src/HOL/Tools/ATP/atp_problem.ML

extended ATP problem syntax to support other applications than Sledgehammer, e.g. experiments with ATPs

(*  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 []

(* "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 |> Long_Name.base_name
                |> 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;