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(* Title: HOL/Tools/ATP/atp_problem.ML
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Author: Jia Meng, Cambridge University Computer Laboratory and NICTA
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Author: Jasmin Blanchette, TU Muenchen
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Abstract representation of ATP problems and TPTP syntax.
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*)
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signature ATP_PROBLEM =
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sig
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datatype ('a, 'b) ho_term =
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ATerm of 'a * ('a, 'b) ho_term list |
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AAbs of ('a * 'b) * ('a, 'b) ho_term
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datatype quantifier = AForall | AExists
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datatype connective = ANot | AAnd | AOr | AImplies | AIff
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datatype ('a, 'b, 'c) formula =
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AQuant of quantifier * ('a * 'b option) list * ('a, 'b, 'c) formula |
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AConn of connective * ('a, 'b, 'c) formula list |
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AAtom of 'c
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datatype 'a ho_type =
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AType of 'a * 'a ho_type list |
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AFun of 'a ho_type * 'a ho_type |
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ATyAbs of 'a list * 'a ho_type
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datatype tptp_polymorphism = TPTP_Monomorphic | TPTP_Polymorphic
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datatype tptp_explicitness = TPTP_Implicit | TPTP_Explicit
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datatype thf_flavor = THF_Without_Choice | THF_With_Choice
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datatype dfg_flavor = DFG_Unsorted | DFG_Sorted
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datatype atp_format =
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CNF |
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CNF_UEQ |
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FOF |
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TFF of tptp_polymorphism * tptp_explicitness |
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THF of tptp_polymorphism * tptp_explicitness * thf_flavor |
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DFG of dfg_flavor
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datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture
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datatype 'a problem_line =
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Decl of string * 'a * 'a ho_type |
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Formula of string * formula_kind
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* ('a, 'a ho_type, ('a, 'a ho_type) ho_term) formula
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* (string, string ho_type) ho_term option
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* (string, string ho_type) ho_term option
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type 'a problem = (string * 'a problem_line list) list
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val isabelle_info_prefix : string
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val isabelle_info : atp_format -> string -> (string, 'a) ho_term option
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val introN : string
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val elimN : string
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val simpN : string
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val tptp_cnf : string
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val tptp_fof : string
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val tptp_tff : string
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val tptp_thf : string
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val tptp_has_type : string
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val tptp_type_of_types : string
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val tptp_bool_type : string
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val tptp_individual_type : string
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val tptp_fun_type : string
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val tptp_product_type : string
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val tptp_forall : string
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val tptp_ho_forall : string
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val tptp_pi_binder : string
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val tptp_exists : string
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val tptp_ho_exists : string
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val tptp_choice : string
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val tptp_not : string
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val tptp_and : string
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val tptp_or : string
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val tptp_implies : string
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val tptp_if : string
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val tptp_iff : string
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val tptp_not_iff : string
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val tptp_app : string
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val tptp_not_infix : string
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val tptp_equal : string
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val tptp_old_equal : string
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val tptp_false : string
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val tptp_true : string
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val tptp_empty_list : string
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val is_tptp_equal : string -> bool
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val is_built_in_tptp_symbol : string -> bool
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val is_tptp_variable : string -> bool
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val is_tptp_user_symbol : string -> bool
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val atype_of_types : (string * string) ho_type
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val bool_atype : (string * string) ho_type
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val individual_atype : (string * string) ho_type
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val mk_anot : ('a, 'b, 'c) formula -> ('a, 'b, 'c) formula
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val mk_aconn :
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connective -> ('a, 'b, 'c) formula -> ('a, 'b, 'c) formula
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-> ('a, 'b, 'c) formula
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val aconn_fold :
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bool option -> (bool option -> 'a -> 'b -> 'b) -> connective * 'a list
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-> 'b -> 'b
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val aconn_map :
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bool option -> (bool option -> 'a -> ('b, 'c, 'd) formula)
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-> connective * 'a list -> ('b, 'c, 'd) formula
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val formula_fold :
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bool option -> (bool option -> 'c -> 'd -> 'd) -> ('a, 'b, 'c) formula
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-> 'd -> 'd
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val formula_map : ('c -> 'd) -> ('a, 'b, 'c) formula -> ('a, 'b, 'd) formula
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val is_format_higher_order : atp_format -> bool
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val is_format_typed : atp_format -> bool
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val lines_for_atp_problem : atp_format -> string problem -> string list
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val ensure_cnf_problem :
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(string * string) problem -> (string * string) problem
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val filter_cnf_ueq_problem :
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(string * string) problem -> (string * string) problem
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val declared_syms_in_problem : (string * ''a) problem -> (string * ''a) list
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val nice_atp_problem :
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bool -> ('a * (string * string) problem_line list) list
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-> ('a * string problem_line list) list
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* (string Symtab.table * string Symtab.table) option
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end;
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structure ATP_Problem : ATP_PROBLEM =
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struct
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open ATP_Util
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(** ATP problem **)
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datatype ('a, 'b) ho_term =
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ATerm of 'a * ('a, 'b) ho_term list |
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AAbs of ('a * 'b) * ('a, 'b) ho_term
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datatype quantifier = AForall | AExists
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datatype connective = ANot | AAnd | AOr | AImplies | AIff
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datatype ('a, 'b, 'c) formula =
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AQuant of quantifier * ('a * 'b option) list * ('a, 'b, 'c) formula |
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AConn of connective * ('a, 'b, 'c) formula list |
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AAtom of 'c
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datatype 'a ho_type =
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AType of 'a * 'a ho_type list |
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AFun of 'a ho_type * 'a ho_type |
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ATyAbs of 'a list * 'a ho_type
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datatype tptp_polymorphism = TPTP_Monomorphic | TPTP_Polymorphic
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datatype tptp_explicitness = TPTP_Implicit | TPTP_Explicit
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datatype thf_flavor = THF_Without_Choice | THF_With_Choice
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datatype dfg_flavor = DFG_Unsorted | DFG_Sorted
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datatype atp_format =
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CNF |
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CNF_UEQ |
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FOF |
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TFF of tptp_polymorphism * tptp_explicitness |
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THF of tptp_polymorphism * tptp_explicitness * thf_flavor |
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DFG of dfg_flavor
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datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture
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datatype 'a problem_line =
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Decl of string * 'a * 'a ho_type |
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Formula of string * formula_kind * ('a, 'a ho_type, ('a, 'a ho_type) ho_term) formula
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* (string, string ho_type) ho_term option * (string, string ho_type) ho_term option
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type 'a problem = (string * 'a problem_line list) list
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val isabelle_info_prefix = "isabelle_"
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(* Currently, only newer versions of SPASS, with sorted DFG format support, can
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process Isabelle metainformation. *)
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fun isabelle_info (DFG DFG_Sorted) s =
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SOME (ATerm ("[]", [ATerm (isabelle_info_prefix ^ s, [])]))
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| isabelle_info _ _ = NONE
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val introN = "intro"
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val elimN = "elim"
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val simpN = "simp"
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fun is_isabelle_info suffix (SOME (ATerm ("[]", [ATerm (s, [])]))) =
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s = isabelle_info_prefix ^ suffix
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| is_isabelle_info _ _ = false
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(* official TPTP syntax *)
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val tptp_cnf = "cnf"
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val tptp_fof = "fof"
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val tptp_tff = "tff"
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val tptp_thf = "thf"
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val tptp_has_type = ":"
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val tptp_type_of_types = "$tType"
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val tptp_bool_type = "$o"
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val tptp_individual_type = "$i"
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val tptp_fun_type = ">"
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val tptp_product_type = "*"
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val tptp_forall = "!"
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val tptp_ho_forall = "!!"
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val tptp_pi_binder = "!>"
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val tptp_exists = "?"
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val tptp_ho_exists = "??"
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val tptp_choice = "@+"
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val tptp_not = "~"
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val tptp_and = "&"
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val tptp_or = "|"
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val tptp_implies = "=>"
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val tptp_if = "<="
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val tptp_iff = "<=>"
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val tptp_not_iff = "<~>"
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val tptp_app = "@"
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val tptp_not_infix = "!"
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val tptp_equal = "="
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val tptp_old_equal = "equal"
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val tptp_false = "$false"
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val tptp_true = "$true"
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val tptp_empty_list = "[]"
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fun is_tptp_equal s = (s = tptp_equal orelse s = tptp_old_equal)
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fun is_built_in_tptp_symbol s =
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s = tptp_old_equal orelse not (Char.isAlpha (String.sub (s, 0)))
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fun is_tptp_variable s = Char.isUpper (String.sub (s, 0))
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val is_tptp_user_symbol = not o (is_tptp_variable orf is_built_in_tptp_symbol)
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val atype_of_types = AType (`I tptp_type_of_types, [])
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val bool_atype = AType (`I tptp_bool_type, [])
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val individual_atype = AType (`I tptp_individual_type, [])
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fun raw_polarities_of_conn ANot = (SOME false, NONE)
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| raw_polarities_of_conn AAnd = (SOME true, SOME true)
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| raw_polarities_of_conn AOr = (SOME true, SOME true)
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| raw_polarities_of_conn AImplies = (SOME false, SOME true)
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| raw_polarities_of_conn AIff = (NONE, NONE)
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fun polarities_of_conn NONE = K (NONE, NONE)
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| polarities_of_conn (SOME pos) =
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raw_polarities_of_conn #> not pos ? pairself (Option.map not)
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fun mk_anot (AConn (ANot, [phi])) = phi
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| mk_anot phi = AConn (ANot, [phi])
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fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
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fun aconn_fold pos f (ANot, [phi]) = f (Option.map not pos) phi
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| aconn_fold pos f (AImplies, [phi1, phi2]) =
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f (Option.map not pos) phi1 #> f pos phi2
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| aconn_fold pos f (AAnd, phis) = fold (f pos) phis
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| aconn_fold pos f (AOr, phis) = fold (f pos) phis
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| aconn_fold _ f (_, phis) = fold (f NONE) phis
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fun aconn_map pos f (ANot, [phi]) = AConn (ANot, [f (Option.map not pos) phi])
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| aconn_map pos f (AImplies, [phi1, phi2]) =
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AConn (AImplies, [f (Option.map not pos) phi1, f pos phi2])
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| aconn_map pos f (AAnd, phis) = AConn (AAnd, map (f pos) phis)
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| aconn_map pos f (AOr, phis) = AConn (AOr, map (f pos) phis)
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| aconn_map _ f (c, phis) = AConn (c, map (f NONE) phis)
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fun formula_fold pos f =
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let
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fun fld pos (AQuant (_, _, phi)) = fld pos phi
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| fld pos (AConn conn) = aconn_fold pos fld conn
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| fld pos (AAtom tm) = f pos tm
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in fld pos end
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fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
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| formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
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| formula_map f (AAtom tm) = AAtom (f tm)
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blanchet@46174
|
256 |
fun is_format_higher_order (THF _) = true
|
blanchet@46174
|
257 |
| is_format_higher_order _ = false
|
blanchet@45354
|
258 |
fun is_format_typed (TFF _) = true
|
blanchet@45618
|
259 |
| is_format_typed (THF _) = true
|
blanchet@46174
|
260 |
| is_format_typed (DFG DFG_Sorted) = true
|
blanchet@45106
|
261 |
| is_format_typed _ = false
|
blanchet@43839
|
262 |
|
blanchet@46172
|
263 |
fun tptp_string_for_kind Axiom = "axiom"
|
blanchet@46172
|
264 |
| tptp_string_for_kind Definition = "definition"
|
blanchet@46172
|
265 |
| tptp_string_for_kind Lemma = "lemma"
|
blanchet@46172
|
266 |
| tptp_string_for_kind Hypothesis = "hypothesis"
|
blanchet@46172
|
267 |
| tptp_string_for_kind Conjecture = "conjecture"
|
blanchet@38854
|
268 |
|
blanchet@46172
|
269 |
fun tptp_string_for_app format func args =
|
blanchet@46174
|
270 |
if is_format_higher_order format then
|
blanchet@45655
|
271 |
"(" ^ space_implode (" " ^ tptp_app ^ " ") (func :: args) ^ ")"
|
blanchet@45655
|
272 |
else
|
blanchet@45655
|
273 |
func ^ "(" ^ commas args ^ ")"
|
blanchet@45655
|
274 |
|
blanchet@45458
|
275 |
fun flatten_type (ATyAbs (tys, ty)) = ATyAbs (tys, flatten_type ty)
|
blanchet@45458
|
276 |
| flatten_type (ty as AFun (ty1 as AType _, ty2)) =
|
blanchet@45458
|
277 |
(case flatten_type ty2 of
|
blanchet@45458
|
278 |
AFun (ty' as AType (s, tys), ty) =>
|
blanchet@45458
|
279 |
AFun (AType (tptp_product_type,
|
blanchet@45458
|
280 |
ty1 :: (if s = tptp_product_type then tys else [ty'])), ty)
|
blanchet@45458
|
281 |
| _ => ty)
|
blanchet@45458
|
282 |
| flatten_type (ty as AType _) = ty
|
blanchet@45458
|
283 |
| flatten_type _ =
|
blanchet@43804
|
284 |
raise Fail "unexpected higher-order type in first-order format"
|
blanchet@43804
|
285 |
|
blanchet@45655
|
286 |
fun str_for_type format ty =
|
blanchet@45457
|
287 |
let
|
blanchet@46174
|
288 |
val dfg = (format = DFG DFG_Sorted)
|
blanchet@46172
|
289 |
fun str _ (AType (s, [])) =
|
blanchet@46172
|
290 |
if dfg andalso s = tptp_individual_type then "Top" else s
|
blanchet@45458
|
291 |
| str _ (AType (s, tys)) =
|
blanchet@45655
|
292 |
let val ss = tys |> map (str false) in
|
blanchet@45655
|
293 |
if s = tptp_product_type then
|
blanchet@46172
|
294 |
ss |> space_implode
|
blanchet@46172
|
295 |
(if dfg then ", " else " " ^ tptp_product_type ^ " ")
|
blanchet@46172
|
296 |
|> (not dfg andalso length ss > 1) ? enclose "(" ")"
|
blanchet@45655
|
297 |
else
|
blanchet@46172
|
298 |
tptp_string_for_app format s ss
|
blanchet@45655
|
299 |
end
|
blanchet@45457
|
300 |
| str rhs (AFun (ty1, ty2)) =
|
blanchet@46172
|
301 |
(str false ty1 |> dfg ? enclose "(" ")") ^ " " ^
|
blanchet@46172
|
302 |
(if dfg then "" else tptp_fun_type ^ " ") ^ str true ty2
|
blanchet@45457
|
303 |
|> not rhs ? enclose "(" ")"
|
blanchet@45458
|
304 |
| str _ (ATyAbs (ss, ty)) =
|
blanchet@45514
|
305 |
tptp_pi_binder ^ "[" ^
|
blanchet@45458
|
306 |
commas (map (suffix (" " ^ tptp_has_type ^ " " ^ tptp_type_of_types))
|
blanchet@45603
|
307 |
ss) ^ "]: " ^ str false ty
|
blanchet@45457
|
308 |
in str true ty end
|
blanchet@45457
|
309 |
|
blanchet@45655
|
310 |
fun string_for_type (format as THF _) ty = str_for_type format ty
|
blanchet@46172
|
311 |
| string_for_type format ty = str_for_type format (flatten_type ty)
|
blanchet@43804
|
312 |
|
blanchet@46172
|
313 |
fun tptp_string_for_quantifier AForall = tptp_forall
|
blanchet@46172
|
314 |
| tptp_string_for_quantifier AExists = tptp_exists
|
blanchet@43804
|
315 |
|
blanchet@46172
|
316 |
fun tptp_string_for_connective ANot = tptp_not
|
blanchet@46172
|
317 |
| tptp_string_for_connective AAnd = tptp_and
|
blanchet@46172
|
318 |
| tptp_string_for_connective AOr = tptp_or
|
blanchet@46172
|
319 |
| tptp_string_for_connective AImplies = tptp_implies
|
blanchet@46172
|
320 |
| tptp_string_for_connective AIff = tptp_iff
|
blanchet@43804
|
321 |
|
blanchet@43803
|
322 |
fun string_for_bound_var format (s, ty) =
|
blanchet@45457
|
323 |
s ^
|
blanchet@45457
|
324 |
(if is_format_typed format then
|
blanchet@45457
|
325 |
" " ^ tptp_has_type ^ " " ^
|
blanchet@45457
|
326 |
(ty |> the_default (AType (tptp_individual_type, []))
|
blanchet@45457
|
327 |
|> string_for_type format)
|
blanchet@45457
|
328 |
else
|
blanchet@45457
|
329 |
"")
|
blanchet@43804
|
330 |
|
blanchet@45618
|
331 |
fun is_format_with_choice (THF (_, _, THF_With_Choice)) = true
|
blanchet@45618
|
332 |
| is_format_with_choice _ = false
|
blanchet@45618
|
333 |
|
blanchet@46172
|
334 |
fun tptp_string_for_term _ (ATerm (s, [])) = s
|
blanchet@46172
|
335 |
| tptp_string_for_term format (ATerm (s, ts)) =
|
blanchet@45655
|
336 |
(if s = tptp_empty_list then
|
blanchet@45655
|
337 |
(* used for lists in the optional "source" field of a derivation *)
|
blanchet@46172
|
338 |
"[" ^ commas (map (tptp_string_for_term format) ts) ^ "]"
|
blanchet@45655
|
339 |
else if is_tptp_equal s then
|
blanchet@46172
|
340 |
space_implode (" " ^ tptp_equal ^ " ")
|
blanchet@46172
|
341 |
(map (tptp_string_for_term format) ts)
|
blanchet@46174
|
342 |
|> is_format_higher_order format ? enclose "(" ")"
|
blanchet@45655
|
343 |
else case (s = tptp_ho_forall orelse s = tptp_ho_exists,
|
blanchet@45655
|
344 |
s = tptp_choice andalso is_format_with_choice format, ts) of
|
blanchet@45655
|
345 |
(true, _, [AAbs ((s', ty), tm)]) =>
|
blanchet@45655
|
346 |
(* Use syntactic sugar "!" and "?" instead of "!!" and "??" whenever
|
blanchet@45655
|
347 |
possible, to work around LEO-II 1.2.8 parser limitation. *)
|
blanchet@46172
|
348 |
tptp_string_for_formula format
|
blanchet@45655
|
349 |
(AQuant (if s = tptp_ho_forall then AForall else AExists,
|
blanchet@45655
|
350 |
[(s', SOME ty)], AAtom tm))
|
blanchet@45655
|
351 |
| (_, true, [AAbs ((s', ty), tm)]) =>
|
blanchet@45655
|
352 |
(* There is code in "ATP_Translate" to ensure that "Eps" is always
|
blanchet@45655
|
353 |
applied to an abstraction. *)
|
blanchet@45655
|
354 |
tptp_choice ^ "[" ^ s' ^ " : " ^ string_for_type format ty ^ "]: " ^
|
blanchet@46172
|
355 |
tptp_string_for_term format tm ^ ""
|
blanchet@45655
|
356 |
|> enclose "(" ")"
|
blanchet@46172
|
357 |
| _ => tptp_string_for_app format s (map (tptp_string_for_term format) ts))
|
blanchet@46172
|
358 |
| tptp_string_for_term (format as THF _) (AAbs ((s, ty), tm)) =
|
blanchet@45603
|
359 |
"(^[" ^ s ^ " : " ^ string_for_type format ty ^ "]: " ^
|
blanchet@46172
|
360 |
tptp_string_for_term format tm ^ ")"
|
blanchet@46172
|
361 |
| tptp_string_for_term _ _ =
|
blanchet@46172
|
362 |
raise Fail "unexpected term in first-order format"
|
blanchet@46172
|
363 |
and tptp_string_for_formula format (AQuant (q, xs, phi)) =
|
blanchet@46172
|
364 |
tptp_string_for_quantifier q ^
|
blanchet@45603
|
365 |
"[" ^ commas (map (string_for_bound_var format) xs) ^ "]: " ^
|
blanchet@46172
|
366 |
tptp_string_for_formula format phi
|
blanchet@43815
|
367 |
|> enclose "(" ")"
|
blanchet@46172
|
368 |
| tptp_string_for_formula format
|
blanchet@43841
|
369 |
(AConn (ANot, [AAtom (ATerm ("=" (* tptp_equal *), ts))])) =
|
blanchet@43809
|
370 |
space_implode (" " ^ tptp_not_infix ^ tptp_equal ^ " ")
|
blanchet@46172
|
371 |
(map (tptp_string_for_term format) ts)
|
blanchet@46174
|
372 |
|> is_format_higher_order format ? enclose "(" ")"
|
blanchet@46172
|
373 |
| tptp_string_for_formula format (AConn (c, [phi])) =
|
blanchet@46172
|
374 |
tptp_string_for_connective c ^ " " ^
|
blanchet@46172
|
375 |
(tptp_string_for_formula format phi
|
blanchet@46174
|
376 |
|> is_format_higher_order format ? enclose "(" ")")
|
blanchet@43815
|
377 |
|> enclose "(" ")"
|
blanchet@46172
|
378 |
| tptp_string_for_formula format (AConn (c, phis)) =
|
blanchet@46172
|
379 |
space_implode (" " ^ tptp_string_for_connective c ^ " ")
|
blanchet@46172
|
380 |
(map (tptp_string_for_formula format) phis)
|
blanchet@43815
|
381 |
|> enclose "(" ")"
|
blanchet@46172
|
382 |
| tptp_string_for_formula format (AAtom tm) = tptp_string_for_term format tm
|
blanchet@38198
|
383 |
|
blanchet@44558
|
384 |
fun the_source (SOME source) = source
|
blanchet@44558
|
385 |
| the_source NONE =
|
blanchet@44558
|
386 |
ATerm ("inference",
|
blanchet@44558
|
387 |
ATerm ("isabelle", []) :: replicate 2 (ATerm ("[]", [])))
|
blanchet@43510
|
388 |
|
blanchet@46172
|
389 |
fun tptp_string_for_format CNF = tptp_cnf
|
blanchet@46172
|
390 |
| tptp_string_for_format CNF_UEQ = tptp_cnf
|
blanchet@46172
|
391 |
| tptp_string_for_format FOF = tptp_fof
|
blanchet@46172
|
392 |
| tptp_string_for_format (TFF _) = tptp_tff
|
blanchet@46172
|
393 |
| tptp_string_for_format (THF _) = tptp_thf
|
blanchet@46174
|
394 |
| tptp_string_for_format (DFG _) = raise Fail "non-TPTP format"
|
blanchet@43803
|
395 |
|
blanchet@46172
|
396 |
fun tptp_string_for_problem_line format (Decl (ident, sym, ty)) =
|
blanchet@46172
|
397 |
tptp_string_for_format format ^ "(" ^ ident ^ ", type,\n " ^ sym ^
|
blanchet@46172
|
398 |
" : " ^ string_for_type format ty ^ ").\n"
|
blanchet@46172
|
399 |
| tptp_string_for_problem_line format
|
blanchet@46172
|
400 |
(Formula (ident, kind, phi, source, info)) =
|
blanchet@46172
|
401 |
tptp_string_for_format format ^ "(" ^ ident ^ ", " ^
|
blanchet@46172
|
402 |
tptp_string_for_kind kind ^ ",\n (" ^
|
blanchet@46172
|
403 |
tptp_string_for_formula format phi ^ ")" ^
|
blanchet@43780
|
404 |
(case (source, info) of
|
blanchet@43580
|
405 |
(NONE, NONE) => ""
|
blanchet@46172
|
406 |
| (SOME tm, NONE) => ", " ^ tptp_string_for_term format tm
|
blanchet@43580
|
407 |
| (_, SOME tm) =>
|
blanchet@46172
|
408 |
", " ^ tptp_string_for_term format (the_source source) ^
|
blanchet@46172
|
409 |
", " ^ tptp_string_for_term format tm) ^ ").\n"
|
blanchet@46172
|
410 |
|
blanchet@46172
|
411 |
fun tptp_lines format =
|
blanchet@37643
|
412 |
maps (fn (_, []) => []
|
blanchet@37643
|
413 |
| (heading, lines) =>
|
wenzelm@41739
|
414 |
"\n% " ^ heading ^ " (" ^ string_of_int (length lines) ^ ")\n" ::
|
blanchet@46172
|
415 |
map (tptp_string_for_problem_line format) lines)
|
blanchet@46172
|
416 |
|
blanchet@46172
|
417 |
fun arity_of_type (AFun (_, ty)) = 1 + arity_of_type ty
|
blanchet@46172
|
418 |
| arity_of_type _ = 0
|
blanchet@46172
|
419 |
|
blanchet@46172
|
420 |
fun binder_atypes (AFun (ty1, ty2)) = ty1 :: binder_atypes ty2
|
blanchet@46172
|
421 |
| binder_atypes _ = []
|
blanchet@46172
|
422 |
|
blanchet@46172
|
423 |
fun is_function_type (AFun (_, ty)) = is_function_type ty
|
blanchet@46172
|
424 |
| is_function_type (AType (s, _)) =
|
blanchet@46172
|
425 |
s <> tptp_type_of_types andalso s <> tptp_bool_type
|
blanchet@46172
|
426 |
| is_function_type _ = false
|
blanchet@46172
|
427 |
|
blanchet@46172
|
428 |
fun is_predicate_type (AFun (_, ty)) = is_predicate_type ty
|
blanchet@46172
|
429 |
| is_predicate_type (AType (s, _)) = (s = tptp_bool_type)
|
blanchet@46172
|
430 |
| is_predicate_type _ = false
|
blanchet@46172
|
431 |
|
blanchet@46174
|
432 |
fun dfg_string_for_formula flavor info =
|
blanchet@46172
|
433 |
let
|
blanchet@46172
|
434 |
fun str_for_term simp (ATerm (s, tms)) =
|
blanchet@46172
|
435 |
(if is_tptp_equal s then "equal" |> simp ? suffix ":lr"
|
blanchet@46172
|
436 |
else if s = tptp_true then "true"
|
blanchet@46172
|
437 |
else if s = tptp_false then "false"
|
blanchet@46172
|
438 |
else s) ^
|
blanchet@46172
|
439 |
(if null tms then ""
|
blanchet@46172
|
440 |
else "(" ^ commas (map (str_for_term false) tms) ^ ")")
|
blanchet@46172
|
441 |
| str_for_term _ _ = raise Fail "unexpected term in first-order format"
|
blanchet@46172
|
442 |
fun str_for_quant AForall = "forall"
|
blanchet@46172
|
443 |
| str_for_quant AExists = "exists"
|
blanchet@46172
|
444 |
fun str_for_conn _ ANot = "not"
|
blanchet@46172
|
445 |
| str_for_conn _ AAnd = "and"
|
blanchet@46172
|
446 |
| str_for_conn _ AOr = "or"
|
blanchet@46172
|
447 |
| str_for_conn _ AImplies = "implies"
|
blanchet@46172
|
448 |
| str_for_conn simp AIff = "equiv" |> simp ? suffix ":lr"
|
blanchet@46172
|
449 |
fun str_for_formula simp (AQuant (q, xs, phi)) =
|
blanchet@46172
|
450 |
str_for_quant q ^ "(" ^ "[" ^
|
blanchet@46174
|
451 |
commas (map (string_for_bound_var (DFG flavor)) xs) ^ "], " ^
|
blanchet@46172
|
452 |
str_for_formula simp phi ^ ")"
|
blanchet@46172
|
453 |
| str_for_formula simp (AConn (c, phis)) =
|
blanchet@46172
|
454 |
str_for_conn simp c ^ "(" ^
|
blanchet@46172
|
455 |
commas (map (str_for_formula false) phis) ^ ")"
|
blanchet@46172
|
456 |
| str_for_formula simp (AAtom tm) = str_for_term simp tm
|
blanchet@46172
|
457 |
in str_for_formula (is_isabelle_info simpN info) end
|
blanchet@46172
|
458 |
|
blanchet@46174
|
459 |
fun dfg_lines flavor problem =
|
blanchet@46172
|
460 |
let
|
blanchet@46175
|
461 |
val sorted = (flavor = DFG_Sorted)
|
blanchet@46174
|
462 |
val format = DFG flavor
|
blanchet@46172
|
463 |
fun ary sym ty =
|
blanchet@46172
|
464 |
"(" ^ sym ^ ", " ^ string_of_int (arity_of_type ty) ^ ")"
|
blanchet@46172
|
465 |
fun fun_typ sym ty =
|
blanchet@46174
|
466 |
"function(" ^ sym ^ ", " ^ string_for_type format ty ^ ")."
|
blanchet@46172
|
467 |
fun pred_typ sym ty =
|
blanchet@46172
|
468 |
"predicate(" ^
|
blanchet@46174
|
469 |
commas (sym :: map (string_for_type format) (binder_atypes ty)) ^ ")."
|
blanchet@46172
|
470 |
fun formula pred (Formula (ident, kind, phi, _, info)) =
|
blanchet@46172
|
471 |
if pred kind then
|
blanchet@46174
|
472 |
SOME ("formula(" ^ dfg_string_for_formula flavor info phi ^ ", " ^
|
blanchet@46174
|
473 |
ident ^ ").")
|
blanchet@46172
|
474 |
else
|
blanchet@46172
|
475 |
NONE
|
blanchet@46172
|
476 |
| formula _ _ = NONE
|
blanchet@46172
|
477 |
fun filt f = problem |> map (map_filter f o snd) |> flat
|
blanchet@46172
|
478 |
val func_aries =
|
blanchet@46172
|
479 |
filt (fn Decl (_, sym, ty) =>
|
blanchet@46172
|
480 |
if is_function_type ty then SOME (ary sym ty) else NONE
|
blanchet@46172
|
481 |
| _ => NONE)
|
blanchet@46172
|
482 |
|> commas |> enclose "functions [" "]."
|
blanchet@46172
|
483 |
val pred_aries =
|
blanchet@46172
|
484 |
filt (fn Decl (_, sym, ty) =>
|
blanchet@46172
|
485 |
if is_predicate_type ty then SOME (ary sym ty) else NONE
|
blanchet@46172
|
486 |
| _ => NONE)
|
blanchet@46172
|
487 |
|> commas |> enclose "predicates [" "]."
|
blanchet@46175
|
488 |
fun sorts () =
|
blanchet@46172
|
489 |
filt (fn Decl (_, sym, AType (s, [])) =>
|
blanchet@46172
|
490 |
if s = tptp_type_of_types then SOME sym else NONE
|
blanchet@46172
|
491 |
| _ => NONE)
|
blanchet@46172
|
492 |
|> commas |> enclose "sorts [" "]."
|
blanchet@46175
|
493 |
val syms = [func_aries, pred_aries] @ (if sorted then [sorts ()] else [])
|
blanchet@46175
|
494 |
fun func_sigs () =
|
blanchet@46172
|
495 |
filt (fn Decl (_, sym, ty) =>
|
blanchet@46172
|
496 |
if is_function_type ty then SOME (fun_typ sym ty) else NONE
|
blanchet@46172
|
497 |
| _ => NONE)
|
blanchet@46175
|
498 |
fun pred_sigs () =
|
blanchet@46172
|
499 |
filt (fn Decl (_, sym, ty) =>
|
blanchet@46172
|
500 |
if is_predicate_type ty then SOME (pred_typ sym ty) else NONE
|
blanchet@46172
|
501 |
| _ => NONE)
|
blanchet@46175
|
502 |
val decls = if sorted then func_sigs () @ pred_sigs () else []
|
blanchet@46172
|
503 |
val axioms = filt (formula (curry (op <>) Conjecture))
|
blanchet@46172
|
504 |
val conjs = filt (formula (curry (op =) Conjecture))
|
blanchet@46172
|
505 |
fun list_of _ [] = []
|
blanchet@46172
|
506 |
| list_of heading ss =
|
blanchet@46172
|
507 |
"list_of_" ^ heading ^ ".\n" :: map (suffix "\n") ss @
|
blanchet@46172
|
508 |
["end_of_list.\n\n"]
|
blanchet@46172
|
509 |
in
|
blanchet@46172
|
510 |
"\nbegin_problem(isabelle).\n\n" ::
|
blanchet@46172
|
511 |
list_of "descriptions"
|
blanchet@46172
|
512 |
["name({**}).", "author({**}).", "status(unknown).",
|
blanchet@46172
|
513 |
"description({**})."] @
|
blanchet@46175
|
514 |
list_of "symbols" syms @
|
blanchet@46175
|
515 |
list_of "declarations" decls @
|
blanchet@46172
|
516 |
list_of "formulae(axioms)" axioms @
|
blanchet@46172
|
517 |
list_of "formulae(conjectures)" conjs @
|
blanchet@46172
|
518 |
["end_problem.\n"]
|
blanchet@46172
|
519 |
end
|
blanchet@46172
|
520 |
|
blanchet@46172
|
521 |
fun lines_for_atp_problem format problem =
|
blanchet@46172
|
522 |
"% This file was generated by Isabelle (most likely Sledgehammer)\n\
|
blanchet@46172
|
523 |
\% " ^ timestamp () ^ "\n" ::
|
blanchet@46174
|
524 |
(case format of
|
blanchet@46174
|
525 |
DFG flavor => dfg_lines flavor
|
blanchet@46174
|
526 |
| _ => tptp_lines format) problem
|
blanchet@37643
|
527 |
|
blanchet@43780
|
528 |
|
blanchet@43939
|
529 |
(** CNF (Metis) and CNF UEQ (Waldmeister) **)
|
blanchet@43780
|
530 |
|
blanchet@43780
|
531 |
fun is_problem_line_negated (Formula (_, _, AConn (ANot, _), _, _)) = true
|
blanchet@43780
|
532 |
| is_problem_line_negated _ = false
|
blanchet@43780
|
533 |
|
blanchet@44034
|
534 |
fun is_problem_line_cnf_ueq (Formula (_, _, AAtom (ATerm ((s, _), _)), _, _)) =
|
blanchet@44034
|
535 |
is_tptp_equal s
|
blanchet@43780
|
536 |
| is_problem_line_cnf_ueq _ = false
|
blanchet@43780
|
537 |
|
blanchet@43785
|
538 |
fun open_conjecture_term (ATerm ((s, s'), tms)) =
|
nik@44535
|
539 |
ATerm (if is_tptp_variable s then (s |> Name.desymbolize false, s')
|
nik@44535
|
540 |
else (s, s'), tms |> map open_conjecture_term)
|
nik@44535
|
541 |
| open_conjecture_term _ = raise Fail "unexpected higher-order term"
|
blanchet@43939
|
542 |
fun open_formula conj =
|
blanchet@43939
|
543 |
let
|
blanchet@44034
|
544 |
(* We are conveniently assuming that all bound variable names are
|
blanchet@44034
|
545 |
distinct, which should be the case for the formulas we generate. *)
|
blanchet@44034
|
546 |
fun opn (pos as SOME true) (AQuant (AForall, _, phi)) = opn pos phi
|
blanchet@44034
|
547 |
| opn (pos as SOME false) (AQuant (AExists, _, phi)) = opn pos phi
|
blanchet@43939
|
548 |
| opn pos (AConn (ANot, [phi])) = mk_anot (opn (Option.map not pos) phi)
|
blanchet@43939
|
549 |
| opn pos (AConn (c, [phi1, phi2])) =
|
blanchet@43939
|
550 |
let val (pos1, pos2) = polarities_of_conn pos c in
|
blanchet@43939
|
551 |
AConn (c, [opn pos1 phi1, opn pos2 phi2])
|
blanchet@43939
|
552 |
end
|
blanchet@43939
|
553 |
| opn _ (AAtom t) = AAtom (t |> conj ? open_conjecture_term)
|
blanchet@44283
|
554 |
| opn _ phi = phi
|
blanchet@43939
|
555 |
in opn (SOME (not conj)) end
|
blanchet@43785
|
556 |
fun open_formula_line (Formula (ident, kind, phi, source, info)) =
|
blanchet@43785
|
557 |
Formula (ident, kind, open_formula (kind = Conjecture) phi, source, info)
|
blanchet@43785
|
558 |
| open_formula_line line = line
|
blanchet@43780
|
559 |
|
blanchet@43780
|
560 |
fun negate_conjecture_line (Formula (ident, Conjecture, phi, source, info)) =
|
blanchet@43783
|
561 |
Formula (ident, Hypothesis, mk_anot phi, source, info)
|
blanchet@43780
|
562 |
| negate_conjecture_line line = line
|
blanchet@43780
|
563 |
|
blanchet@43939
|
564 |
exception CLAUSIFY of unit
|
blanchet@43939
|
565 |
|
blanchet@43967
|
566 |
(* This "clausification" only expands syntactic sugar, such as "phi => psi" to
|
blanchet@43967
|
567 |
"~ phi | psi" and "phi <=> psi" to "~ phi | psi" and "~ psi | phi". We don't
|
blanchet@43967
|
568 |
attempt to distribute conjunctions over disjunctions. *)
|
blanchet@44034
|
569 |
fun clausify_formula pos (phi as AAtom _) = [phi |> not pos ? mk_anot]
|
blanchet@44034
|
570 |
| clausify_formula pos (AConn (ANot, [phi])) = clausify_formula (not pos) phi
|
blanchet@44034
|
571 |
| clausify_formula true (AConn (AOr, [phi1, phi2])) =
|
blanchet@44034
|
572 |
(phi1, phi2) |> pairself (clausify_formula true)
|
blanchet@44034
|
573 |
|> uncurry (map_product (mk_aconn AOr))
|
blanchet@44034
|
574 |
| clausify_formula false (AConn (AAnd, [phi1, phi2])) =
|
blanchet@44034
|
575 |
(phi1, phi2) |> pairself (clausify_formula false)
|
blanchet@44034
|
576 |
|> uncurry (map_product (mk_aconn AOr))
|
blanchet@44034
|
577 |
| clausify_formula true (AConn (AImplies, [phi1, phi2])) =
|
blanchet@44034
|
578 |
clausify_formula true (AConn (AOr, [mk_anot phi1, phi2]))
|
blanchet@44034
|
579 |
| clausify_formula true (AConn (AIff, phis)) =
|
blanchet@44034
|
580 |
clausify_formula true (AConn (AImplies, phis)) @
|
blanchet@44034
|
581 |
clausify_formula true (AConn (AImplies, rev phis))
|
blanchet@44034
|
582 |
| clausify_formula _ _ = raise CLAUSIFY ()
|
blanchet@43939
|
583 |
|
blanchet@43939
|
584 |
fun clausify_formula_line (Formula (ident, kind, phi, source, info)) =
|
blanchet@43967
|
585 |
let
|
blanchet@43967
|
586 |
val (n, phis) = phi |> try (clausify_formula true) |> these |> `length
|
blanchet@43967
|
587 |
in
|
blanchet@43967
|
588 |
map2 (fn phi => fn j =>
|
blanchet@44153
|
589 |
Formula (ident ^ replicate_string (j - 1) "x", kind, phi, source,
|
blanchet@44153
|
590 |
info))
|
blanchet@43967
|
591 |
phis (1 upto n)
|
blanchet@43967
|
592 |
end
|
blanchet@43967
|
593 |
| clausify_formula_line _ = []
|
blanchet@43939
|
594 |
|
blanchet@43939
|
595 |
fun ensure_cnf_problem_line line =
|
blanchet@43939
|
596 |
line |> open_formula_line |> negate_conjecture_line |> clausify_formula_line
|
blanchet@43939
|
597 |
|
blanchet@43939
|
598 |
fun ensure_cnf_problem problem =
|
blanchet@43967
|
599 |
problem |> map (apsnd (maps ensure_cnf_problem_line))
|
blanchet@43933
|
600 |
|
blanchet@43803
|
601 |
fun filter_cnf_ueq_problem problem =
|
blanchet@43803
|
602 |
problem
|
blanchet@43803
|
603 |
|> map (apsnd (map open_formula_line
|
blanchet@43803
|
604 |
#> filter is_problem_line_cnf_ueq
|
blanchet@43803
|
605 |
#> map negate_conjecture_line))
|
blanchet@43803
|
606 |
|> (fn problem =>
|
blanchet@43780
|
607 |
let
|
blanchet@44688
|
608 |
val lines = problem |> maps snd
|
blanchet@44688
|
609 |
val conjs = lines |> filter is_problem_line_negated
|
blanchet@44688
|
610 |
in if length conjs = 1 andalso conjs <> lines then problem else [] end)
|
blanchet@38251
|
611 |
|
blanchet@37643
|
612 |
|
blanchet@43839
|
613 |
(** Symbol declarations **)
|
blanchet@43839
|
614 |
|
blanchet@43839
|
615 |
fun add_declared_syms_in_problem_line (Decl (_, sym, _)) = insert (op =) sym
|
blanchet@43839
|
616 |
| add_declared_syms_in_problem_line _ = I
|
blanchet@43839
|
617 |
fun declared_syms_in_problem problem =
|
blanchet@43839
|
618 |
fold (fold add_declared_syms_in_problem_line o snd) problem []
|
blanchet@43839
|
619 |
|
blanchet@37643
|
620 |
(** Nice names **)
|
blanchet@37643
|
621 |
|
blanchet@37624
|
622 |
fun empty_name_pool readable_names =
|
blanchet@37643
|
623 |
if readable_names then SOME (Symtab.empty, Symtab.empty) else NONE
|
blanchet@37624
|
624 |
|
blanchet@37624
|
625 |
fun pool_fold f xs z = pair z #> fold_rev (fn x => uncurry (f x)) xs
|
blanchet@37624
|
626 |
fun pool_map f xs =
|
blanchet@37624
|
627 |
pool_fold (fn x => fn ys => fn pool => f x pool |>> (fn y => y :: ys)) xs []
|
blanchet@37624
|
628 |
|
blanchet@43088
|
629 |
val no_qualifiers =
|
blanchet@43088
|
630 |
let
|
blanchet@43088
|
631 |
fun skip [] = []
|
blanchet@43088
|
632 |
| skip (#"." :: cs) = skip cs
|
blanchet@43088
|
633 |
| skip (c :: cs) = if Char.isAlphaNum c then skip cs else c :: keep cs
|
blanchet@43088
|
634 |
and keep [] = []
|
blanchet@43088
|
635 |
| keep (#"." :: cs) = skip cs
|
blanchet@43088
|
636 |
| keep (c :: cs) = c :: keep cs
|
blanchet@43088
|
637 |
in String.explode #> rev #> keep #> rev #> String.implode end
|
blanchet@43088
|
638 |
|
blanchet@43626
|
639 |
(* Long names can slow down the ATPs. *)
|
blanchet@43589
|
640 |
val max_readable_name_size = 20
|
blanchet@43438
|
641 |
|
blanchet@43841
|
642 |
(* "equal" is reserved by some ATPs. "op" is also reserved, to avoid the
|
blanchet@43841
|
643 |
unreadable "op_1", "op_2", etc., in the problem files. "eq" is reserved to
|
blanchet@43841
|
644 |
ensure that "HOL.eq" is correctly mapped to equality (not clear whether this
|
blanchet@43841
|
645 |
is still necessary). *)
|
blanchet@46172
|
646 |
val spass_reserved_nice_names =
|
blanchet@46172
|
647 |
["forall", "exists", "le", "ls", "ge", "gs", "plus", "minus", "mult", "fract",
|
blanchet@46172
|
648 |
"equal", "true", "false", "or", "and", "not", "implies", "implied", "equiv",
|
blanchet@46172
|
649 |
"lr", "def"]
|
blanchet@46172
|
650 |
val reserved_nice_names =
|
blanchet@46172
|
651 |
[tptp_old_equal, "op", "eq"] @ spass_reserved_nice_names
|
blanchet@43780
|
652 |
|
blanchet@37624
|
653 |
fun readable_name full_name s =
|
blanchet@37643
|
654 |
if s = full_name then
|
blanchet@37643
|
655 |
s
|
blanchet@37643
|
656 |
else
|
blanchet@43438
|
657 |
s |> no_qualifiers
|
blanchet@45266
|
658 |
|> perhaps (try (unprefix "'"))
|
blanchet@43438
|
659 |
|> Name.desymbolize (Char.isUpper (String.sub (full_name, 0)))
|
blanchet@43454
|
660 |
|> (fn s =>
|
blanchet@43530
|
661 |
if size s > max_readable_name_size then
|
blanchet@43530
|
662 |
String.substring (s, 0, max_readable_name_size div 2 - 4) ^
|
blanchet@44691
|
663 |
string_of_int (hash_string full_name) ^
|
blanchet@43530
|
664 |
String.extract (s, size s - max_readable_name_size div 2 + 4,
|
blanchet@43530
|
665 |
NONE)
|
blanchet@43454
|
666 |
else
|
blanchet@43454
|
667 |
s)
|
blanchet@43438
|
668 |
|> (fn s => if member (op =) reserved_nice_names s then full_name else s)
|
blanchet@37624
|
669 |
|
blanchet@37624
|
670 |
fun nice_name (full_name, _) NONE = (full_name, NONE)
|
blanchet@37624
|
671 |
| nice_name (full_name, desired_name) (SOME the_pool) =
|
blanchet@43839
|
672 |
if is_built_in_tptp_symbol full_name then
|
blanchet@39630
|
673 |
(full_name, SOME the_pool)
|
blanchet@39630
|
674 |
else case Symtab.lookup (fst the_pool) full_name of
|
blanchet@37624
|
675 |
SOME nice_name => (nice_name, SOME the_pool)
|
blanchet@37624
|
676 |
| NONE =>
|
blanchet@37624
|
677 |
let
|
blanchet@37624
|
678 |
val nice_prefix = readable_name full_name desired_name
|
blanchet@37624
|
679 |
fun add j =
|
blanchet@37624
|
680 |
let
|
blanchet@43515
|
681 |
val nice_name =
|
blanchet@45266
|
682 |
nice_prefix ^ (if j = 0 then "" else string_of_int j)
|
blanchet@37624
|
683 |
in
|
blanchet@37624
|
684 |
case Symtab.lookup (snd the_pool) nice_name of
|
blanchet@37624
|
685 |
SOME full_name' =>
|
blanchet@37624
|
686 |
if full_name = full_name' then (nice_name, the_pool)
|
blanchet@37624
|
687 |
else add (j + 1)
|
blanchet@37624
|
688 |
| NONE =>
|
blanchet@37624
|
689 |
(nice_name,
|
blanchet@37624
|
690 |
(Symtab.update_new (full_name, nice_name) (fst the_pool),
|
blanchet@37624
|
691 |
Symtab.update_new (nice_name, full_name) (snd the_pool)))
|
blanchet@37624
|
692 |
end
|
blanchet@37624
|
693 |
in add 0 |> apsnd SOME end
|
blanchet@37624
|
694 |
|
blanchet@45457
|
695 |
fun nice_type (AType (name, tys)) =
|
blanchet@45457
|
696 |
nice_name name ##>> pool_map nice_type tys #>> AType
|
blanchet@43804
|
697 |
| nice_type (AFun (ty1, ty2)) = nice_type ty1 ##>> nice_type ty2 #>> AFun
|
blanchet@45458
|
698 |
| nice_type (ATyAbs (names, ty)) =
|
blanchet@45458
|
699 |
pool_map nice_name names ##>> nice_type ty #>> ATyAbs
|
nik@44535
|
700 |
fun nice_term (ATerm (name, ts)) =
|
nik@44535
|
701 |
nice_name name ##>> pool_map nice_term ts #>> ATerm
|
nik@44535
|
702 |
| nice_term (AAbs ((name, ty), tm)) =
|
nik@44535
|
703 |
nice_name name ##>> nice_type ty ##>> nice_term tm #>> AAbs
|
blanchet@38198
|
704 |
fun nice_formula (AQuant (q, xs, phi)) =
|
blanchet@43397
|
705 |
pool_map nice_name (map fst xs)
|
blanchet@43397
|
706 |
##>> pool_map (fn NONE => pair NONE
|
blanchet@43804
|
707 |
| SOME ty => nice_type ty #>> SOME) (map snd xs)
|
blanchet@43397
|
708 |
##>> nice_formula phi
|
blanchet@43397
|
709 |
#>> (fn ((ss, ts), phi) => AQuant (q, ss ~~ ts, phi))
|
blanchet@38198
|
710 |
| nice_formula (AConn (c, phis)) =
|
blanchet@38198
|
711 |
pool_map nice_formula phis #>> curry AConn c
|
blanchet@38280
|
712 |
| nice_formula (AAtom tm) = nice_term tm #>> AAtom
|
blanchet@43804
|
713 |
fun nice_problem_line (Decl (ident, sym, ty)) =
|
blanchet@43839
|
714 |
nice_name sym ##>> nice_type ty #>> (fn (sym, ty) => Decl (ident, sym, ty))
|
blanchet@43780
|
715 |
| nice_problem_line (Formula (ident, kind, phi, source, info)) =
|
blanchet@43780
|
716 |
nice_formula phi #>> (fn phi => Formula (ident, kind, phi, source, info))
|
blanchet@38171
|
717 |
fun nice_problem problem =
|
blanchet@37643
|
718 |
pool_map (fn (heading, lines) =>
|
blanchet@38171
|
719 |
pool_map nice_problem_line lines #>> pair heading) problem
|
blanchet@39692
|
720 |
fun nice_atp_problem readable_names problem =
|
blanchet@38251
|
721 |
nice_problem problem (empty_name_pool readable_names)
|
blanchet@37509
|
722 |
|
blanchet@37509
|
723 |
end;
|