(* Title: HOL/Tools/ATP/atp_proof.ML
Author: Lawrence C. Paulson, Cambridge University Computer Laboratory
Author: Claire Quigley, Cambridge University Computer Laboratory
Author: Jasmin Blanchette, TU Muenchen
Abstract representation of ATP proofs and TSTP/SPASS syntax.
*)
signature ATP_PROOF =
sig
type ('a, 'b) ho_term = ('a, 'b) ATP_Problem.ho_term
type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
type 'a problem = 'a ATP_Problem.problem
exception UNRECOGNIZED_ATP_PROOF of unit
datatype failure =
Unprovable |
GaveUp |
ProofMissing |
ProofIncomplete |
UnsoundProof of bool option * string list | (* FIXME: doesn't belong here *)
CantConnect |
TimedOut |
Inappropriate |
OutOfResources |
SpassTooOld |
VampireTooOld |
NoPerl |
NoLibwwwPerl |
MalformedInput |
MalformedOutput |
Interrupted |
Crashed |
InternalError |
UnknownError of string
type step_name = string * string list option
datatype 'a step =
Definition of step_name * 'a * 'a |
Inference of step_name * 'a * step_name list
type 'a proof = ('a, 'a, ('a, 'a) ho_term) formula step list
val short_output : bool -> string -> string
val string_for_failure : failure -> string
val extract_important_message : string -> string
val extract_known_failure :
(failure * string) list -> string -> failure option
val extract_tstplike_proof_and_outcome :
bool -> bool -> (string * string) list -> (failure * string) list -> string
-> string * failure option
val is_same_atp_step : step_name -> step_name -> bool
val scan_general_id : string list -> string * string list
val parse_formula :
string list -> (string, 'a, (string, 'a) ho_term) formula * string list
val atp_proof_from_tstplike_proof :
string problem -> string -> string -> string proof
val clean_up_atp_proof_dependencies : string proof -> string proof
val map_term_names_in_atp_proof :
(string -> string) -> string proof -> string proof
val nasty_atp_proof : string Symtab.table -> string proof -> string proof
end;
structure ATP_Proof : ATP_PROOF =
struct
open ATP_Util
open ATP_Problem
exception UNRECOGNIZED_ATP_PROOF of unit
datatype failure =
Unprovable |
GaveUp |
ProofMissing |
ProofIncomplete |
UnsoundProof of bool option * string list |
CantConnect |
TimedOut |
Inappropriate |
OutOfResources |
SpassTooOld |
VampireTooOld |
NoPerl |
NoLibwwwPerl |
MalformedInput |
MalformedOutput |
Interrupted |
Crashed |
InternalError |
UnknownError of string
fun elide_string threshold s =
if size s > threshold then
String.extract (s, 0, SOME (threshold div 2 - 5)) ^ " ...... " ^
String.extract (s, size s - (threshold + 1) div 2 + 6, NONE)
else
s
fun short_output verbose output =
if verbose then
if output = "" then "No details available" else elide_string 1000 output
else
""
val missing_message_tail =
" appears to be missing. You will need to install it if you want to invoke \
\remote provers."
fun involving [] = ""
| involving ss =
"involving " ^ space_implode " " (Try.serial_commas "and" (map quote ss)) ^
" "
fun string_for_failure Unprovable = "The problem is unprovable."
| string_for_failure GaveUp = "The prover gave up."
| string_for_failure ProofMissing =
"The prover claims the conjecture is a theorem but did not provide a proof."
| string_for_failure ProofIncomplete =
"The prover claims the conjecture is a theorem but provided an incomplete \
\proof."
| string_for_failure (UnsoundProof (NONE, ss)) =
"The prover found a type-unsound proof " ^ involving ss ^
"(or, less likely, your axioms are inconsistent). Specify a sound type \
\encoding or omit the \"type_enc\" option."
| string_for_failure (UnsoundProof (SOME false, ss)) =
"The prover found a type-unsound proof " ^ involving ss ^
"(or, less likely, your axioms are inconsistent). Try passing the \
\\"sound\" option to Sledgehammer to avoid such spurious proofs."
| string_for_failure (UnsoundProof (SOME true, ss)) =
"The prover found a type-unsound proof " ^ involving ss ^
"even though a supposedly type-sound encoding was used (or, less likely, \
\your axioms are inconsistent). Please report this to the Isabelle \
\developers."
| string_for_failure CantConnect = "Cannot connect to remote server."
| string_for_failure TimedOut = "Timed out."
| string_for_failure Inappropriate =
"The problem lies outside the prover's scope."
| string_for_failure OutOfResources = "The prover ran out of resources."
| string_for_failure SpassTooOld =
"Isabelle requires a more recent version of SPASS with support for the \
\TPTP syntax. To install it, download and extract the package \
\\"http://isabelle.in.tum.de/dist/contrib/spass-3.7.tar.gz\" and add the \
\\"spass-3.7\" directory's absolute path to " ^
Path.print (Path.expand (Path.explode "$ISABELLE_HOME_USER/etc/components")) ^
" on a line of its own."
| string_for_failure VampireTooOld =
"Isabelle requires a more recent version of Vampire. To install it, follow \
\the instructions from the Sledgehammer manual (\"isabelle doc\
\ sledgehammer\")."
| string_for_failure NoPerl = "Perl" ^ missing_message_tail
| string_for_failure NoLibwwwPerl =
"The Perl module \"libwww-perl\"" ^ missing_message_tail
| string_for_failure MalformedInput =
"The generated problem is malformed. Please report this to the Isabelle \
\developers."
| string_for_failure MalformedOutput = "The prover output is malformed."
| string_for_failure Interrupted = "The prover was interrupted."
| string_for_failure Crashed = "The prover crashed."
| string_for_failure InternalError = "An internal prover error occurred."
| string_for_failure (UnknownError string) =
"A prover error occurred" ^
(if string = "" then ". (Pass the \"verbose\" option for details.)"
else ":\n" ^ string)
fun extract_delimited (begin_delim, end_delim) output =
output |> first_field begin_delim |> the |> snd
|> first_field end_delim |> the |> fst
|> first_field "\n" |> the |> snd
handle Option.Option => ""
val tstp_important_message_delims =
("% SZS start RequiredInformation", "% SZS end RequiredInformation")
fun extract_important_message output =
case extract_delimited tstp_important_message_delims output of
"" => ""
| s => s |> space_explode "\n" |> filter_out (curry (op =) "")
|> map (perhaps (try (unprefix "%")))
|> map (perhaps (try (unprefix " ")))
|> space_implode "\n " |> quote
(* Splits by the first possible of a list of delimiters. *)
fun extract_tstplike_proof delims output =
case pairself (find_first (fn s => String.isSubstring s output))
(ListPair.unzip delims) of
(SOME begin_delim, SOME end_delim) =>
extract_delimited (begin_delim, end_delim) output
| _ => ""
fun extract_known_failure known_failures output =
known_failures
|> find_first (fn (_, pattern) => String.isSubstring pattern output)
|> Option.map fst
fun extract_tstplike_proof_and_outcome verbose complete proof_delims
known_failures output =
case (extract_tstplike_proof proof_delims output,
extract_known_failure known_failures output) of
(_, SOME ProofIncomplete) => ("", SOME ProofIncomplete)
| ("", SOME ProofMissing) => ("", NONE)
| ("", SOME failure) =>
("", SOME (if failure = GaveUp andalso complete then Unprovable
else failure))
| ("", NONE) => ("", SOME (UnknownError (short_output verbose output)))
| (tstplike_proof, _) => (tstplike_proof, NONE)
type step_name = string * string list option
fun is_same_atp_step (s1, _) (s2, _) = s1 = s2
val vampire_fact_prefix = "f"
fun step_name_ord p =
let val q = pairself fst p in
(* The "unprefix" part is to cope with remote Vampire's output. The proper
solution would be to perform a topological sort, e.g. using the nice
"Graph" functor. *)
case pairself (Int.fromString
o perhaps (try (unprefix vampire_fact_prefix))) q of
(NONE, NONE) => string_ord q
| (NONE, SOME _) => LESS
| (SOME _, NONE) => GREATER
| (SOME i, SOME j) => int_ord (i, j)
end
datatype 'a step =
Definition of step_name * 'a * 'a |
Inference of step_name * 'a * step_name list
type 'a proof = ('a, 'a, ('a, 'a) ho_term) formula step list
fun step_name (Definition (name, _, _)) = name
| step_name (Inference (name, _, _)) = name
(**** PARSING OF TSTP FORMAT ****)
(* FIXME: temporary hack *)
fun repair_waldmeister_step_name s =
case space_explode "." s of
[a, b, c, d] =>
(case a of "0" => "X" | "1" => "Y" | _ => "Z" ^ a) ^
(if size b = 1 then "0" else "") ^ b ^ c ^ d
| _ => s
(* Strings enclosed in single quotes (e.g., file names) *)
val scan_general_id =
$$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'"
>> implode >> repair_waldmeister_step_name
|| Scan.repeat ($$ "$") -- Scan.many1 Symbol.is_letdig
>> (fn (ss1, ss2) => implode ss1 ^ implode ss2)
(* Generalized first-order terms, which include file names, numbers, etc. *)
fun parse_annotation x =
((scan_general_id ::: Scan.repeat ($$ " " |-- scan_general_id))
-- Scan.optional parse_annotation [] >> op @
|| $$ "(" |-- parse_annotations --| $$ ")"
|| $$ "[" |-- parse_annotations --| $$ "]") x
and parse_annotations x =
(Scan.optional (parse_annotation
::: Scan.repeat ($$ "," |-- parse_annotation)) []
>> flat) x
fun list_app (f, args) =
fold (fn arg => fn f => ATerm (tptp_app, [f, arg])) args f
(* We ignore TFF and THF types for now. *)
fun parse_type_stuff x =
Scan.repeat (($$ tptp_has_type || $$ tptp_fun_type) |-- parse_arg) x
and parse_arg x =
($$ "(" |-- parse_term --| $$ ")" --| parse_type_stuff
|| scan_general_id --| parse_type_stuff
-- Scan.optional ($$ "(" |-- parse_terms --| $$ ")") []
>> ATerm) x
and parse_app x =
(parse_arg -- Scan.repeat ($$ tptp_app |-- parse_arg) >> list_app) x
and parse_term x =
(parse_app -- Scan.option (Scan.option ($$ tptp_not_infix) --| $$ tptp_equal
-- parse_app)
>> (fn (u1, NONE) => u1
| (u1, SOME (NONE, u2)) => ATerm ("equal", [u1, u2])
| (u1, SOME (SOME _, u2)) =>
ATerm (tptp_not, [ATerm ("equal", [u1, u2])]))) x
and parse_terms x =
(parse_term ::: Scan.repeat ($$ "," |-- parse_term)) x
(* TODO: Avoid duplication with "parse_term" above. *)
fun parse_atom x =
(parse_term -- Scan.option (Scan.option ($$ tptp_not_infix) --| $$ tptp_equal
-- parse_term)
>> (fn (u1, NONE) => AAtom u1
| (u1, SOME (NONE, u2)) => AAtom (ATerm ("equal", [u1, u2]))
| (u1, SOME (SOME _, u2)) =>
mk_anot (AAtom (ATerm ("equal", [u1, u2]))))) x
fun ho_term_head (ATerm (s, _)) = s
(* TPTP formulas are fully parenthesized, so we don't need to worry about
operator precedence. *)
fun parse_literal x =
((Scan.repeat ($$ tptp_not) >> length)
-- ($$ "(" |-- parse_formula --| $$ ")"
|| parse_quantified_formula
|| parse_atom)
>> (fn (n, phi) => phi |> n mod 2 = 1 ? mk_anot)) x
and parse_formula x =
(parse_literal
-- Scan.option ((Scan.this_string tptp_implies
|| Scan.this_string tptp_iff
|| Scan.this_string tptp_not_iff
|| Scan.this_string tptp_if
|| $$ tptp_or
|| $$ tptp_and) -- parse_formula)
>> (fn (phi1, NONE) => phi1
| (phi1, SOME (c, phi2)) =>
if c = tptp_implies then mk_aconn AImplies phi1 phi2
else if c = tptp_iff then mk_aconn AIff phi1 phi2
else if c = tptp_not_iff then mk_anot (mk_aconn AIff phi1 phi2)
else if c = tptp_if then mk_aconn AImplies phi2 phi1
else if c = tptp_or then mk_aconn AOr phi1 phi2
else if c = tptp_and then mk_aconn AAnd phi1 phi2
else raise Fail ("impossible connective " ^ quote c))) x
and parse_quantified_formula x =
(($$ tptp_forall >> K AForall || $$ tptp_exists >> K AExists)
--| $$ "[" -- parse_terms --| $$ "]" --| $$ ":" -- parse_literal
>> (fn ((q, ts), phi) =>
(* We ignore TFF and THF types for now. *)
AQuant (q, map (rpair NONE o ho_term_head) ts, phi))) x
fun skip_formula ss =
let
fun skip _ [] = []
| skip 0 (ss as "," :: _) = ss
| skip 0 (ss as ")" :: _) = ss
| skip 0 (ss as "]" :: _) = ss
| skip n ("(" :: ss) = skip (n + 1) ss
| skip n ("[" :: ss) = skip (n + 1) ss
| skip n ("]" :: ss) = skip (n - 1) ss
| skip n (")" :: ss) = skip (n - 1) ss
| skip n (_ :: ss) = skip n ss
in (AAtom (ATerm ("", [])), skip 0 ss) end
val parse_tstp_extra_arguments =
Scan.optional ($$ "," |-- parse_annotation
--| Scan.option ($$ "," |-- parse_annotations)) []
val waldmeister_conjecture = "conjecture_1"
val tofof_fact_prefix = "fof_"
fun is_same_term subst tm1 tm2 =
let
fun do_term_pair _ NONE = NONE
| do_term_pair (ATerm (s1, tm1), ATerm (s2, tm2)) (SOME subst) =
case pairself is_tptp_variable (s1, s2) of
(true, true) =>
(case AList.lookup (op =) subst s1 of
SOME s2' => if s2' = s2 then SOME subst else NONE
| NONE =>
if null (AList.find (op =) subst s2) then SOME ((s1, s2) :: subst)
else NONE)
| (false, false) =>
if s1 = s2 andalso length tm1 = length tm2 then
SOME subst |> fold do_term_pair (tm1 ~~ tm2)
else
NONE
| _ => NONE
in SOME subst |> do_term_pair (tm1, tm2) |> is_some end
fun is_same_formula subst (AQuant (q1, xs1, phi1)) (AQuant (q2, xs2, phi2)) =
q1 = q2 andalso length xs1 = length xs2 andalso
is_same_formula ((map fst xs1 ~~ map fst xs2) @ subst) phi1 phi2
| is_same_formula subst (AConn (c1, phis1)) (AConn (c2, phis2)) =
c1 = c2 andalso length phis1 = length phis2 andalso
forall (uncurry (is_same_formula subst)) (phis1 ~~ phis2)
| is_same_formula subst (AAtom (ATerm ("equal", [tm11, tm12]))) (AAtom tm2) =
is_same_term subst (ATerm ("equal", [tm11, tm12])) tm2 orelse
is_same_term subst (ATerm ("equal", [tm12, tm11])) tm2
| is_same_formula subst (AAtom tm1) (AAtom tm2) = is_same_term subst tm1 tm2
| is_same_formula _ _ _ = false
fun matching_formula_line_identifier phi (Formula (ident, _, phi', _, _)) =
if is_same_formula [] phi phi' then SOME ident else NONE
| matching_formula_line_identifier _ _ = NONE
fun find_formula_in_problem problem phi =
problem |> maps snd |> map_filter (matching_formula_line_identifier phi)
|> try (single o hd)
(* Syntax: (cnf|fof|tff|thf)\(<num>, <formula_role>,
<formula> <extra_arguments>\).
The <num> could be an identifier, but we assume integers. *)
fun parse_tstp_line problem =
((Scan.this_string tptp_cnf || Scan.this_string tptp_fof
|| Scan.this_string tptp_tff || Scan.this_string tptp_thf) -- $$ "(")
|-- scan_general_id --| $$ "," -- Symbol.scan_id --| $$ ","
-- (parse_formula || skip_formula) -- parse_tstp_extra_arguments --| $$ ")"
--| $$ "."
>> (fn (((num, role), phi), deps) =>
let
val (name, deps) =
(* Waldmeister isn't exactly helping. *)
case deps of
["file", _, s] =>
((num,
if s = waldmeister_conjecture then
find_formula_in_problem problem (mk_anot phi)
else
SOME [s |> perhaps (try (unprefix tofof_fact_prefix))]),
[])
| ["file", _] => ((num, find_formula_in_problem problem phi), [])
| _ => ((num, NONE), deps)
in
case role of
"definition" =>
(case phi of
AConn (AIff, [phi1 as AAtom _, phi2]) =>
Definition (name, phi1, phi2)
| AAtom (ATerm ("equal", _)) =>
(* Vampire's equality proxy axiom *)
Inference (name, phi, map (rpair NONE) deps)
| _ => raise UNRECOGNIZED_ATP_PROOF ())
| _ => Inference (name, phi, map (rpair NONE) deps)
end)
(**** PARSING OF SPASS OUTPUT ****)
(* SPASS returns clause references of the form "x.y". We ignore "y", whose role
is not clear anyway. *)
val parse_dot_name = scan_general_id --| $$ "." --| scan_general_id
val parse_spass_annotations =
Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name
--| Scan.option ($$ ","))) []
(* It is not clear why some literals are followed by sequences of stars and/or
pluses. We ignore them. *)
fun parse_decorated_atom x =
(parse_atom --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")) x
fun mk_horn ([], []) = AAtom (ATerm ("c_False", []))
| mk_horn ([], pos_lits) = foldr1 (uncurry (mk_aconn AOr)) pos_lits
| mk_horn (neg_lits, []) = mk_anot (foldr1 (uncurry (mk_aconn AAnd)) neg_lits)
| mk_horn (neg_lits, pos_lits) =
mk_aconn AImplies (foldr1 (uncurry (mk_aconn AAnd)) neg_lits)
(foldr1 (uncurry (mk_aconn AOr)) pos_lits)
fun parse_horn_clause x =
(Scan.repeat parse_decorated_atom --| $$ "|" --| $$ "|"
-- Scan.repeat parse_decorated_atom --| $$ "-" --| $$ ">"
-- Scan.repeat parse_decorated_atom
>> (mk_horn o apfst (op @))) x
fun resolve_spass_num spass_names num =
case Int.fromString num of
SOME j => if j > 0 andalso j <= Vector.length spass_names then
SOME (Vector.sub (spass_names, j - 1))
else
NONE
| NONE => NONE
(* Syntax: <num>[0:<inference><annotations>]
<atoms> || <atoms> -> <atoms>. *)
fun parse_spass_line spass_names x =
(scan_general_id --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id
-- parse_spass_annotations --| $$ "]" -- parse_horn_clause --| $$ "."
>> (fn ((num, deps), u) =>
Inference ((num, resolve_spass_num spass_names num), u,
map (swap o `(resolve_spass_num spass_names)) deps))) x
fun parse_line problem spass_names =
parse_tstp_line problem || parse_spass_line spass_names
fun parse_proof problem spass_names tstp =
tstp |> strip_spaces_except_between_idents
|> raw_explode
|> Scan.finite Symbol.stopper
(Scan.error (!! (fn _ => raise UNRECOGNIZED_ATP_PROOF ())
(Scan.repeat1 (parse_line problem spass_names))))
|> fst
(** SPASS's FLOTTER hack **)
(* This is a hack required for keeping track of facts after they have been
clausified by SPASS's FLOTTER preprocessor. The "ATP/scripts/spass" script is
also part of this hack. *)
val set_ClauseFormulaRelationN = "set_ClauseFormulaRelation"
fun extract_clause_sequence output =
let
val tokens_of = String.tokens (not o Char.isAlphaNum)
fun extract_num ("clause" :: (ss as _ :: _)) = Int.fromString (List.last ss)
| extract_num _ = NONE
in output |> split_lines |> map_filter (extract_num o tokens_of) end
fun is_head_digit s = Char.isDigit (String.sub (s, 0))
val scan_integer = Scan.many1 is_head_digit >> (the o Int.fromString o implode)
val parse_clause_formula_pair =
$$ "(" |-- scan_integer --| $$ ","
-- (Symbol.scan_id ::: Scan.repeat ($$ "," |-- Symbol.scan_id)) --| $$ ")"
--| Scan.option ($$ ",")
val parse_clause_formula_relation =
Scan.this_string set_ClauseFormulaRelationN |-- $$ "("
|-- Scan.repeat parse_clause_formula_pair
val extract_clause_formula_relation =
Substring.full #> Substring.position set_ClauseFormulaRelationN
#> snd #> Substring.position "." #> fst #> Substring.string
#> raw_explode #> filter_out Symbol.is_blank #> parse_clause_formula_relation
#> fst
fun extract_spass_name_vector output =
(if String.isSubstring set_ClauseFormulaRelationN output then
let
val num_seq = extract_clause_sequence output
val name_map = extract_clause_formula_relation output
val name_seq = num_seq |> map (these o AList.lookup (op =) name_map)
in name_seq end
else
[])
|> Vector.fromList
fun atp_proof_from_tstplike_proof _ _ "" = []
| atp_proof_from_tstplike_proof problem output tstp =
tstp ^ "$" (* the $ sign acts as a sentinel (FIXME: needed?) *)
|> parse_proof problem (extract_spass_name_vector output)
|> sort (step_name_ord o pairself step_name)
fun clean_up_dependencies _ [] = []
| clean_up_dependencies seen ((step as Definition (name, _, _)) :: steps) =
step :: clean_up_dependencies (name :: seen) steps
| clean_up_dependencies seen (Inference (name, u, deps) :: steps) =
Inference (name, u,
map_filter (fn dep => find_first (is_same_atp_step dep) seen)
deps) ::
clean_up_dependencies (name :: seen) steps
fun clean_up_atp_proof_dependencies proof = clean_up_dependencies [] proof
fun map_term_names_in_term f (ATerm (s, ts)) =
ATerm (f s, map (map_term_names_in_term f) ts)
fun map_term_names_in_formula f (AQuant (q, xs, phi)) =
AQuant (q, xs, map_term_names_in_formula f phi)
| map_term_names_in_formula f (AConn (c, phis)) =
AConn (c, map (map_term_names_in_formula f) phis)
| map_term_names_in_formula f (AAtom t) = AAtom (map_term_names_in_term f t)
fun map_term_names_in_step f (Definition (name, phi1, phi2)) =
Definition (name, map_term_names_in_formula f phi1,
map_term_names_in_formula f phi2)
| map_term_names_in_step f (Inference (name, phi, deps)) =
Inference (name, map_term_names_in_formula f phi, deps)
fun map_term_names_in_atp_proof f = map (map_term_names_in_step f)
fun nasty_name pool s = s |> Symtab.lookup pool |> the_default s
fun nasty_atp_proof pool =
if Symtab.is_empty pool then I
else map_term_names_in_atp_proof (nasty_name pool)
end;