(*  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) formula =

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

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

    AAtom of 'b

  type 'a uniform_formula = ('a, 'a fo_term) formula

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

  datatype 'a problem_line =

    Fof of string * kind * ('a, 'a fo_term) formula * string fo_term option

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

  val timestamp : unit -> string

  val is_atp_variable : string -> bool

  val tptp_strings_for_atp_problem :

    bool -> (string * string problem_line list) list -> 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) formula =

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

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

  AAtom of 'b

type 'a uniform_formula = ('a, 'a fo_term) formula

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

datatype 'a problem_line =

  Fof of string * kind * ('a, 'a fo_term) formula * string fo_term option

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

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

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_formula (AQuant (q, xs, phi)) =

    "(" ^ string_for_quantifier q ^ "[" ^ commas xs ^ "] : " ^

    string_for_formula phi ^ ")"

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

    space_implode " != " (map string_for_term ts)

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

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

  | string_for_formula (AConn (c, phis)) =

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

                        (map string_for_formula phis) ^ ")"

  | string_for_formula (AAtom tm) = string_for_term tm

fun string_for_problem_line use_conjecture_for_hypotheses

                            (Fof (ident, kind, phi, source)) =

  let

    val (kind, phi) =

      if kind = Hypothesis andalso use_conjecture_for_hypotheses then

        (Conjecture, AConn (ANot, [phi]))

      else

        (kind, phi)

  in

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

    string_for_formula phi ^ ")" ^

    (case source of

       SOME tm => ", " ^ string_for_term tm

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

  end

fun tptp_strings_for_atp_problem use_conjecture_for_hypotheses 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 use_conjecture_for_hypotheses) 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

(* "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

    let

      val s = s |> no_qualifiers

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

    in if member (op =) reserved_nice_names s then full_name else s end

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

            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 xs ##>> nice_formula phi

    #>> (fn (xs, phi) => AQuant (q, xs, 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 (Fof (ident, kind, phi, source)) =

  nice_formula phi #>> (fn phi => Fof (ident, kind, phi, source))

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;