet@43934
|
1370 |
val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
|
blanchet@43934
|
1371 |
val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
|
blanchet@43926
|
1372 |
|
blanchet@43926
|
1373 |
(*fold type constructors*)
|
blanchet@44030
|
1374 |
fun fold_type_constrs f (Type (a, Ts)) x =
|
blanchet@44030
|
1375 |
fold (fold_type_constrs f) Ts (f (a,x))
|
blanchet@44030
|
1376 |
| fold_type_constrs _ _ x = x
|
blanchet@43926
|
1377 |
|
blanchet@43926
|
1378 |
(*Type constructors used to instantiate overloaded constants are the only ones needed.*)
|
blanchet@44030
|
1379 |
fun add_type_constrs_in_term thy =
|
blanchet@43926
|
1380 |
let
|
blanchet@44029
|
1381 |
fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
|
blanchet@44022
|
1382 |
| add (t $ u) = add t #> add u
|
blanchet@44029
|
1383 |
| add (Const (x as (s, _))) =
|
blanchet@44029
|
1384 |
if String.isPrefix skolem_const_prefix s then I
|
blanchet@44030
|
1385 |
else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
|
blanchet@44022
|
1386 |
| add (Abs (_, _, u)) = add u
|
blanchet@44022
|
1387 |
| add _ = I
|
blanchet@44022
|
1388 |
in add end
|
blanchet@43926
|
1389 |
|
blanchet@44030
|
1390 |
fun type_constrs_of_terms thy ts =
|
blanchet@44030
|
1391 |
Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
|
blanchet@43926
|
1392 |
|
blanchet@43937
|
1393 |
fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
|
blanchet@43803
|
1394 |
rich_facts =
|
blanchet@43444
|
1395 |
let
|
blanchet@43444
|
1396 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@43444
|
1397 |
val fact_ts = map (prop_of o snd o snd) rich_facts
|
blanchet@43444
|
1398 |
val (facts, fact_names) =
|
blanchet@43444
|
1399 |
rich_facts
|
blanchet@43444
|
1400 |
|> map_filter (fn (NONE, _) => NONE
|
blanchet@43444
|
1401 |
| (SOME fact, (name, _)) => SOME (fact, name))
|
blanchet@43444
|
1402 |
|> ListPair.unzip
|
blanchet@43444
|
1403 |
(* Remove existing facts from the conjecture, as this can dramatically
|
blanchet@43444
|
1404 |
boost an ATP's performance (for some reason). *)
|
blanchet@44033
|
1405 |
val hyp_ts =
|
blanchet@44033
|
1406 |
hyp_ts
|
blanchet@44033
|
1407 |
|> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
|
blanchet@43444
|
1408 |
val goal_t = Logic.list_implies (hyp_ts, concl_t)
|
blanchet@43444
|
1409 |
val all_ts = goal_t :: fact_ts
|
blanchet@43444
|
1410 |
val subs = tfree_classes_of_terms all_ts
|
blanchet@43444
|
1411 |
val supers = tvar_classes_of_terms all_ts
|
blanchet@44030
|
1412 |
val tycons = type_constrs_of_terms thy all_ts
|
blanchet@43835
|
1413 |
val conjs =
|
blanchet@43937
|
1414 |
hyp_ts @ [concl_t]
|
blanchet@43937
|
1415 |
|> make_conjecture ctxt format prem_kind type_sys preproc
|
blanchet@43444
|
1416 |
val (supers', arity_clauses) =
|
blanchet@43460
|
1417 |
if level_of_type_sys type_sys = No_Types then ([], [])
|
blanchet@43444
|
1418 |
else make_arity_clauses thy tycons supers
|
blanchet@43444
|
1419 |
val class_rel_clauses = make_class_rel_clauses thy subs supers'
|
blanchet@43444
|
1420 |
in
|
blanchet@43444
|
1421 |
(fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
|
blanchet@43444
|
1422 |
end
|
blanchet@43444
|
1423 |
|
blanchet@43444
|
1424 |
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
|
blanchet@43444
|
1425 |
(true, ATerm (class, [ATerm (name, [])]))
|
blanchet@43444
|
1426 |
| fo_literal_from_type_literal (TyLitFree (class, name)) =
|
blanchet@43444
|
1427 |
(true, ATerm (class, [ATerm (name, [])]))
|
blanchet@43444
|
1428 |
|
blanchet@43444
|
1429 |
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
|
blanchet@43444
|
1430 |
|
blanchet@43971
|
1431 |
val type_pred = `make_fixed_const type_pred_name
|
blanchet@43971
|
1432 |
|
blanchet@44020
|
1433 |
fun type_pred_combterm ctxt format type_sys T tm =
|
blanchet@44020
|
1434 |
CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
|
blanchet@44020
|
1435 |
|> enforce_type_arg_policy_in_combterm ctxt format type_sys, tm)
|
blanchet@43444
|
1436 |
|
blanchet@43747
|
1437 |
fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
|
blanchet@43747
|
1438 |
| var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
|
blanchet@43841
|
1439 |
accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
|
blanchet@43747
|
1440 |
fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
|
blanchet@43747
|
1441 |
| is_var_nonmonotonic_in_formula pos phi _ name =
|
blanchet@43747
|
1442 |
formula_fold pos (var_occurs_positively_naked_in_term name) phi false
|
blanchet@43705
|
1443 |
|
blanchet@44019
|
1444 |
fun mk_const_aterm format type_sys x T_args args =
|
blanchet@44019
|
1445 |
ATerm (x, map (fo_term_from_typ format type_sys) T_args @ args)
|
blanchet@43835
|
1446 |
|
blanchet@43803
|
1447 |
fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
|
blanchet@43971
|
1448 |
CombConst (type_tag, T --> T, [T])
|
blanchet@44020
|
1449 |
|> enforce_type_arg_policy_in_combterm ctxt format type_sys
|
blanchet@43803
|
1450 |
|> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
|
blanchet@43700
|
1451 |
|> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
|
blanchet@43803
|
1452 |
and term_from_combterm ctxt format nonmono_Ts type_sys =
|
blanchet@43444
|
1453 |
let
|
blanchet@43803
|
1454 |
fun aux site u =
|
blanchet@43803
|
1455 |
let
|
blanchet@43803
|
1456 |
val (head, args) = strip_combterm_comb u
|
blanchet@43803
|
1457 |
val (x as (s, _), T_args) =
|
blanchet@43803
|
1458 |
case head of
|
blanchet@43803
|
1459 |
CombConst (name, _, T_args) => (name, T_args)
|
blanchet@43803
|
1460 |
| CombVar (name, _) => (name, [])
|
blanchet@43803
|
1461 |
| CombApp _ => raise Fail "impossible \"CombApp\""
|
blanchet@43841
|
1462 |
val arg_site = if site = Top_Level andalso is_tptp_equal s then Eq_Arg
|
blanchet@43803
|
1463 |
else Elsewhere
|
blanchet@44019
|
1464 |
val t = mk_const_aterm format type_sys x T_args
|
blanchet@44019
|
1465 |
(map (aux arg_site) args)
|
blanchet@43803
|
1466 |
val T = combtyp_of u
|
blanchet@43803
|
1467 |
in
|
blanchet@43803
|
1468 |
t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
|
blanchet@43803
|
1469 |
tag_with_type ctxt format nonmono_Ts type_sys T
|
blanchet@43803
|
1470 |
else
|
blanchet@43803
|
1471 |
I)
|
blanchet@43803
|
1472 |
end
|
blanchet@43803
|
1473 |
in aux end
|
blanchet@43803
|
1474 |
and formula_from_combformula ctxt format nonmono_Ts type_sys
|
blanchet@43803
|
1475 |
should_predicate_on_var =
|
blanchet@43700
|
1476 |
let
|
blanchet@43803
|
1477 |
val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
|
blanchet@43444
|
1478 |
val do_bound_type =
|
blanchet@43552
|
1479 |
case type_sys of
|
blanchet@43587
|
1480 |
Simple_Types level =>
|
blanchet@43835
|
1481 |
homogenized_type ctxt nonmono_Ts level 0
|
blanchet@44019
|
1482 |
#> mangled_type format type_sys false 0 #> SOME
|
blanchet@43552
|
1483 |
| _ => K NONE
|
blanchet@43747
|
1484 |
fun do_out_of_bound_type pos phi universal (name, T) =
|
blanchet@43705
|
1485 |
if should_predicate_on_type ctxt nonmono_Ts type_sys
|
blanchet@43747
|
1486 |
(fn () => should_predicate_on_var pos phi universal name) T then
|
blanchet@43705
|
1487 |
CombVar (name, T)
|
blanchet@44020
|
1488 |
|> type_pred_combterm ctxt format type_sys T
|
blanchet@43747
|
1489 |
|> do_term |> AAtom |> SOME
|
blanchet@43444
|
1490 |
else
|
blanchet@43444
|
1491 |
NONE
|
blanchet@43747
|
1492 |
fun do_formula pos (AQuant (q, xs, phi)) =
|
blanchet@43747
|
1493 |
let
|
blanchet@43747
|
1494 |
val phi = phi |> do_formula pos
|
blanchet@43747
|
1495 |
val universal = Option.map (q = AExists ? not) pos
|
blanchet@43747
|
1496 |
in
|
blanchet@43705
|
1497 |
AQuant (q, xs |> map (apsnd (fn NONE => NONE
|
blanchet@43705
|
1498 |
| SOME T => do_bound_type T)),
|
blanchet@43705
|
1499 |
(if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
|
blanchet@43705
|
1500 |
(map_filter
|
blanchet@43705
|
1501 |
(fn (_, NONE) => NONE
|
blanchet@43705
|
1502 |
| (s, SOME T) =>
|
blanchet@43747
|
1503 |
do_out_of_bound_type pos phi universal (s, T))
|
blanchet@43747
|
1504 |
xs)
|
blanchet@43705
|
1505 |
phi)
|
blanchet@43705
|
1506 |
end
|
blanchet@43747
|
1507 |
| do_formula pos (AConn conn) = aconn_map pos do_formula conn
|
blanchet@43747
|
1508 |
| do_formula _ (AAtom tm) = AAtom (do_term tm)
|
blanchet@43747
|
1509 |
in do_formula o SOME end
|
blanchet@43444
|
1510 |
|
blanchet@43939
|
1511 |
fun bound_tvars type_sys Ts =
|
blanchet@43592
|
1512 |
mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
|
blanchet@43939
|
1513 |
(type_literals_for_types type_sys sorts_on_tvar Ts))
|
blanchet@43592
|
1514 |
|
blanchet@43797
|
1515 |
fun formula_for_fact ctxt format nonmono_Ts type_sys
|
blanchet@43444
|
1516 |
({combformula, atomic_types, ...} : translated_formula) =
|
blanchet@43592
|
1517 |
combformula
|
blanchet@43592
|
1518 |
|> close_combformula_universally
|
blanchet@43803
|
1519 |
|> formula_from_combformula ctxt format nonmono_Ts type_sys
|
blanchet@43747
|
1520 |
is_var_nonmonotonic_in_formula true
|
blanchet@43939
|
1521 |
|> bound_tvars type_sys atomic_types
|
blanchet@43444
|
1522 |
|> close_formula_universally
|
blanchet@43444
|
1523 |
|
blanchet@43444
|
1524 |
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
|
blanchet@43444
|
1525 |
of monomorphization). The TPTP explicitly forbids name clashes, and some of
|
blanchet@43444
|
1526 |
the remote provers might care. *)
|
blanchet@44000
|
1527 |
fun formula_line_for_fact ctxt format prefix encode freshen nonmono_Ts type_sys
|
blanchet@43511
|
1528 |
(j, formula as {name, locality, kind, ...}) =
|
blanchet@44000
|
1529 |
Formula (prefix ^
|
blanchet@44000
|
1530 |
(if freshen andalso
|
blanchet@44000
|
1531 |
polymorphism_of_type_sys type_sys <> Polymorphic then
|
blanchet@44000
|
1532 |
string_of_int j ^ "_"
|
blanchet@44000
|
1533 |
else
|
blanchet@44000
|
1534 |
"") ^ encode name,
|
blanchet@43797
|
1535 |
kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
|
blanchet@43748
|
1536 |
case locality of
|
blanchet@43748
|
1537 |
Intro => intro_info
|
blanchet@43748
|
1538 |
| Elim => elim_info
|
blanchet@43748
|
1539 |
| Simp => simp_info
|
blanchet@43748
|
1540 |
| _ => NONE)
|
blanchet@43444
|
1541 |
|
blanchet@43927
|
1542 |
fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
|
blanchet@43927
|
1543 |
: class_rel_clause) =
|
blanchet@43444
|
1544 |
let val ty_arg = ATerm (`I "T", []) in
|
blanchet@43448
|
1545 |
Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
|
blanchet@43444
|
1546 |
AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
|
blanchet@43444
|
1547 |
AAtom (ATerm (superclass, [ty_arg]))])
|
blanchet@43748
|
1548 |
|> close_formula_universally, intro_info, NONE)
|
blanchet@43444
|
1549 |
end
|
blanchet@43444
|
1550 |
|
blanchet@43444
|
1551 |
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
|
blanchet@43444
|
1552 |
(true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
|
blanchet@43444
|
1553 |
| fo_literal_from_arity_literal (TVarLit (c, sort)) =
|
blanchet@43444
|
1554 |
(false, ATerm (c, [ATerm (sort, [])]))
|
blanchet@43444
|
1555 |
|
blanchet@43927
|
1556 |
fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
|
blanchet@43927
|
1557 |
: arity_clause) =
|
blanchet@43448
|
1558 |
Formula (arity_clause_prefix ^ ascii_of name, Axiom,
|
blanchet@43444
|
1559 |
mk_ahorn (map (formula_from_fo_literal o apfst not
|
blanchet@43766
|
1560 |
o fo_literal_from_arity_literal) prem_lits)
|
blanchet@43444
|
1561 |
(formula_from_fo_literal
|
blanchet@43766
|
1562 |
(fo_literal_from_arity_literal concl_lits))
|
blanchet@43748
|
1563 |
|> close_formula_universally, intro_info, NONE)
|
blanchet@43444
|
1564 |
|
blanchet@43803
|
1565 |
fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
|
blanchet@43939
|
1566 |
({name, kind, combformula, atomic_types, ...} : translated_formula) =
|
blanchet@43448
|
1567 |
Formula (conjecture_prefix ^ name, kind,
|
blanchet@43803
|
1568 |
formula_from_combformula ctxt format nonmono_Ts type_sys
|
blanchet@43780
|
1569 |
is_var_nonmonotonic_in_formula false
|
blanchet@43780
|
1570 |
(close_combformula_universally combformula)
|
blanchet@43939
|
1571 |
|> bound_tvars type_sys atomic_types
|
blanchet@43444
|
1572 |
|> close_formula_universally, NONE, NONE)
|
blanchet@43444
|
1573 |
|
blanchet@43939
|
1574 |
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
|
blanchet@43939
|
1575 |
atomic_types |> type_literals_for_types type_sys sorts_on_tfree
|
blanchet@43444
|
1576 |
|> map fo_literal_from_type_literal
|
blanchet@43444
|
1577 |
|
blanchet@43444
|
1578 |
fun formula_line_for_free_type j lit =
|
blanchet@43926
|
1579 |
Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
|
blanchet@43444
|
1580 |
formula_from_fo_literal lit, NONE, NONE)
|
blanchet@43939
|
1581 |
fun formula_lines_for_free_types type_sys facts =
|
blanchet@43444
|
1582 |
let
|
blanchet@43939
|
1583 |
val litss = map (free_type_literals type_sys) facts
|
blanchet@43444
|
1584 |
val lits = fold (union (op =)) litss []
|
blanchet@43444
|
1585 |
in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
|
blanchet@43444
|
1586 |
|
blanchet@43444
|
1587 |
(** Symbol declarations **)
|
blanchet@43415
|
1588 |
|
blanchet@43445
|
1589 |
fun should_declare_sym type_sys pred_sym s =
|
blanchet@43839
|
1590 |
is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
|
blanchet@43765
|
1591 |
(case type_sys of
|
blanchet@43765
|
1592 |
Simple_Types _ => true
|
blanchet@43969
|
1593 |
| Tags (_, _, Lightweight) => true
|
blanchet@43765
|
1594 |
| _ => not pred_sym)
|
blanchet@43413
|
1595 |
|
blanchet@43755
|
1596 |
fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
|
blanchet@43445
|
1597 |
let
|
blanchet@43568
|
1598 |
fun add_combterm in_conj tm =
|
blanchet@43445
|
1599 |
let val (head, args) = strip_combterm_comb tm in
|
blanchet@43445
|
1600 |
(case head of
|
blanchet@43445
|
1601 |
CombConst ((s, s'), T, T_args) =>
|
blanchet@43445
|
1602 |
let val pred_sym = is_pred_sym repaired_sym_tab s in
|
blanchet@43445
|
1603 |
if should_declare_sym type_sys pred_sym s then
|
blanchet@43447
|
1604 |
Symtab.map_default (s, [])
|
blanchet@43755
|
1605 |
(insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
|
blanchet@43755
|
1606 |
in_conj))
|
blanchet@43445
|
1607 |
else
|
blanchet@43445
|
1608 |
I
|
blanchet@43445
|
1609 |
end
|
blanchet@43445
|
1610 |
| _ => I)
|
blanchet@43568
|
1611 |
#> fold (add_combterm in_conj) args
|
blanchet@43445
|
1612 |
end
|
blanchet@43568
|
1613 |
fun add_fact in_conj =
|
blanchet@43705
|
1614 |
fact_lift (formula_fold NONE (K (add_combterm in_conj)))
|
blanchet@43568
|
1615 |
in
|
blanchet@43568
|
1616 |
Symtab.empty
|
blanchet@43568
|
1617 |
|> is_type_sys_fairly_sound type_sys
|
blanchet@43568
|
1618 |
? (fold (add_fact true) conjs #> fold (add_fact false) facts)
|
blanchet@43568
|
1619 |
end
|
blanchet@43445
|
1620 |
|
blanchet@43755
|
1621 |
(* These types witness that the type classes they belong to allow infinite
|
blanchet@43755
|
1622 |
models and hence that any types with these type classes is monotonic. *)
|
blanchet@43926
|
1623 |
val known_infinite_types =
|
blanchet@43926
|
1624 |
[@{typ nat}, Type ("Int.int", []), @{typ "nat => bool"}]
|
blanchet@43755
|
1625 |
|
blanchet@43555
|
1626 |
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
|
blanchet@43555
|
1627 |
out with monotonicity" paper presented at CADE 2011. *)
|
blanchet@43755
|
1628 |
fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
|
blanchet@43700
|
1629 |
| add_combterm_nonmonotonic_types ctxt level _
|
blanchet@44020
|
1630 |
(CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
|
blanchet@44020
|
1631 |
tm2)) =
|
blanchet@43841
|
1632 |
(is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
|
blanchet@43700
|
1633 |
(case level of
|
blanchet@43755
|
1634 |
Nonmonotonic_Types =>
|
blanchet@43755
|
1635 |
not (is_type_surely_infinite ctxt known_infinite_types T)
|
blanchet@43700
|
1636 |
| Finite_Types => is_type_surely_finite ctxt T
|
blanchet@43755
|
1637 |
| _ => true)) ? insert_type ctxt I (deep_freeze_type T)
|
blanchet@43700
|
1638 |
| add_combterm_nonmonotonic_types _ _ _ _ = I
|
blanchet@43700
|
1639 |
fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
|
blanchet@43700
|
1640 |
: translated_formula) =
|
blanchet@43705
|
1641 |
formula_fold (SOME (kind <> Conjecture))
|
blanchet@43700
|
1642 |
(add_combterm_nonmonotonic_types ctxt level) combformula
|
blanchet@43755
|
1643 |
fun nonmonotonic_types_for_facts ctxt type_sys facts =
|
blanchet@43700
|
1644 |
let val level = level_of_type_sys type_sys in
|
blanchet@43755
|
1645 |
if level = Nonmonotonic_Types orelse level = Finite_Types then
|
blanchet@43755
|
1646 |
[] |> fold (add_fact_nonmonotonic_types ctxt level) facts
|
blanchet@43755
|
1647 |
(* We must add "bool" in case the helper "True_or_False" is added
|
blanchet@43755
|
1648 |
later. In addition, several places in the code rely on the list of
|
blanchet@43755
|
1649 |
nonmonotonic types not being empty. *)
|
blanchet@43755
|
1650 |
|> insert_type ctxt I @{typ bool}
|
blanchet@43755
|
1651 |
else
|
blanchet@43755
|
1652 |
[]
|
blanchet@43700
|
1653 |
end
|
blanchet@43547
|
1654 |
|
blanchet@43835
|
1655 |
fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
|
blanchet@43835
|
1656 |
(s', T_args, T, pred_sym, ary, _) =
|
blanchet@43835
|
1657 |
let
|
blanchet@44019
|
1658 |
val (T_arg_Ts, level) =
|
blanchet@43835
|
1659 |
case type_sys of
|
blanchet@44019
|
1660 |
Simple_Types level => ([], level)
|
blanchet@44019
|
1661 |
| _ => (replicate (length T_args) homo_infinite_type, No_Types)
|
blanchet@43835
|
1662 |
in
|
blanchet@43839
|
1663 |
Decl (sym_decl_prefix ^ s, (s, s'),
|
blanchet@43835
|
1664 |
(T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
|
blanchet@44019
|
1665 |
|> mangled_type format type_sys pred_sym (length T_arg_Ts + ary))
|
blanchet@43835
|
1666 |
end
|
blanchet@43450
|
1667 |
|
blanchet@43463
|
1668 |
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
|
blanchet@43463
|
1669 |
|
blanchet@43966
|
1670 |
fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
|
blanchet@43966
|
1671 |
type_sys n s j (s', T_args, T, _, ary, in_conj) =
|
blanchet@43450
|
1672 |
let
|
blanchet@43580
|
1673 |
val (kind, maybe_negate) =
|
blanchet@43580
|
1674 |
if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
|
blanchet@43580
|
1675 |
else (Axiom, I)
|
blanchet@43618
|
1676 |
val (arg_Ts, res_T) = chop_fun ary T
|
blanchet@43450
|
1677 |
val bound_names =
|
blanchet@43450
|
1678 |
1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
|
blanchet@43700
|
1679 |
val bounds =
|
blanchet@43450
|
1680 |
bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
|
blanchet@43450
|
1681 |
val bound_Ts =
|
blanchet@43463
|
1682 |
arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
|
blanchet@43463
|
1683 |
else NONE)
|
blanchet@43450
|
1684 |
in
|
blanchet@43966
|
1685 |
Formula (preds_sym_formula_prefix ^ s ^
|
blanchet@43580
|
1686 |
(if n > 1 then "_" ^ string_of_int j else ""), kind,
|
blanchet@43450
|
1687 |
CombConst ((s, s'), T, T_args)
|
blanchet@43700
|
1688 |
|> fold (curry (CombApp o swap)) bounds
|
blanchet@44020
|
1689 |
|> type_pred_combterm ctxt format type_sys res_T
|
blanchet@43804
|
1690 |
|> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
|
blanchet@43803
|
1691 |
|> formula_from_combformula ctxt format nonmono_Ts type_sys
|
blanchet@43747
|
1692 |
(K (K (K (K true)))) true
|
blanchet@43939
|
1693 |
|> n > 1 ? bound_tvars type_sys (atyps_of T)
|
blanchet@43580
|
1694 |
|> close_formula_universally
|
blanchet@43580
|
1695 |
|> maybe_negate,
|
blanchet@43748
|
1696 |
intro_info, NONE)
|
blanchet@43450
|
1697 |
end
|
blanchet@43450
|
1698 |
|
blanchet@43970
|
1699 |
fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
|
blanchet@43970
|
1700 |
nonmono_Ts type_sys n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
|
blanchet@43700
|
1701 |
let
|
blanchet@43700
|
1702 |
val ident_base =
|
blanchet@43970
|
1703 |
lightweight_tags_sym_formula_prefix ^ s ^
|
blanchet@43966
|
1704 |
(if n > 1 then "_" ^ string_of_int j else "")
|
blanchet@43721
|
1705 |
val (kind, maybe_negate) =
|
blanchet@43721
|
1706 |
if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
|
blanchet@43721
|
1707 |
else (Axiom, I)
|
blanchet@43700
|
1708 |
val (arg_Ts, res_T) = chop_fun ary T
|
blanchet@43700
|
1709 |
val bound_names =
|
blanchet@43700
|
1710 |
1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
|
blanchet@43700
|
1711 |
val bounds = bound_names |> map (fn name => ATerm (name, []))
|
blanchet@44019
|
1712 |
val cst = mk_const_aterm format type_sys (s, s') T_args
|
blanchet@43701
|
1713 |
val atomic_Ts = atyps_of T
|
blanchet@43705
|
1714 |
fun eq tms =
|
blanchet@43705
|
1715 |
(if pred_sym then AConn (AIff, map AAtom tms)
|
blanchet@43841
|
1716 |
else AAtom (ATerm (`I tptp_equal, tms)))
|
blanchet@43939
|
1717 |
|> bound_tvars type_sys atomic_Ts
|
blanchet@43701
|
1718 |
|> close_formula_universally
|
blanchet@43721
|
1719 |
|> maybe_negate
|
blanchet@43707
|
1720 |
val should_encode = should_encode_type ctxt nonmono_Ts All_Types
|
blanchet@43803
|
1721 |
val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
|
blanchet@43700
|
1722 |
val add_formula_for_res =
|
blanchet@43700
|
1723 |
if should_encode res_T then
|
blanchet@43721
|
1724 |
cons (Formula (ident_base ^ "_res", kind,
|
blanchet@43835
|
1725 |
eq [tag_with res_T (cst bounds), cst bounds],
|
blanchet@43748
|
1726 |
simp_info, NONE))
|
blanchet@43700
|
1727 |
else
|
blanchet@43700
|
1728 |
I
|
blanchet@43700
|
1729 |
fun add_formula_for_arg k =
|
blanchet@43700
|
1730 |
let val arg_T = nth arg_Ts k in
|
blanchet@43700
|
1731 |
if should_encode arg_T then
|
blanchet@43700
|
1732 |
case chop k bounds of
|
blanchet@43700
|
1733 |
(bounds1, bound :: bounds2) =>
|
blanchet@43721
|
1734 |
cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
|
blanchet@43835
|
1735 |
eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
|
blanchet@43835
|
1736 |
cst bounds],
|
blanchet@43748
|
1737 |
simp_info, NONE))
|
blanchet@43700
|
1738 |
| _ => raise Fail "expected nonempty tail"
|
blanchet@43700
|
1739 |
else
|
blanchet@43700
|
1740 |
I
|
blanchet@43700
|
1741 |
end
|
blanchet@43700
|
1742 |
in
|
blanchet@43705
|
1743 |
[] |> not pred_sym ? add_formula_for_res
|
blanchet@43700
|
1744 |
|> fold add_formula_for_arg (ary - 1 downto 0)
|
blanchet@43700
|
1745 |
end
|
blanchet@43700
|
1746 |
|
blanchet@43707
|
1747 |
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
|
blanchet@43707
|
1748 |
|
blanchet@43797
|
1749 |
fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
|
blanchet@43580
|
1750 |
(s, decls) =
|
blanchet@43839
|
1751 |
case type_sys of
|
blanchet@43839
|
1752 |
Simple_Types _ =>
|
blanchet@43839
|
1753 |
decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
|
blanchet@43839
|
1754 |
| Preds _ =>
|
blanchet@43839
|
1755 |
let
|
blanchet@43839
|
1756 |
val decls =
|
blanchet@43839
|
1757 |
case decls of
|
blanchet@43839
|
1758 |
decl :: (decls' as _ :: _) =>
|
blanchet@43839
|
1759 |
let val T = result_type_of_decl decl in
|
blanchet@43839
|
1760 |
if forall (curry (type_instance ctxt o swap) T
|
blanchet@43839
|
1761 |
o result_type_of_decl) decls' then
|
blanchet@43839
|
1762 |
[decl]
|
blanchet@43839
|
1763 |
else
|
blanchet@43839
|
1764 |
decls
|
blanchet@43839
|
1765 |
end
|
blanchet@43839
|
1766 |
| _ => decls
|
blanchet@43839
|
1767 |
val n = length decls
|
blanchet@43839
|
1768 |
val decls =
|
blanchet@43839
|
1769 |
decls
|
blanchet@43839
|
1770 |
|> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
|
blanchet@43839
|
1771 |
o result_type_of_decl)
|
blanchet@43839
|
1772 |
in
|
blanchet@43839
|
1773 |
(0 upto length decls - 1, decls)
|
blanchet@43966
|
1774 |
|-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
|
blanchet@43966
|
1775 |
nonmono_Ts type_sys n s)
|
blanchet@43839
|
1776 |
end
|
blanchet@43839
|
1777 |
| Tags (_, _, heaviness) =>
|
blanchet@43839
|
1778 |
(case heaviness of
|
blanchet@43969
|
1779 |
Heavyweight => []
|
blanchet@43969
|
1780 |
| Lightweight =>
|
blanchet@43839
|
1781 |
let val n = length decls in
|
blanchet@43839
|
1782 |
(0 upto n - 1 ~~ decls)
|
blanchet@43970
|
1783 |
|> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
|
blanchet@43970
|
1784 |
conj_sym_kind nonmono_Ts type_sys n s)
|
blanchet@43839
|
1785 |
end)
|
blanchet@43450
|
1786 |
|
blanchet@43797
|
1787 |
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
|
blanchet@43797
|
1788 |
type_sys sym_decl_tab =
|
blanchet@43839
|
1789 |
sym_decl_tab
|
blanchet@43839
|
1790 |
|> Symtab.dest
|
blanchet@43839
|
1791 |
|> sort_wrt fst
|
blanchet@43839
|
1792 |
|> rpair []
|
blanchet@43839
|
1793 |
|-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
|
blanchet@43839
|
1794 |
nonmono_Ts type_sys)
|
blanchet@43414
|
1795 |
|
blanchet@44026
|
1796 |
fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
|
blanchet@44026
|
1797 |
poly <> Mangled_Monomorphic andalso
|
blanchet@44026
|
1798 |
((level = All_Types andalso heaviness = Lightweight) orelse
|
blanchet@44026
|
1799 |
level = Nonmonotonic_Types orelse level = Finite_Types)
|
blanchet@44000
|
1800 |
| needs_type_tag_idempotence _ = false
|
blanchet@43702
|
1801 |
|
blanchet@43780
|
1802 |
fun offset_of_heading_in_problem _ [] j = j
|
blanchet@43780
|
1803 |
| offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
|
blanchet@43780
|
1804 |
if heading = needle then j
|
blanchet@43780
|
1805 |
else offset_of_heading_in_problem needle problem (j + length lines)
|
blanchet@43780
|
1806 |
|
blanchet@43839
|
1807 |
val implicit_declsN = "Should-be-implicit typings"
|
blanchet@43839
|
1808 |
val explicit_declsN = "Explicit typings"
|
blanchet@41405
|
1809 |
val factsN = "Relevant facts"
|
blanchet@41405
|
1810 |
val class_relsN = "Class relationships"
|
blanchet@43414
|
1811 |
val aritiesN = "Arities"
|
blanchet@41405
|
1812 |
val helpersN = "Helper facts"
|
blanchet@41405
|
1813 |
val conjsN = "Conjectures"
|
blanchet@41561
|
1814 |
val free_typesN = "Type variables"
|
blanchet@41405
|
1815 |
|
blanchet@43780
|
1816 |
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
|
blanchet@43937
|
1817 |
explicit_apply readable_names preproc hyp_ts concl_t
|
blanchet@43937
|
1818 |
facts =
|
blanchet@38506
|
1819 |
let
|
blanchet@43942
|
1820 |
val (format, type_sys) = choose_format [format] type_sys
|
blanchet@41561
|
1821 |
val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
|
blanchet@43937
|
1822 |
translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
|
blanchet@43937
|
1823 |
facts
|
blanchet@43905
|
1824 |
val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
|
blanchet@43755
|
1825 |
val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
|
blanchet@44020
|
1826 |
val repair = repair_fact ctxt format type_sys sym_tab
|
blanchet@43552
|
1827 |
val (conjs, facts) = (conjs, facts) |> pairself (map repair)
|
blanchet@43905
|
1828 |
val repaired_sym_tab =
|
blanchet@43905
|
1829 |
conjs @ facts |> sym_table_for_facts ctxt (SOME false)
|
blanchet@43444
|
1830 |
val helpers =
|
blanchet@43803
|
1831 |
repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
|
blanchet@43803
|
1832 |
|> map repair
|
blanchet@43765
|
1833 |
val lavish_nonmono_Ts =
|
blanchet@43765
|
1834 |
if null nonmono_Ts orelse
|
blanchet@43765
|
1835 |
polymorphism_of_type_sys type_sys <> Polymorphic then
|
blanchet@43765
|
1836 |
nonmono_Ts
|
blanchet@43765
|
1837 |
else
|
blanchet@43765
|
1838 |
[TVar (("'a", 0), HOLogic.typeS)]
|
blanchet@43550
|
1839 |
val sym_decl_lines =
|
blanchet@43596
|
1840 |
(conjs, helpers @ facts)
|
blanchet@43755
|
1841 |
|> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
|
blanchet@43797
|
1842 |
|> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
|
blanchet@43797
|
1843 |
lavish_nonmono_Ts type_sys
|
blanchet@43750
|
1844 |
val helper_lines =
|
blanchet@43797
|
1845 |
0 upto length helpers - 1 ~~ helpers
|
blanchet@44000
|
1846 |
|> map (formula_line_for_fact ctxt format helper_prefix I false
|
blanchet@44000
|
1847 |
lavish_nonmono_Ts type_sys)
|
blanchet@44000
|
1848 |
|> (if needs_type_tag_idempotence type_sys then
|
blanchet@44000
|
1849 |
cons (type_tag_idempotence_fact ())
|
blanchet@44000
|
1850 |
else
|
blanchet@44000
|
1851 |
I)
|
blanchet@43393
|
1852 |
(* Reordering these might confuse the proof reconstruction code or the SPASS
|
blanchet@43880
|
1853 |
FLOTTER hack. *)
|
blanchet@38506
|
1854 |
val problem =
|
blanchet@43839
|
1855 |
[(explicit_declsN, sym_decl_lines),
|
blanchet@43797
|
1856 |
(factsN,
|
blanchet@44000
|
1857 |
map (formula_line_for_fact ctxt format fact_prefix ascii_of true
|
blanchet@44000
|
1858 |
nonmono_Ts type_sys)
|
blanchet@43797
|
1859 |
(0 upto length facts - 1 ~~ facts)),
|
blanchet@43416
|
1860 |
(class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
|
blanchet@43416
|
1861 |
(aritiesN, map formula_line_for_arity_clause arity_clauses),
|
blanchet@43750
|
1862 |
(helpersN, helper_lines),
|
blanchet@43803
|
1863 |
(conjsN,
|
blanchet@43803
|
1864 |
map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
|
blanchet@43803
|
1865 |
conjs),
|
blanchet@43939
|
1866 |
(free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
|
blanchet@43414
|
1867 |
val problem =
|
blanchet@43432
|
1868 |
problem
|
blanchet@43933
|
1869 |
|> (case format of
|
blanchet@43933
|
1870 |
CNF => ensure_cnf_problem
|
blanchet@43933
|
1871 |
| CNF_UEQ => filter_cnf_ueq_problem
|
blanchet@43933
|
1872 |
| _ => I)
|
blanchet@43839
|
1873 |
|> (if is_format_typed format then
|
blanchet@43839
|
1874 |
declare_undeclared_syms_in_atp_problem type_decl_prefix
|
blanchet@43839
|
1875 |
implicit_declsN
|
blanchet@43839
|
1876 |
else
|
blanchet@43839
|
1877 |
I)
|
blanchet@43933
|
1878 |
val (problem, pool) = problem |> nice_atp_problem readable_names
|
blanchet@43750
|
1879 |
val helpers_offset = offset_of_heading_in_problem helpersN problem 0
|
blanchet@43750
|
1880 |
val typed_helpers =
|
blanchet@43750
|
1881 |
map_filter (fn (j, {name, ...}) =>
|
blanchet@43750
|
1882 |
if String.isSuffix typed_helper_suffix name then SOME j
|
blanchet@43750
|
1883 |
else NONE)
|
blanchet@43750
|
1884 |
((helpers_offset + 1 upto helpers_offset + length helpers)
|
blanchet@43750
|
1885 |
~~ helpers)
|
blanchet@43649
|
1886 |
fun add_sym_arity (s, {min_ary, ...} : sym_info) =
|
blanchet@43620
|
1887 |
if min_ary > 0 then
|
blanchet@43620
|
1888 |
case strip_prefix_and_unascii const_prefix s of
|
blanchet@43620
|
1889 |
SOME s => Symtab.insert (op =) (s, min_ary)
|
blanchet@43620
|
1890 |
| NONE => I
|
blanchet@43620
|
1891 |
else
|
blanchet@43620
|
1892 |
I
|
blanchet@38506
|
1893 |
in
|
blanchet@38506
|
1894 |
(problem,
|
blanchet@38506
|
1895 |
case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
|
blanchet@43456
|
1896 |
offset_of_heading_in_problem conjsN problem 0,
|
blanchet@43412
|
1897 |
offset_of_heading_in_problem factsN problem 0,
|
blanchet@43620
|
1898 |
fact_names |> Vector.fromList,
|
blanchet@43750
|
1899 |
typed_helpers,
|
blanchet@43620
|
1900 |
Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
|
blanchet@38506
|
1901 |
end
|
blanchet@38506
|
1902 |
|
blanchet@41561
|
1903 |
(* FUDGE *)
|
blanchet@41561
|
1904 |
val conj_weight = 0.0
|
blanchet@42641
|
1905 |
val hyp_weight = 0.1
|
blanchet@42641
|
1906 |
val fact_min_weight = 0.2
|
blanchet@41561
|
1907 |
val fact_max_weight = 1.0
|
blanchet@43479
|
1908 |
val type_info_default_weight = 0.8
|
blanchet@41561
|
1909 |
|
blanchet@41561
|
1910 |
fun add_term_weights weight (ATerm (s, tms)) =
|
blanchet@43839
|
1911 |
is_tptp_user_symbol s ? Symtab.default (s, weight)
|
blanchet@41561
|
1912 |
#> fold (add_term_weights weight) tms
|
blanchet@43448
|
1913 |
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
|
blanchet@43705
|
1914 |
formula_fold NONE (K (add_term_weights weight)) phi
|
blanchet@43399
|
1915 |
| add_problem_line_weights _ _ = I
|
blanchet@41561
|
1916 |
|
blanchet@41561
|
1917 |
fun add_conjectures_weights [] = I
|
blanchet@41561
|
1918 |
| add_conjectures_weights conjs =
|
blanchet@41561
|
1919 |
let val (hyps, conj) = split_last conjs in
|
blanchet@41561
|
1920 |
add_problem_line_weights conj_weight conj
|
blanchet@41561
|
1921 |
#> fold (add_problem_line_weights hyp_weight) hyps
|
blanchet@41561
|
1922 |
end
|
blanchet@41561
|
1923 |
|
blanchet@41561
|
1924 |
fun add_facts_weights facts =
|
blanchet@41561
|
1925 |
let
|
blanchet@41561
|
1926 |
val num_facts = length facts
|
blanchet@41561
|
1927 |
fun weight_of j =
|
blanchet@41561
|
1928 |
fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
|
blanchet@41561
|
1929 |
/ Real.fromInt num_facts
|
blanchet@41561
|
1930 |
in
|
blanchet@41561
|
1931 |
map weight_of (0 upto num_facts - 1) ~~ facts
|
blanchet@41561
|
1932 |
|> fold (uncurry add_problem_line_weights)
|
blanchet@41561
|
1933 |
end
|
blanchet@41561
|
1934 |
|
blanchet@41561
|
1935 |
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
|
blanchet@41561
|
1936 |
fun atp_problem_weights problem =
|
blanchet@43479
|
1937 |
let val get = these o AList.lookup (op =) problem in
|
blanchet@43479
|
1938 |
Symtab.empty
|
blanchet@43479
|
1939 |
|> add_conjectures_weights (get free_typesN @ get conjsN)
|
blanchet@43479
|
1940 |
|> add_facts_weights (get factsN)
|
blanchet@43479
|
1941 |
|> fold (fold (add_problem_line_weights type_info_default_weight) o get)
|
blanchet@43839
|
1942 |
[explicit_declsN, class_relsN, aritiesN]
|
blanchet@43479
|
1943 |
|> Symtab.dest
|
blanchet@43479
|
1944 |
|> sort (prod_ord Real.compare string_ord o pairself swap)
|
blanchet@43479
|
1945 |
end
|
blanchet@41561
|
1946 |
|
blanchet@38506
|
1947 |
end;
|