wneuper/isa: src/HOL/Tools/ATP/atp_problem.ML@2168126446bb

     1 (*  Title:      HOL/Tools/ATP/atp_problem.ML

     2     Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA

     3     Author:     Jasmin Blanchette, TU Muenchen

     5 Abstract representation of ATP problems and TPTP syntax.

     6 *)

     8 signature ATP_PROBLEM =

     9 sig

    10   datatype ('a, 'b) ho_term =

    11     ATerm of 'a * ('a, 'b) ho_term list |

    12     AAbs of (('a * 'b) * ('a, 'b) ho_term) * ('a, 'b) ho_term list

    13   datatype quantifier = AForall | AExists

    14   datatype connective = ANot | AAnd | AOr | AImplies | AIff

    15   datatype ('a, 'b, 'c) formula =

    16     AQuant of quantifier * ('a * 'b option) list * ('a, 'b, 'c) formula |

    17     AConn of connective * ('a, 'b, 'c) formula list |

    18     AAtom of 'c

    20   datatype 'a ho_type =

    21     AType of 'a * 'a ho_type list |

    22     AFun of 'a ho_type * 'a ho_type |

    23     ATyAbs of 'a list * 'a ho_type

    25   type term_order =

    26     {is_lpo : bool,

    27      gen_weights : bool,

    28      gen_prec : bool,

    29      gen_simp : bool}

    31   datatype tptp_polymorphism = TPTP_Monomorphic | TPTP_Polymorphic

    32   datatype tptp_explicitness = TPTP_Implicit | TPTP_Explicit

    33   datatype thf_flavor = THF_Without_Choice | THF_With_Choice

    34   datatype dfg_flavor = DFG_Unsorted | DFG_Sorted

    36   datatype atp_format =

    37     CNF |

    38     CNF_UEQ |

    39     FOF |

    40     TFF of tptp_polymorphism * tptp_explicitness |

    41     THF of tptp_polymorphism * tptp_explicitness * thf_flavor |

    42     DFG of dfg_flavor

    44   datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture

    45   datatype 'a problem_line =

    46     Decl of string * 'a * 'a ho_type |

    47     Formula of string * formula_kind

    48                * ('a, 'a ho_type, ('a, 'a ho_type) ho_term) formula

    49                * (string, string ho_type) ho_term option

    50                * (string, string ho_type) ho_term list

    51   type 'a problem = (string * 'a problem_line list) list

    53   val tptp_cnf : string

    54   val tptp_fof : string

    55   val tptp_tff : string

    56   val tptp_thf : string

    57   val tptp_has_type : string

    58   val tptp_type_of_types : string

    59   val tptp_bool_type : string

    60   val tptp_individual_type : string

    61   val tptp_fun_type : string

    62   val tptp_product_type : string

    63   val tptp_forall : string

    64   val tptp_ho_forall : string

    65   val tptp_pi_binder : string

    66   val tptp_exists : string

    67   val tptp_ho_exists : string

    68   val tptp_choice : string

    69   val tptp_not : string

    70   val tptp_and : string

    71   val tptp_or : string

    72   val tptp_implies : string

    73   val tptp_if : string

    74   val tptp_iff : string

    75   val tptp_not_iff : string

    76   val tptp_app : string

    77   val tptp_not_infix : string

    78   val tptp_equal : string

    79   val tptp_old_equal : string

    80   val tptp_false : string

    81   val tptp_true : string

    82   val tptp_empty_list : string

    83   val isabelle_info_prefix : string

    84   val isabelle_info : string -> int -> (string, 'a) ho_term list

    85   val extract_isabelle_status : (string, 'a) ho_term list -> string option

    86   val extract_isabelle_rank : (string, 'a) ho_term list -> int

    87   val introN : string

    88   val inductiveN : string

    89   val elimN : string

    90   val simpN : string

    91   val defN : string

    92   val rankN : string

    93   val minimum_rank : int

    94   val default_rank : int

    95   val default_term_order_weight : int

    96   val is_tptp_equal : string -> bool

    97   val is_built_in_tptp_symbol : string -> bool

    98   val is_tptp_variable : string -> bool

    99   val is_tptp_user_symbol : string -> bool

   100   val atype_of_types : (string * string) ho_type

   101   val bool_atype : (string * string) ho_type

   102   val individual_atype : (string * string) ho_type

   103   val mk_anot : ('a, 'b, 'c) formula -> ('a, 'b, 'c) formula

   104   val mk_aconn :

   105     connective -> ('a, 'b, 'c) formula -> ('a, 'b, 'c) formula

   106     -> ('a, 'b, 'c) formula

   107   val aconn_fold :

   108     bool option -> (bool option -> 'a -> 'b -> 'b) -> connective * 'a list

   109     -> 'b -> 'b

   110   val aconn_map :

   111     bool option -> (bool option -> 'a -> ('b, 'c, 'd) formula)

   112     -> connective * 'a list -> ('b, 'c, 'd) formula

   113   val formula_fold :

   114     bool option -> (bool option -> 'c -> 'd -> 'd) -> ('a, 'b, 'c) formula

   115     -> 'd -> 'd

   116   val formula_map : ('c -> 'd) -> ('a, 'b, 'c) formula -> ('a, 'b, 'd) formula

   117   val is_function_type : string ho_type -> bool

   118   val is_predicate_type : string ho_type -> bool

   119   val is_format_higher_order : atp_format -> bool

   120   val lines_for_atp_problem :

   121     atp_format -> term_order -> (unit -> (string * int) list) -> string problem

   122     -> string list

   123   val ensure_cnf_problem :

   124     (string * string) problem -> (string * string) problem

   125   val filter_cnf_ueq_problem :

   126     (string * string) problem -> (string * string) problem

   127   val declared_syms_in_problem : 'a problem -> 'a list

   128   val nice_atp_problem :

   129     bool -> atp_format -> ('a * (string * string) problem_line list) list

   130     -> ('a * string problem_line list) list

   131        * (string Symtab.table * string Symtab.table) option

   132 end;

   134 structure ATP_Problem : ATP_PROBLEM =

   135 struct

   137 open ATP_Util

   140 (** ATP problem **)

   142 datatype ('a, 'b) ho_term =

   143   ATerm of 'a * ('a, 'b) ho_term list |

   144   AAbs of (('a * 'b) * ('a, 'b) ho_term) * ('a, 'b) ho_term list

   145 datatype quantifier = AForall | AExists

   146 datatype connective = ANot | AAnd | AOr | AImplies | AIff

   147 datatype ('a, 'b, 'c) formula =

   148   AQuant of quantifier * ('a * 'b option) list * ('a, 'b, 'c) formula |

   149   AConn of connective * ('a, 'b, 'c) formula list |

   150   AAtom of 'c

   152 datatype 'a ho_type =

   153   AType of 'a * 'a ho_type list |

   154   AFun of 'a ho_type * 'a ho_type |

   155   ATyAbs of 'a list * 'a ho_type

   157 type term_order =

   158   {is_lpo : bool,

   159    gen_weights : bool,

   160    gen_prec : bool,

   161    gen_simp : bool}

   163 datatype tptp_polymorphism = TPTP_Monomorphic | TPTP_Polymorphic

   164 datatype tptp_explicitness = TPTP_Implicit | TPTP_Explicit

   165 datatype thf_flavor = THF_Without_Choice | THF_With_Choice

   166 datatype dfg_flavor = DFG_Unsorted | DFG_Sorted

   168 datatype atp_format =

   169   CNF |

   170   CNF_UEQ |

   171   FOF |

   172   TFF of tptp_polymorphism * tptp_explicitness |

   173   THF of tptp_polymorphism * tptp_explicitness * thf_flavor |

   174   DFG of dfg_flavor

   176 datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture

   177 datatype 'a problem_line =

   178   Decl of string * 'a * 'a ho_type |

   179   Formula of string * formula_kind

   180              * ('a, 'a ho_type, ('a, 'a ho_type) ho_term) formula

   181              * (string, string ho_type) ho_term option

   182              * (string, string ho_type) ho_term list

   183 type 'a problem = (string * 'a problem_line list) list

   185 (* official TPTP syntax *)

   186 val tptp_cnf = "cnf"

   187 val tptp_fof = "fof"

   188 val tptp_tff = "tff"

   189 val tptp_thf = "thf"

   190 val tptp_has_type = ":"

   191 val tptp_type_of_types = "$tType"

   192 val tptp_bool_type = "$o"

   193 val tptp_individual_type = "$i"

   194 val tptp_fun_type = ">"

   195 val tptp_product_type = "*"

   196 val tptp_forall = "!"

   197 val tptp_ho_forall = "!!"

   198 val tptp_pi_binder = "!>"

   199 val tptp_exists = "?"

   200 val tptp_ho_exists = "??"

   201 val tptp_choice = "@+"

   202 val tptp_not = "~"

   203 val tptp_and = "&"

   204 val tptp_or = "|"

   205 val tptp_implies = "=>"

   206 val tptp_if = "<="

   207 val tptp_iff = "<=>"

   208 val tptp_not_iff = "<~>"

   209 val tptp_app = "@"

   210 val tptp_not_infix = "!"

   211 val tptp_equal = "="

   212 val tptp_old_equal = "equal"

   213 val tptp_false = "$false"

   214 val tptp_true = "$true"

   215 val tptp_empty_list = "[]"

   217 val isabelle_info_prefix = "isabelle_"

   219 val introN = "intro"

   220 val inductiveN = "inductive"

   221 val elimN = "elim"

   222 val simpN = "simp"

   223 val defN = "def"

   224 val rankN = "rank"

   226 val minimum_rank = 0

   227 val default_rank = 1000

   228 val default_term_order_weight = 1

   230 (* Currently, only newer versions of SPASS, with sorted DFG format support, can

   231    process Isabelle metainformation. *)

   232 fun isabelle_info status rank =

   233   [] |> rank <> default_rank

   234         ? cons (ATerm (isabelle_info_prefix ^ rankN,

   235                        [ATerm (string_of_int rank, [])]))

   236      |> status <> "" ? cons (ATerm (isabelle_info_prefix ^ status, []))

   238 fun extract_isabelle_status (ATerm (s, []) :: _) =

   239     try (unprefix isabelle_info_prefix) s

   240   | extract_isabelle_status _ = NONE

   242 fun extract_isabelle_rank (tms as _ :: _) =

   243     (case List.last tms of

   244        ATerm (_, [ATerm (rank, [])]) => the (Int.fromString rank)

   245      | _ => default_rank)

   246   | extract_isabelle_rank _ = default_rank

   248 fun is_tptp_equal s = (s = tptp_equal orelse s = tptp_old_equal)

   249 fun is_built_in_tptp_symbol s =

   250   s = tptp_old_equal orelse not (Char.isAlpha (String.sub (s, 0)))

   251 fun is_tptp_variable s = Char.isUpper (String.sub (s, 0))

   252 val is_tptp_user_symbol = not o (is_tptp_variable orf is_built_in_tptp_symbol)

   254 val atype_of_types = AType (`I tptp_type_of_types, [])

   255 val bool_atype = AType (`I tptp_bool_type, [])

   256 val individual_atype = AType (`I tptp_individual_type, [])

   258 fun raw_polarities_of_conn ANot = (SOME false, NONE)

   259   | raw_polarities_of_conn AAnd = (SOME true, SOME true)

   260   | raw_polarities_of_conn AOr = (SOME true, SOME true)

   261   | raw_polarities_of_conn AImplies = (SOME false, SOME true)

   262   | raw_polarities_of_conn AIff = (NONE, NONE)

   263 fun polarities_of_conn NONE = K (NONE, NONE)

   264   | polarities_of_conn (SOME pos) =

   265     raw_polarities_of_conn #> not pos ? pairself (Option.map not)

   267 fun mk_anot (AConn (ANot, [phi])) = phi

   268   | mk_anot phi = AConn (ANot, [phi])

   269 fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])

   271 fun aconn_fold pos f (ANot, [phi]) = f (Option.map not pos) phi

   272   | aconn_fold pos f (AImplies, [phi1, phi2]) =

   273     f (Option.map not pos) phi1 #> f pos phi2

   274   | aconn_fold pos f (AAnd, phis) = fold (f pos) phis

   275   | aconn_fold pos f (AOr, phis) = fold (f pos) phis

   276   | aconn_fold _ f (_, phis) = fold (f NONE) phis

   278 fun aconn_map pos f (ANot, [phi]) = AConn (ANot, [f (Option.map not pos) phi])

   279   | aconn_map pos f (AImplies, [phi1, phi2]) =

   280     AConn (AImplies, [f (Option.map not pos) phi1, f pos phi2])

   281   | aconn_map pos f (AAnd, phis) = AConn (AAnd, map (f pos) phis)

   282   | aconn_map pos f (AOr, phis) = AConn (AOr, map (f pos) phis)

   283   | aconn_map _ f (c, phis) = AConn (c, map (f NONE) phis)

   285 fun formula_fold pos f =

   286   let

   287     fun fld pos (AQuant (_, _, phi)) = fld pos phi

   288       | fld pos (AConn conn) = aconn_fold pos fld conn

   289       | fld pos (AAtom tm) = f pos tm

   290   in fld pos end

   292 fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)

   293   | formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)

   294   | formula_map f (AAtom tm) = AAtom (f tm)

   296 fun is_function_type (AFun (_, ty)) = is_function_type ty

   297   | is_function_type (AType (s, _)) =

   298     s <> tptp_type_of_types andalso s <> tptp_bool_type

   299   | is_function_type _ = false

   300 fun is_predicate_type (AFun (_, ty)) = is_predicate_type ty

   301   | is_predicate_type (AType (s, _)) = (s = tptp_bool_type)

   302   | is_predicate_type _ = false

   303 fun is_nontrivial_predicate_type (AFun (_, ty)) = is_predicate_type ty

   304   | is_nontrivial_predicate_type _ = false

   306 fun is_format_higher_order (THF _) = true

   307   | is_format_higher_order _ = false

   308 fun is_format_typed (TFF _) = true

   309   | is_format_typed (THF _) = true

   310   | is_format_typed (DFG DFG_Sorted) = true

   311   | is_format_typed _ = false

   313 fun tptp_string_for_kind Axiom = "axiom"

   314   | tptp_string_for_kind Definition = "definition"

   315   | tptp_string_for_kind Lemma = "lemma"

   316   | tptp_string_for_kind Hypothesis = "hypothesis"

   317   | tptp_string_for_kind Conjecture = "conjecture"

   319 fun tptp_string_for_app format func args =

   320   if is_format_higher_order format then

   321     "(" ^ space_implode (" " ^ tptp_app ^ " ") (func :: args) ^ ")"

   322   else

   323     func ^ "(" ^ commas args ^ ")"

   325 fun flatten_type (ATyAbs (tys, ty)) = ATyAbs (tys, flatten_type ty)

   326   | flatten_type (ty as AFun (ty1 as AType _, ty2)) =

   327     (case flatten_type ty2 of

   328        AFun (ty' as AType (s, tys), ty) =>

   329        AFun (AType (tptp_product_type,

   330                     ty1 :: (if s = tptp_product_type then tys else [ty'])), ty)

   331      | _ => ty)

   332   | flatten_type (ty as AType _) = ty

   333   | flatten_type _ =

   334     raise Fail "unexpected higher-order type in first-order format"

   336 val dfg_individual_type = "iii" (* cannot clash *)

   338 fun str_for_type format ty =

   339   let

   340     val dfg = (format = DFG DFG_Sorted)

   341     fun str _ (AType (s, [])) =

   342         if dfg andalso s = tptp_individual_type then dfg_individual_type else s

   343       | str _ (AType (s, tys)) =

   344         let val ss = tys |> map (str false) in

   345           if s = tptp_product_type then

   346             ss |> space_implode

   347                       (if dfg then ", " else " " ^ tptp_product_type ^ " ")

   348                |> (not dfg andalso length ss > 1) ? enclose "(" ")"

   349           else

   350             tptp_string_for_app format s ss

   351         end

   352       | str rhs (AFun (ty1, ty2)) =

   353         (str false ty1 |> dfg ? enclose "(" ")") ^ " " ^

   354         (if dfg then "" else tptp_fun_type ^ " ") ^ str true ty2

   355         |> not rhs ? enclose "(" ")"

   356       | str _ (ATyAbs (ss, ty)) =

   357         tptp_pi_binder ^ "[" ^

   358         commas (map (suffix (" " ^ tptp_has_type ^ " " ^ tptp_type_of_types))

   359                     ss) ^ "]: " ^ str false ty

   360   in str true ty end

   362 fun string_for_type (format as THF _) ty = str_for_type format ty

   363   | string_for_type format ty = str_for_type format (flatten_type ty)

   365 fun tptp_string_for_quantifier AForall = tptp_forall

   366   | tptp_string_for_quantifier AExists = tptp_exists

   368 fun tptp_string_for_connective ANot = tptp_not

   369   | tptp_string_for_connective AAnd = tptp_and

   370   | tptp_string_for_connective AOr = tptp_or

   371   | tptp_string_for_connective AImplies = tptp_implies

   372   | tptp_string_for_connective AIff = tptp_iff

   374 fun string_for_bound_var format (s, ty) =

   375   s ^

   376   (if is_format_typed format then

   377      " " ^ tptp_has_type ^ " " ^

   378      (ty |> the_default (AType (tptp_individual_type, []))

   379          |> string_for_type format)

   380    else

   381      "")

   383 fun is_format_with_choice (THF (_, _, THF_With_Choice)) = true

   384   | is_format_with_choice _ = false

   386 fun tptp_string_for_term _ (ATerm (s, [])) = s

   387   | tptp_string_for_term format (ATerm (s, ts)) =

   388     (if s = tptp_empty_list then

   389        (* used for lists in the optional "source" field of a derivation *)

   390        "[" ^ commas (map (tptp_string_for_term format) ts) ^ "]"

   391      else if is_tptp_equal s then

   392        space_implode (" " ^ tptp_equal ^ " ")

   393                      (map (tptp_string_for_term format) ts)

   394        |> is_format_higher_order format ? enclose "(" ")"

   395      else case (s = tptp_ho_forall orelse s = tptp_ho_exists,

   396                 s = tptp_choice andalso is_format_with_choice format, ts) of

   397        (true, _, [AAbs (((s', ty), tm), [])]) =>

   398        (* Use syntactic sugar "!" and "?" instead of "!!" and "??" whenever

   399           possible, to work around LEO-II 1.2.8 parser limitation. *)

   400        tptp_string_for_formula format

   401            (AQuant (if s = tptp_ho_forall then AForall else AExists,

   402                     [(s', SOME ty)], AAtom tm))

   403      | (_, true, [AAbs (((s', ty), tm), args)]) =>

   404        (* There is code in "ATP_Problem_Generate" to ensure that "Eps" is always

   405           applied to an abstraction. *)

   406        tptp_string_for_app format

   407            (tptp_choice ^ "[" ^ s' ^ " : " ^ string_for_type format ty ^ "]: " ^

   408             tptp_string_for_term format tm ^ ""

   409             |> enclose "(" ")")

   410            (map (tptp_string_for_term format) args)

   411      | _ => tptp_string_for_app format s (map (tptp_string_for_term format) ts))

   412   | tptp_string_for_term (format as THF _) (AAbs (((s, ty), tm), args)) =

   413     tptp_string_for_app format

   414         ("(^[" ^ s ^ " : " ^ string_for_type format ty ^ "]: " ^

   415          tptp_string_for_term format tm ^ ")")

   416         (map (tptp_string_for_term format) args)

   417   | tptp_string_for_term _ _ =

   418     raise Fail "unexpected term in first-order format"

   419 and tptp_string_for_formula format (AQuant (q, xs, phi)) =

   420     tptp_string_for_quantifier q ^

   421     "[" ^ commas (map (string_for_bound_var format) xs) ^ "]: " ^

   422     tptp_string_for_formula format phi

   423     |> enclose "(" ")"

   424   | tptp_string_for_formula format

   425         (AConn (ANot, [AAtom (ATerm ("=" (* tptp_equal *), ts))])) =

   426     space_implode (" " ^ tptp_not_infix ^ tptp_equal ^ " ")

   427                   (map (tptp_string_for_term format) ts)

   428     |> is_format_higher_order format ? enclose "(" ")"

   429   | tptp_string_for_formula format (AConn (c, [phi])) =

   430     tptp_string_for_connective c ^ " " ^

   431     (tptp_string_for_formula format phi

   432      |> is_format_higher_order format ? enclose "(" ")")

   433     |> enclose "(" ")"

   434   | tptp_string_for_formula format (AConn (c, phis)) =

   435     space_implode (" " ^ tptp_string_for_connective c ^ " ")

   436                   (map (tptp_string_for_formula format) phis)

   437     |> enclose "(" ")"

   438   | tptp_string_for_formula format (AAtom tm) = tptp_string_for_term format tm

   440 fun tptp_string_for_format CNF = tptp_cnf

   441   | tptp_string_for_format CNF_UEQ = tptp_cnf

   442   | tptp_string_for_format FOF = tptp_fof

   443   | tptp_string_for_format (TFF _) = tptp_tff

   444   | tptp_string_for_format (THF _) = tptp_thf

   445   | tptp_string_for_format (DFG _) = raise Fail "non-TPTP format"

   447 fun tptp_string_for_problem_line format (Decl (ident, sym, ty)) =

   448     tptp_string_for_format format ^ "(" ^ ident ^ ", type,\n    " ^ sym ^

   449     " : " ^ string_for_type format ty ^ ").\n"

   450   | tptp_string_for_problem_line format

   451                                  (Formula (ident, kind, phi, source, _)) =

   452     tptp_string_for_format format ^ "(" ^ ident ^ ", " ^

   453     tptp_string_for_kind kind ^ ",\n    (" ^

   454     tptp_string_for_formula format phi ^ ")" ^

   455     (case source of

   456        SOME tm => ", " ^ tptp_string_for_term format tm

   457      | NONE => "") ^ ").\n"

   459 fun tptp_lines format =

   460   maps (fn (_, []) => []

   461          | (heading, lines) =>

   462            "\n% " ^ heading ^ " (" ^ string_of_int (length lines) ^ ")\n" ::

   463            map (tptp_string_for_problem_line format) lines)

   465 fun arity_of_type (AFun (_, ty)) = 1 + arity_of_type ty

   466   | arity_of_type _ = 0

   468 fun binder_atypes (AFun (ty1, ty2)) = ty1 :: binder_atypes ty2

   469   | binder_atypes _ = []

   471 fun dfg_string_for_formula gen_simp flavor info =

   472   let

   473     fun suffix_tag top_level s =

   474       if flavor = DFG_Sorted andalso top_level then

   475         case extract_isabelle_status info of

   476           SOME s' => if s' = defN then s ^ ":lt"

   477                      else if s' = simpN andalso gen_simp then s ^ ":lr"

   478                      else s

   479         | NONE => s

   480       else

   481         s

   482     fun str_for_term top_level (ATerm (s, tms)) =

   483         (if is_tptp_equal s then "equal" |> suffix_tag top_level

   484          else if s = tptp_true then "true"

   485          else if s = tptp_false then "false"

   486          else s) ^

   487         (if null tms then ""

   488          else "(" ^ commas (map (str_for_term false) tms) ^ ")")

   489       | str_for_term _ _ = raise Fail "unexpected term in first-order format"

   490     fun str_for_quant AForall = "forall"

   491       | str_for_quant AExists = "exists"

   492     fun str_for_conn _ ANot = "not"

   493       | str_for_conn _ AAnd = "and"

   494       | str_for_conn _ AOr = "or"

   495       | str_for_conn _ AImplies = "implies"

   496       | str_for_conn top_level AIff = "equiv" |> suffix_tag top_level

   497     fun str_for_formula top_level (AQuant (q, xs, phi)) =

   498         str_for_quant q ^ "(" ^ "[" ^

   499         commas (map (string_for_bound_var (DFG flavor)) xs) ^ "], " ^

   500         str_for_formula top_level phi ^ ")"

   501       | str_for_formula top_level (AConn (c, phis)) =

   502         str_for_conn top_level c ^ "(" ^

   503         commas (map (str_for_formula false) phis) ^ ")"

   504       | str_for_formula top_level (AAtom tm) = str_for_term top_level tm

   505   in str_for_formula true end

   507 fun maybe_enclose bef aft "" = "% " ^ bef ^ aft

   508   | maybe_enclose bef aft s = bef ^ s ^ aft

   510 fun dfg_lines flavor {is_lpo, gen_weights, gen_prec, gen_simp} ord_info

   511               problem =

   512   let

   513     val sorted = (flavor = DFG_Sorted)

   514     val format = DFG flavor

   515     fun spair (sym, k) = "(" ^ sym ^ ", " ^ string_of_int k ^ ")"

   516     fun ary sym = curry spair sym o arity_of_type

   517     fun fun_typ sym ty =

   518       "function(" ^ sym ^ ", " ^ string_for_type format ty ^ ")."

   519     fun pred_typ sym ty =

   520       "predicate(" ^

   521       commas (sym :: map (string_for_type format) (binder_atypes ty)) ^ ")."

   522     fun formula pred (Formula (ident, kind, phi, _, info)) =

   523         if pred kind then

   524           let

   525             val rank =

   526               if flavor = DFG_Sorted then extract_isabelle_rank info

   527               else default_rank

   528           in

   529             "formula(" ^ dfg_string_for_formula gen_simp flavor info phi ^

   530             ", " ^ ident ^

   531             (if rank = default_rank then "" else ", " ^ string_of_int rank) ^

   532             ")." |> SOME

   533           end

   534         else

   535           NONE

   536       | formula _ _ = NONE

   537     fun filt f = problem |> map (map_filter f o snd) |> filter_out null

   538     val func_aries =

   539       filt (fn Decl (_, sym, ty) =>

   540                if is_function_type ty then SOME (ary sym ty) else NONE

   541              | _ => NONE)

   542       |> flat |> commas |> maybe_enclose "functions [" "]."

   543     val pred_aries =

   544       filt (fn Decl (_, sym, ty) =>

   545                if is_predicate_type ty then SOME (ary sym ty) else NONE

   546              | _ => NONE)

   547       |> flat |> commas |> maybe_enclose "predicates [" "]."

   548     fun sorts () =

   549       filt (fn Decl (_, sym, AType (s, [])) =>

   550                if s = tptp_type_of_types then SOME sym else NONE

   551              | _ => NONE) @ [[dfg_individual_type]]

   552       |> flat |> commas |> maybe_enclose "sorts [" "]."

   553     val ord_info =

   554       if sorted andalso (gen_weights orelse gen_prec) then ord_info () else []

   555     fun do_term_order_weights () =

   556       (if gen_weights then ord_info else [])

   557       |> map spair |> commas |> maybe_enclose "weights [" "]."

   558     val syms =

   559       [func_aries, pred_aries] @

   560       (if sorted then [do_term_order_weights (), sorts ()] else [])

   561     fun func_sigs () =

   562       filt (fn Decl (_, sym, ty) =>

   563                if is_function_type ty then SOME (fun_typ sym ty) else NONE

   564              | _ => NONE)

   565       |> flat

   566     fun pred_sigs () =

   567       filt (fn Decl (_, sym, ty) =>

   568                if is_nontrivial_predicate_type ty then SOME (pred_typ sym ty)

   569                else NONE

   570              | _ => NONE)

   571       |> flat

   572     val decls = if sorted then func_sigs () @ pred_sigs () else []

   573     val axioms =

   574       filt (formula (curry (op <>) Conjecture)) |> separate [""] |> flat

   575     val conjs =

   576       filt (formula (curry (op =) Conjecture)) |> separate [""] |> flat

   577     val settings =

   578       (if is_lpo then ["set_flag(Ordering, 1)."] else []) @

   579       (if gen_prec then

   580          [ord_info |> map fst |> rev |> commas

   581                    |> maybe_enclose "set_precedence(" ")."]

   582        else

   583          [])

   584     fun list_of _ [] = []

   585       | list_of heading ss =

   586         "list_of_" ^ heading ^ ".\n" :: map (suffix "\n") ss @

   587         ["end_of_list.\n\n"]

   588   in

   589     "\nbegin_problem(isabelle).\n\n" ::

   590     list_of "descriptions"

   591             ["name({**}).", "author({**}).", "status(unknown).",

   592              "description({**})."] @

   593     list_of "symbols" syms @

   594     list_of "declarations" decls @

   595     list_of "formulae(axioms)" axioms @

   596     list_of "formulae(conjectures)" conjs @

   597     list_of "settings(SPASS)" settings @

   598     ["end_problem.\n"]

   599   end

   601 fun lines_for_atp_problem format ord ord_info problem =

   602   "% This file was generated by Isabelle (most likely Sledgehammer)\n\

   603   \% " ^ timestamp () ^ "\n" ::

   604   (case format of

   605      DFG flavor => dfg_lines flavor ord ord_info

   606    | _ => tptp_lines format) problem

   609 (** CNF (Metis) and CNF UEQ (Waldmeister) **)

   611 fun is_problem_line_negated (Formula (_, _, AConn (ANot, _), _, _)) = true

   612   | is_problem_line_negated _ = false

   614 fun is_problem_line_cnf_ueq (Formula (_, _, AAtom (ATerm ((s, _), _)), _, _)) =

   615     is_tptp_equal s

   616   | is_problem_line_cnf_ueq _ = false

   618 fun open_conjecture_term (ATerm ((s, s'), tms)) =

   619     ATerm (if is_tptp_variable s then (s |> Name.desymbolize false, s')

   620            else (s, s'), tms |> map open_conjecture_term)

   621   | open_conjecture_term _ = raise Fail "unexpected higher-order term"

   622 fun open_formula conj =

   623   let

   624     (* We are conveniently assuming that all bound variable names are

   625        distinct, which should be the case for the formulas we generate. *)

   626     fun opn (pos as SOME true) (AQuant (AForall, _, phi)) = opn pos phi

   627       | opn (pos as SOME false) (AQuant (AExists, _, phi)) = opn pos phi

   628       | opn pos (AConn (ANot, [phi])) = mk_anot (opn (Option.map not pos) phi)

   629       | opn pos (AConn (c, [phi1, phi2])) =

   630         let val (pos1, pos2) = polarities_of_conn pos c in

   631           AConn (c, [opn pos1 phi1, opn pos2 phi2])

   632         end

   633       | opn _ (AAtom t) = AAtom (t |> conj ? open_conjecture_term)

   634       | opn _ phi = phi

   635   in opn (SOME (not conj)) end

   636 fun open_formula_line (Formula (ident, kind, phi, source, info)) =

   637     Formula (ident, kind, open_formula (kind = Conjecture) phi, source, info)

   638   | open_formula_line line = line

   640 fun negate_conjecture_line (Formula (ident, Conjecture, phi, source, info)) =

   641     Formula (ident, Hypothesis, mk_anot phi, source, info)

   642   | negate_conjecture_line line = line

   644 exception CLAUSIFY of unit

   646 (* This "clausification" only expands syntactic sugar, such as "phi => psi" to

   647    "~ phi | psi" and "phi <=> psi" to "~ phi | psi" and "~ psi | phi". We don't

   648    attempt to distribute conjunctions over disjunctions. *)

   649 fun clausify_formula pos (phi as AAtom _) = [phi |> not pos ? mk_anot]

   650   | clausify_formula pos (AConn (ANot, [phi])) = clausify_formula (not pos) phi

   651   | clausify_formula true (AConn (AOr, [phi1, phi2])) =

   652     (phi1, phi2) |> pairself (clausify_formula true)

   653                  |> uncurry (map_product (mk_aconn AOr))

   654   | clausify_formula false (AConn (AAnd, [phi1, phi2])) =

   655     (phi1, phi2) |> pairself (clausify_formula false)

   656                  |> uncurry (map_product (mk_aconn AOr))

   657   | clausify_formula true (AConn (AImplies, [phi1, phi2])) =

   658     clausify_formula true (AConn (AOr, [mk_anot phi1, phi2]))

   659   | clausify_formula true (AConn (AIff, phis)) =

   660     clausify_formula true (AConn (AImplies, phis)) @

   661     clausify_formula true (AConn (AImplies, rev phis))

   662   | clausify_formula _ _ = raise CLAUSIFY ()

   664 fun clausify_formula_line (Formula (ident, kind, phi, source, info)) =

   665     let

   666       val (n, phis) = phi |> try (clausify_formula true) |> these |> `length

   667     in

   668       map2 (fn phi => fn j =>

   669                Formula (ident ^ replicate_string (j - 1) "x", kind, phi, source,

   670                         info))

   671            phis (1 upto n)

   672     end

   673   | clausify_formula_line _ = []

   675 fun ensure_cnf_problem_line line =

   676   line |> open_formula_line |> negate_conjecture_line |> clausify_formula_line

   678 fun ensure_cnf_problem problem =

   679   problem |> map (apsnd (maps ensure_cnf_problem_line))

   681 fun filter_cnf_ueq_problem problem =

   682   problem

   683   |> map (apsnd (map open_formula_line

   684                  #> filter is_problem_line_cnf_ueq

   685                  #> map negate_conjecture_line))

   686   |> (fn problem =>

   687          let

   688            val lines = problem |> maps snd

   689            val conjs = lines |> filter is_problem_line_negated

   690          in if length conjs = 1 andalso conjs <> lines then problem else [] end)

   693 (** Symbol declarations **)

   695 fun add_declared_syms_in_problem_line (Decl (_, sym, _)) = cons sym

   696   | add_declared_syms_in_problem_line _ = I

   697 fun declared_syms_in_problem problem =

   698   fold (fold add_declared_syms_in_problem_line o snd) problem []

   700 (** Nice names **)

   702 fun pool_fold f xs z = pair z #> fold_rev (fn x => uncurry (f x)) xs

   703 fun pool_map f xs =

   704   pool_fold (fn x => fn ys => fn pool => f x pool |>> (fn y => y :: ys)) xs []

   706 val no_qualifiers =

   707   let

   708     fun skip [] = []

   709       | skip (#"." :: cs) = skip cs

   710       | skip (c :: cs) = if Char.isAlphaNum c then skip cs else c :: keep cs

   711     and keep [] = []

   712       | keep (#"." :: cs) = skip cs

   713       | keep (c :: cs) = c :: keep cs

   714   in String.explode #> rev #> keep #> rev #> String.implode end

   716 (* Long names can slow down the ATPs. *)

   717 val max_readable_name_size = 20

   719 (* "equal" is reserved by some ATPs. "op" is also reserved, to avoid the

   720    unreadable "op_1", "op_2", etc., in the problem files. "eq" is reserved to

   721    ensure that "HOL.eq" is correctly mapped to equality (not clear whether this

   722    is still necessary). *)

   723 val reserved_nice_names = [tptp_old_equal, "op", "eq"]

   725 (* hack to get the same hashing across Mirabelle runs (see "mirabelle.pl") *)

   726 fun cleanup_mirabelle_name s =

   727   let

   728     val mirabelle_infix = "_Mirabelle_"

   729     val random_suffix_len = 10

   730     val (s1, s2) = Substring.position mirabelle_infix (Substring.full s)

   731   in

   732     if Substring.isEmpty s2 then

   733       s

   734     else

   735       Substring.string s1 ^

   736       Substring.string (Substring.triml (size mirabelle_infix + random_suffix_len) s2)

   737   end

   739 fun readable_name protect full_name s =

   740   (if s = full_name then

   741      s

   742    else

   743      s |> no_qualifiers

   744        |> perhaps (try (unprefix "'"))

   745        |> Name.desymbolize (Char.isUpper (String.sub (full_name, 0)))

   746        |> (fn s =>

   747               if size s > max_readable_name_size then

   748                 String.substring (s, 0, max_readable_name_size div 2 - 4) ^

   749                 string_of_int (hash_string (cleanup_mirabelle_name full_name)) ^

   750                 String.extract (s, size s - max_readable_name_size div 2 + 4,

   751                                 NONE)

   752               else

   753                 s)

   754        |> (fn s =>

   755               if member (op =) reserved_nice_names s then full_name else s))

   756   |> protect

   758 fun nice_name _ (full_name, _) NONE = (full_name, NONE)

   759   | nice_name protect (full_name, desired_name) (SOME the_pool) =

   760     if is_built_in_tptp_symbol full_name then

   761       (full_name, SOME the_pool)

   762     else case Symtab.lookup (fst the_pool) full_name of

   763       SOME nice_name => (nice_name, SOME the_pool)

   764     | NONE =>

   765       let

   766         val nice_prefix = readable_name protect full_name desired_name

   767         fun add j =

   768           let

   769             val nice_name =

   770               nice_prefix ^ (if j = 1 then "" else string_of_int j)

   771           in

   772             case Symtab.lookup (snd the_pool) nice_name of

   773               SOME full_name' =>

   774               if full_name = full_name' then (nice_name, the_pool)

   775               else add (j + 1)

   776             | NONE =>

   777               (nice_name,

   778                (Symtab.update_new (full_name, nice_name) (fst the_pool),

   779                 Symtab.update_new (nice_name, full_name) (snd the_pool)))

   780           end

   781       in add 1 |> apsnd SOME end

   783 fun avoid_clash_with_alt_ergo_type_vars s =

   784   if is_tptp_variable s then s else s ^ "_"

   786 fun avoid_clash_with_dfg_keywords s =

   787   let val n = String.size s in

   788     if n < 2 orelse (n = 2 andalso String.sub (s, 0) = String.sub (s, 1)) orelse

   789        String.isSubstring "_" s then

   790       s

   791     else if is_tptp_variable s then

   792       (* "DL" appears to be a SPASS 3.7 keyword *)

   793       if s = "DL" then s ^ "_" else s

   794     else

   795       String.substring (s, 0, n - 1) ^

   796       String.str (Char.toUpper (String.sub (s, n - 1)))

   797   end

   799 fun nice_atp_problem readable_names format problem =

   800   let

   801     val empty_pool =

   802       if readable_names then SOME (Symtab.empty, Symtab.empty) else NONE

   803     val avoid_clash =

   804       case format of

   805         TFF (TPTP_Polymorphic, _) => avoid_clash_with_alt_ergo_type_vars

   806       | DFG _ => avoid_clash_with_dfg_keywords

   807       | _ => I

   808     val nice_name = nice_name avoid_clash

   809     fun nice_type (AType (name, tys)) =

   810         nice_name name ##>> pool_map nice_type tys #>> AType

   811       | nice_type (AFun (ty1, ty2)) = nice_type ty1 ##>> nice_type ty2 #>> AFun

   812       | nice_type (ATyAbs (names, ty)) =

   813         pool_map nice_name names ##>> nice_type ty #>> ATyAbs

   814     fun nice_term (ATerm (name, ts)) =

   815         nice_name name ##>> pool_map nice_term ts #>> ATerm

   816       | nice_term (AAbs (((name, ty), tm), args)) =

   817         nice_name name ##>> nice_type ty ##>> nice_term tm

   818         ##>> pool_map nice_term args #>> AAbs

   819     fun nice_formula (AQuant (q, xs, phi)) =

   820         pool_map nice_name (map fst xs)

   821         ##>> pool_map (fn NONE => pair NONE

   822                         | SOME ty => nice_type ty #>> SOME) (map snd xs)

   823         ##>> nice_formula phi

   824         #>> (fn ((ss, ts), phi) => AQuant (q, ss ~~ ts, phi))

   825       | nice_formula (AConn (c, phis)) =

   826         pool_map nice_formula phis #>> curry AConn c

   827       | nice_formula (AAtom tm) = nice_term tm #>> AAtom

   828     fun nice_problem_line (Decl (ident, sym, ty)) =

   829         nice_name sym ##>> nice_type ty #>> (fn (sym, ty) => Decl (ident, sym, ty))

   830       | nice_problem_line (Formula (ident, kind, phi, source, info)) =

   831         nice_formula phi #>> (fn phi => Formula (ident, kind, phi, source, info))

   832     fun nice_problem problem =

   833       pool_map (fn (heading, lines) =>

   834                    pool_map nice_problem_line lines #>> pair heading) problem

   835   in nice_problem problem empty_pool end

   837 end;

author	blanchet
	Sun, 13 May 2012 16:31:01 +0200
changeset 48926	2168126446bb
parent 48638	0b2b7ff31867
child 48991	6b13451135a9
permissions	-rw-r--r--