author | blanchet |
Thu, 16 Sep 2010 15:16:08 +0200 | |
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permissions | -rw-r--r-- |
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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 uniform_formula = 'a ATP_Problem.uniform_formula |
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datatype failure = |
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Unprovable | IncompleteUnprovable | CantConnect | TimedOut | |
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OutOfResources | SpassTooOld | VampireTooOld | NoPerl | NoLibwwwPerl | |
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MalformedInput | MalformedOutput | Interrupted | InternalError | |
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UnknownError |
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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 uniform_formula step list |
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val strip_spaces : (char -> 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 -> int -> (string * string) list -> (failure * string) list -> string |
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-> 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_string : 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 | CantConnect | TimedOut | OutOfResources | |
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SpassTooOld | VampireTooOld | NoPerl | NoLibwwwPerl | MalformedInput | |
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MalformedOutput | Interrupted | InternalError | UnknownError |
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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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val missing_message_tail = |
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" appears to be missing. You will need to install it if you want to run \ |
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\ATPs remotely." |
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fun string_for_failure Unprovable = "The ATP problem is unprovable." |
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| string_for_failure IncompleteUnprovable = |
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"The ATP cannot prove the problem." |
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| string_for_failure CantConnect = "Can't connect to remote server." |
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| string_for_failure TimedOut = "Timed out." |
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| string_for_failure OutOfResources = "The ATP 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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quote (Path.implode (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 MalformedInput = |
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"The ATP problem is malformed. Please report this to the Isabelle \ |
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\developers." |
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| string_for_failure MalformedOutput = "The ATP output is malformed." |
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| string_for_failure Interrupted = "The ATP was interrupted." |
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| string_for_failure InternalError = "An internal ATP error occurred." |
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| string_for_failure UnknownError = "An unknown ATP error occurred." |
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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 complete res_code proof_delims |
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known_failures output = |
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case extract_known_failure known_failures output of |
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NONE => (case extract_tstplike_proof proof_delims output of |
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"" => ("", SOME (if res_code = 0 andalso output = "" then |
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Interrupted |
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else |
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UnknownError)) |
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| tstplike_proof => if res_code = 0 then (tstplike_proof, NONE) |
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else ("", SOME UnknownError)) |
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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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|
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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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||
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type step_name = string * string option |
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|
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fun is_same_step p = p |> pairself fst |> op = |
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|
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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 |
165 |
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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||
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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 uniform_formula step list |
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|
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fun step_name (Definition (name, _, _)) = name |
|
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| step_name (Inference (name, _, _)) = name |
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||
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(**** PARSING OF TSTP FORMAT ****) |
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||
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(*Strings enclosed in single quotes, e.g. filenames*) |
|
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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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||
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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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||
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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 |-- $$ ":" --| scan_general_id >> K []) x |
|
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||
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fun parse_term x = |
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(scan_general_id |
|
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-- Scan.optional ($$ "(" |-- (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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|
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val parse_atom = |
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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])))) |
|
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||
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fun fo_term_head (ATerm (s, _)) = s |
|
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||
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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 = |
230 |
(($$ "(" |-- parse_formula --| $$ ")" |
|
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|| ($$ "!" >> K AForall || $$ "?" >> K AExists) |
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--| $$ "[" -- parse_terms --| $$ "]" --| $$ ":" -- parse_formula |
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>> (fn ((q, ts), phi) => AQuant (q, map fo_term_head ts, phi)) |
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|| $$ "~" |-- parse_formula >> mk_anot |
235 |
|| parse_atom) |
|
39452 | 236 |
-- Scan.option ((Scan.this_string "=>" >> K AImplies |
237 |
|| 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) |
|
39454 | 241 |
-- parse_formula) |
39452 | 242 |
>> (fn (phi1, NONE) => phi1 |
243 |
| (phi1, SOME (c, phi2)) => mk_aconn c (phi1, phi2))) x |
|
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||
245 |
val parse_tstp_extra_arguments = |
|
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Scan.optional ($$ "," |-- parse_annotation false |
|
247 |
--| Scan.option ($$ "," |-- parse_annotations false)) [] |
|
248 |
||
249 |
(* Syntax: (fof|cnf)\(<num>, <formula_role>, <formula> <extra_arguments>\). |
|
250 |
The <num> could be an identifier, but we assume integers. *) |
|
39454 | 251 |
val parse_tstp_line = |
252 |
((Scan.this_string "fof" || Scan.this_string "cnf") -- $$ "(") |
|
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|-- scan_general_id --| $$ "," -- Symbol.scan_id --| $$ "," |
|
254 |
-- parse_formula -- parse_tstp_extra_arguments --| $$ ")" --| $$ "." |
|
255 |
>> (fn (((num, role), phi), deps) => |
|
256 |
let |
|
257 |
val (name, deps) = |
|
258 |
case deps of |
|
39455 | 259 |
["file", _, s] => ((num, SOME s), []) |
260 |
| _ => ((num, NONE), deps) |
|
39454 | 261 |
in |
262 |
case role of |
|
263 |
"definition" => |
|
264 |
(case phi of |
|
265 |
AConn (AIff, [phi1 as AAtom _, phi2]) => |
|
266 |
Definition (name, phi1, phi2) |
|
267 |
| AAtom (ATerm ("c_equal", _)) => |
|
268 |
(* Vampire's equality proxy axiom *) |
|
39455 | 269 |
Inference (name, phi, map (rpair NONE) deps) |
39454 | 270 |
| _ => raise Fail "malformed definition") |
39455 | 271 |
| _ => Inference (name, phi, map (rpair NONE) deps) |
39454 | 272 |
end) |
39452 | 273 |
|
274 |
(**** PARSING OF VAMPIRE OUTPUT ****) |
|
275 |
||
276 |
(* Syntax: <num>. <formula> <annotation> *) |
|
39454 | 277 |
val parse_vampire_line = |
278 |
scan_general_id --| $$ "." -- parse_formula -- parse_annotation true |
|
39455 | 279 |
>> (fn ((num, phi), deps) => |
280 |
Inference ((num, NONE), phi, map (rpair NONE) deps)) |
|
39452 | 281 |
|
282 |
(**** PARSING OF SPASS OUTPUT ****) |
|
283 |
||
284 |
(* SPASS returns clause references of the form "x.y". We ignore "y", whose role |
|
285 |
is not clear anyway. *) |
|
286 |
val parse_dot_name = scan_general_id --| $$ "." --| scan_general_id |
|
287 |
||
288 |
val parse_spass_annotations = |
|
289 |
Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name |
|
290 |
--| Scan.option ($$ ","))) [] |
|
291 |
||
292 |
(* It is not clear why some literals are followed by sequences of stars and/or |
|
293 |
pluses. We ignore them. *) |
|
39454 | 294 |
val parse_decorated_atom = |
295 |
parse_atom --| Scan.repeat ($$ "*" || $$ "+" || $$ " ") |
|
39452 | 296 |
|
297 |
fun mk_horn ([], []) = AAtom (ATerm ("c_False", [])) |
|
298 |
| mk_horn ([], pos_lits) = foldr1 (mk_aconn AOr) pos_lits |
|
299 |
| mk_horn (neg_lits, []) = mk_anot (foldr1 (mk_aconn AAnd) neg_lits) |
|
300 |
| mk_horn (neg_lits, pos_lits) = |
|
301 |
mk_aconn AImplies (foldr1 (mk_aconn AAnd) neg_lits, |
|
302 |
foldr1 (mk_aconn AOr) pos_lits) |
|
303 |
||
39454 | 304 |
val parse_horn_clause = |
305 |
Scan.repeat parse_decorated_atom --| $$ "|" --| $$ "|" |
|
306 |
-- Scan.repeat parse_decorated_atom --| $$ "-" --| $$ ">" |
|
307 |
-- Scan.repeat parse_decorated_atom |
|
39452 | 308 |
>> (mk_horn o apfst (op @)) |
309 |
||
310 |
(* Syntax: <num>[0:<inference><annotations>] |
|
311 |
<atoms> || <atoms> -> <atoms>. *) |
|
39454 | 312 |
val parse_spass_line = |
39452 | 313 |
scan_general_id --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id |
39454 | 314 |
-- parse_spass_annotations --| $$ "]" -- parse_horn_clause --| $$ "." |
39455 | 315 |
>> (fn ((num, deps), u) => Inference ((num, NONE), u, map (rpair NONE) deps)) |
39452 | 316 |
|
39454 | 317 |
val parse_line = parse_tstp_line || parse_vampire_line || parse_spass_line |
318 |
val parse_proof = |
|
39452 | 319 |
fst o Scan.finite Symbol.stopper |
320 |
(Scan.error (!! (fn _ => raise Fail "unrecognized ATP output") |
|
39454 | 321 |
(Scan.repeat1 parse_line))) |
39457 | 322 |
o explode o strip_spaces_except_between_ident_chars |
39452 | 323 |
|
324 |
fun clean_up_dependency seen dep = find_first (curry is_same_step dep) seen |
|
325 |
fun clean_up_dependencies _ [] = [] |
|
326 |
| clean_up_dependencies seen ((step as Definition (name, _, _)) :: steps) = |
|
327 |
step :: clean_up_dependencies (name :: seen) steps |
|
328 |
| clean_up_dependencies seen (Inference (name, u, deps) :: steps) = |
|
329 |
Inference (name, u, map_filter (clean_up_dependency seen) deps) :: |
|
330 |
clean_up_dependencies (name :: seen) steps |
|
331 |
||
39454 | 332 |
val atp_proof_from_tstplike_string = |
39452 | 333 |
suffix "$" (* the $ sign acts as a sentinel (FIXME: needed?) *) |
39454 | 334 |
#> parse_proof |
39452 | 335 |
#> sort (step_name_ord o pairself step_name) |
336 |
#> clean_up_dependencies [] |
|
337 |
||
39454 | 338 |
fun map_term_names_in_term f (ATerm (s, ts)) = |
339 |
ATerm (f s, map (map_term_names_in_term f) ts) |
|
340 |
fun map_term_names_in_formula f (AQuant (q, xs, phi)) = |
|
341 |
AQuant (q, xs, map_term_names_in_formula f phi) |
|
342 |
| map_term_names_in_formula f (AConn (c, phis)) = |
|
343 |
AConn (c, map (map_term_names_in_formula f) phis) |
|
344 |
| map_term_names_in_formula f (AAtom t) = AAtom (map_term_names_in_term f t) |
|
345 |
fun map_term_names_in_step f (Definition (name, phi1, phi2)) = |
|
346 |
Definition (name, map_term_names_in_formula f phi1, |
|
347 |
map_term_names_in_formula f phi2) |
|
348 |
| map_term_names_in_step f (Inference (name, phi, deps)) = |
|
349 |
Inference (name, map_term_names_in_formula f phi, deps) |
|
350 |
fun map_term_names_in_atp_proof f = map (map_term_names_in_step f) |
|
351 |
||
352 |
fun nasty_name pool s = s |> Symtab.lookup pool |> the_default s |
|
353 |
fun nasty_atp_proof pool = |
|
354 |
if Symtab.is_empty pool then I |
|
355 |
else map_term_names_in_atp_proof (nasty_name pool) |
|
356 |
||
39452 | 357 |
end; |