src/HOL/Tools/ATP/atp_proof.ML
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(*  Title:      HOL/Tools/ATP/atp_proof.ML
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    Author:     Lawrence C. Paulson, Cambridge University Computer Laboratory
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    Author:     Claire Quigley, Cambridge University Computer Laboratory
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    Author:     Jasmin Blanchette, TU Muenchen
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Abstract representation of ATP proofs and TSTP/Vampire/SPASS syntax.
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*)
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signature ATP_PROOF =
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sig
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  type 'a fo_term = 'a ATP_Problem.fo_term
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  type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
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  datatype failure =
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    Unprovable | IncompleteUnprovable | ProofMissing | UnsoundProof |
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    CantConnect | TimedOut | OutOfResources | SpassTooOld | VampireTooOld |
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    NoPerl | NoLibwwwPerl | NoRealZ3 | MalformedInput | MalformedOutput |
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    Interrupted | Crashed | InternalError | UnknownError of string
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  type step_name = string * string option
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  datatype 'a step =
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    Definition of step_name * 'a * 'a |
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    Inference of step_name * 'a * step_name list
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  type 'a proof = ('a, 'a, 'a fo_term) formula step list
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  val strip_spaces : (char -> bool) -> string -> string
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  val short_output : bool -> string -> string
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  val string_for_failure : failure -> string
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  val extract_important_message : string -> string
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  val extract_known_failure :
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    (failure * string) list -> string -> failure option
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  val extract_tstplike_proof_and_outcome :
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    bool -> bool -> bool -> int -> (string * string) list
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    -> (failure * string) list -> string -> string * failure option
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  val is_same_step : step_name * step_name -> bool
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  val atp_proof_from_tstplike_proof : string -> string proof
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  val map_term_names_in_atp_proof :
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    (string -> string) -> string proof -> string proof
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  val nasty_atp_proof : string Symtab.table -> string proof -> string proof
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end;
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structure ATP_Proof : ATP_PROOF =
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struct
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open ATP_Problem
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datatype failure =
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  Unprovable | IncompleteUnprovable | ProofMissing | UnsoundProof |
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  CantConnect | TimedOut | OutOfResources | SpassTooOld | VampireTooOld |
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  NoPerl | NoLibwwwPerl | NoRealZ3 | MalformedInput | MalformedOutput |
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  Interrupted | Crashed | InternalError | UnknownError of string
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fun strip_spaces_in_list _ [] = []
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  | strip_spaces_in_list _ [c1] = if Char.isSpace c1 then [] else [str c1]
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  | strip_spaces_in_list is_evil [c1, c2] =
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    strip_spaces_in_list is_evil [c1] @ strip_spaces_in_list is_evil [c2]
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  | strip_spaces_in_list is_evil (c1 :: c2 :: c3 :: cs) =
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    if Char.isSpace c1 then
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      strip_spaces_in_list is_evil (c2 :: c3 :: cs)
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    else if Char.isSpace c2 then
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      if Char.isSpace c3 then
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        strip_spaces_in_list is_evil (c1 :: c3 :: cs)
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      else
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        str c1 :: (if forall is_evil [c1, c3] then [" "] else []) @
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        strip_spaces_in_list is_evil (c3 :: cs)
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    else
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      str c1 :: strip_spaces_in_list is_evil (c2 :: c3 :: cs)
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fun strip_spaces is_evil =
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  implode o strip_spaces_in_list is_evil o String.explode
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fun is_ident_char c = Char.isAlphaNum c orelse c = #"_"
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val strip_spaces_except_between_ident_chars = strip_spaces is_ident_char
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fun elide_string threshold s =
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  if size s > threshold then
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    String.extract (s, 0, SOME (threshold div 2 - 5)) ^ " ...... " ^
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    String.extract (s, size s - (threshold + 1) div 2 + 6, NONE)
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  else
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    s
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fun short_output verbose output =
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  if verbose then
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    if output = "" then "No details available" else elide_string 1000 output
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  else
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    ""
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val missing_message_tail =
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  " appears to be missing. You will need to install it if you want to invoke \
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  \remote provers."
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fun string_for_failure Unprovable =
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    "The problem is unprovable."
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  | string_for_failure IncompleteUnprovable =
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    "The prover gave up."
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  | string_for_failure ProofMissing =
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    "The prover claims the conjecture is a theorem but did not provide a proof."
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  | string_for_failure UnsoundProof =
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    "The prover found a type-unsound proof. (Or, very unlikely, your axioms \
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    \are inconsistent.)"
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  | string_for_failure CantConnect = "Cannot connect to remote server."
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  | string_for_failure TimedOut = "Timed out."
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  | string_for_failure OutOfResources = "The prover ran out of resources."
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  | string_for_failure SpassTooOld =
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    "Isabelle requires a more recent version of SPASS with support for the \
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    \TPTP syntax. To install it, download and extract the package \
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    \\"http://isabelle.in.tum.de/dist/contrib/spass-3.7.tar.gz\" and add the \
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    \\"spass-3.7\" directory's absolute path to " ^
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    Path.print (Path.expand (Path.appends
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               (Path.variable "ISABELLE_HOME_USER" ::
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                map Path.basic ["etc", "components"]))) ^
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    " on a line of its own."
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  | string_for_failure VampireTooOld =
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    "Isabelle requires a more recent version of Vampire. To install it, follow \
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    \the instructions from the Sledgehammer manual (\"isabelle doc\
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    \ sledgehammer\")."
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  | string_for_failure NoPerl = "Perl" ^ missing_message_tail
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  | string_for_failure NoLibwwwPerl =
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    "The Perl module \"libwww-perl\"" ^ missing_message_tail
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  | string_for_failure NoRealZ3 =
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    "The environment variable \"Z3_REAL_SOLVER\" must be set to Z3's full path."
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  | string_for_failure MalformedInput =
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    "The generated problem is malformed. Please report this to the Isabelle \
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    \developers."
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  | string_for_failure MalformedOutput = "The prover output is malformed."
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  | string_for_failure Crashed = "The prover crashed."
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  | string_for_failure InternalError = "An internal prover error occurred."
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  | string_for_failure (UnknownError string) =
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    "A prover error occurred" ^
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    (if string = "" then ". (Pass the \"verbose\" option for details.)"
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     else ":\n" ^ string)
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fun extract_delimited (begin_delim, end_delim) output =
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  output |> first_field begin_delim |> the |> snd
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         |> first_field end_delim |> the |> fst
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         |> first_field "\n" |> the |> snd
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  handle Option.Option => ""
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val tstp_important_message_delims =
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  ("% SZS start RequiredInformation", "% SZS end RequiredInformation")
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fun extract_important_message output =
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  case extract_delimited tstp_important_message_delims output of
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    "" => ""
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  | s => s |> space_explode "\n" |> filter_out (curry (op =) "")
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           |> map (perhaps (try (unprefix "%")))
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           |> map (perhaps (try (unprefix " ")))
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           |> space_implode "\n " |> quote
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(* Splits by the first possible of a list of delimiters. *)
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fun extract_tstplike_proof delims output =
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  case pairself (find_first (fn s => String.isSubstring s output))
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                (ListPair.unzip delims) of
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    (SOME begin_delim, SOME end_delim) =>
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    extract_delimited (begin_delim, end_delim) output
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  | _ => ""
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fun extract_known_failure known_failures output =
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  known_failures
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  |> find_first (fn (_, pattern) => String.isSubstring pattern output)
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  |> Option.map fst
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fun extract_tstplike_proof_and_outcome debug verbose complete res_code
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                                       proof_delims known_failures output =
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  case extract_known_failure known_failures output of
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    NONE =>
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    (case extract_tstplike_proof proof_delims output of
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       "" =>
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       ("", SOME (if res_code = 0 andalso (not debug orelse output = "") then
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                    ProofMissing
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                  else
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                    UnknownError (short_output verbose output)))
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     | tstplike_proof =>
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       if res_code = 0 then (tstplike_proof, NONE)
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       else ("", SOME (UnknownError (short_output verbose output))))
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  | SOME failure =>
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    ("", SOME (if failure = IncompleteUnprovable andalso complete then
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                 Unprovable
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               else
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                 failure))
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fun mk_anot (AConn (ANot, [phi])) = phi
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  | mk_anot phi = AConn (ANot, [phi])
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fun mk_aconn c (phi1, phi2) = AConn (c, [phi1, phi2])
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type step_name = string * string option
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fun is_same_step p = p |> pairself fst |> op =
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fun step_name_ord p =
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  let val q = pairself fst p in
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    (* The "unprefix" part is to cope with remote Vampire's output. The proper
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       solution would be to perform a topological sort, e.g. using the nice
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       "Graph" functor. *)
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    case pairself (Int.fromString o perhaps (try (unprefix "f"))) q of
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      (NONE, NONE) => string_ord q
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    | (NONE, SOME _) => LESS
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    | (SOME _, NONE) => GREATER
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    | (SOME i, SOME j) => int_ord (i, j)
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  end
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datatype 'a step =
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  Definition of step_name * 'a * 'a |
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  Inference of step_name * 'a * step_name list
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type 'a proof = ('a, 'a, 'a fo_term) formula step list
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fun step_name (Definition (name, _, _)) = name
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  | step_name (Inference (name, _, _)) = name
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(**** PARSING OF TSTP FORMAT ****)
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(* Strings enclosed in single quotes (e.g., file names) *)
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val scan_general_id =
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  $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode
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  || Scan.repeat ($$ "$") -- Scan.many1 Symbol.is_letdig
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     >> (fn (ss1, ss2) => implode ss1 ^ implode ss2)
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(* Generalized first-order terms, which include file names, numbers, etc. *)
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fun parse_annotation strict x =
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  ((scan_general_id ::: Scan.repeat ($$ " " |-- scan_general_id)
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      >> (strict ? filter (is_some o Int.fromString)))
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   -- Scan.optional (parse_annotation strict) [] >> op @
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   || $$ "(" |-- parse_annotations strict --| $$ ")"
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   || $$ "[" |-- parse_annotations strict --| $$ "]") x
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and parse_annotations strict x =
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  (Scan.optional (parse_annotation strict
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                  ::: Scan.repeat ($$ "," |-- parse_annotation strict)) []
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   >> flat) x
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(* Vampire proof lines sometimes contain needless information such as "(0:3)",
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   which can be hard to disambiguate from function application in an LL(1)
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   parser. As a workaround, we extend the TPTP term syntax with such detritus
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   and ignore it. *)
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fun parse_vampire_detritus x =
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  (scan_general_id |-- $$ ":" --| scan_general_id >> K []) x
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fun parse_term x =
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  (scan_general_id
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     -- Scan.optional ($$ "(" |-- (parse_vampire_detritus || parse_terms)
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                       --| $$ ")") []
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     --| Scan.optional ($$ "(" |-- parse_vampire_detritus --| $$ ")") []
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   >> ATerm) x
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and parse_terms x = (parse_term ::: Scan.repeat ($$ "," |-- parse_term)) x
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fun parse_atom x =
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  (parse_term -- Scan.option (Scan.option ($$ "!") --| $$ "=" -- parse_term)
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   >> (fn (u1, NONE) => AAtom u1
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        | (u1, SOME (NONE, u2)) => AAtom (ATerm ("c_equal", [u1, u2]))
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        | (u1, SOME (SOME _, u2)) =>
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          mk_anot (AAtom (ATerm ("c_equal", [u1, u2]))))) x
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fun fo_term_head (ATerm (s, _)) = s
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(* TPTP formulas are fully parenthesized, so we don't need to worry about
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   operator precedence. *)
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fun parse_formula x =
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  (($$ "(" |-- parse_formula --| $$ ")"
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    || ($$ "!" >> K AForall || $$ "?" >> K AExists)
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       --| $$ "[" -- parse_terms --| $$ "]" --| $$ ":" -- parse_formula
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       >> (fn ((q, ts), phi) =>
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              (* FIXME: TFF *)
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              AQuant (q, map (rpair NONE o fo_term_head) ts, phi))
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    || $$ "~" |-- parse_formula >> mk_anot
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    || parse_atom)
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   -- Scan.option ((Scan.this_string "=>" >> K AImplies
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                    || Scan.this_string "<=>" >> K AIff
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                    || Scan.this_string "<~>" >> K ANotIff
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                    || Scan.this_string "<=" >> K AIf
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                    || $$ "|" >> K AOr || $$ "&" >> K AAnd)
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                   -- parse_formula)
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   >> (fn (phi1, NONE) => phi1
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        | (phi1, SOME (c, phi2)) => mk_aconn c (phi1, phi2))) x
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val parse_tstp_extra_arguments =
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  Scan.optional ($$ "," |-- parse_annotation false
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                 --| Scan.option ($$ "," |-- parse_annotations false)) []
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val vampire_unknown_fact = "unknown"
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val tofof_fact_prefix = "fof_"
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(* Syntax: (cnf|fof|tff)\(<num>, <formula_role>, <formula> <extra_arguments>\).
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   The <num> could be an identifier, but we assume integers. *)
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val parse_tstp_line =
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  ((Scan.this_string "cnf" || Scan.this_string "fof" || Scan.this_string "tff")
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      -- $$ "(")
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    |-- scan_general_id --| $$ "," -- Symbol.scan_id --| $$ ","
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    -- parse_formula -- parse_tstp_extra_arguments --| $$ ")" --| $$ "."
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   >> (fn (((num, role), phi), deps) =>
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          let
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            val (name, deps) =
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              case deps of
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                ["file", _, s] =>
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                ((num,
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                  if s = vampire_unknown_fact then NONE
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                  else SOME (s |> perhaps (try (unprefix tofof_fact_prefix)))),
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                 [])
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              | _ => ((num, NONE), deps)
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          in
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            case role of
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              "definition" =>
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              (case phi of
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                 AConn (AIff, [phi1 as AAtom _, phi2]) =>
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                 Definition (name, phi1, phi2)
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               | AAtom (ATerm ("c_equal", _)) =>
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                 (* Vampire's equality proxy axiom *)
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                 Inference (name, phi, map (rpair NONE) deps)
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               | _ => raise Fail "malformed definition")
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            | _ => Inference (name, phi, map (rpair NONE) deps)
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          end)
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(**** PARSING OF VAMPIRE OUTPUT ****)
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val parse_vampire_braced_stuff =
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  $$ "{" -- Scan.repeat (scan_general_id --| Scan.option ($$ ",")) -- $$ "}"
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val parse_vampire_parenthesized_detritus =
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  $$ "(" |-- parse_vampire_detritus --| $$ ")"
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(* Syntax: <num>. <formula> <annotation> *)
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val parse_vampire_line =
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  scan_general_id --| $$ "." -- parse_formula
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    --| Scan.option parse_vampire_braced_stuff
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    --| Scan.option parse_vampire_parenthesized_detritus
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    -- parse_annotation true
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  >> (fn ((num, phi), deps) =>
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         Inference ((num, NONE), phi, map (rpair NONE) deps))
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(**** PARSING OF SPASS OUTPUT ****)
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(* SPASS returns clause references of the form "x.y". We ignore "y", whose role
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   is not clear anyway. *)
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val parse_dot_name = scan_general_id --| $$ "." --| scan_general_id
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val parse_spass_annotations =
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  Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name
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                                         --| Scan.option ($$ ","))) []
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(* It is not clear why some literals are followed by sequences of stars and/or
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   pluses. We ignore them. *)
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fun parse_decorated_atom x =
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  (parse_atom --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")) x
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fun mk_horn ([], []) = AAtom (ATerm ("c_False", []))
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  | mk_horn ([], pos_lits) = foldr1 (mk_aconn AOr) pos_lits
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  | mk_horn (neg_lits, []) = mk_anot (foldr1 (mk_aconn AAnd) neg_lits)
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  | mk_horn (neg_lits, pos_lits) =
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    mk_aconn AImplies (foldr1 (mk_aconn AAnd) neg_lits,
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                       foldr1 (mk_aconn AOr) pos_lits)
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fun parse_horn_clause x =
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  (Scan.repeat parse_decorated_atom --| $$ "|" --| $$ "|"
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     -- Scan.repeat parse_decorated_atom --| $$ "-" --| $$ ">"
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     -- Scan.repeat parse_decorated_atom
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   >> (mk_horn o apfst (op @))) x
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(* Syntax: <num>[0:<inference><annotations>]
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   <atoms> || <atoms> -> <atoms>. *)
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fun parse_spass_line x =
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  (scan_general_id --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id
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     -- parse_spass_annotations --| $$ "]" -- parse_horn_clause --| $$ "."
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   >> (fn ((num, deps), u) =>
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          Inference ((num, NONE), u, map (rpair NONE) deps))) x
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fun parse_line x = (parse_tstp_line || parse_vampire_line || parse_spass_line) x
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val parse_proof =
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  fst o Scan.finite Symbol.stopper
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            (Scan.error (!! (fn _ => raise Fail "unrecognized ATP output")
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                            (Scan.repeat1 parse_line)))
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  o raw_explode o strip_spaces_except_between_ident_chars
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fun clean_up_dependency seen dep = find_first (curry is_same_step dep) seen
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fun clean_up_dependencies _ [] = []
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  | clean_up_dependencies seen ((step as Definition (name, _, _)) :: steps) =
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    step :: clean_up_dependencies (name :: seen) steps
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  | clean_up_dependencies seen (Inference (name, u, deps) :: steps) =
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    Inference (name, u, map_filter (clean_up_dependency seen) deps) ::
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    clean_up_dependencies (name :: seen) steps
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fun atp_proof_from_tstplike_proof "" = []
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  | atp_proof_from_tstplike_proof s =
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    s ^ "$" (* the $ sign acts as a sentinel (FIXME: needed?) *)
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    |> parse_proof
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    |> sort (step_name_ord o pairself step_name)
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    |> clean_up_dependencies []
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fun map_term_names_in_term f (ATerm (s, ts)) =
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  ATerm (f s, map (map_term_names_in_term f) ts)
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fun map_term_names_in_formula f (AQuant (q, xs, phi)) =
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    AQuant (q, xs, map_term_names_in_formula f phi)
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  | map_term_names_in_formula f (AConn (c, phis)) =
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    AConn (c, map (map_term_names_in_formula f) phis)
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  | map_term_names_in_formula f (AAtom t) = AAtom (map_term_names_in_term f t)
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fun map_term_names_in_step f (Definition (name, phi1, phi2)) =
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    Definition (name, map_term_names_in_formula f phi1,
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                map_term_names_in_formula f phi2)
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  | map_term_names_in_step f (Inference (name, phi, deps)) =
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    Inference (name, map_term_names_in_formula f phi, deps)
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fun map_term_names_in_atp_proof f = map (map_term_names_in_step f)
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fun nasty_name pool s = s |> Symtab.lookup pool |> the_default s
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fun nasty_atp_proof pool =
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  if Symtab.is_empty pool then I
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  else map_term_names_in_atp_proof (nasty_name pool)
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end;