author | blanchet |
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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 | 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 uniform_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)) |
39452 | 181 |
|
182 |
fun mk_anot (AConn (ANot, [phi])) = phi |
|
183 |
| mk_anot phi = AConn (ANot, [phi]) |
|
184 |
fun mk_aconn c (phi1, phi2) = AConn (c, [phi1, phi2]) |
|
185 |
||
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type step_name = string * string option |
39452 | 187 |
|
39455 | 188 |
fun is_same_step p = p |> pairself fst |> op = |
39452 | 189 |
|
190 |
fun step_name_ord p = |
|
39455 | 191 |
let val q = pairself fst p in |
39452 | 192 |
(* The "unprefix" part is to cope with remote Vampire's output. The proper |
193 |
solution would be to perform a topological sort, e.g. using the nice |
|
194 |
"Graph" functor. *) |
|
195 |
case pairself (Int.fromString o perhaps (try (unprefix "f"))) q of |
|
196 |
(NONE, NONE) => string_ord q |
|
197 |
| (NONE, SOME _) => LESS |
|
198 |
| (SOME _, NONE) => GREATER |
|
199 |
| (SOME i, SOME j) => int_ord (i, j) |
|
200 |
end |
|
201 |
||
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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 |
39452 | 205 |
|
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type 'a proof = 'a uniform_formula step list |
39452 | 207 |
|
208 |
fun step_name (Definition (name, _, _)) = name |
|
209 |
| step_name (Inference (name, _, _)) = name |
|
210 |
||
211 |
(**** PARSING OF TSTP FORMAT ****) |
|
212 |
||
213 |
(*Strings enclosed in single quotes, e.g. filenames*) |
|
214 |
val scan_general_id = |
|
215 |
$$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode |
|
216 |
|| Scan.repeat ($$ "$") -- Scan.many1 Symbol.is_letdig |
|
217 |
>> (fn (ss1, ss2) => implode ss1 ^ implode ss2) |
|
218 |
||
219 |
(* Generalized first-order terms, which include file names, numbers, etc. *) |
|
220 |
fun parse_annotation strict x = |
|
221 |
((scan_general_id ::: Scan.repeat ($$ " " |-- scan_general_id) |
|
222 |
>> (strict ? filter (is_some o Int.fromString))) |
|
223 |
-- Scan.optional (parse_annotation strict) [] >> op @ |
|
224 |
|| $$ "(" |-- parse_annotations strict --| $$ ")" |
|
225 |
|| $$ "[" |-- parse_annotations strict --| $$ "]") x |
|
226 |
and parse_annotations strict x = |
|
227 |
(Scan.optional (parse_annotation strict |
|
228 |
::: Scan.repeat ($$ "," |-- parse_annotation strict)) [] |
|
229 |
>> flat) x |
|
230 |
||
231 |
(* Vampire proof lines sometimes contain needless information such as "(0:3)", |
|
232 |
which can be hard to disambiguate from function application in an LL(1) |
|
233 |
parser. As a workaround, we extend the TPTP term syntax with such detritus |
|
234 |
and ignore it. *) |
|
235 |
fun parse_vampire_detritus x = |
|
236 |
(scan_general_id |-- $$ ":" --| scan_general_id >> K []) x |
|
237 |
||
39454 | 238 |
fun parse_term x = |
239 |
(scan_general_id |
|
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-- Scan.optional ($$ "(" |-- (parse_vampire_detritus || parse_terms) |
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--| $$ ")") [] |
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--| Scan.optional ($$ "(" |-- parse_vampire_detritus --| $$ ")") [] |
39452 | 243 |
>> ATerm) x |
39454 | 244 |
and parse_terms x = (parse_term ::: Scan.repeat ($$ "," |-- parse_term)) x |
39452 | 245 |
|
39598 | 246 |
fun parse_atom x = |
247 |
(parse_term -- Scan.option (Scan.option ($$ "!") --| $$ "=" -- parse_term) |
|
248 |
>> (fn (u1, NONE) => AAtom u1 |
|
249 |
| (u1, SOME (NONE, u2)) => AAtom (ATerm ("c_equal", [u1, u2])) |
|
250 |
| (u1, SOME (SOME _, u2)) => |
|
251 |
mk_anot (AAtom (ATerm ("c_equal", [u1, u2]))))) x |
|
39452 | 252 |
|
253 |
fun fo_term_head (ATerm (s, _)) = s |
|
254 |
||
255 |
(* TPTP formulas are fully parenthesized, so we don't need to worry about |
|
256 |
operator precedence. *) |
|
39454 | 257 |
fun parse_formula x = |
258 |
(($$ "(" |-- parse_formula --| $$ ")" |
|
39452 | 259 |
|| ($$ "!" >> K AForall || $$ "?" >> K AExists) |
39454 | 260 |
--| $$ "[" -- parse_terms --| $$ "]" --| $$ ":" -- parse_formula |
39452 | 261 |
>> (fn ((q, ts), phi) => AQuant (q, map fo_term_head ts, phi)) |
39454 | 262 |
|| $$ "~" |-- parse_formula >> mk_anot |
263 |
|| parse_atom) |
|
39452 | 264 |
-- Scan.option ((Scan.this_string "=>" >> K AImplies |
265 |
|| Scan.this_string "<=>" >> K AIff |
|
266 |
|| Scan.this_string "<~>" >> K ANotIff |
|
267 |
|| Scan.this_string "<=" >> K AIf |
|
268 |
|| $$ "|" >> K AOr || $$ "&" >> K AAnd) |
|
39454 | 269 |
-- parse_formula) |
39452 | 270 |
>> (fn (phi1, NONE) => phi1 |
271 |
| (phi1, SOME (c, phi2)) => mk_aconn c (phi1, phi2))) x |
|
272 |
||
273 |
val parse_tstp_extra_arguments = |
|
274 |
Scan.optional ($$ "," |-- parse_annotation false |
|
275 |
--| Scan.option ($$ "," |-- parse_annotations false)) [] |
|
276 |
||
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277 |
val vampire_unknown_fact = "unknown" |
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278 |
|
39452 | 279 |
(* Syntax: (fof|cnf)\(<num>, <formula_role>, <formula> <extra_arguments>\). |
280 |
The <num> could be an identifier, but we assume integers. *) |
|
39454 | 281 |
val parse_tstp_line = |
282 |
((Scan.this_string "fof" || Scan.this_string "cnf") -- $$ "(") |
|
283 |
|-- scan_general_id --| $$ "," -- Symbol.scan_id --| $$ "," |
|
284 |
-- parse_formula -- parse_tstp_extra_arguments --| $$ ")" --| $$ "." |
|
285 |
>> (fn (((num, role), phi), deps) => |
|
286 |
let |
|
287 |
val (name, deps) = |
|
288 |
case deps of |
|
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289 |
["file", _, s] => |
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290 |
((num, if s = vampire_unknown_fact then NONE else SOME s), []) |
39455 | 291 |
| _ => ((num, NONE), deps) |
39454 | 292 |
in |
293 |
case role of |
|
294 |
"definition" => |
|
295 |
(case phi of |
|
296 |
AConn (AIff, [phi1 as AAtom _, phi2]) => |
|
297 |
Definition (name, phi1, phi2) |
|
298 |
| AAtom (ATerm ("c_equal", _)) => |
|
299 |
(* Vampire's equality proxy axiom *) |
|
39455 | 300 |
Inference (name, phi, map (rpair NONE) deps) |
39454 | 301 |
| _ => raise Fail "malformed definition") |
39455 | 302 |
| _ => Inference (name, phi, map (rpair NONE) deps) |
39454 | 303 |
end) |
39452 | 304 |
|
305 |
(**** PARSING OF VAMPIRE OUTPUT ****) |
|
306 |
||
41146 | 307 |
val parse_vampire_braced_stuff = |
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|
308 |
$$ "{" -- Scan.repeat (scan_general_id --| Scan.option ($$ ",")) -- $$ "}" |
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309 |
val parse_vampire_parenthesized_detritus = |
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|
310 |
$$ "(" |-- parse_vampire_detritus --| $$ ")" |
41146 | 311 |
|
39452 | 312 |
(* Syntax: <num>. <formula> <annotation> *) |
39454 | 313 |
val parse_vampire_line = |
41146 | 314 |
scan_general_id --| $$ "." -- parse_formula |
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|
315 |
--| Scan.option parse_vampire_braced_stuff |
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|
316 |
--| Scan.option parse_vampire_parenthesized_detritus |
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|
317 |
-- parse_annotation true |
39455 | 318 |
>> (fn ((num, phi), deps) => |
319 |
Inference ((num, NONE), phi, map (rpair NONE) deps)) |
|
39452 | 320 |
|
321 |
(**** PARSING OF SPASS OUTPUT ****) |
|
322 |
||
323 |
(* SPASS returns clause references of the form "x.y". We ignore "y", whose role |
|
324 |
is not clear anyway. *) |
|
325 |
val parse_dot_name = scan_general_id --| $$ "." --| scan_general_id |
|
326 |
||
327 |
val parse_spass_annotations = |
|
328 |
Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name |
|
329 |
--| Scan.option ($$ ","))) [] |
|
330 |
||
331 |
(* It is not clear why some literals are followed by sequences of stars and/or |
|
332 |
pluses. We ignore them. *) |
|
39602 | 333 |
fun parse_decorated_atom x = |
334 |
(parse_atom --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")) x |
|
39452 | 335 |
|
336 |
fun mk_horn ([], []) = AAtom (ATerm ("c_False", [])) |
|
337 |
| mk_horn ([], pos_lits) = foldr1 (mk_aconn AOr) pos_lits |
|
338 |
| mk_horn (neg_lits, []) = mk_anot (foldr1 (mk_aconn AAnd) neg_lits) |
|
339 |
| mk_horn (neg_lits, pos_lits) = |
|
340 |
mk_aconn AImplies (foldr1 (mk_aconn AAnd) neg_lits, |
|
341 |
foldr1 (mk_aconn AOr) pos_lits) |
|
342 |
||
39645 | 343 |
fun parse_horn_clause x = |
344 |
(Scan.repeat parse_decorated_atom --| $$ "|" --| $$ "|" |
|
345 |
-- Scan.repeat parse_decorated_atom --| $$ "-" --| $$ ">" |
|
346 |
-- Scan.repeat parse_decorated_atom |
|
347 |
>> (mk_horn o apfst (op @))) x |
|
39452 | 348 |
|
349 |
(* Syntax: <num>[0:<inference><annotations>] |
|
350 |
<atoms> || <atoms> -> <atoms>. *) |
|
39645 | 351 |
fun parse_spass_line x = |
352 |
(scan_general_id --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id |
|
353 |
-- parse_spass_annotations --| $$ "]" -- parse_horn_clause --| $$ "." |
|
354 |
>> (fn ((num, deps), u) => |
|
355 |
Inference ((num, NONE), u, map (rpair NONE) deps))) x |
|
39452 | 356 |
|
39645 | 357 |
fun parse_line x = (parse_tstp_line || parse_vampire_line || parse_spass_line) x |
39454 | 358 |
val parse_proof = |
39452 | 359 |
fst o Scan.finite Symbol.stopper |
360 |
(Scan.error (!! (fn _ => raise Fail "unrecognized ATP output") |
|
39454 | 361 |
(Scan.repeat1 parse_line))) |
40627
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changeset
|
362 |
o raw_explode o strip_spaces_except_between_ident_chars |
39452 | 363 |
|
364 |
fun clean_up_dependency seen dep = find_first (curry is_same_step dep) seen |
|
365 |
fun clean_up_dependencies _ [] = [] |
|
366 |
| clean_up_dependencies seen ((step as Definition (name, _, _)) :: steps) = |
|
367 |
step :: clean_up_dependencies (name :: seen) steps |
|
368 |
| clean_up_dependencies seen (Inference (name, u, deps) :: steps) = |
|
369 |
Inference (name, u, map_filter (clean_up_dependency seen) deps) :: |
|
370 |
clean_up_dependencies (name :: seen) steps |
|
371 |
||
42449
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|
372 |
fun atp_proof_from_tstplike_proof "" = [] |
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|
373 |
| atp_proof_from_tstplike_proof s = |
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|
374 |
s ^ "$" (* the $ sign acts as a sentinel (FIXME: needed?) *) |
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|
375 |
|> parse_proof |
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|
376 |
|> sort (step_name_ord o pairself step_name) |
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|
377 |
|> clean_up_dependencies [] |
39452 | 378 |
|
39454 | 379 |
fun map_term_names_in_term f (ATerm (s, ts)) = |
380 |
ATerm (f s, map (map_term_names_in_term f) ts) |
|
381 |
fun map_term_names_in_formula f (AQuant (q, xs, phi)) = |
|
382 |
AQuant (q, xs, map_term_names_in_formula f phi) |
|
383 |
| map_term_names_in_formula f (AConn (c, phis)) = |
|
384 |
AConn (c, map (map_term_names_in_formula f) phis) |
|
385 |
| map_term_names_in_formula f (AAtom t) = AAtom (map_term_names_in_term f t) |
|
386 |
fun map_term_names_in_step f (Definition (name, phi1, phi2)) = |
|
387 |
Definition (name, map_term_names_in_formula f phi1, |
|
388 |
map_term_names_in_formula f phi2) |
|
389 |
| map_term_names_in_step f (Inference (name, phi, deps)) = |
|
390 |
Inference (name, map_term_names_in_formula f phi, deps) |
|
391 |
fun map_term_names_in_atp_proof f = map (map_term_names_in_step f) |
|
392 |
||
393 |
fun nasty_name pool s = s |> Symtab.lookup pool |> the_default s |
|
394 |
fun nasty_atp_proof pool = |
|
395 |
if Symtab.is_empty pool then I |
|
396 |
else map_term_names_in_atp_proof (nasty_name pool) |
|
397 |
||
39452 | 398 |
end; |