(*  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;