(*  Title:      HOL/Tools/Nitpick/nitrox.ML

    Author:     Jasmin Blanchette, TU Muenchen

    Copyright   2010, 2011

Finite model generation for TPTP first-order formulas (FOF and CNF) via Nitpick.

*)

signature NITROX =

sig

  val pick_nits_in_fof_file : string -> string

end;

structure Nitrox : NITROX =

struct

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 formula =

  AQuant of quantifier * 'a list * 'a formula |

  AConn of connective * 'a formula list |

  APred of 'a fo_term

exception SYNTAX of string

fun is_ident_char c = Char.isAlphaNum c orelse c = #"_"

fun takewhile _ [] = []

  | takewhile p (x :: xs) = if p x then x :: takewhile p xs else []

fun dropwhile _ [] = []

  | dropwhile p (x :: xs) =  if p x then dropwhile p xs else x :: xs

fun strip_c_style_comment [] = ""

  | strip_c_style_comment (#"*" :: #"/" :: cs) = strip_spaces_in_list cs

  | strip_c_style_comment (_ :: cs) = strip_c_style_comment cs

and strip_spaces_in_list [] = ""

  | strip_spaces_in_list (#"%" :: cs) =

    strip_spaces_in_list (dropwhile (not_equal #"\n") cs)

  | strip_spaces_in_list (#"/" :: #"*" :: cs) = strip_c_style_comment cs

  | strip_spaces_in_list [c1] = if Char.isSpace c1 then "" else str c1

  | strip_spaces_in_list [c1, c2] =

    strip_spaces_in_list [c1] ^ strip_spaces_in_list [c2]

  | strip_spaces_in_list (c1 :: c2 :: c3 :: cs) =

    if Char.isSpace c1 then

      strip_spaces_in_list (c2 :: c3 :: cs)

    else if Char.isSpace c2 then

      if Char.isSpace c3 then

        strip_spaces_in_list (c1 :: c3 :: cs)

      else

        str c1 ^ (if forall is_ident_char [c1, c3] then " " else "") ^

        strip_spaces_in_list (c3 :: cs)

    else

      str c1 ^ strip_spaces_in_list (c2 :: c3 :: cs)

val strip_spaces = strip_spaces_in_list o String.explode

val parse_keyword = Scan.this_string

fun parse_file_path ("'" :: ss) =

    (takewhile (not_equal "'") ss |> implode,

     List.drop (dropwhile (not_equal "'") ss, 1))

  | parse_file_path ("\"" :: ss) =

    (takewhile (not_equal "\"") ss |> implode,

     List.drop (dropwhile (not_equal "\"") ss, 1))

  | parse_file_path _ = raise SYNTAX "invalid file path"

fun parse_include x =

  let

    val (file_name, rest) =

      (parse_keyword "include" |-- $$ "(" |-- parse_file_path --| $$ ")"

       --| $$ ".") x

  in

    ((), raw_explode (strip_spaces (File.read (Path.explode file_name))) @ rest)

  end

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

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

val parse_dollar_name =

  Scan.repeat ($$ "$") -- Symbol.scan_id >> (fn (ss, s) => implode ss ^ s)

fun parse_term x =

  (parse_dollar_name

   -- Scan.optional ($$ "(" |-- parse_terms --| $$ ")") [] >> ATerm) x

and parse_terms x = (parse_term ::: Scan.repeat ($$ "," |-- parse_term)) x

(* Apply equal or not-equal to a term. *)

val parse_predicate_term =

  parse_term -- Scan.option (Scan.option ($$ "!") --| $$ "=" -- parse_term)

  >> (fn (u, NONE) => APred u

       | (u1, SOME (NONE, u2)) => APred (ATerm ("=", [u1, u2]))

       | (u1, SOME (SOME _, u2)) => mk_anot (APred (ATerm ("=", [u1, u2]))))

fun fo_term_head (ATerm (s, _)) = s

fun parse_formula x =

  (($$ "(" |-- parse_formula --| $$ ")"

    || ($$ "!" >> K AForall || $$ "?" >> K AExists)

       --| $$ "[" -- parse_terms --| $$ "]" --| $$ ":" -- parse_formula

       >> (fn ((q, ts), phi) => AQuant (q, map fo_term_head ts, phi))

    || $$ "~" |-- parse_formula >> mk_anot

    || parse_predicate_term)

   -- Scan.option ((Scan.this_string "=>" >> K AImplies

                    || Scan.this_string "<=>" >> K AIff

                    || Scan.this_string "<~>" >> K ANotIff

                    || Scan.this_string "<=" >> K AIf

                    || $$ "|" >> K AOr || $$ "&" >> K AAnd) -- parse_formula)

   >> (fn (phi1, NONE) => phi1

        | (phi1, SOME (c, phi2)) => mk_aconn c (phi1, phi2))) x

val parse_fof_or_cnf =

  (parse_keyword "fof" || parse_keyword "cnf") |-- $$ "(" |--

  Scan.many (not_equal ",") |-- $$ "," |--

  (parse_keyword "axiom" || parse_keyword "definition"

   || parse_keyword "theorem" || parse_keyword "lemma"

   || parse_keyword "hypothesis" || parse_keyword "conjecture"

   || parse_keyword "negated_conjecture") --| $$ "," -- parse_formula

      --| $$ ")" --| $$ "."

  >> (fn ("conjecture", phi) => AConn (ANot, [phi]) | (_, phi) => phi)

val parse_problem =

  Scan.repeat parse_include

  |-- Scan.repeat (parse_fof_or_cnf --| Scan.repeat parse_include)

val parse_tptp_problem =

  Scan.finite Symbol.stopper

      (Scan.error (!! (fn _ => raise SYNTAX "malformed TPTP input")

                  parse_problem))

  o raw_explode o strip_spaces

val boolT = @{typ bool}

val iotaT = @{typ iota}

val quantT = (iotaT --> boolT) --> boolT

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

fun hol_term_from_fo_term res_T (ATerm (x, us)) =

  let val ts = map (hol_term_from_fo_term iotaT) us in

    list_comb ((case x of

                  "$true" => @{const_name True}

                | "$false" => @{const_name False}

                | "=" => @{const_name HOL.eq}

                | _ => x, map fastype_of ts ---> res_T)

               |> (if is_variable x then Free else Const), ts)

  end

fun hol_prop_from_formula phi =

  case phi of

    AQuant (_, [], phi') => hol_prop_from_formula phi'

  | AQuant (q, x :: xs, phi') =>

    Const (case q of AForall => @{const_name All} | AExists => @{const_name Ex},

           quantT)

    $ lambda (Free (x, iotaT)) (hol_prop_from_formula (AQuant (q, xs, phi')))

  | AConn (ANot, [u']) => HOLogic.mk_not (hol_prop_from_formula u')

  | AConn (c, [u1, u2]) =>

    pairself hol_prop_from_formula (u1, u2)

    |> (case c of

          AAnd => HOLogic.mk_conj

        | AOr => HOLogic.mk_disj

        | AImplies => HOLogic.mk_imp

        | AIf => HOLogic.mk_imp o swap

        | AIff => HOLogic.mk_eq

        | ANotIff => HOLogic.mk_not o HOLogic.mk_eq

        | ANot => raise Fail "binary \"ANot\"")

  | AConn _ => raise Fail "malformed AConn"

  | APred u => hol_term_from_fo_term boolT u

fun mk_all x t = Const (@{const_name All}, quantT) $ lambda x t

fun close_hol_prop t = fold (mk_all o Free) (Term.add_frees t []) t

fun pick_nits_in_fof_file file_name =

  case parse_tptp_problem (File.read (Path.explode file_name)) of

    (_, s :: ss) => raise SYNTAX ("cannot parse " ^ quote (implode (s :: ss)))

  | (phis, []) =>

    let

      val ts = map (HOLogic.mk_Trueprop o close_hol_prop

                    o hol_prop_from_formula) phis

(*

      val _ = warning (PolyML.makestring phis)

      val _ = app (warning o Syntax.string_of_term @{context}) ts

*)

      val state = Proof.init @{context}

      val params =

        [("card", "1\<emdash>8"),

         ("box", "false"),

         ("sat_solver", "smart"),

         ("max_threads", "1"),

         ("batch_size", "10"),

         (* ("debug", "true"), *)

         ("verbose", "true"),

         (* ("overlord", "true"), *)

         ("show_consts", "true"),

         ("format", "1000"),

         ("max_potential", "0"),

         (* ("timeout", "240 s"), *)

         ("expect", "genuine")]

        |> Nitpick_Isar.default_params @{theory}

      val auto = false

      val i = 1

      val n = 1

      val step = 0

      val subst = []

    in

      Nitpick.pick_nits_in_term state params auto i n step subst ts

                                @{prop False} |> fst

    end

end;