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

    Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA

    Author:     Jasmin Blanchette, TU Muenchen

Abstract representation of ATP problems and TPTP syntax.

*)

signature ATP_PROBLEM =

sig

  datatype 'a fo_term = ATerm of 'a * 'a fo_term list

  datatype quantifier = AForall | AExists

  datatype connective = ANot | AAnd | AOr | AImplies | AIf | AIff | ANotIff

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

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

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

    AAtom of 'c

  datatype format = UEQ | FOF | TFF

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

  datatype 'a problem_line =

    Decl of string * 'a * 'a list * 'a |

    Formula of string * formula_kind * ('a, 'a, 'a fo_term) formula

               * string fo_term option * string fo_term option

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

(* official TPTP syntax *)

  val tptp_special_prefix : string

  val tptp_false : string

  val tptp_true : string

  val tptp_tff_type_of_types : string

  val tptp_tff_bool_type : string

  val tptp_tff_individual_type : string

  val timestamp : unit -> string

  val hashw : word * word -> word

  val hashw_string : string * word -> word

  val is_atp_variable : string -> bool

  val tptp_strings_for_atp_problem : format -> string problem -> string list

  val nice_atp_problem :

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

    -> ('a * string problem_line list) list

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

end;

structure ATP_Problem : ATP_PROBLEM =

struct

(** ATP problem **)

datatype 'a fo_term = ATerm of 'a * 'a fo_term list

datatype quantifier = AForall | AExists

datatype connective = ANot | AAnd | AOr | AImplies | AIf | AIff | ANotIff

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

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

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

  AAtom of 'c

datatype format = UEQ | FOF | TFF

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

datatype 'a problem_line =

  Decl of string * 'a * 'a list * 'a |

  Formula of string * formula_kind * ('a, 'a, 'a fo_term) formula

             * string fo_term option * string fo_term option

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

(* official TPTP syntax *)

val tptp_special_prefix = "$"

val tptp_false = "$false"

val tptp_true = "$true"

val tptp_tff_type_of_types = "$tType"

val tptp_tff_bool_type = "$o"

val tptp_tff_individual_type = "$i"

val timestamp = Date.fmt "%Y-%m-%d %H:%M:%S" o Date.fromTimeLocal o Time.now

(* This hash function is recommended in Compilers: Principles, Techniques, and

   Tools, by Aho, Sethi, and Ullman. The "hashpjw" function, which they

   particularly recommend, triggers a bug in versions of Poly/ML up to 4.2.0. *)

fun hashw (u, w) = Word.+ (u, Word.* (0w65599, w))

fun hashw_char (c, w) = hashw (Word.fromInt (Char.ord c), w)

fun hashw_string (s : string, w) = CharVector.foldl hashw_char w s

fun string_for_kind Axiom = "axiom"

  | string_for_kind Definition = "definition"

  | string_for_kind Lemma = "lemma"

  | string_for_kind Hypothesis = "hypothesis"

  | string_for_kind Conjecture = "conjecture"

fun string_for_term (ATerm (s, [])) = s

  | string_for_term (ATerm ("equal", ts)) =

    space_implode " = " (map string_for_term ts)

  | string_for_term (ATerm ("[]", ts)) =

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

    "[" ^ commas (map string_for_term ts) ^ "]"

  | string_for_term (ATerm (s, ts)) =

    s ^ "(" ^ commas (map string_for_term ts) ^ ")"

fun string_for_quantifier AForall = "!"

  | string_for_quantifier AExists = "?"

fun string_for_connective ANot = "~"

  | string_for_connective AAnd = "&"

  | string_for_connective AOr = "|"

  | string_for_connective AImplies = "=>"

  | string_for_connective AIf = "<="

  | string_for_connective AIff = "<=>"

  | string_for_connective ANotIff = "<~>"

fun string_for_bound_var TFF (s, ty) =

    s ^ " : " ^ (ty |> the_default tptp_tff_individual_type)

  | string_for_bound_var _ (s, _) = s

fun string_for_formula format (AQuant (q, xs, phi)) =

    "(" ^ string_for_quantifier q ^

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

    string_for_formula format phi ^ ")"

  | string_for_formula _ (AConn (ANot, [AAtom (ATerm ("equal", ts))])) =

    space_implode " != " (map string_for_term ts)

  | string_for_formula format (AConn (c, [phi])) =

    "(" ^ string_for_connective c ^ " " ^ string_for_formula format phi ^ ")"

  | string_for_formula format (AConn (c, phis)) =

    "(" ^ space_implode (" " ^ string_for_connective c ^ " ")

                        (map (string_for_formula format) phis) ^ ")"

  | string_for_formula _ (AAtom tm) = string_for_term tm

fun string_for_symbol_type [] res_ty = res_ty

  | string_for_symbol_type [arg_ty] res_ty = arg_ty ^ " > " ^ res_ty

  | string_for_symbol_type arg_tys res_ty =

    string_for_symbol_type ["(" ^ space_implode " * " arg_tys ^ ")"] res_ty

val default_source =

  ATerm ("inference", ATerm ("isabelle", []) :: replicate 2 (ATerm ("[]", [])))

fun string_for_problem_line _ (Decl (ident, sym, arg_tys, res_ty)) =

    "tff(" ^ ident ^ ", type,\n    " ^ sym ^ " : " ^

    string_for_symbol_type arg_tys res_ty ^ ").\n"

  | string_for_problem_line format

                            (Formula (ident, kind, phi, source, useful_info)) =

    (case format of UEQ => "cnf" | FOF => "fof" | TFF => "tff") ^

    "(" ^ ident ^ ", " ^ string_for_kind kind ^ ",\n    (" ^

    string_for_formula format phi ^ ")" ^

    (case (source, useful_info) of

       (NONE, NONE) => ""

     | (SOME tm, NONE) => ", " ^ string_for_term tm

     | (_, SOME tm) =>

       ", " ^ string_for_term (source |> the_default default_source) ^

       ", " ^ string_for_term tm) ^ ").\n"

fun tptp_strings_for_atp_problem format problem =

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

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

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

         | (heading, lines) =>

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

           map (string_for_problem_line format) lines)

       problem

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

(** Nice names **)

fun empty_name_pool readable_names =

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

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

fun pool_map f xs =

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

val no_qualifiers =

  let

    fun skip [] = []

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

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

    and keep [] = []

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

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

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

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

val max_readable_name_size = 20

(* "op" is also reserved, to avoid the unreadable "op_1", "op_2", etc., in the

   problem files. "equal" is reserved by some ATPs. "eq" is reserved to ensure

   that "HOL.eq" is correctly mapped to equality. *)

val reserved_nice_names = ["op", "equal", "eq"]

fun readable_name full_name s =

  if s = full_name then

    s

  else

    s |> no_qualifiers

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

         (* SNARK doesn't like sort (type) names that end with digits. We make

            an effort to avoid this here. *)

      |> (fn s => if Char.isDigit (String.sub (s, size s - 1)) then s ^ "_"

                  else s)

      |> (fn s =>

             if size s > max_readable_name_size then

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

               Word.toString (hashw_string (full_name, 0w0)) ^

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

                               NONE)

             else

               s)

      |> (fn s => if member (op =) reserved_nice_names s then full_name else s)

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

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

    if String.isPrefix "$" full_name then

      (full_name, SOME the_pool)

    else case Symtab.lookup (fst the_pool) full_name of

      SOME nice_name => (nice_name, SOME the_pool)

    | NONE =>

      let

        val nice_prefix = readable_name full_name desired_name

        fun add j =

          let

            (* The trailing "_" is for SNARK (cf. comment above). *)

            val nice_name =

              nice_prefix ^ (if j = 0 then "" else "_" ^ string_of_int j ^ "_")

          in

            case Symtab.lookup (snd the_pool) nice_name of

              SOME full_name' =>

              if full_name = full_name' then (nice_name, the_pool)

              else add (j + 1)

            | NONE =>

              (nice_name,

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

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

          end

      in add 0 |> apsnd SOME end

fun nice_term (ATerm (name, ts)) =

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

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

    pool_map nice_name (map fst xs)

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

                    | SOME ty => nice_name ty #>> SOME) (map snd xs)

    ##>> nice_formula phi

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

  | nice_formula (AConn (c, phis)) =

    pool_map nice_formula phis #>> curry AConn c

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

fun nice_problem_line (Decl (ident, sym, arg_tys, res_ty)) =

    nice_name sym

    ##>> pool_map nice_name arg_tys

    ##>> nice_name res_ty

    #>> (fn ((sym, arg_tys), res_ty) => Decl (ident, sym, arg_tys, res_ty))

  | nice_problem_line (Formula (ident, kind, phi, source, useful_info)) =

    nice_formula phi

    #>> (fn phi => Formula (ident, kind, phi, source, useful_info))

fun nice_problem problem =

  pool_map (fn (heading, lines) =>

               pool_map nice_problem_line lines #>> pair heading) problem

fun nice_atp_problem readable_names problem =

  nice_problem problem (empty_name_pool readable_names)

end;