1 (* Title: HOL/Tools/ATP/atp_proof.ML
2 Author: Lawrence C. Paulson, Cambridge University Computer Laboratory
3 Author: Claire Quigley, Cambridge University Computer Laboratory
4 Author: Jasmin Blanchette, TU Muenchen
6 Abstract representation of ATP proofs and TSTP/Vampire/SPASS syntax.
11 type 'a fo_term = 'a ATP_Problem.fo_term
12 type 'a uniform_formula = 'a ATP_Problem.uniform_formula
15 Unprovable | IncompleteUnprovable | CantConnect | TimedOut |
16 OutOfResources | SpassTooOld | VampireTooOld | NoPerl | NoLibwwwPerl |
17 NoRealZ3 | MalformedInput | MalformedOutput | Interrupted | Crashed |
18 InternalError | UnknownError
20 type step_name = string * string option
23 Definition of step_name * 'a * 'a |
24 Inference of step_name * 'a * step_name list
26 type 'a proof = 'a uniform_formula step list
28 val strip_spaces : (char -> bool) -> string -> string
29 val string_for_failure : string -> failure -> string
30 val extract_important_message : string -> string
31 val extract_known_failure :
32 (failure * string) list -> string -> failure option
33 val extract_tstplike_proof_and_outcome :
34 bool -> int -> (string * string) list -> (failure * string) list -> string
35 -> string * failure option
36 val is_same_step : step_name * step_name -> bool
37 val atp_proof_from_tstplike_string : bool -> string -> string proof
38 val map_term_names_in_atp_proof :
39 (string -> string) -> string proof -> string proof
40 val nasty_atp_proof : string Symtab.table -> string proof -> string proof
43 structure ATP_Proof : ATP_PROOF =
49 Unprovable | IncompleteUnprovable | CantConnect | TimedOut | OutOfResources |
50 SpassTooOld | VampireTooOld | NoPerl | NoLibwwwPerl | NoRealZ3 |
51 MalformedInput | MalformedOutput | Interrupted | Crashed | InternalError |
54 fun strip_spaces_in_list _ [] = []
55 | strip_spaces_in_list _ [c1] = if Char.isSpace c1 then [] else [str c1]
56 | strip_spaces_in_list is_evil [c1, c2] =
57 strip_spaces_in_list is_evil [c1] @ strip_spaces_in_list is_evil [c2]
58 | strip_spaces_in_list is_evil (c1 :: c2 :: c3 :: cs) =
59 if Char.isSpace c1 then
60 strip_spaces_in_list is_evil (c2 :: c3 :: cs)
61 else if Char.isSpace c2 then
62 if Char.isSpace c3 then
63 strip_spaces_in_list is_evil (c1 :: c3 :: cs)
65 str c1 :: (if forall is_evil [c1, c3] then [" "] else []) @
66 strip_spaces_in_list is_evil (c3 :: cs)
68 str c1 :: strip_spaces_in_list is_evil (c2 :: c3 :: cs)
69 fun strip_spaces is_evil =
70 implode o strip_spaces_in_list is_evil o String.explode
72 fun is_ident_char c = Char.isAlphaNum c orelse c = #"_"
73 val strip_spaces_except_between_ident_chars = strip_spaces is_ident_char
75 fun missing_message_tail prover =
76 " appears to be missing. You will need to install it if you want to run " ^
77 prover ^ "s remotely."
79 fun string_for_failure prover Unprovable =
80 "The " ^ prover ^ " problem is unprovable."
81 | string_for_failure prover IncompleteUnprovable =
82 "The " ^ prover ^ " cannot prove the problem."
83 | string_for_failure _ CantConnect = "Cannot connect to remote server."
84 | string_for_failure _ TimedOut = "Timed out."
85 | string_for_failure prover OutOfResources =
86 "The " ^ prover ^ " ran out of resources."
87 | string_for_failure _ SpassTooOld =
88 "Isabelle requires a more recent version of SPASS with support for the \
89 \TPTP syntax. To install it, download and extract the package \
90 \\"http://isabelle.in.tum.de/dist/contrib/spass-3.7.tar.gz\" and add the \
91 \\"spass-3.7\" directory's absolute path to " ^
92 quote (Path.implode (Path.expand (Path.appends
93 (Path.variable "ISABELLE_HOME_USER" ::
94 map Path.basic ["etc", "components"])))) ^
95 " on a line of its own."
96 | string_for_failure _ VampireTooOld =
97 "Isabelle requires a more recent version of Vampire. To install it, follow \
98 \the instructions from the Sledgehammer manual (\"isabelle doc\
100 | string_for_failure prover NoPerl = "Perl" ^ missing_message_tail prover
101 | string_for_failure prover NoLibwwwPerl =
102 "The Perl module \"libwww-perl\"" ^ missing_message_tail prover
103 | string_for_failure prover NoRealZ3 =
104 "The environment variable \"Z3_REAL_SOLVER\" must be set to Z3's full path."
105 | string_for_failure prover MalformedInput =
106 "The " ^ prover ^ " problem is malformed. Please report this to the \
107 \Isabelle developers."
108 | string_for_failure prover MalformedOutput =
109 "The " ^ prover ^ " output is malformed."
110 | string_for_failure prover Interrupted =
111 "The " ^ prover ^ " was interrupted."
112 | string_for_failure prover Crashed = "The " ^ prover ^ " crashed."
113 | string_for_failure prover InternalError =
114 "An internal " ^ prover ^ " error occurred."
115 | string_for_failure prover UnknownError =
116 (* "An" is correct for "ATP" and "SMT". *)
117 "An " ^ prover ^ " error occurred."
119 fun extract_delimited (begin_delim, end_delim) output =
120 output |> first_field begin_delim |> the |> snd
121 |> first_field end_delim |> the |> fst
122 |> first_field "\n" |> the |> snd
123 handle Option.Option => ""
125 val tstp_important_message_delims =
126 ("% SZS start RequiredInformation", "% SZS end RequiredInformation")
128 fun extract_important_message output =
129 case extract_delimited tstp_important_message_delims output of
131 | s => s |> space_explode "\n" |> filter_out (curry (op =) "")
132 |> map (perhaps (try (unprefix "%")))
133 |> map (perhaps (try (unprefix " ")))
134 |> space_implode "\n " |> quote
136 (* Splits by the first possible of a list of delimiters. *)
137 fun extract_tstplike_proof delims output =
138 case pairself (find_first (fn s => String.isSubstring s output))
139 (ListPair.unzip delims) of
140 (SOME begin_delim, SOME end_delim) =>
141 extract_delimited (begin_delim, end_delim) output
144 fun extract_known_failure known_failures output =
146 |> find_first (fn (_, pattern) => String.isSubstring pattern output)
149 fun extract_tstplike_proof_and_outcome complete res_code proof_delims
150 known_failures output =
151 case extract_known_failure known_failures output of
152 NONE => (case extract_tstplike_proof proof_delims output of
153 "" => ("", SOME (if res_code = 0 andalso output = "" then
157 | tstplike_proof => if res_code = 0 then (tstplike_proof, NONE)
158 else ("", SOME UnknownError))
160 ("", SOME (if failure = IncompleteUnprovable andalso complete then
165 fun mk_anot (AConn (ANot, [phi])) = phi
166 | mk_anot phi = AConn (ANot, [phi])
167 fun mk_aconn c (phi1, phi2) = AConn (c, [phi1, phi2])
169 type step_name = string * string option
171 fun is_same_step p = p |> pairself fst |> op =
173 fun step_name_ord p =
174 let val q = pairself fst p in
175 (* The "unprefix" part is to cope with remote Vampire's output. The proper
176 solution would be to perform a topological sort, e.g. using the nice
178 case pairself (Int.fromString o perhaps (try (unprefix "f"))) q of
179 (NONE, NONE) => string_ord q
180 | (NONE, SOME _) => LESS
181 | (SOME _, NONE) => GREATER
182 | (SOME i, SOME j) => int_ord (i, j)
186 Definition of step_name * 'a * 'a |
187 Inference of step_name * 'a * step_name list
189 type 'a proof = 'a uniform_formula step list
191 fun step_name (Definition (name, _, _)) = name
192 | step_name (Inference (name, _, _)) = name
194 (**** PARSING OF TSTP FORMAT ****)
196 (*Strings enclosed in single quotes, e.g. filenames*)
197 val scan_general_id =
198 $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode
199 || Scan.repeat ($$ "$") -- Scan.many1 Symbol.is_letdig
200 >> (fn (ss1, ss2) => implode ss1 ^ implode ss2)
202 (* Generalized first-order terms, which include file names, numbers, etc. *)
203 fun parse_annotation strict x =
204 ((scan_general_id ::: Scan.repeat ($$ " " |-- scan_general_id)
205 >> (strict ? filter (is_some o Int.fromString)))
206 -- Scan.optional (parse_annotation strict) [] >> op @
207 || $$ "(" |-- parse_annotations strict --| $$ ")"
208 || $$ "[" |-- parse_annotations strict --| $$ "]") x
209 and parse_annotations strict x =
210 (Scan.optional (parse_annotation strict
211 ::: Scan.repeat ($$ "," |-- parse_annotation strict)) []
214 (* Vampire proof lines sometimes contain needless information such as "(0:3)",
215 which can be hard to disambiguate from function application in an LL(1)
216 parser. As a workaround, we extend the TPTP term syntax with such detritus
218 fun parse_vampire_detritus x =
219 (scan_general_id |-- $$ ":" --| scan_general_id >> K []) x
223 -- Scan.optional ($$ "(" |-- (parse_vampire_detritus || parse_terms)
225 --| Scan.optional ($$ "(" |-- parse_vampire_detritus --| $$ ")") []
227 and parse_terms x = (parse_term ::: Scan.repeat ($$ "," |-- parse_term)) x
230 (parse_term -- Scan.option (Scan.option ($$ "!") --| $$ "=" -- parse_term)
231 >> (fn (u1, NONE) => AAtom u1
232 | (u1, SOME (NONE, u2)) => AAtom (ATerm ("c_equal", [u1, u2]))
233 | (u1, SOME (SOME _, u2)) =>
234 mk_anot (AAtom (ATerm ("c_equal", [u1, u2]))))) x
236 fun fo_term_head (ATerm (s, _)) = s
238 (* TPTP formulas are fully parenthesized, so we don't need to worry about
239 operator precedence. *)
240 fun parse_formula x =
241 (($$ "(" |-- parse_formula --| $$ ")"
242 || ($$ "!" >> K AForall || $$ "?" >> K AExists)
243 --| $$ "[" -- parse_terms --| $$ "]" --| $$ ":" -- parse_formula
244 >> (fn ((q, ts), phi) => AQuant (q, map fo_term_head ts, phi))
245 || $$ "~" |-- parse_formula >> mk_anot
247 -- Scan.option ((Scan.this_string "=>" >> K AImplies
248 || Scan.this_string "<=>" >> K AIff
249 || Scan.this_string "<~>" >> K ANotIff
250 || Scan.this_string "<=" >> K AIf
251 || $$ "|" >> K AOr || $$ "&" >> K AAnd)
253 >> (fn (phi1, NONE) => phi1
254 | (phi1, SOME (c, phi2)) => mk_aconn c (phi1, phi2))) x
256 val parse_tstp_extra_arguments =
257 Scan.optional ($$ "," |-- parse_annotation false
258 --| Scan.option ($$ "," |-- parse_annotations false)) []
260 val vampire_unknown_fact = "unknown"
262 (* Syntax: (fof|cnf)\(<num>, <formula_role>, <formula> <extra_arguments>\).
263 The <num> could be an identifier, but we assume integers. *)
264 val parse_tstp_line =
265 ((Scan.this_string "fof" || Scan.this_string "cnf") -- $$ "(")
266 |-- scan_general_id --| $$ "," -- Symbol.scan_id --| $$ ","
267 -- parse_formula -- parse_tstp_extra_arguments --| $$ ")" --| $$ "."
268 >> (fn (((num, role), phi), deps) =>
273 ((num, if s = vampire_unknown_fact then NONE else SOME s), [])
274 | _ => ((num, NONE), deps)
279 AConn (AIff, [phi1 as AAtom _, phi2]) =>
280 Definition (name, phi1, phi2)
281 | AAtom (ATerm ("c_equal", _)) =>
282 (* Vampire's equality proxy axiom *)
283 Inference (name, phi, map (rpair NONE) deps)
284 | _ => raise Fail "malformed definition")
285 | _ => Inference (name, phi, map (rpair NONE) deps)
288 (**** PARSING OF VAMPIRE OUTPUT ****)
290 val parse_vampire_braced_stuff =
291 $$ "{" -- Scan.repeat (scan_general_id --| Scan.option ($$ ",")) -- $$ "}"
292 val parse_vampire_parenthesized_detritus =
293 $$ "(" |-- parse_vampire_detritus --| $$ ")"
295 (* Syntax: <num>. <formula> <annotation> *)
296 val parse_vampire_line =
297 scan_general_id --| $$ "." -- parse_formula
298 --| Scan.option parse_vampire_braced_stuff
299 --| Scan.option parse_vampire_parenthesized_detritus
300 -- parse_annotation true
301 >> (fn ((num, phi), deps) =>
302 Inference ((num, NONE), phi, map (rpair NONE) deps))
304 (**** PARSING OF SPASS OUTPUT ****)
306 (* SPASS returns clause references of the form "x.y". We ignore "y", whose role
307 is not clear anyway. *)
308 val parse_dot_name = scan_general_id --| $$ "." --| scan_general_id
310 val parse_spass_annotations =
311 Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name
312 --| Scan.option ($$ ","))) []
314 (* It is not clear why some literals are followed by sequences of stars and/or
315 pluses. We ignore them. *)
316 fun parse_decorated_atom x =
317 (parse_atom --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")) x
319 fun mk_horn ([], []) = AAtom (ATerm ("c_False", []))
320 | mk_horn ([], pos_lits) = foldr1 (mk_aconn AOr) pos_lits
321 | mk_horn (neg_lits, []) = mk_anot (foldr1 (mk_aconn AAnd) neg_lits)
322 | mk_horn (neg_lits, pos_lits) =
323 mk_aconn AImplies (foldr1 (mk_aconn AAnd) neg_lits,
324 foldr1 (mk_aconn AOr) pos_lits)
326 fun parse_horn_clause x =
327 (Scan.repeat parse_decorated_atom --| $$ "|" --| $$ "|"
328 -- Scan.repeat parse_decorated_atom --| $$ "-" --| $$ ">"
329 -- Scan.repeat parse_decorated_atom
330 >> (mk_horn o apfst (op @))) x
332 (* Syntax: <num>[0:<inference><annotations>]
333 <atoms> || <atoms> -> <atoms>. *)
334 fun parse_spass_line x =
335 (scan_general_id --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id
336 -- parse_spass_annotations --| $$ "]" -- parse_horn_clause --| $$ "."
337 >> (fn ((num, deps), u) =>
338 Inference ((num, NONE), u, map (rpair NONE) deps))) x
340 fun parse_line x = (parse_tstp_line || parse_vampire_line || parse_spass_line) x
342 fst o Scan.finite Symbol.stopper
343 (Scan.error (!! (fn _ => raise Fail "unrecognized ATP output")
344 (Scan.repeat1 parse_line)))
345 o raw_explode o strip_spaces_except_between_ident_chars
347 fun clean_up_dependency seen dep = find_first (curry is_same_step dep) seen
348 fun clean_up_dependencies _ [] = []
349 | clean_up_dependencies seen ((step as Definition (name, _, _)) :: steps) =
350 step :: clean_up_dependencies (name :: seen) steps
351 | clean_up_dependencies seen (Inference (name, u, deps) :: steps) =
352 Inference (name, u, map_filter (clean_up_dependency seen) deps) ::
353 clean_up_dependencies (name :: seen) steps
355 fun atp_proof_from_tstplike_string clean =
356 suffix "$" (* the $ sign acts as a sentinel (FIXME: needed?) *)
358 #> clean ? (sort (step_name_ord o pairself step_name)
359 #> clean_up_dependencies [])
361 fun map_term_names_in_term f (ATerm (s, ts)) =
362 ATerm (f s, map (map_term_names_in_term f) ts)
363 fun map_term_names_in_formula f (AQuant (q, xs, phi)) =
364 AQuant (q, xs, map_term_names_in_formula f phi)
365 | map_term_names_in_formula f (AConn (c, phis)) =
366 AConn (c, map (map_term_names_in_formula f) phis)
367 | map_term_names_in_formula f (AAtom t) = AAtom (map_term_names_in_term f t)
368 fun map_term_names_in_step f (Definition (name, phi1, phi2)) =
369 Definition (name, map_term_names_in_formula f phi1,
370 map_term_names_in_formula f phi2)
371 | map_term_names_in_step f (Inference (name, phi, deps)) =
372 Inference (name, map_term_names_in_formula f phi, deps)
373 fun map_term_names_in_atp_proof f = map (map_term_names_in_step f)
375 fun nasty_name pool s = s |> Symtab.lookup pool |> the_default s
376 fun nasty_atp_proof pool =
377 if Symtab.is_empty pool then I
378 else map_term_names_in_atp_proof (nasty_name pool)