(* 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
Author: Mathias Fleury, ENS Rennes
Abstract representation of ATP proofs and TSTP/SPASS syntax.
*)
signature ATP_PROOF =
sig
type 'a atp_type = 'a ATP_Problem.atp_type
type ('a, 'b) atp_term = ('a, 'b) ATP_Problem.atp_term
type atp_formula_role = ATP_Problem.atp_formula_role
type ('a, 'b, 'c, 'd) atp_formula = ('a, 'b, 'c, 'd) ATP_Problem.atp_formula
type 'a atp_problem = 'a ATP_Problem.atp_problem
exception UNRECOGNIZED_ATP_PROOF of unit
datatype atp_failure =
MaybeUnprovable |
Unprovable |
GaveUp |
ProofMissing |
ProofIncomplete |
ProofUnparsable |
UnsoundProof of bool * string list |
CantConnect |
TimedOut |
Inappropriate |
OutOfResources |
NoPerl |
NoLibwwwPerl |
MalformedInput |
MalformedOutput |
Interrupted |
Crashed |
InternalError |
UnknownError of string
type atp_step_name = string * string list
type ('a, 'b) atp_step =
atp_step_name * atp_formula_role * 'a * 'b * atp_step_name list
type 'a atp_proof = (('a, 'a, ('a, 'a atp_type) atp_term, 'a) atp_formula, string) atp_step list
val agsyholN : string
val alt_ergoN : string
val eN : string
val iproverN : string
val leo2N : string
val leo3N : string
val pirateN : string
val satallaxN : string
val spassN : string
val vampireN : string
val waldmeisterN : string
val z3_tptpN : string
val zipperpositionN : string
val remote_prefix : string
val agsyhol_core_rule : string
val spass_input_rule : string
val spass_pre_skolemize_rule : string
val spass_skolemize_rule : string
val z3_tptp_core_rule : string
val short_output : bool -> string -> string
val string_of_atp_failure : atp_failure -> string
val extract_important_message : string -> string
val extract_known_atp_failure : (atp_failure * string) list -> string -> atp_failure option
val extract_tstplike_proof_and_outcome :
bool -> (string * string) list -> (atp_failure * string) list -> string
-> string * atp_failure option
val is_same_atp_step : atp_step_name -> atp_step_name -> bool
val scan_general_id : string list -> string * string list
val parse_fol_formula : string list ->
(string, string atp_type, (string, string atp_type) atp_term, string) atp_formula * string list
val clean_up_atp_proof_dependencies : string atp_proof -> string atp_proof
val map_term_names_in_atp_proof : (string -> string) -> string atp_proof -> string atp_proof
val nasty_atp_proof : string Symtab.table -> string atp_proof -> string atp_proof
val skip_term : string list -> string * string list
val parse_hol_formula : string list ->
('a, 'b, (string, string ATP_Problem.atp_type) ATP_Problem.atp_term, 'c) ATP_Problem.atp_formula *
string list
val dummy_atype : string ATP_Problem.atp_type
val role_of_tptp_string : string -> ATP_Problem.atp_formula_role
val parse_line : string -> ('a * string ATP_Problem.atp_problem_line list) list ->
string list -> ((string * string list) * ATP_Problem.atp_formula_role *
(string, 'b, (string, string ATP_Problem.atp_type) ATP_Problem.atp_term,
'c) ATP_Problem.atp_formula
* string * (string * 'd list) list) list * string list
val core_inference : 'a -> 'b -> ('b * 'b list) * ATP_Problem.atp_formula_role *
('c, 'd, (string, 'e) ATP_Problem.atp_term, 'f) ATP_Problem.atp_formula * 'a * 'g list
val vampire_step_name_ord : (string * 'a) ord
val core_of_agsyhol_proof : string -> string list option
val string_of_atp_step : ('a -> string) -> ('b -> string) -> ('a, 'b) atp_step -> string
val atp_proof_of_tstplike_proof : string -> string atp_problem -> string -> string atp_proof
end;
structure ATP_Proof : ATP_PROOF =
struct
open ATP_Util
open ATP_Problem
val agsyholN = "agsyhol"
val alt_ergoN = "alt_ergo"
val eN = "e"
val iproverN = "iprover"
val leo2N = "leo2"
val leo3N = "leo3"
val pirateN = "pirate"
val satallaxN = "satallax"
val spassN = "spass"
val vampireN = "vampire"
val waldmeisterN = "waldmeister"
val z3_tptpN = "z3_tptp"
val zipperpositionN = "zipperposition"
val remote_prefix = "remote_"
val agsyhol_core_rule = "__agsyhol_core" (* arbitrary *)
val spass_input_rule = "Inp"
val spass_pre_skolemize_rule = "__Sko0" (* arbitrary *)
val spass_skolemize_rule = "__Sko" (* arbitrary *)
val z3_tptp_core_rule = "__z3_tptp_core" (* arbitrary *)
exception UNRECOGNIZED_ATP_PROOF of unit
datatype atp_failure =
MaybeUnprovable |
Unprovable |
GaveUp |
ProofMissing |
ProofIncomplete |
ProofUnparsable |
UnsoundProof of bool * string list |
CantConnect |
TimedOut |
Inappropriate |
OutOfResources |
NoPerl |
NoLibwwwPerl |
MalformedInput |
MalformedOutput |
Interrupted |
Crashed |
InternalError |
UnknownError of string
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 from_lemmas [] = ""
| from_lemmas ss = " from " ^ space_implode " " (Try.serial_commas "and" (map quote ss))
fun string_of_atp_failure MaybeUnprovable = "The generated problem is maybe unprovable"
| string_of_atp_failure Unprovable = "The generated problem is unprovable"
| string_of_atp_failure GaveUp = "The prover gave up"
| string_of_atp_failure ProofMissing =
"The prover claims the conjecture is a theorem but did not provide a proof"
| string_of_atp_failure ProofIncomplete =
"The prover claims the conjecture is a theorem but provided an incomplete proof"
| string_of_atp_failure ProofUnparsable =
"The prover claims the conjecture is a theorem but provided an unparsable proof"
| string_of_atp_failure (UnsoundProof (false, ss)) =
"The prover derived \"False\"" ^ from_lemmas ss ^
"; specify a sound type encoding or omit the \"type_enc\" option"
| string_of_atp_failure (UnsoundProof (true, ss)) =
"The prover derived \"False\"" ^ from_lemmas ss ^
", which could be due to a bug in Sledgehammer or to inconsistent axioms (including \"sorry\"s)"
| string_of_atp_failure CantConnect = "Cannot connect to server"
| string_of_atp_failure TimedOut = "Timed out"
| string_of_atp_failure Inappropriate =
"The generated problem lies outside the prover's scope"
| string_of_atp_failure OutOfResources = "The prover ran out of resources"
| string_of_atp_failure NoPerl = "Perl" ^ missing_message_tail
| string_of_atp_failure NoLibwwwPerl =
"The Perl module \"libwww-perl\"" ^ missing_message_tail
| string_of_atp_failure MalformedInput = "The generated problem is malformed"
| string_of_atp_failure MalformedOutput = "The prover output is malformed"
| string_of_atp_failure Interrupted = "The prover was interrupted"
| string_of_atp_failure Crashed = "The prover crashed"
| string_of_atp_failure InternalError = "An internal prover error occurred"
| string_of_atp_failure (UnknownError s) =
"A prover error occurred" ^
(if s = "" then " (pass the \"verbose\" option for details)" else ":\n" ^ s)
fun extract_delimited (begin_delim, end_delim) output =
(case first_field begin_delim output of
SOME (_, tail) =>
(case first_field "\n" tail of
SOME (_, tail') =>
if end_delim = "" then
tail'
else
(case first_field end_delim tail' of
SOME (body, _) => body
| NONE => "")
| NONE => "")
| NONE => "")
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 apply2 (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_atp_failure known_failures output =
known_failures
|> find_first (fn (_, pattern) => String.isSubstring pattern output)
|> Option.map fst
fun extract_tstplike_proof_and_outcome verbose proof_delims known_failures output =
(case (extract_tstplike_proof proof_delims output,
extract_known_atp_failure known_failures output) of
(_, SOME ProofIncomplete) => ("", NONE)
| (_, SOME ProofUnparsable) => ("", NONE)
| ("", SOME ProofMissing) => ("", NONE)
| ("", NONE) => ("", SOME (UnknownError (short_output verbose output)))
| res as ("", _) => res
| (tstplike_proof, _) => (tstplike_proof, NONE))
type atp_step_name = string * string list
fun is_same_atp_step (s1, _) (s2, _) = s1 = s2
val vampire_fact_prefix = "f"
fun vampire_step_name_ord p =
let val q = apply2 fst p in
(* The "unprefix" part is to cope with Vampire's output. *)
(case apply2 (Int.fromString o perhaps (try (unprefix vampire_fact_prefix))) q of
(SOME i, SOME j) => int_ord (i, j)
| _ => raise Fail "not Vampire")
end
type ('a, 'b) atp_step = atp_step_name * atp_formula_role * 'a * 'b * atp_step_name list
type 'a atp_proof = (('a, 'a, ('a, 'a atp_type) atp_term, 'a) atp_formula, string) atp_step list
(**** PARSING OF TSTP FORMAT ****)
(* Strings enclosed in single quotes (e.g., file names), identifiers possibly starting
with "$" and possibly with "!" in them (for "z3_tptp"). *)
val scan_general_id =
$$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode
|| (Scan.repeat ($$ "$") -- Scan.many1 Symbol.is_letdig >> (op ^ o apply2 implode))
-- Scan.optional (Scan.repeat ($$ "!") -- Scan.many1 Symbol.is_letdig >> (op ^ o apply2 implode)) ""
>> op ^
fun skip_term x =
let
fun skip _ accum [] = (accum, [])
| skip n accum (ss as s :: ss') =
if (s = "," orelse s = ".") andalso n = 0 then
(accum, ss)
else if member (op =) [")", "]"] s then
if n = 0 then (accum, ss) else skip (n - 1) (s :: accum) ss'
else if member (op =) ["(", "["] s then
skip (n + 1) (s :: accum) ss'
else
skip n (s :: accum) ss'
in
(skip 0 [] #>> (rev #> implode)) x
end
and skip_terms x = (skip_term ::: Scan.repeat ($$ "," |-- skip_term)) x
datatype source =
File_Source of string * string option |
Inference_Source of string * string list |
Introduced_Source of string
val dummy_phi = AAtom (ATerm (("", []), []))
val dummy_inference = Inference_Source ("", [])
val dummy_atype = AType (("", []), [])
(* "skip_term" is there to cope with Waldmeister nonsense such as "theory(equality)". *)
fun parse_dependency x =
(parse_inference_source >> snd
|| scan_general_id --| skip_term >> single) x
and parse_dependencies x =
(Scan.repeats (Scan.option ($$ ",") |-- parse_dependency)
>> (filter_out (curry (op =) "theory"))) x
and parse_file_source x =
(Scan.this_string "file" |-- $$ "(" |-- scan_general_id
-- Scan.option ($$ "," |-- scan_general_id
--| Scan.option ($$ "," |-- $$ "[" -- Scan.option scan_general_id --| $$ "]")) --| $$ ")") x
and parse_inference_source x =
(Scan.this_string "inference" |-- $$ "(" |-- scan_general_id
--| skip_term --| $$ "," --| skip_term --| $$ "," --| $$ "["
-- parse_dependencies --| $$ "]" --| $$ ")") x
and parse_introduced_source x =
(Scan.this_string "introduced" |-- $$ "(" |-- scan_general_id
--| Scan.option ($$ "," |-- skip_term) --| $$ ")") x
and parse_source x =
(parse_file_source >> File_Source
|| parse_inference_source >> Inference_Source
|| parse_introduced_source >> Introduced_Source
|| scan_general_id >> (fn s => Inference_Source ("", [s])) (* for E *)
|| skip_term >> K dummy_inference) x
fun list_app (f, args) = fold (fn arg => fn f => ATerm ((tptp_app, []), [f, arg])) args f
fun parse_class x = scan_general_id x
and parse_classes x = (parse_class ::: Scan.repeat ($$ "&" |-- parse_class)) x
fun parse_type x =
(($$ "(" |-- parse_type --| $$ ")"
|| Scan.this_string tptp_pi_binder |-- $$ "[" |-- skip_terms --| $$ "]" --| $$ ":" -- parse_type
>> (fn (_, ty) => ty (* currently ignoring type constructor declarations anyway *))
|| (scan_general_id -- Scan.optional ($$ "{" |-- parse_classes --| $$ "}") [])
-- Scan.optional ($$ "(" |-- parse_types --| $$ ")") []
>> AType)
-- Scan.option (($$ tptp_app || $$ tptp_fun_type || $$ tptp_product_type) -- parse_type)
>> (fn (a, NONE) => a
| (a, SOME (bin_op, b)) =>
if bin_op = tptp_app then
(case a of
AType (s_clss, tys) => AType (s_clss, tys @ [b])
| _ => raise UNRECOGNIZED_ATP_PROOF ())
else if bin_op = tptp_fun_type then
AFun (a, b)
else if bin_op = tptp_product_type then
AType ((tptp_product_type, []), [a, b])
else
raise Fail "impossible case")) x
and parse_types x =
(parse_type ::: Scan.repeat ($$ "," |-- parse_type)) x
(* We currently half ignore types. *)
fun parse_fol_optional_type_signature x =
(Scan.option ($$ tptp_has_type |-- parse_type)
>> (fn some as SOME (AType ((s, []), [])) => if s = dfg_individual_type then NONE else some
| res => res)) x
and parse_fol_arg x =
($$ "(" |-- parse_fol_term --| $$ ")" --| parse_fol_optional_type_signature
|| scan_general_id -- parse_fol_optional_type_signature
-- Scan.optional ($$ "<" |-- parse_types --| $$ ">") []
-- Scan.optional ($$ "(" |-- parse_fol_terms --| $$ ")") []
>> (fn (((s, ty_opt), tyargs), args) =>
if is_tptp_variable s andalso null tyargs andalso null args andalso is_some ty_opt then
ATerm ((s, the_list ty_opt), [])
else
ATerm ((s, tyargs), args))) x
and parse_fol_term x =
(parse_fol_arg -- Scan.repeat ($$ tptp_app |-- parse_fol_arg)
--| parse_fol_optional_type_signature >> list_app) x
and parse_fol_terms x = (parse_fol_term ::: Scan.repeat ($$ "," |-- parse_fol_term)) x
fun parse_fol_atom x =
(parse_fol_term --
Scan.option (Scan.option ($$ tptp_not_infix) --| $$ tptp_equal -- parse_fol_term)
>> (fn (u1, NONE) => AAtom u1
| (u1, SOME (neg, u2)) =>
AAtom (ATerm (("equal", []), [u1, u2])) |> is_some neg ? mk_anot)) x
(* TPTP formulas are fully parenthesized, so we don't need to worry about operator precedence. *)
fun parse_fol_literal x =
((Scan.repeat ($$ tptp_not) >> length)
-- ($$ "(" |-- parse_fol_formula --| $$ ")"
|| parse_fol_quantified_formula
|| parse_fol_atom)
>> (fn (n, phi) => phi |> n mod 2 = 1 ? mk_anot)) x
and parse_fol_formula x =
(parse_fol_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_fol_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_fol_quantified_formula x =
(($$ tptp_forall >> K AForall || $$ tptp_exists >> K AExists)
--| $$ "[" -- parse_fol_terms --| $$ "]" --| $$ ":" -- parse_fol_literal
>> (fn ((q, ts), phi) => AQuant (q, map (fn ATerm ((s, _), _) => (s, NONE)) ts, phi))) x
val parse_tstp_extra_arguments =
Scan.optional ($$ "," |-- parse_source --| Scan.option ($$ "," |-- skip_term)) dummy_inference
val waldmeister_conjecture_name = "conjecture_1"
fun is_same_term subst tm1 tm2 =
let
fun do_term_pair (AAbs (((var1, typ1), body1), args1)) (AAbs (((var2, typ2), body2), args2))
(SOME subst) =
if typ1 <> typ2 andalso length args1 = length args2 then NONE
else
let val ls = length subst in
SOME ((var1, var2) :: subst)
|> do_term_pair body1 body2
|> (fn SOME subst => SOME (nth_drop (length subst - ls - 1) subst)
| NONE => NONE)
|> (if length args1 = length args2
then fold2 do_term_pair args1 args2
else K NONE)
end
| do_term_pair (ATerm ((s1, _), args1)) (ATerm ((s2, _), args2)) (SOME subst) =
(case apply2 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 then
SOME subst
else
NONE
| _ => NONE) |> (if length args1 = length args2
then fold2 do_term_pair args1 args2
else K NONE)
| do_term_pair _ _ _ = NONE
in
SOME subst |> do_term_pair tm1 tm2 |> is_some
end
fun is_same_formula comm subst (AQuant (q1, xs1, phi1)) (AQuant (q2, xs2, phi2)) =
q1 = q2 andalso length xs1 = length xs2 andalso
is_same_formula comm ((map fst xs1 ~~ map fst xs2) @ subst) phi1 phi2
| is_same_formula comm subst (AConn (c1, phis1)) (AConn (c2, phis2)) =
c1 = c2 andalso length phis1 = length phis2 andalso
forall (uncurry (is_same_formula comm subst)) (phis1 ~~ phis2)
| is_same_formula comm subst (AAtom (tm1 as ATerm (("equal", tys), [tm11, tm12]))) (AAtom tm2) =
is_same_term subst tm1 tm2 orelse
(comm andalso is_same_term subst (ATerm (("equal", tys), [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 true [] phi phi' then SOME (ident, phi') else NONE
| matching_formula_line_identifier _ _ = NONE
fun find_formula_in_problem phi =
maps snd
#> map_filter (matching_formula_line_identifier phi)
#> try (single o hd)
#> the_default []
fun commute_eq (AAtom (ATerm ((s, tys), tms))) = AAtom (ATerm ((s, tys), rev tms))
| commute_eq _ = raise Fail "expected equation"
fun role_of_tptp_string "axiom" = Axiom
| role_of_tptp_string "definition" = Definition
| role_of_tptp_string "lemma" = Lemma
| role_of_tptp_string "hypothesis" = Hypothesis
| role_of_tptp_string "conjecture" = Conjecture
| role_of_tptp_string "negated_conjecture" = Negated_Conjecture
| role_of_tptp_string "plain" = Plain
| role_of_tptp_string "type" = Type_Role
| role_of_tptp_string _ = Unknown
val tptp_binary_ops =
[tptp_and, tptp_not_and, tptp_or, tptp_not_or, tptp_implies, tptp_if, tptp_iff, tptp_not_iff,
tptp_equal, tptp_not_equal, tptp_app]
fun parse_one_in_list xs =
foldl1 (op ||) (map Scan.this_string xs)
fun parse_binary_op x =
(parse_one_in_list tptp_binary_ops
>> (fn c => if c = tptp_equal then "equal" else c)) x
val parse_fol_quantifier =
parse_one_in_list [tptp_forall, tptp_exists, tptp_lambda, tptp_hilbert_choice, tptp_hilbert_the]
val parse_hol_quantifier =
parse_one_in_list [tptp_ho_forall, tptp_ho_exists, tptp_hilbert_choice, tptp_hilbert_the]
fun mk_ho_of_fo_quant q =
if q = tptp_forall then tptp_ho_forall
else if q = tptp_exists then tptp_ho_exists
else if q = tptp_hilbert_choice then tptp_hilbert_choice
else if q = tptp_hilbert_the then tptp_hilbert_the
else raise Fail ("unrecognized quantification: " ^ q)
fun remove_hol_app (ATerm ((x, ty), arg)) =
if x = tptp_app then
(case arg of
ATerm ((x, ty), arg) :: t => remove_hol_app (ATerm ((x, ty), map remove_hol_app arg @ t))
| [AAbs ((var, tvar), phi), t] =>
remove_hol_app (AAbs ((var, tvar), map remove_hol_app phi @ [t])))
else
ATerm ((x, ty), map remove_hol_app arg)
| remove_hol_app (AAbs (((x, ty), arg), t)) = AAbs (((x, ty), remove_hol_app arg), t)
fun parse_hol_typed_var x =
(Scan.repeat (scan_general_id -- Scan.option ($$ tptp_has_type |-- parse_type)
--| Scan.option (Scan.this_string ","))
|| $$ "(" |-- parse_hol_typed_var --| $$ ")") x
fun parse_simple_hol_term x =
(parse_fol_quantifier -- ($$ "[" |-- parse_hol_typed_var --| $$ "]" --| $$ ":") -- parse_hol_term
>> (fn ((q, ys), t) =>
fold_rev
(fn (var, ty) => fn r =>
AAbs (((var, the_default dummy_atype ty), r), [])
|> (if tptp_lambda <> q then
mk_app (q |> mk_ho_of_fo_quant
|> mk_simple_aterm)
else I))
ys t)
|| Scan.this_string tptp_not |-- parse_hol_term >> mk_app (mk_simple_aterm tptp_not)
|| scan_general_id -- Scan.option ($$ tptp_has_type |-- parse_type)
>> (fn (var, typ_opt) => ATerm ((var, the_list typ_opt), []))
|| parse_hol_quantifier >> mk_simple_aterm
|| $$ "(" |-- parse_hol_term --| $$ ")"
|| parse_binary_op >> mk_simple_aterm) x
and parse_hol_term x =
(parse_simple_hol_term -- Scan.option (parse_binary_op -- parse_hol_term)
>> (fn (t1, SOME (c, t2)) =>
if c = tptp_app then mk_app t1 t2 else mk_apps (mk_simple_aterm c) [t1, t2]
| (t, NONE) => t)) x
fun parse_hol_formula x = (parse_hol_term #>> remove_hol_app #>> AAtom) x
fun parse_tstp_hol_line problem =
(Scan.this_string tptp_thf -- $$ "(") |-- scan_general_id --| $$ ","
-- Symbol.scan_ascii_id --| $$ "," -- (parse_hol_formula || skip_term >> K dummy_phi)
-- parse_tstp_extra_arguments --| $$ ")"
--| $$ "."
>> (fn (((num, role), phi), deps) =>
let
val role' = role_of_tptp_string role
val ((name, phi), rule, deps) =
(case deps of
File_Source (_, SOME s) =>
if role' = Definition then
(((num, map fst (find_formula_in_problem phi problem)), phi), "", [])
else
(((num, [s]), phi), "", [])
| Inference_Source (rule, deps) => (((num, []), phi), rule, deps))
in
[(name, role', phi, rule, map (rpair []) deps)]
end)
fun parse_tstp_fol_line problem =
((Scan.this_string tptp_cnf || Scan.this_string tptp_fof || Scan.this_string tptp_tff) -- $$ "(")
|-- scan_general_id --| $$ "," -- Symbol.scan_ascii_id --| $$ ","
-- (parse_fol_formula || skip_term >> K dummy_phi) -- parse_tstp_extra_arguments
--| $$ ")" --| $$ "."
>> (fn (((num, role0), phi), src) =>
let
val role = role_of_tptp_string role0
val ((name, phi), role', rule, deps) =
(* Waldmeister isn't exactly helping. *)
(case src of
File_Source (_, SOME s) =>
(if s = waldmeister_conjecture_name then
(case find_formula_in_problem (mk_anot phi) problem of
(* Waldmeister hack: Get the original orientation of the equation to avoid
confusing Isar. *)
[(s, phi')] =>
((num, [s]),
phi |> not (is_same_formula false [] (mk_anot phi) phi') ? commute_eq)
| _ => ((num, []), phi))
else
((num, [s]), phi),
role, "", [])
| File_Source _ =>
(((num, map fst (find_formula_in_problem phi problem)), phi), role, "", [])
| Inference_Source (rule, deps) => (((num, []), phi), role, rule, deps)
| Introduced_Source rule => (((num, []), phi), Lemma, rule, []))
fun mk_step () = (name, role', phi, rule, map (rpair []) deps)
in
[(case role' of
Definition =>
(case phi of
AAtom (ATerm (("equal", _), _)) =>
(* Vampire's equality proxy axiom *)
(name, Definition, phi, rule, map (rpair []) deps)
| _ => mk_step ())
| _ => mk_step ())]
end)
fun parse_tstp_line problem = parse_tstp_fol_line problem || parse_tstp_hol_line problem
(**** PARSING OF SPASS OUTPUT ****)
(* SPASS returns clause references of the form "x.y". We ignore "y". *)
val parse_dot_name = scan_general_id --| $$ "." --| scan_general_id
val parse_spass_annotations =
Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name --| Scan.option ($$ ","))) []
(* We ignore the stars and the pluses that follow literals. *)
fun parse_decorated_atom x =
(parse_fol_atom --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")) x
fun mk_horn ([], []) = AAtom (ATerm (("c_False", []), []))
| mk_horn (neg_lits, pos_lits) = foldr1 (uncurry (mk_aconn AOr)) (map mk_anot neg_lits @ 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
val parse_spass_debug =
Scan.option ($$ "(" |-- Scan.repeat (scan_general_id --| Scan.option ($$ ",")) --| $$ ")")
(* Syntax: <num>[0:<inference><annotations>] <atoms> || <atoms> -> <atoms> .
derived from formulae <ident>* *)
fun parse_spass_line x =
(parse_spass_debug |-- scan_general_id --| $$ "[" --| Scan.many1 Symbol.is_digit --| $$ ":"
-- Symbol.scan_ascii_id -- parse_spass_annotations --| $$ "]" -- parse_horn_clause --| $$ "."
-- Scan.option (Scan.this_string "derived from formulae "
|-- Scan.repeat (scan_general_id --| Scan.option ($$ " ")))
>> (fn ((((num, rule), deps), u), names) =>
[((num, these names), Unknown, u, rule, map (rpair []) deps)])) x
fun parse_pirate_dependency x = (Scan.option ($$ "-") |-- scan_general_id) x
fun parse_pirate_dependencies x =
Scan.repeat (parse_pirate_dependency --| Scan.option ($$ "," || $$ " ")) x
fun parse_pirate_file_source x =
((Scan.this_string "Input" || Scan.this_string "Conj") |-- $$ "(" |-- scan_general_id
--| $$ ")") x
fun parse_pirate_inference_source x =
(scan_general_id -- ($$ "(" |-- parse_pirate_dependencies --| $$ ")")) x
fun parse_pirate_source x =
(parse_pirate_file_source >> (fn s => File_Source ("", SOME s))
|| parse_pirate_inference_source >> Inference_Source) x
(* Syntax: <num> <stuff> || <atoms> -> <atoms> . origin\(<origin>\) *)
fun parse_pirate_line x =
(scan_general_id --| Scan.repeat (~$$ "|") -- parse_horn_clause --| $$ "."
--| Scan.this_string "origin" --| $$ "(" -- parse_pirate_source --| $$ ")"
>> (fn ((((num, u), source))) =>
let
val (names, rule, deps) =
(case source of
File_Source (_, SOME s) => ([s], spass_input_rule, [])
| Inference_Source (rule, deps) => ([], rule, deps))
in
[((num, names), Unknown, u, rule, map (rpair []) deps)]
end)) x
fun core_inference inf fact = ((fact, [fact]), Unknown, dummy_phi, inf, [])
(* Syntax: SZS core <name> ... <name> *)
fun parse_z3_tptp_core_line x =
(Scan.this_string "SZS core" |-- Scan.repeat ($$ " " |-- scan_general_id)
>> map (core_inference z3_tptp_core_rule)) x
fun parse_line local_name problem =
(* Satallax is handled separately, in "atp_satallax.ML". *)
if local_name = spassN then parse_spass_line
else if local_name = pirateN then parse_pirate_line
else if local_name = z3_tptpN then parse_z3_tptp_core_line
else parse_tstp_line problem
fun core_of_agsyhol_proof s =
(case split_lines s of
"The transformed problem consists of the following conjectures:" :: conj ::
_ :: proof_term :: _ => SOME (unprefix " " conj :: find_enclosed "<<" ">>" proof_term)
| _ => NONE)
fun clean_up_dependencies _ [] = []
| clean_up_dependencies seen ((name, role, u, rule, deps) :: steps) =
(name, role, u, rule, 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_atp_proof f =
let
fun map_type (AType ((s, clss), tys)) = AType ((f s, map f clss), map map_type tys)
| map_type (AFun (ty, ty')) = AFun (map_type ty, map_type ty')
| map_type (APi (ss, ty)) = APi (map f ss, map_type ty)
fun map_term (ATerm ((s, tys), ts)) = ATerm ((f s, map map_type tys), map map_term ts)
| map_term (AAbs (((s, ty), tm), args)) =
AAbs (((f s, map_type ty), map_term tm), map map_term args)
fun map_formula (AQuant (q, xs, phi)) = AQuant (q, map (apfst f) xs, map_formula phi)
| map_formula (AConn (c, phis)) = AConn (c, map map_formula phis)
| map_formula (AAtom t) = AAtom (map_term t)
fun map_step (name, role, phi, rule, deps) = (name, role, map_formula phi, rule, deps)
in
map map_step
end
fun nasty_name pool s = Symtab.lookup pool s |> the_default s
fun nasty_atp_proof pool =
not (Symtab.is_empty pool) ? map_term_names_in_atp_proof (nasty_name pool)
fun string_of_list f xs = enclose "[" "]" (commas (map f xs))
fun string_of_atp_step_name (s, ss) = "(" ^ s ^ ", " ^ string_of_list I ss ^ ")"
fun string_of_atp_step f g (name, role, x, y, names) =
let
val name' = string_of_atp_step_name name
val role' = ATP_Problem.tptp_string_of_role role
val x' = f x
val y' = g y
val names' = string_of_list string_of_atp_step_name names
in
"(" ^ name' ^ ", " ^ role' ^ ", " ^ x' ^ ", " ^ y' ^ ", " ^ names' ^ ")"
end
fun parse_proof local_name problem =
strip_spaces_except_between_idents
#> raw_explode
#> Scan.error (!! (fn _ => raise UNRECOGNIZED_ATP_PROOF ())
(Scan.finite Symbol.stopper (Scan.repeats1 (parse_line local_name problem))))
#> fst
fun atp_proof_of_tstplike_proof _ _ "" = []
| atp_proof_of_tstplike_proof local_prover problem tstp =
(case core_of_agsyhol_proof tstp of
SOME facts => facts |> map (core_inference agsyhol_core_rule)
| NONE =>
tstp ^ "$" (* the $ sign acts as a sentinel (FIXME: needed?) *)
|> parse_proof local_prover problem
|> local_prover = vampireN ? perhaps (try (sort (vampire_step_name_ord o apply2 #1)))
|> local_prover = zipperpositionN ? rev)
end;