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

    Author:     Lawrence C. Paulson, Cambridge University Computer Laboratory

    Author:     Claire Quigley, Cambridge University Computer Laboratory

    Author:     Jasmin Blanchette, TU Muenchen

Abstract representation of ATP proofs and TSTP/Vampire/SPASS syntax.

*)

signature ATP_PROOF =

sig

  type 'a fo_term = 'a ATP_Problem.fo_term

  type 'a uniform_formula = 'a ATP_Problem.uniform_formula

  datatype failure =

    Unprovable | IncompleteUnprovable | ProofMissing | CantConnect | TimedOut |

    OutOfResources | SpassTooOld | VampireTooOld | NoPerl | NoLibwwwPerl |

    NoRealZ3 | MalformedInput | MalformedOutput | Interrupted | Crashed |

    InternalError | UnknownError of string

  type step_name = string * string option

  datatype 'a step =

    Definition of step_name * 'a * 'a |

    Inference of step_name * 'a * step_name list

  type 'a proof = 'a uniform_formula step list

  val strip_spaces : (char -> bool) -> string -> string

  val short_output : bool -> string -> string

  val string_for_failure : string -> failure -> string

  val extract_important_message : string -> string

  val extract_known_failure :

    (failure * string) list -> string -> failure option

  val extract_tstplike_proof_and_outcome :

    bool -> bool -> int -> (string * string) list -> (failure * string) list

    -> string -> string * failure option

  val is_same_step : step_name * step_name -> bool

  val atp_proof_from_tstplike_string : bool -> string -> string proof

  val map_term_names_in_atp_proof :

    (string -> string) -> string proof -> string proof

  val nasty_atp_proof : string Symtab.table -> string proof -> string proof

end;

structure ATP_Proof : ATP_PROOF =

struct

open ATP_Problem

datatype failure =

  Unprovable | IncompleteUnprovable | ProofMissing | CantConnect | TimedOut |

  OutOfResources | SpassTooOld | VampireTooOld | NoPerl | NoLibwwwPerl |

  NoRealZ3 | MalformedInput | MalformedOutput | Interrupted | Crashed |

  InternalError | UnknownError of string

fun strip_spaces_in_list _ [] = []

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

  | strip_spaces_in_list is_evil [c1, c2] =

    strip_spaces_in_list is_evil [c1] @ strip_spaces_in_list is_evil [c2]

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

    if Char.isSpace c1 then

      strip_spaces_in_list is_evil (c2 :: c3 :: cs)

    else if Char.isSpace c2 then

      if Char.isSpace c3 then

        strip_spaces_in_list is_evil (c1 :: c3 :: cs)

      else

        str c1 :: (if forall is_evil [c1, c3] then [" "] else []) @

        strip_spaces_in_list is_evil (c3 :: cs)

    else

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

fun strip_spaces is_evil =

  implode o strip_spaces_in_list is_evil o String.explode

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

val strip_spaces_except_between_ident_chars = strip_spaces is_ident_char

fun elide_string threshold s =

  if size s > threshold then

    String.extract (s, 0, SOME (threshold div 2 - 5)) ^ " ...... " ^

    String.extract (s, size s - (threshold + 1) div 2 + 6, NONE)

  else

    s

fun short_output verbose output =

  if verbose then elide_string 1000 output else ""

fun missing_message_tail prover =

  " appears to be missing. You will need to install it if you want to run " ^

  prover ^ "s remotely."

fun string_for_failure prover Unprovable =

    "The " ^ prover ^ " problem is unprovable."

  | string_for_failure prover IncompleteUnprovable =

    "The " ^ prover ^ " cannot prove the problem."

  | string_for_failure prover ProofMissing =

    "The " ^ prover ^ " claims the conjecture is a theorem but did not provide \

    \a proof."

  | string_for_failure _ CantConnect = "Cannot connect to remote server."

  | string_for_failure _ TimedOut = "Timed out."

  | string_for_failure prover OutOfResources =

    "The " ^ prover ^ " ran out of resources."

  | string_for_failure _ SpassTooOld =

    "Isabelle requires a more recent version of SPASS with support for the \

    \TPTP syntax. To install it, download and extract the package \

    \\"http://isabelle.in.tum.de/dist/contrib/spass-3.7.tar.gz\" and add the \

    \\"spass-3.7\" directory's absolute path to " ^

    quote (Path.implode (Path.expand (Path.appends

               (Path.variable "ISABELLE_HOME_USER" ::

                map Path.basic ["etc", "components"])))) ^

    " on a line of its own."

  | string_for_failure _ VampireTooOld =

    "Isabelle requires a more recent version of Vampire. To install it, follow \

    \the instructions from the Sledgehammer manual (\"isabelle doc\

    \ sledgehammer\")."

  | string_for_failure prover NoPerl = "Perl" ^ missing_message_tail prover

  | string_for_failure prover NoLibwwwPerl =

    "The Perl module \"libwww-perl\"" ^ missing_message_tail prover

  | string_for_failure _ NoRealZ3 =

    "The environment variable \"Z3_REAL_SOLVER\" must be set to Z3's full path."

  | string_for_failure prover MalformedInput =

    "The " ^ prover ^ " problem is malformed. Please report this to the \

    \Isabelle developers."

  | string_for_failure prover MalformedOutput =

    "The " ^ prover ^ " output is malformed."

  | string_for_failure prover Crashed = "The " ^ prover ^ " crashed."

  | string_for_failure prover InternalError =

    "An internal " ^ prover ^ " error occurred."

  | string_for_failure prover (UnknownError string) =

    (* "An" is correct for "ATP" and "SMT". *)

    "An " ^ prover ^ " error occurred" ^

    (if string = "" then ". (Pass the \"verbose\" option for details.)"

     else ":\n" ^ string)

fun extract_delimited (begin_delim, end_delim) output =

  output |> first_field begin_delim |> the |> snd

         |> first_field end_delim |> the |> fst

         |> first_field "\n" |> the |> snd

  handle Option.Option => ""

val tstp_important_message_delims =

  ("% SZS start RequiredInformation", "% SZS end RequiredInformation")

fun extract_important_message output =

  case extract_delimited tstp_important_message_delims output of

    "" => ""

  | s => s |> space_explode "\n" |> filter_out (curry (op =) "")

           |> map (perhaps (try (unprefix "%")))

           |> map (perhaps (try (unprefix " ")))

           |> space_implode "\n " |> quote

(* Splits by the first possible of a list of delimiters. *)

fun extract_tstplike_proof delims output =

  case pairself (find_first (fn s => String.isSubstring s output))

                (ListPair.unzip delims) of

    (SOME begin_delim, SOME end_delim) =>

    extract_delimited (begin_delim, end_delim) output

  | _ => ""

fun extract_known_failure known_failures output =

  known_failures

  |> find_first (fn (_, pattern) => String.isSubstring pattern output)

  |> Option.map fst

fun extract_tstplike_proof_and_outcome verbose complete res_code proof_delims

                                       known_failures output =

  case extract_known_failure known_failures output of

    NONE => (case extract_tstplike_proof proof_delims output of

             "" => ("", SOME (if res_code = 0 andalso output = "" then

                                ProofMissing

                              else

                                UnknownError (short_output verbose output)))

           | tstplike_proof =>

             if res_code = 0 then (tstplike_proof, NONE)

             else ("", SOME (UnknownError (short_output verbose output))))

  | SOME failure =>

    ("", SOME (if failure = IncompleteUnprovable andalso complete then

                 Unprovable

               else

                 failure))

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

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

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

type step_name = string * string option

fun is_same_step p = p |> pairself fst |> op =

fun step_name_ord p =

  let val q = pairself fst p in

    (* The "unprefix" part is to cope with remote Vampire's output. The proper

       solution would be to perform a topological sort, e.g. using the nice

       "Graph" functor. *)

    case pairself (Int.fromString o perhaps (try (unprefix "f"))) q of

      (NONE, NONE) => string_ord q

    | (NONE, SOME _) => LESS

    | (SOME _, NONE) => GREATER

    | (SOME i, SOME j) => int_ord (i, j)

  end

datatype 'a step =

  Definition of step_name * 'a * 'a |

  Inference of step_name * 'a * step_name list

type 'a proof = 'a uniform_formula step list

fun step_name (Definition (name, _, _)) = name

  | step_name (Inference (name, _, _)) = name

(**** PARSING OF TSTP FORMAT ****)

(*Strings enclosed in single quotes, e.g. filenames*)

val scan_general_id =

  $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode

  || Scan.repeat ($$ "$") -- Scan.many1 Symbol.is_letdig

     >> (fn (ss1, ss2) => implode ss1 ^ implode ss2)

(* Generalized first-order terms, which include file names, numbers, etc. *)

fun parse_annotation strict x =

  ((scan_general_id ::: Scan.repeat ($$ " " |-- scan_general_id)

      >> (strict ? filter (is_some o Int.fromString)))

   -- Scan.optional (parse_annotation strict) [] >> op @

   || $$ "(" |-- parse_annotations strict --| $$ ")"

   || $$ "[" |-- parse_annotations strict --| $$ "]") x

and parse_annotations strict x =

  (Scan.optional (parse_annotation strict

                  ::: Scan.repeat ($$ "," |-- parse_annotation strict)) []

   >> flat) x

(* Vampire proof lines sometimes contain needless information such as "(0:3)",

   which can be hard to disambiguate from function application in an LL(1)

   parser. As a workaround, we extend the TPTP term syntax with such detritus

   and ignore it. *)

fun parse_vampire_detritus x =

  (scan_general_id |-- $$ ":" --| scan_general_id >> K []) x

fun parse_term x =

  (scan_general_id

     -- Scan.optional ($$ "(" |-- (parse_vampire_detritus || parse_terms)

                       --| $$ ")") []

     --| Scan.optional ($$ "(" |-- parse_vampire_detritus --| $$ ")") []

   >> ATerm) x

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

fun parse_atom x =

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

   >> (fn (u1, NONE) => AAtom u1

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

        | (u1, SOME (SOME _, u2)) =>

          mk_anot (AAtom (ATerm ("c_equal", [u1, u2]))))) x

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

(* TPTP formulas are fully parenthesized, so we don't need to worry about

   operator precedence. *)

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_atom)

   -- 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_tstp_extra_arguments =

  Scan.optional ($$ "," |-- parse_annotation false

                 --| Scan.option ($$ "," |-- parse_annotations false)) []

val vampire_unknown_fact = "unknown"

(* Syntax: (fof|cnf)\(<num>, <formula_role>, <formula> <extra_arguments>\).

   The <num> could be an identifier, but we assume integers. *)

val parse_tstp_line =

  ((Scan.this_string "fof" || Scan.this_string "cnf") -- $$ "(")

    |-- scan_general_id --| $$ "," -- Symbol.scan_id --| $$ ","

    -- parse_formula -- parse_tstp_extra_arguments --| $$ ")" --| $$ "."

   >> (fn (((num, role), phi), deps) =>

          let

            val (name, deps) =

              case deps of

                ["file", _, s] =>

                ((num, if s = vampire_unknown_fact then NONE else SOME s), [])

              | _ => ((num, NONE), deps)

          in

            case role of

              "definition" =>

              (case phi of

                 AConn (AIff, [phi1 as AAtom _, phi2]) =>

                 Definition (name, phi1, phi2)

               | AAtom (ATerm ("c_equal", _)) =>

                 (* Vampire's equality proxy axiom *)

                 Inference (name, phi, map (rpair NONE) deps)

               | _ => raise Fail "malformed definition")

            | _ => Inference (name, phi, map (rpair NONE) deps)

          end)

(**** PARSING OF VAMPIRE OUTPUT ****)

val parse_vampire_braced_stuff =

  $$ "{" -- Scan.repeat (scan_general_id --| Scan.option ($$ ",")) -- $$ "}"

val parse_vampire_parenthesized_detritus =

  $$ "(" |-- parse_vampire_detritus --| $$ ")"

(* Syntax: <num>. <formula> <annotation> *)

val parse_vampire_line =

  scan_general_id --| $$ "." -- parse_formula

    --| Scan.option parse_vampire_braced_stuff

    --| Scan.option parse_vampire_parenthesized_detritus

    -- parse_annotation true

  >> (fn ((num, phi), deps) =>

         Inference ((num, NONE), phi, map (rpair NONE) deps))

(**** PARSING OF SPASS OUTPUT ****)

(* SPASS returns clause references of the form "x.y". We ignore "y", whose role

   is not clear anyway. *)

val parse_dot_name = scan_general_id --| $$ "." --| scan_general_id

val parse_spass_annotations =

  Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name

                                         --| Scan.option ($$ ","))) []

(* It is not clear why some literals are followed by sequences of stars and/or

   pluses. We ignore them. *)

fun parse_decorated_atom x =

  (parse_atom --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")) x

fun mk_horn ([], []) = AAtom (ATerm ("c_False", []))

  | mk_horn ([], pos_lits) = foldr1 (mk_aconn AOr) pos_lits

  | mk_horn (neg_lits, []) = mk_anot (foldr1 (mk_aconn AAnd) neg_lits)

  | mk_horn (neg_lits, pos_lits) =

    mk_aconn AImplies (foldr1 (mk_aconn AAnd) neg_lits,

                       foldr1 (mk_aconn AOr) pos_lits)

fun parse_horn_clause x =

  (Scan.repeat parse_decorated_atom --| $$ "|" --| $$ "|"

     -- Scan.repeat parse_decorated_atom --| $$ "-" --| $$ ">"

     -- Scan.repeat parse_decorated_atom

   >> (mk_horn o apfst (op @))) x

(* Syntax: <num>[0:<inference><annotations>]

   <atoms> || <atoms> -> <atoms>. *)

fun parse_spass_line x =

  (scan_general_id --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id

     -- parse_spass_annotations --| $$ "]" -- parse_horn_clause --| $$ "."

   >> (fn ((num, deps), u) =>

          Inference ((num, NONE), u, map (rpair NONE) deps))) x

fun parse_line x = (parse_tstp_line || parse_vampire_line || parse_spass_line) x

val parse_proof =

  fst o Scan.finite Symbol.stopper

            (Scan.error (!! (fn _ => raise Fail "unrecognized ATP output")

                            (Scan.repeat1 parse_line)))

  o raw_explode o strip_spaces_except_between_ident_chars

fun clean_up_dependency seen dep = find_first (curry is_same_step dep) seen

fun clean_up_dependencies _ [] = []

  | clean_up_dependencies seen ((step as Definition (name, _, _)) :: steps) =

    step :: clean_up_dependencies (name :: seen) steps

  | clean_up_dependencies seen (Inference (name, u, deps) :: steps) =

    Inference (name, u, map_filter (clean_up_dependency seen) deps) ::

    clean_up_dependencies (name :: seen) steps

fun atp_proof_from_tstplike_string clean =

  suffix "$" (* the $ sign acts as a sentinel (FIXME: needed?) *)

  #> parse_proof

  #> clean ? (sort (step_name_ord o pairself step_name)

              #> clean_up_dependencies [])

fun map_term_names_in_term f (ATerm (s, ts)) =

  ATerm (f s, map (map_term_names_in_term f) ts)

fun map_term_names_in_formula f (AQuant (q, xs, phi)) =

    AQuant (q, xs, map_term_names_in_formula f phi)

  | map_term_names_in_formula f (AConn (c, phis)) =

    AConn (c, map (map_term_names_in_formula f) phis)

  | map_term_names_in_formula f (AAtom t) = AAtom (map_term_names_in_term f t)

fun map_term_names_in_step f (Definition (name, phi1, phi2)) =

    Definition (name, map_term_names_in_formula f phi1,

                map_term_names_in_formula f phi2)

  | map_term_names_in_step f (Inference (name, phi, deps)) =

    Inference (name, map_term_names_in_formula f phi, deps)

fun map_term_names_in_atp_proof f = map (map_term_names_in_step f)

fun nasty_name pool s = s |> Symtab.lookup pool |> the_default s

fun nasty_atp_proof pool =

  if Symtab.is_empty pool then I

  else map_term_names_in_atp_proof (nasty_name pool)

end;