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/SPASS syntax.
11 type ('a, 'b) ho_term = ('a, 'b) ATP_Problem.ho_term
12 type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
13 type 'a problem = 'a ATP_Problem.problem
15 exception UNRECOGNIZED_ATP_PROOF of unit
22 UnsoundProof of bool option * string list | (* FIXME: doesn't belong here *)
36 UnknownError of string
38 type step_name = string * string list option
41 Definition of step_name * 'a * 'a |
42 Inference of step_name * 'a * step_name list
44 type 'a proof = ('a, 'a, ('a, 'a) ho_term) formula step list
46 val short_output : bool -> string -> string
47 val string_for_failure : failure -> string
48 val extract_important_message : string -> string
49 val extract_known_failure :
50 (failure * string) list -> string -> failure option
51 val extract_tstplike_proof_and_outcome :
52 bool -> bool -> (string * string) list -> (failure * string) list -> string
53 -> string * failure option
54 val is_same_atp_step : step_name -> step_name -> bool
55 val scan_general_id : string list -> string * string list
57 string list -> (string, 'a, (string, 'a) ho_term) formula * string list
58 val atp_proof_from_tstplike_proof :
59 string problem -> string -> string -> string proof
60 val clean_up_atp_proof_dependencies : string proof -> string proof
61 val map_term_names_in_atp_proof :
62 (string -> string) -> string proof -> string proof
63 val nasty_atp_proof : string Symtab.table -> string proof -> string proof
66 structure ATP_Proof : ATP_PROOF =
72 exception UNRECOGNIZED_ATP_PROOF of unit
79 UnsoundProof of bool option * string list |
93 UnknownError of string
95 fun elide_string threshold s =
96 if size s > threshold then
97 String.extract (s, 0, SOME (threshold div 2 - 5)) ^ " ...... " ^
98 String.extract (s, size s - (threshold + 1) div 2 + 6, NONE)
101 fun short_output verbose output =
103 if output = "" then "No details available" else elide_string 1000 output
107 val missing_message_tail =
108 " appears to be missing. You will need to install it if you want to invoke \
111 fun involving [] = ""
113 "involving " ^ space_implode " " (Try.serial_commas "and" (map quote ss)) ^
116 fun string_for_failure Unprovable = "The problem is unprovable."
117 | string_for_failure GaveUp = "The prover gave up."
118 | string_for_failure ProofMissing =
119 "The prover claims the conjecture is a theorem but did not provide a proof."
120 | string_for_failure ProofIncomplete =
121 "The prover claims the conjecture is a theorem but provided an incomplete \
123 | string_for_failure (UnsoundProof (NONE, ss)) =
124 "The prover found a type-unsound proof " ^ involving ss ^
125 "(or, less likely, your axioms are inconsistent). Specify a sound type \
126 \encoding or omit the \"type_enc\" option."
127 | string_for_failure (UnsoundProof (SOME false, ss)) =
128 "The prover found a type-unsound proof " ^ involving ss ^
129 "(or, less likely, your axioms are inconsistent). Try passing the \
130 \\"sound\" option to Sledgehammer to avoid such spurious proofs."
131 | string_for_failure (UnsoundProof (SOME true, ss)) =
132 "The prover found a type-unsound proof " ^ involving ss ^
133 "even though a supposedly type-sound encoding was used (or, less likely, \
134 \your axioms are inconsistent). Please report this to the Isabelle \
136 | string_for_failure CantConnect = "Cannot connect to remote server."
137 | string_for_failure TimedOut = "Timed out."
138 | string_for_failure Inappropriate =
139 "The problem lies outside the prover's scope."
140 | string_for_failure OutOfResources = "The prover ran out of resources."
141 | string_for_failure SpassTooOld =
142 "Isabelle requires a more recent version of SPASS with support for the \
143 \TPTP syntax. To install it, download and extract the package \
144 \\"http://isabelle.in.tum.de/dist/contrib/spass-3.7.tar.gz\" and add the \
145 \\"spass-3.7\" directory's absolute path to " ^
146 Path.print (Path.expand (Path.explode "$ISABELLE_HOME_USER/etc/components")) ^
147 " on a line of its own."
148 | string_for_failure VampireTooOld =
149 "Isabelle requires a more recent version of Vampire. To install it, follow \
150 \the instructions from the Sledgehammer manual (\"isabelle doc\
152 | string_for_failure NoPerl = "Perl" ^ missing_message_tail
153 | string_for_failure NoLibwwwPerl =
154 "The Perl module \"libwww-perl\"" ^ missing_message_tail
155 | string_for_failure MalformedInput =
156 "The generated problem is malformed. Please report this to the Isabelle \
158 | string_for_failure MalformedOutput = "The prover output is malformed."
159 | string_for_failure Interrupted = "The prover was interrupted."
160 | string_for_failure Crashed = "The prover crashed."
161 | string_for_failure InternalError = "An internal prover error occurred."
162 | string_for_failure (UnknownError string) =
163 "A prover error occurred" ^
164 (if string = "" then ". (Pass the \"verbose\" option for details.)"
167 fun extract_delimited (begin_delim, end_delim) output =
168 output |> first_field begin_delim |> the |> snd
169 |> first_field end_delim |> the |> fst
170 |> first_field "\n" |> the |> snd
171 handle Option.Option => ""
173 val tstp_important_message_delims =
174 ("% SZS start RequiredInformation", "% SZS end RequiredInformation")
176 fun extract_important_message output =
177 case extract_delimited tstp_important_message_delims output of
179 | s => s |> space_explode "\n" |> filter_out (curry (op =) "")
180 |> map (perhaps (try (unprefix "%")))
181 |> map (perhaps (try (unprefix " ")))
182 |> space_implode "\n " |> quote
184 (* Splits by the first possible of a list of delimiters. *)
185 fun extract_tstplike_proof delims output =
186 case pairself (find_first (fn s => String.isSubstring s output))
187 (ListPair.unzip delims) of
188 (SOME begin_delim, SOME end_delim) =>
189 extract_delimited (begin_delim, end_delim) output
192 fun extract_known_failure known_failures output =
194 |> find_first (fn (_, pattern) => String.isSubstring pattern output)
197 fun extract_tstplike_proof_and_outcome verbose complete proof_delims
198 known_failures output =
199 case (extract_tstplike_proof proof_delims output,
200 extract_known_failure known_failures output) of
201 (_, SOME ProofIncomplete) => ("", SOME ProofIncomplete)
202 | ("", SOME ProofMissing) => ("", NONE)
203 | ("", SOME failure) =>
204 ("", SOME (if failure = GaveUp andalso complete then Unprovable
206 | ("", NONE) => ("", SOME (UnknownError (short_output verbose output)))
207 | (tstplike_proof, _) => (tstplike_proof, NONE)
209 type step_name = string * string list option
211 fun is_same_atp_step (s1, _) (s2, _) = s1 = s2
213 val vampire_fact_prefix = "f"
215 fun step_name_ord p =
216 let val q = pairself fst p in
217 (* The "unprefix" part is to cope with remote Vampire's output. The proper
218 solution would be to perform a topological sort, e.g. using the nice
220 case pairself (Int.fromString
221 o perhaps (try (unprefix vampire_fact_prefix))) q of
222 (NONE, NONE) => string_ord q
223 | (NONE, SOME _) => LESS
224 | (SOME _, NONE) => GREATER
225 | (SOME i, SOME j) => int_ord (i, j)
229 Definition of step_name * 'a * 'a |
230 Inference of step_name * 'a * step_name list
232 type 'a proof = ('a, 'a, ('a, 'a) ho_term) formula step list
234 fun step_name (Definition (name, _, _)) = name
235 | step_name (Inference (name, _, _)) = name
237 (**** PARSING OF TSTP FORMAT ****)
239 (* FIXME: temporary hack *)
240 fun repair_waldmeister_step_name s =
241 case space_explode "." s of
243 (case a of "0" => "X" | "1" => "Y" | _ => "Z" ^ a) ^
244 (if size b = 1 then "0" else "") ^ b ^ c ^ d
247 (* Strings enclosed in single quotes (e.g., file names) *)
248 val scan_general_id =
249 $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'"
250 >> implode >> repair_waldmeister_step_name
251 || Scan.repeat ($$ "$") -- Scan.many1 Symbol.is_letdig
252 >> (fn (ss1, ss2) => implode ss1 ^ implode ss2)
254 (* Generalized first-order terms, which include file names, numbers, etc. *)
255 fun parse_annotation x =
256 ((scan_general_id ::: Scan.repeat ($$ " " |-- scan_general_id))
257 -- Scan.optional parse_annotation [] >> op @
258 || $$ "(" |-- parse_annotations --| $$ ")"
259 || $$ "[" |-- parse_annotations --| $$ "]") x
260 and parse_annotations x =
261 (Scan.optional (parse_annotation
262 ::: Scan.repeat ($$ "," |-- parse_annotation)) []
265 fun list_app (f, args) =
266 fold (fn arg => fn f => ATerm (tptp_app, [f, arg])) args f
268 (* We ignore TFF and THF types for now. *)
269 fun parse_type_stuff x =
270 Scan.repeat (($$ tptp_has_type || $$ tptp_fun_type) |-- parse_arg) x
272 ($$ "(" |-- parse_term --| $$ ")" --| parse_type_stuff
273 || scan_general_id --| parse_type_stuff
274 -- Scan.optional ($$ "(" |-- parse_terms --| $$ ")") []
277 (parse_arg -- Scan.repeat ($$ tptp_app |-- parse_arg) >> list_app) x
279 (parse_app -- Scan.option (Scan.option ($$ tptp_not_infix) --| $$ tptp_equal
281 >> (fn (u1, NONE) => u1
282 | (u1, SOME (NONE, u2)) => ATerm ("equal", [u1, u2])
283 | (u1, SOME (SOME _, u2)) =>
284 ATerm (tptp_not, [ATerm ("equal", [u1, u2])]))) x
286 (parse_term ::: Scan.repeat ($$ "," |-- parse_term)) x
288 (* TODO: Avoid duplication with "parse_term" above. *)
290 (parse_term -- Scan.option (Scan.option ($$ tptp_not_infix) --| $$ tptp_equal
292 >> (fn (u1, NONE) => AAtom u1
293 | (u1, SOME (NONE, u2)) => AAtom (ATerm ("equal", [u1, u2]))
294 | (u1, SOME (SOME _, u2)) =>
295 mk_anot (AAtom (ATerm ("equal", [u1, u2]))))) x
297 fun ho_term_head (ATerm (s, _)) = s
299 (* TPTP formulas are fully parenthesized, so we don't need to worry about
300 operator precedence. *)
301 fun parse_literal x =
302 ((Scan.repeat ($$ tptp_not) >> length)
303 -- ($$ "(" |-- parse_formula --| $$ ")"
304 || parse_quantified_formula
306 >> (fn (n, phi) => phi |> n mod 2 = 1 ? mk_anot)) x
307 and parse_formula x =
309 -- Scan.option ((Scan.this_string tptp_implies
310 || Scan.this_string tptp_iff
311 || Scan.this_string tptp_not_iff
312 || Scan.this_string tptp_if
314 || $$ tptp_and) -- parse_formula)
315 >> (fn (phi1, NONE) => phi1
316 | (phi1, SOME (c, phi2)) =>
317 if c = tptp_implies then mk_aconn AImplies phi1 phi2
318 else if c = tptp_iff then mk_aconn AIff phi1 phi2
319 else if c = tptp_not_iff then mk_anot (mk_aconn AIff phi1 phi2)
320 else if c = tptp_if then mk_aconn AImplies phi2 phi1
321 else if c = tptp_or then mk_aconn AOr phi1 phi2
322 else if c = tptp_and then mk_aconn AAnd phi1 phi2
323 else raise Fail ("impossible connective " ^ quote c))) x
324 and parse_quantified_formula x =
325 (($$ tptp_forall >> K AForall || $$ tptp_exists >> K AExists)
326 --| $$ "[" -- parse_terms --| $$ "]" --| $$ ":" -- parse_literal
327 >> (fn ((q, ts), phi) =>
328 (* We ignore TFF and THF types for now. *)
329 AQuant (q, map (rpair NONE o ho_term_head) ts, phi))) x
331 fun skip_formula ss =
334 | skip 0 (ss as "," :: _) = ss
335 | skip 0 (ss as ")" :: _) = ss
336 | skip 0 (ss as "]" :: _) = ss
337 | skip n ("(" :: ss) = skip (n + 1) ss
338 | skip n ("[" :: ss) = skip (n + 1) ss
339 | skip n ("]" :: ss) = skip (n - 1) ss
340 | skip n (")" :: ss) = skip (n - 1) ss
341 | skip n (_ :: ss) = skip n ss
342 in (AAtom (ATerm ("", [])), skip 0 ss) end
344 val parse_tstp_extra_arguments =
345 Scan.optional ($$ "," |-- parse_annotation
346 --| Scan.option ($$ "," |-- parse_annotations)) []
348 val waldmeister_conjecture = "conjecture_1"
350 val tofof_fact_prefix = "fof_"
352 fun is_same_term subst tm1 tm2 =
354 fun do_term_pair _ NONE = NONE
355 | do_term_pair (ATerm (s1, tm1), ATerm (s2, tm2)) (SOME subst) =
356 case pairself is_tptp_variable (s1, s2) of
358 (case AList.lookup (op =) subst s1 of
359 SOME s2' => if s2' = s2 then SOME subst else NONE
361 if null (AList.find (op =) subst s2) then SOME ((s1, s2) :: subst)
364 if s1 = s2 andalso length tm1 = length tm2 then
365 SOME subst |> fold do_term_pair (tm1 ~~ tm2)
369 in SOME subst |> do_term_pair (tm1, tm2) |> is_some end
371 fun is_same_formula subst (AQuant (q1, xs1, phi1)) (AQuant (q2, xs2, phi2)) =
372 q1 = q2 andalso length xs1 = length xs2 andalso
373 is_same_formula ((map fst xs1 ~~ map fst xs2) @ subst) phi1 phi2
374 | is_same_formula subst (AConn (c1, phis1)) (AConn (c2, phis2)) =
375 c1 = c2 andalso length phis1 = length phis2 andalso
376 forall (uncurry (is_same_formula subst)) (phis1 ~~ phis2)
377 | is_same_formula subst (AAtom (ATerm ("equal", [tm11, tm12]))) (AAtom tm2) =
378 is_same_term subst (ATerm ("equal", [tm11, tm12])) tm2 orelse
379 is_same_term subst (ATerm ("equal", [tm12, tm11])) tm2
380 | is_same_formula subst (AAtom tm1) (AAtom tm2) = is_same_term subst tm1 tm2
381 | is_same_formula _ _ _ = false
383 fun matching_formula_line_identifier phi (Formula (ident, _, phi', _, _)) =
384 if is_same_formula [] phi phi' then SOME ident else NONE
385 | matching_formula_line_identifier _ _ = NONE
387 fun find_formula_in_problem problem phi =
388 problem |> maps snd |> map_filter (matching_formula_line_identifier phi)
391 (* Syntax: (cnf|fof|tff|thf)\(<num>, <formula_role>,
392 <formula> <extra_arguments>\).
393 The <num> could be an identifier, but we assume integers. *)
394 fun parse_tstp_line problem =
395 ((Scan.this_string tptp_cnf || Scan.this_string tptp_fof
396 || Scan.this_string tptp_tff || Scan.this_string tptp_thf) -- $$ "(")
397 |-- scan_general_id --| $$ "," -- Symbol.scan_id --| $$ ","
398 -- (parse_formula || skip_formula) -- parse_tstp_extra_arguments --| $$ ")"
400 >> (fn (((num, role), phi), deps) =>
403 (* Waldmeister isn't exactly helping. *)
407 if s = waldmeister_conjecture then
408 find_formula_in_problem problem (mk_anot phi)
410 SOME [s |> perhaps (try (unprefix tofof_fact_prefix))]),
412 | ["file", _] => ((num, find_formula_in_problem problem phi), [])
413 | _ => ((num, NONE), deps)
418 AConn (AIff, [phi1 as AAtom _, phi2]) =>
419 Definition (name, phi1, phi2)
420 | AAtom (ATerm ("equal", _)) =>
421 (* Vampire's equality proxy axiom *)
422 Inference (name, phi, map (rpair NONE) deps)
423 | _ => raise UNRECOGNIZED_ATP_PROOF ())
424 | _ => Inference (name, phi, map (rpair NONE) deps)
427 (**** PARSING OF SPASS OUTPUT ****)
429 (* SPASS returns clause references of the form "x.y". We ignore "y", whose role
430 is not clear anyway. *)
431 val parse_dot_name = scan_general_id --| $$ "." --| scan_general_id
433 val parse_spass_annotations =
434 Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name
435 --| Scan.option ($$ ","))) []
437 (* It is not clear why some literals are followed by sequences of stars and/or
438 pluses. We ignore them. *)
439 fun parse_decorated_atom x =
440 (parse_atom --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")) x
442 fun mk_horn ([], []) = AAtom (ATerm ("c_False", []))
443 | mk_horn ([], pos_lits) = foldr1 (uncurry (mk_aconn AOr)) pos_lits
444 | mk_horn (neg_lits, []) = mk_anot (foldr1 (uncurry (mk_aconn AAnd)) neg_lits)
445 | mk_horn (neg_lits, pos_lits) =
446 mk_aconn AImplies (foldr1 (uncurry (mk_aconn AAnd)) neg_lits)
447 (foldr1 (uncurry (mk_aconn AOr)) pos_lits)
449 fun parse_horn_clause x =
450 (Scan.repeat parse_decorated_atom --| $$ "|" --| $$ "|"
451 -- Scan.repeat parse_decorated_atom --| $$ "-" --| $$ ">"
452 -- Scan.repeat parse_decorated_atom
453 >> (mk_horn o apfst (op @))) x
455 fun resolve_spass_num spass_names num =
456 case Int.fromString num of
457 SOME j => if j > 0 andalso j <= Vector.length spass_names then
458 SOME (Vector.sub (spass_names, j - 1))
463 (* Syntax: <num>[0:<inference><annotations>]
464 <atoms> || <atoms> -> <atoms>. *)
465 fun parse_spass_line spass_names x =
466 (scan_general_id --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id
467 -- parse_spass_annotations --| $$ "]" -- parse_horn_clause --| $$ "."
468 >> (fn ((num, deps), u) =>
469 Inference ((num, resolve_spass_num spass_names num), u,
470 map (swap o `(resolve_spass_num spass_names)) deps))) x
472 fun parse_line problem spass_names =
473 parse_tstp_line problem || parse_spass_line spass_names
474 fun parse_proof problem spass_names tstp =
475 tstp |> strip_spaces_except_between_idents
477 |> Scan.finite Symbol.stopper
478 (Scan.error (!! (fn _ => raise UNRECOGNIZED_ATP_PROOF ())
479 (Scan.repeat1 (parse_line problem spass_names))))
482 (** SPASS's FLOTTER hack **)
484 (* This is a hack required for keeping track of facts after they have been
485 clausified by SPASS's FLOTTER preprocessor. The "ATP/scripts/spass" script is
486 also part of this hack. *)
488 val set_ClauseFormulaRelationN = "set_ClauseFormulaRelation"
490 fun extract_clause_sequence output =
492 val tokens_of = String.tokens (not o Char.isAlphaNum)
493 fun extract_num ("clause" :: (ss as _ :: _)) = Int.fromString (List.last ss)
494 | extract_num _ = NONE
495 in output |> split_lines |> map_filter (extract_num o tokens_of) end
497 fun is_head_digit s = Char.isDigit (String.sub (s, 0))
498 val scan_integer = Scan.many1 is_head_digit >> (the o Int.fromString o implode)
500 val parse_clause_formula_pair =
501 $$ "(" |-- scan_integer --| $$ ","
502 -- (Symbol.scan_id ::: Scan.repeat ($$ "," |-- Symbol.scan_id)) --| $$ ")"
503 --| Scan.option ($$ ",")
504 val parse_clause_formula_relation =
505 Scan.this_string set_ClauseFormulaRelationN |-- $$ "("
506 |-- Scan.repeat parse_clause_formula_pair
507 val extract_clause_formula_relation =
508 Substring.full #> Substring.position set_ClauseFormulaRelationN
509 #> snd #> Substring.position "." #> fst #> Substring.string
510 #> raw_explode #> filter_out Symbol.is_blank #> parse_clause_formula_relation
513 fun extract_spass_name_vector output =
514 (if String.isSubstring set_ClauseFormulaRelationN output then
516 val num_seq = extract_clause_sequence output
517 val name_map = extract_clause_formula_relation output
518 val name_seq = num_seq |> map (these o AList.lookup (op =) name_map)
524 fun atp_proof_from_tstplike_proof _ _ "" = []
525 | atp_proof_from_tstplike_proof problem output tstp =
526 tstp ^ "$" (* the $ sign acts as a sentinel (FIXME: needed?) *)
527 |> parse_proof problem (extract_spass_name_vector output)
528 |> sort (step_name_ord o pairself step_name)
530 fun clean_up_dependencies _ [] = []
531 | clean_up_dependencies seen ((step as Definition (name, _, _)) :: steps) =
532 step :: clean_up_dependencies (name :: seen) steps
533 | clean_up_dependencies seen (Inference (name, u, deps) :: steps) =
535 map_filter (fn dep => find_first (is_same_atp_step dep) seen)
537 clean_up_dependencies (name :: seen) steps
539 fun clean_up_atp_proof_dependencies proof = clean_up_dependencies [] proof
541 fun map_term_names_in_term f (ATerm (s, ts)) =
542 ATerm (f s, map (map_term_names_in_term f) ts)
543 fun map_term_names_in_formula f (AQuant (q, xs, phi)) =
544 AQuant (q, xs, map_term_names_in_formula f phi)
545 | map_term_names_in_formula f (AConn (c, phis)) =
546 AConn (c, map (map_term_names_in_formula f) phis)
547 | map_term_names_in_formula f (AAtom t) = AAtom (map_term_names_in_term f t)
548 fun map_term_names_in_step f (Definition (name, phi1, phi2)) =
549 Definition (name, map_term_names_in_formula f phi1,
550 map_term_names_in_formula f phi2)
551 | map_term_names_in_step f (Inference (name, phi, deps)) =
552 Inference (name, map_term_names_in_formula f phi, deps)
553 fun map_term_names_in_atp_proof f = map (map_term_names_in_step f)
555 fun nasty_name pool s = s |> Symtab.lookup pool |> the_default s
556 fun nasty_atp_proof pool =
557 if Symtab.is_empty pool then I
558 else map_term_names_in_atp_proof (nasty_name pool)