|
(* Title: HOL/Tools/ATP/atp_problem.ML
Author: Jia Meng, Cambridge University Computer Laboratory and NICTA
Author: Jasmin Blanchette, TU Muenchen
Abstract representation of ATP problems and TPTP syntax.
*)
signature ATP_PROBLEM =
sig
datatype ('a, 'b) atp_term =
ATerm of ('a * 'b list) * ('a, 'b) atp_term list |
AAbs of (('a * 'b) * ('a, 'b) atp_term) * ('a, 'b) atp_term list
datatype atp_quantifier = AForall | AExists
datatype atp_connective = ANot | AAnd | AOr | AImplies | AIff
datatype ('a, 'b, 'c, 'd) atp_formula =
ATyQuant of atp_quantifier * ('b * 'd list) list
* ('a, 'b, 'c, 'd) atp_formula |
AQuant of atp_quantifier * ('a * 'b option) list
* ('a, 'b, 'c, 'd) atp_formula |
AConn of atp_connective * ('a, 'b, 'c, 'd) atp_formula list |
AAtom of 'c
datatype 'a atp_type =
AType of ('a * 'a list) * 'a atp_type list |
AFun of 'a atp_type * 'a atp_type |
APi of 'a list * 'a atp_type
type term_order =
{is_lpo : bool,
gen_weights : bool,
gen_prec : bool,
gen_simp : bool}
datatype fool = Without_FOOL | With_FOOL
datatype polymorphism = Monomorphic | Polymorphic
datatype thf_flavor = THF_Lambda_Free | THF_Without_Choice | THF_With_Choice
datatype atp_format =
CNF |
CNF_UEQ |
FOF |
TFF of fool * polymorphism |
THF of fool * polymorphism * thf_flavor |
DFG of polymorphism
datatype atp_formula_role =
Axiom | Definition | Lemma | Hypothesis | Conjecture | Negated_Conjecture |
Plain | Type_Role | Unknown
datatype 'a atp_problem_line =
Class_Decl of string * 'a * 'a list |
Type_Decl of string * 'a * int |
Sym_Decl of string * 'a * 'a atp_type |
Datatype_Decl of
string * ('a * 'a list) list * 'a atp_type * ('a, 'a atp_type) atp_term list * bool |
Class_Memb of string * ('a * 'a list) list * 'a atp_type * 'a |
Formula of (string * string) * atp_formula_role
* ('a, 'a atp_type, ('a, 'a atp_type) atp_term, 'a) atp_formula
* (string, string atp_type) atp_term option
* (string, string atp_type) atp_term list
type 'a atp_problem = (string * 'a atp_problem_line list) list
val tptp_cnf : string
val tptp_fof : string
val tptp_tff : string
val tptp_thf : string
val tptp_has_type : string
val tptp_type_of_types : string
val tptp_bool_type : string
val tptp_individual_type : string
val tptp_fun_type : string
val tptp_product_type : string
val tptp_forall : string
val tptp_ho_forall : string
val tptp_pi_binder : string
val tptp_exists : string
val tptp_ho_exists : string
val tptp_choice : string
val tptp_ho_choice : string
val tptp_hilbert_choice : string
val tptp_hilbert_the : string
val tptp_not : string
val tptp_and : string
val tptp_not_and : string
val tptp_or : string
val tptp_not_or : string
val tptp_implies : string
val tptp_if : string
val tptp_iff : string
val tptp_not_iff : string
val tptp_app : string
val tptp_not_infix : string
val tptp_equal : string
val tptp_not_equal : string
val tptp_old_equal : string
val tptp_false : string
val tptp_true : string
val tptp_lambda : string
val tptp_empty_list : string
val tptp_unary_builtins : string list
val tptp_binary_builtins : string list
val dfg_individual_type : string
val isabelle_info_prefix : string
val isabelle_info : bool -> string -> int -> (string, 'a) atp_term list
val extract_isabelle_status : (string, 'a) atp_term list -> string option
val extract_isabelle_rank : (string, 'a) atp_term list -> int
val inductionN : string
val introN : string
val inductiveN : string
val elimN : string
val simpN : string
val non_rec_defN : string
val rec_defN : string
val rankN : string
val minimum_rank : int
val default_rank : int
val default_term_order_weight : int
val is_tptp_equal : string -> bool
val is_built_in_tptp_symbol : string -> bool
val is_tptp_variable : string -> bool
val is_tptp_user_symbol : string -> bool
val bool_atype : (string * string) atp_type
val individual_atype : (string * string) atp_type
val mk_anot : ('a, 'b, 'c, 'd) atp_formula -> ('a, 'b, 'c, 'd) atp_formula
val mk_aconn :
atp_connective -> ('a, 'b, 'c, 'd) atp_formula
-> ('a, 'b, 'c, 'd) atp_formula -> ('a, 'b, 'c, 'd) atp_formula
val mk_app : (string, 'a) atp_term -> (string, 'a) atp_term -> (string, 'a) atp_term
val mk_apps : (string, 'a) atp_term -> (string, 'a) atp_term list -> (string, 'a) atp_term
val mk_simple_aterm: 'a -> ('a, 'b) atp_term
val aconn_fold :
bool option -> (bool option -> 'a -> 'b -> 'b) -> atp_connective * 'a list
-> 'b -> 'b
val aconn_map :
bool option -> (bool option -> 'a -> ('b, 'c, 'd, 'e) atp_formula)
-> atp_connective * 'a list -> ('b, 'c, 'd, 'e) atp_formula
val formula_fold :
bool option -> (bool option -> 'c -> 'e -> 'e)
-> ('a, 'b, 'c, 'd) atp_formula -> 'e -> 'e
val formula_map :
('c -> 'e) -> ('a, 'b, 'c, 'd) atp_formula -> ('a, 'b, 'e, 'd) atp_formula
val strip_atype : 'a atp_type -> 'a list * ('a atp_type list * 'a atp_type)
val is_format_higher_order : atp_format -> bool
val tptp_string_of_format : atp_format -> string
val tptp_string_of_role : atp_formula_role -> string
val tptp_string_of_line : atp_format -> string atp_problem_line -> string
val lines_of_atp_problem :
atp_format -> term_order -> (unit -> (string * int) list)
-> string atp_problem -> string list
val ensure_cnf_problem :
(string * string) atp_problem -> (string * string) atp_problem
val filter_cnf_ueq_problem :
(string * string) atp_problem -> (string * string) atp_problem
val declared_in_atp_problem : 'a atp_problem -> ('a list * 'a list) * 'a list
val nice_atp_problem :
bool -> atp_format -> ('a * (string * string) atp_problem_line list) list
-> ('a * string atp_problem_line list) list
* (string Symtab.table * string Symtab.table) option
end;
structure ATP_Problem : ATP_PROBLEM =
struct
open ATP_Util
val parens = enclose "(" ")"
(** ATP problem **)
datatype ('a, 'b) atp_term =
ATerm of ('a * 'b list) * ('a, 'b) atp_term list |
AAbs of (('a * 'b) * ('a, 'b) atp_term) * ('a, 'b) atp_term list
datatype atp_quantifier = AForall | AExists
datatype atp_connective = ANot | AAnd | AOr | AImplies | AIff
datatype ('a, 'b, 'c, 'd) atp_formula =
ATyQuant of atp_quantifier * ('b * 'd list) list
* ('a, 'b, 'c, 'd) atp_formula |
AQuant of atp_quantifier * ('a * 'b option) list
* ('a, 'b, 'c, 'd) atp_formula |
AConn of atp_connective * ('a, 'b, 'c, 'd) atp_formula list |
AAtom of 'c
datatype 'a atp_type =
AType of ('a * 'a list) * 'a atp_type list |
AFun of 'a atp_type * 'a atp_type |
APi of 'a list * 'a atp_type
type term_order =
{is_lpo : bool,
gen_weights : bool,
gen_prec : bool,
gen_simp : bool}
datatype fool = Without_FOOL | With_FOOL
datatype polymorphism = Monomorphic | Polymorphic
datatype thf_flavor = THF_Lambda_Free | THF_Without_Choice | THF_With_Choice
datatype atp_format =
CNF |
CNF_UEQ |
FOF |
TFF of fool * polymorphism |
THF of fool * polymorphism * thf_flavor |
DFG of polymorphism
datatype atp_formula_role =
Axiom | Definition | Lemma | Hypothesis | Conjecture | Negated_Conjecture |
Plain | Type_Role | Unknown
datatype 'a atp_problem_line =
Class_Decl of string * 'a * 'a list |
Type_Decl of string * 'a * int |
Sym_Decl of string * 'a * 'a atp_type |
Datatype_Decl of
string * ('a * 'a list) list * 'a atp_type * ('a, 'a atp_type) atp_term list * bool |
Class_Memb of string * ('a * 'a list) list * 'a atp_type * 'a |
Formula of (string * string) * atp_formula_role
* ('a, 'a atp_type, ('a, 'a atp_type) atp_term, 'a) atp_formula
* (string, string atp_type) atp_term option
* (string, string atp_type) atp_term list
type 'a atp_problem = (string * 'a atp_problem_line list) list
(* official TPTP syntax *)
val tptp_cnf = "cnf"
val tptp_fof = "fof"
val tptp_tff = "tff"
val tptp_thf = "thf"
val tptp_has_type = ":"
val tptp_type_of_types = "$tType"
val tptp_bool_type = "$o"
val tptp_individual_type = "$i"
val tptp_fun_type = ">"
val tptp_product_type = "*"
val tptp_forall = "!"
val tptp_ho_forall = "!!"
val tptp_pi_binder = "!>"
val tptp_exists = "?"
val tptp_ho_exists = "??"
val tptp_choice = "@+"
val tptp_ho_choice = "@@+"
val tptp_not = "~"
val tptp_and = "&"
val tptp_not_and = "~&"
val tptp_or = "|"
val tptp_not_or = "~|"
val tptp_implies = "=>"
val tptp_if = "<="
val tptp_iff = "<=>"
val tptp_not_iff = "<~>"
val tptp_app = "@"
val tptp_hilbert_choice = "@+"
val tptp_hilbert_the = "@-"
val tptp_not_infix = "!"
val tptp_equal = "="
val tptp_not_equal = "!="
val tptp_old_equal = "equal"
val tptp_false = "$false"
val tptp_true = "$true"
val tptp_lambda = "^"
val tptp_empty_list = "[]"
val tptp_unary_builtins = [tptp_not]
val tptp_binary_builtins =
[tptp_and, tptp_or, tptp_implies, tptp_if, tptp_iff, tptp_not_iff, tptp_equal]
val dfg_individual_type = "iii" (* cannot clash *)
val isabelle_info_prefix = "isabelle_"
val inductionN = "induction"
val introN = "intro"
val inductiveN = "inductive"
val elimN = "elim"
val simpN = "simp"
val non_rec_defN = "non_rec_def"
val rec_defN = "rec_def"
val rankN = "rank"
val minimum_rank = 0
val default_rank = 1000
val default_term_order_weight = 1
(* Currently, only SPASS 3.8ds and (to a lesser extent) Metis can process Isabelle
metainformation. *)
fun isabelle_info generate_info status rank =
if generate_info then
[] |> rank <> default_rank
? cons (ATerm ((isabelle_info_prefix ^ rankN, []),
[ATerm ((string_of_int rank, []), [])]))
|> status <> "" ? cons (ATerm ((isabelle_info_prefix ^ status, []), []))
else
[]
fun extract_isabelle_status (ATerm ((s, []), []) :: _) =
try (unprefix isabelle_info_prefix) s
| extract_isabelle_status _ = NONE
fun extract_isabelle_rank (tms as _ :: _) =
(case List.last tms of
ATerm ((_, []), [ATerm ((rank, []), [])]) => the (Int.fromString rank)
| _ => default_rank)
| extract_isabelle_rank _ = default_rank
fun is_tptp_equal s = (s = tptp_equal orelse s = tptp_old_equal)
fun is_built_in_tptp_symbol s =
s = tptp_old_equal orelse not (Char.isAlpha (String.sub (s, 0)))
fun is_tptp_variable s = s <> "" andalso Char.isUpper (String.sub (s, 0))
val is_tptp_user_symbol = not o (is_tptp_variable orf is_built_in_tptp_symbol)
val bool_atype = AType ((`I tptp_bool_type, []), [])
val individual_atype = AType ((`I tptp_individual_type, []), [])
fun raw_polarities_of_conn ANot = (SOME false, NONE)
| raw_polarities_of_conn AAnd = (SOME true, SOME true)
| raw_polarities_of_conn AOr = (SOME true, SOME true)
| raw_polarities_of_conn AImplies = (SOME false, SOME true)
| raw_polarities_of_conn AIff = (NONE, NONE)
fun polarities_of_conn NONE = K (NONE, NONE)
| polarities_of_conn (SOME pos) =
raw_polarities_of_conn #> not pos ? apply2 (Option.map not)
fun mk_anot (AConn (ANot, [phi])) = phi
| mk_anot phi = AConn (ANot, [phi])
fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
fun mk_app t u = ATerm ((tptp_app, []), [t, u])
fun mk_apps f xs = fold (fn x => fn f => mk_app f x) xs f
fun mk_simple_aterm p = ATerm ((p, []), [])
fun aconn_fold pos f (ANot, [phi]) = f (Option.map not pos) phi
| aconn_fold pos f (AImplies, [phi1, phi2]) =
f (Option.map not pos) phi1 #> f pos phi2
| aconn_fold pos f (AAnd, phis) = fold (f pos) phis
| aconn_fold pos f (AOr, phis) = fold (f pos) phis
| aconn_fold _ f (_, phis) = fold (f NONE) phis
fun aconn_map pos f (ANot, [phi]) = AConn (ANot, [f (Option.map not pos) phi])
| aconn_map pos f (AImplies, [phi1, phi2]) =
AConn (AImplies, [f (Option.map not pos) phi1, f pos phi2])
| aconn_map pos f (AAnd, phis) = AConn (AAnd, map (f pos) phis)
| aconn_map pos f (AOr, phis) = AConn (AOr, map (f pos) phis)
| aconn_map _ f (c, phis) = AConn (c, map (f NONE) phis)
fun formula_fold pos f =
let
fun fld pos (AQuant (_, _, phi)) = fld pos phi
| fld pos (ATyQuant (_, _, phi)) = fld pos phi
| fld pos (AConn conn) = aconn_fold pos fld conn
| fld pos (AAtom tm) = f pos tm
in fld pos end
fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
| formula_map f (ATyQuant (q, xs, phi)) = ATyQuant (q, xs, formula_map f phi)
| formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
| formula_map f (AAtom tm) = AAtom (f tm)
fun strip_api (APi (tys, ty)) = strip_api ty |>> append tys
| strip_api ty = ([], ty)
fun strip_afun (AFun (ty1, ty2)) = strip_afun ty2 |>> cons ty1
| strip_afun ty = ([], ty)
fun strip_atype ty = ty |> strip_api ||> strip_afun
fun is_function_atype ty = snd (snd (strip_atype ty)) <> AType ((tptp_bool_type, []), [])
fun is_predicate_atype ty = not (is_function_atype ty)
fun is_nontrivial_predicate_atype (AType _) = false
| is_nontrivial_predicate_atype ty = is_predicate_atype ty
fun is_format_higher_order (THF _) = true
| is_format_higher_order _ = false
fun is_format_typed (TFF _) = true
| is_format_typed (THF _) = true
| is_format_typed (DFG _) = true
| is_format_typed _ = false
fun is_format_with_fool (THF (With_FOOL, _, _)) = true
| is_format_with_fool (TFF (With_FOOL, _)) = true
| is_format_with_fool _ = false
fun tptp_string_of_role Axiom = "axiom"
| tptp_string_of_role Definition = "definition"
| tptp_string_of_role Lemma = "lemma"
| tptp_string_of_role Hypothesis = "hypothesis"
| tptp_string_of_role Conjecture = "conjecture"
| tptp_string_of_role Negated_Conjecture = "negated_conjecture"
| tptp_string_of_role Plain = "plain"
| tptp_string_of_role Type_Role = "type"
| tptp_string_of_role Unknown = "unknown"
fun tptp_string_of_app _ func [] = func
| tptp_string_of_app format func args =
if is_format_higher_order format then
"(" ^ space_implode (" " ^ tptp_app ^ " ") (func :: args) ^ ")"
else
func ^ "(" ^ commas args ^ ")"
fun uncurry_type (APi (tys, ty)) = APi (tys, uncurry_type ty)
| uncurry_type (ty as AFun (ty1 as AType _, ty2)) =
(case uncurry_type ty2 of
AFun (ty' as AType ((s, _), tys), ty) =>
AFun (AType ((tptp_product_type, []),
ty1 :: (if s = tptp_product_type then tys else [ty'])), ty)
| _ => ty)
| uncurry_type (ty as AType _) = ty
| uncurry_type _ =
raise Fail "unexpected higher-order type in first-order format"
val suffix_type_of_types = suffix (" " ^ tptp_has_type ^ " " ^ tptp_type_of_types)
fun str_of_type format ty =
let
val dfg = (case format of DFG _ => true | _ => false)
fun str _ (AType ((s, _), [])) =
if dfg andalso s = tptp_individual_type then dfg_individual_type else s
| str rhs (AType ((s, _), tys)) =
if s = tptp_fun_type then
let val [ty1, ty2] = tys in
str rhs (AFun (ty1, ty2))
end
else
let val ss = tys |> map (str false) in
if s = tptp_product_type then
ss |> space_implode
(if dfg then ", " else " " ^ tptp_product_type ^ " ")
|> (not dfg andalso length ss > 1) ? parens
else
tptp_string_of_app format s ss
end
| str rhs (AFun (ty1, ty2)) =
(str false ty1 |> dfg ? parens) ^ " " ^
(if dfg then "" else tptp_fun_type ^ " ") ^ str true ty2
|> not rhs ? parens
| str _ (APi (ss, ty)) =
if dfg then
"[" ^ commas ss ^ "], " ^ str true ty
else
tptp_pi_binder ^ "[" ^ commas (map suffix_type_of_types ss) ^ "]: " ^
str false ty
in str true ty end
fun string_of_type (format as THF _) ty = str_of_type format ty
| string_of_type format ty = str_of_type format (uncurry_type ty)
fun tptp_string_of_quantifier AForall = tptp_forall
| tptp_string_of_quantifier AExists = tptp_exists
fun tptp_string_of_connective ANot = tptp_not
| tptp_string_of_connective AAnd = tptp_and
| tptp_string_of_connective AOr = tptp_or
| tptp_string_of_connective AImplies = tptp_implies
| tptp_string_of_connective AIff = tptp_iff
fun string_of_bound_var format (s, ty) =
s ^
(if is_format_typed format then
" " ^ tptp_has_type ^ " " ^
(ty |> the_default (AType ((tptp_individual_type, []), [])) |> string_of_type format)
else
"")
fun tptp_string_of_term _ (ATerm ((s, []), [])) =
s |> member (op =) (tptp_unary_builtins @ tptp_binary_builtins) s ? parens
| tptp_string_of_term format (ATerm ((s, tys), ts)) =
let
val of_type = string_of_type format
val of_term = tptp_string_of_term format
fun app () =
tptp_string_of_app format s
(map (of_type #> is_format_higher_order format ? parens) tys @ map of_term ts)
in
if s = tptp_empty_list then
(* used for lists in the optional "source" field of a derivation *)
"[" ^ commas (map of_term ts) ^ "]"
else if is_tptp_equal s then
space_implode (" " ^ tptp_equal ^ " ") (map of_term ts)
|> (is_format_higher_order format orelse is_format_with_fool format) ? parens
else if s = tptp_ho_forall orelse s = tptp_ho_exists then
(case ts of
[AAbs (((s', ty), tm), [])] =>
(* Use syntactic sugar "!" and "?" instead of "!!" and "??" whenever possible, to work
around LEO-II, Leo-III, and Satallax parser limitation. *)
tptp_string_of_formula format
(AQuant (if s = tptp_ho_forall then AForall else AExists,
[(s', SOME ty)], AAtom tm))
| _ => app ())
else if s = tptp_choice then
(case ts of
[AAbs (((s', ty), tm), args)] =>
(* There is code in "ATP_Problem_Generate" to ensure that "Eps" is always applied to an
abstraction. *)
tptp_string_of_app format
(tptp_choice ^ "[" ^ s' ^ " : " ^ of_type ty ^
"]: " ^ of_term tm ^ ""
|> parens) (map of_term args)
| _ => app ())
else if member (op =) tptp_unary_builtins s then
(* generate e.g. "~ t" instead of "~ @ t". *)
(case ts of [t] => s ^ " " ^ (of_term t |> parens) |> parens)
else if member (op =) tptp_binary_builtins s then
(* generate e.g. "t1 & t2" instead of "& @ t1 @ t2". *)
(case ts of
[t1, t2] => (of_term t1 |> parens) ^ " " ^ s ^ " " ^ (of_term t2 |> parens) |> parens
| _ => app ())
else
app ()
end
| tptp_string_of_term (format as THF _) (AAbs (((s, ty), tm), args)) =
tptp_string_of_app format
("(^[" ^ s ^ " : " ^ string_of_type format ty ^ "]: " ^
tptp_string_of_term format tm ^ ")")
(map (tptp_string_of_term format) args)
| tptp_string_of_term _ _ =
raise Fail "unexpected term in first-order format"
and tptp_string_of_formula format (ATyQuant (q, xs, phi)) =
tptp_string_of_quantifier q ^
"[" ^
commas (map (suffix_type_of_types o string_of_type format o fst) xs) ^
"]: " ^ tptp_string_of_formula format phi
|> parens
| tptp_string_of_formula format (AQuant (q, xs, phi)) =
tptp_string_of_quantifier q ^
"[" ^ commas (map (string_of_bound_var format) xs) ^ "]: " ^
tptp_string_of_formula format phi
|> parens
| tptp_string_of_formula format
(AConn (ANot, [AAtom (ATerm (("=" (* tptp_equal *), []), ts))])) =
space_implode (" " ^ tptp_not_infix ^ tptp_equal ^ " ")
(map (tptp_string_of_term format) ts)
|> is_format_higher_order format ? parens
| tptp_string_of_formula format (AConn (c, [phi])) =
tptp_string_of_connective c ^ " " ^
(tptp_string_of_formula format phi
|> is_format_higher_order format ? parens)
|> parens
| tptp_string_of_formula format (AConn (c, phis)) =
space_implode (" " ^ tptp_string_of_connective c ^ " ")
(map (tptp_string_of_formula format) phis)
|> parens
| tptp_string_of_formula format (AAtom tm) = tptp_string_of_term format tm
fun tptp_string_of_format CNF = tptp_cnf
| tptp_string_of_format CNF_UEQ = tptp_cnf
| tptp_string_of_format FOF = tptp_fof
| tptp_string_of_format (TFF _) = tptp_tff
| tptp_string_of_format (THF _) = tptp_thf
| tptp_string_of_format (DFG _) = raise Fail "non-TPTP format"
val atype_of_types = AType ((tptp_type_of_types, []), [])
fun nary_type_decl_type n = funpow n (curry AFun atype_of_types) atype_of_types
fun maybe_alt "" = ""
| maybe_alt s = " % " ^ s
fun tptp_string_of_line format (Type_Decl (ident, ty, ary)) =
tptp_string_of_line format (Sym_Decl (ident, ty, nary_type_decl_type ary))
| tptp_string_of_line format (Sym_Decl (ident, sym, ty)) =
tptp_string_of_format format ^ "(" ^ ident ^ ", type,\n " ^ sym ^
" : " ^ string_of_type format ty ^ ").\n"
| tptp_string_of_line format (Formula ((ident, alt), kind, phi, source, info)) =
tptp_string_of_format format ^ "(" ^ ident ^ ", " ^
tptp_string_of_role kind ^ "," ^ "\n (" ^
tptp_string_of_formula format phi ^ ")" ^
(case source of
SOME tm => ", " ^ tptp_string_of_term format tm
| NONE => if null info then "" else ", []") ^
(case info of
[] => ""
| tms => ", [" ^ commas (map (tptp_string_of_term format) tms) ^ "]") ^
")." ^ maybe_alt alt ^ "\n"
fun tptp_lines format =
maps (fn (_, []) => []
| (heading, lines) =>
"\n% " ^ heading ^ " (" ^ string_of_int (length lines) ^ ")\n" ::
map (tptp_string_of_line format) lines)
fun arity_of_type (APi (tys, ty)) =
arity_of_type ty |>> Integer.add (length tys)
| arity_of_type (AFun (_, ty)) = arity_of_type ty ||> Integer.add 1
| arity_of_type _ = (0, 0)
fun string_of_arity (0, n) = string_of_int n
| string_of_arity (m, n) = string_of_int m ^ "+" ^ string_of_int n
val dfg_class_inter = space_implode " & "
fun dfg_string_of_term (ATerm ((s, tys), tms)) =
s ^
(if null tys then ""
else "<" ^ commas (map (string_of_type (DFG Polymorphic)) tys) ^ ">") ^
(if null tms then ""
else "(" ^ commas (map dfg_string_of_term tms) ^ ")")
| dfg_string_of_term _ = raise Fail "unexpected atom in first-order format"
fun dfg_string_of_formula poly gen_simp info =
let
val str_of_typ = string_of_type (DFG poly)
fun str_of_bound_typ (ty, []) = str_of_typ ty
| str_of_bound_typ (ty, cls) = str_of_typ ty ^ " : " ^ dfg_class_inter cls
fun suffix_tag top_level s =
if top_level then
(case extract_isabelle_status info of
SOME s' =>
if s' = non_rec_defN then s ^ ":lt"
else if (s' = simpN orelse s' = rec_defN) andalso gen_simp then s ^ ":lr"
else s
| NONE => s)
else
s
fun str_of_atom top_level (ATerm ((s, tys), tms)) =
let
val s' =
if is_tptp_equal s then "equal" |> suffix_tag top_level
else if s = tptp_true then "true"
else if s = tptp_false then "false"
else s
in dfg_string_of_term (ATerm ((s', tys), tms)) end
| str_of_atom _ _ = raise Fail "unexpected atom in first-order format"
fun str_of_quant AForall = "forall"
| str_of_quant AExists = "exists"
fun str_of_conn _ ANot = "not"
| str_of_conn _ AAnd = "and"
| str_of_conn _ AOr = "or"
| str_of_conn _ AImplies = "implies"
| str_of_conn top_level AIff = "equiv" |> suffix_tag top_level
fun str_of_formula top_level (ATyQuant (q, xs, phi)) =
str_of_quant q ^ "_sorts([" ^ commas (map str_of_bound_typ xs) ^ "], " ^
str_of_formula top_level phi ^ ")"
| str_of_formula top_level (AQuant (q, xs, phi)) =
str_of_quant q ^ "([" ^
commas (map (string_of_bound_var (DFG poly)) xs) ^ "], " ^
str_of_formula top_level phi ^ ")"
| str_of_formula top_level (AConn (c, phis)) =
str_of_conn top_level c ^ "(" ^
commas (map (str_of_formula false) phis) ^ ")"
| str_of_formula top_level (AAtom tm) = str_of_atom top_level tm
in str_of_formula true end
fun maybe_enclose bef aft "" = "% " ^ bef ^ aft
| maybe_enclose bef aft s = bef ^ s ^ aft
fun dfg_lines poly {is_lpo, gen_weights, gen_prec, gen_simp} ord_info problem =
let
val typ = string_of_type (DFG poly)
val term = dfg_string_of_term
fun spair (s, s') = "(" ^ s ^ ", " ^ s' ^ ")"
fun tm_ary sym ty = spair (sym, string_of_arity (arity_of_type ty))
fun ty_ary 0 ty = ty
| ty_ary n ty = "(" ^ ty ^ ", " ^ string_of_int n ^ ")"
fun fun_typ sym ty = "function(" ^ sym ^ ", " ^ typ ty ^ ")."
fun pred_typ sym ty =
let
val (ty_vars, (tys, _)) =
strip_atype ty
|>> (fn [] => [] | xs => ["[" ^ commas xs ^ "]"])
in "predicate(" ^ commas (sym :: ty_vars @ map typ tys) ^ ")." end
fun bound_tvar (ty, []) = ty
| bound_tvar (ty, cls) = ty ^ " : " ^ dfg_class_inter cls
fun binder_typ xs ty =
(if null xs then "" else "[" ^ commas (map bound_tvar xs) ^ "], ") ^
typ ty
fun sort_decl xs ty cl = "sort(" ^ binder_typ xs ty ^ ", " ^ cl ^ ")."
fun datatype_decl xs ty tms exhaust =
"datatype(" ^ commas (binder_typ xs ty :: map term tms @ (if exhaust then [] else ["..."])) ^
")."
fun subclass_of sub super = "subclass(" ^ sub ^ ", " ^ super ^ ")."
fun formula pred (Formula ((ident, alt), kind, phi, _, info)) =
if pred kind then
let val rank = extract_isabelle_rank info in
"formula(" ^ dfg_string_of_formula poly gen_simp info phi ^ ", " ^ ident ^
(if rank = default_rank then "" else ", " ^ string_of_int rank) ^
")." ^ maybe_alt alt
|> SOME
end
else
NONE
| formula _ _ = NONE
fun filt f = problem |> map (map_filter f o snd) |> filter_out null
val func_aries =
filt (fn Sym_Decl (_, sym, ty) =>
if is_function_atype ty then SOME (tm_ary sym ty) else NONE
| _ => NONE)
|> flat |> commas |> maybe_enclose "functions [" "]."
val pred_aries =
filt (fn Sym_Decl (_, sym, ty) =>
if is_predicate_atype ty then SOME (tm_ary sym ty) else NONE
| _ => NONE)
|> flat |> commas |> maybe_enclose "predicates [" "]."
val sorts =
filt (try (fn Type_Decl (_, ty, ary) => ty_ary ary ty)) @
[[ty_ary 0 dfg_individual_type]]
|> flat |> commas |> maybe_enclose "sorts [" "]."
val classes =
filt (try (fn Class_Decl (_, cl, _) => cl))
|> flat |> commas |> maybe_enclose "classes [" "]."
val ord_info = if gen_weights orelse gen_prec then ord_info () else []
val do_term_order_weights =
(if gen_weights then ord_info else [])
|> map (spair o apsnd string_of_int) |> commas
|> maybe_enclose "weights [" "]."
val syms = [func_aries, pred_aries, do_term_order_weights, sorts, classes]
val func_decls =
filt (fn Sym_Decl (_, sym, ty) =>
if is_function_atype ty then SOME (fun_typ sym ty) else NONE
| _ => NONE) |> flat
val pred_decls =
filt (fn Sym_Decl (_, sym, ty) =>
if is_nontrivial_predicate_atype ty then SOME (pred_typ sym ty)
else NONE
| _ => NONE) |> flat
val datatype_decls =
filt (try (fn Datatype_Decl (_, xs, ty, tms, exhaust) => datatype_decl xs ty tms exhaust))
|> flat
val sort_decls =
filt (try (fn Class_Memb (_, xs, ty, cl) => sort_decl xs ty cl)) |> flat
val subclass_decls =
filt (try (fn Class_Decl (_, sub, supers) =>
map (subclass_of sub) supers))
|> flat |> flat
val decls =
func_decls @ pred_decls @ datatype_decls @ sort_decls @ subclass_decls
val axioms =
filt (formula (curry (op <>) Conjecture)) |> separate [""] |> flat
val conjs =
filt (formula (curry (op =) Conjecture)) |> separate [""] |> flat
val settings =
(if is_lpo then ["set_flag(Ordering, 1)."] else []) @
(if gen_prec then
[ord_info |> map fst |> rev |> commas
|> maybe_enclose "set_precedence(" ")."]
else
[])
fun list_of _ [] = []
| list_of heading ss =
"list_of_" ^ heading ^ ".\n" :: map (suffix "\n") ss @
["end_of_list.\n\n"]
in
"\nbegin_problem(isabelle).\n\n" ::
list_of "descriptions"
["name({**}).", "author({**}).", "status(unknown).",
"description({**})."] @
list_of "symbols" syms @
list_of "declarations" decls @
list_of "formulae(axioms)" axioms @
list_of "formulae(conjectures)" conjs @
list_of "settings(SPASS)" settings @
["end_problem.\n"]
end
fun lines_of_atp_problem format ord ord_info problem =
"% This file was generated by Isabelle (most likely Sledgehammer)\n\
\% " ^ timestamp () ^ "\n" ::
(case format of
DFG poly => dfg_lines poly ord ord_info
| _ => tptp_lines format) problem
(** CNF (Metis) and CNF UEQ (Waldmeister) **)
fun is_line_negated (Formula (_, _, AConn (ANot, _), _, _)) = true
| is_line_negated _ = false
fun is_line_cnf_ueq (Formula (_, _, AAtom (ATerm (((s, _), _), _)), _, _)) =
is_tptp_equal s
| is_line_cnf_ueq _ = false
fun open_conjecture_term (ATerm (((s, s'), tys), tms)) =
ATerm ((if is_tptp_variable s then (s |> Name.desymbolize (SOME false), s')
else (s, s'), tys), tms |> map open_conjecture_term)
| open_conjecture_term _ = raise Fail "unexpected higher-order term"
fun open_formula conj =
let
(* We are conveniently assuming that all bound variable names are
distinct, which should be the case for the formulas we generate. *)
fun opn (pos as SOME true) (AQuant (AForall, _, phi)) = opn pos phi
| opn (pos as SOME false) (AQuant (AExists, _, phi)) = opn pos phi
| opn pos (AConn (ANot, [phi])) = mk_anot (opn (Option.map not pos) phi)
| opn pos (AConn (c, [phi1, phi2])) =
let val (pos1, pos2) = polarities_of_conn pos c in
AConn (c, [opn pos1 phi1, opn pos2 phi2])
end
| opn _ (AAtom t) = AAtom (t |> conj ? open_conjecture_term)
| opn _ phi = phi
in opn (SOME (not conj)) end
fun open_formula_line (Formula (ident, kind, phi, source, info)) =
Formula (ident, kind, open_formula (kind = Conjecture) phi, source, info)
| open_formula_line line = line
fun negate_conjecture_line (Formula (ident, Conjecture, phi, source, info)) =
Formula (ident, Hypothesis, mk_anot phi, source, info)
| negate_conjecture_line line = line
exception CLAUSIFY of unit
(* This "clausification" only expands syntactic sugar, such as "phi => psi" to
"~ phi | psi" and "phi <=> psi" to "~ phi | psi" and "~ psi | phi". We don't
attempt to distribute conjunctions over disjunctions. *)
fun clausify_formula pos (phi as AAtom _) = [phi |> not pos ? mk_anot]
| clausify_formula pos (AConn (ANot, [phi])) = clausify_formula (not pos) phi
| clausify_formula true (AConn (AOr, [phi1, phi2])) =
(phi1, phi2) |> apply2 (clausify_formula true)
|> uncurry (map_product (mk_aconn AOr))
| clausify_formula false (AConn (AAnd, [phi1, phi2])) =
(phi1, phi2) |> apply2 (clausify_formula false)
|> uncurry (map_product (mk_aconn AOr))
| clausify_formula true (AConn (AImplies, [phi1, phi2])) =
clausify_formula true (AConn (AOr, [mk_anot phi1, phi2]))
| clausify_formula true (AConn (AIff, phis)) =
clausify_formula true (AConn (AImplies, phis)) @
clausify_formula true (AConn (AImplies, rev phis))
| clausify_formula _ _ = raise CLAUSIFY ()
fun clausify_formula_line (Formula ((ident, alt), kind, phi, source, info)) =
let
val (n, phis) = phi |> try (clausify_formula true) |> these |> `length
in
map2 (fn phi => fn j =>
Formula ((ident ^ replicate_string (j - 1) "x", alt), kind, phi,
source, info))
phis (1 upto n)
end
| clausify_formula_line _ = []
fun ensure_cnf_line line =
line |> open_formula_line |> negate_conjecture_line |> clausify_formula_line
fun ensure_cnf_problem problem = problem |> map (apsnd (maps ensure_cnf_line))
fun filter_cnf_ueq_problem problem =
problem
|> map (apsnd (map open_formula_line #> filter is_line_cnf_ueq
#> map negate_conjecture_line))
|> (fn problem =>
let
val lines = problem |> maps snd
val conjs = lines |> filter is_line_negated
in if length conjs = 1 andalso conjs <> lines then problem else [] end)
(** Symbol declarations **)
fun add_declared_in_line (Class_Decl (_, cl, _)) = apfst (apfst (cons cl))
| add_declared_in_line (Type_Decl (_, ty, _)) = apfst (apsnd (cons ty))
| add_declared_in_line (Sym_Decl (_, sym, _)) = apsnd (cons sym)
| add_declared_in_line _ = I
fun declared_in_atp_problem problem =
fold (fold add_declared_in_line o snd) problem (([], []), [])
(** Nice names **)
val no_qualifiers =
let
fun skip [] = []
| skip (#"." :: cs) = skip cs
| skip (c :: cs) = if Char.isAlphaNum c then skip cs else c :: keep cs
and keep [] = []
| keep (#"." :: cs) = skip cs
| keep (c :: cs) = c :: keep cs
in String.explode #> rev #> keep #> rev #> String.implode end
(* Long names can slow down the ATPs. *)
val max_readable_name_size = 20
(* "equal" is reserved by some ATPs. "op" is also reserved, to avoid the
unreadable "op_1", "op_2", etc., in the problem files. "eq" is reserved to
ensure that "HOL.eq" is correctly mapped to equality (not clear whether this
is still necessary). *)
val reserved_nice_names = [tptp_old_equal, "op", "eq"]
(* hack to get the same hashing across Mirabelle runs (see "mirabelle.pl") *)
fun cleanup_mirabelle_name s =
let
val mirabelle_infix = "_Mirabelle_"
val random_suffix_len = 10
val (s1, s2) = Substring.position mirabelle_infix (Substring.full s)
in
if Substring.isEmpty s2 then
s
else
Substring.string s1 ^
Substring.string (Substring.triml (size mirabelle_infix + random_suffix_len) s2)
end
fun readable_name protect full_name s =
(if s = full_name then
s
else
s |> no_qualifiers
|> unquote_tvar
|> Name.desymbolize (SOME (Char.isUpper (String.sub (full_name, 0))))
|> (fn s =>
if size s > max_readable_name_size then
String.substring (s, 0, max_readable_name_size div 2 - 4) ^
string_of_int (hash_string (cleanup_mirabelle_name full_name)) ^
String.extract (s, size s - max_readable_name_size div 2 + 4, NONE)
else
s)
|> (fn s =>
if member (op =) reserved_nice_names s then full_name else s))
|> protect
fun nice_name _ (full_name, _) NONE = (full_name, NONE)
| nice_name protect (full_name, desired_name) (SOME the_pool) =
if is_built_in_tptp_symbol full_name then
(full_name, SOME the_pool)
else
(case Symtab.lookup (fst the_pool) full_name of
SOME nice_name => (nice_name, SOME the_pool)
| NONE =>
let
val nice_prefix = readable_name protect full_name desired_name
fun add j =
let
val nice_name = nice_prefix ^ (if j = 1 then "" else string_of_int j)
in
(case Symtab.lookup (snd the_pool) nice_name of
SOME full_name' =>
if full_name = full_name' then (nice_name, the_pool) else add (j + 1)
| NONE =>
(nice_name,
(Symtab.update_new (full_name, nice_name) (fst the_pool),
Symtab.update_new (nice_name, full_name) (snd the_pool))))
end
in add 1 |> apsnd SOME end)
fun avoid_clash_with_dfg_keywords s =
let val n = String.size s in
if n < 2 orelse (n = 2 andalso String.sub (s, 0) = String.sub (s, 1)) orelse
String.isSubstring "_" s then
s
else if is_tptp_variable s then
s ^ "_"
else
String.substring (s, 0, n - 1) ^
String.str (Char.toUpper (String.sub (s, n - 1)))
end
fun nice_atp_problem readable_names format problem =
let
val empty_pool =
if readable_names then SOME (Symtab.empty, Symtab.empty) else NONE
val avoid_clash =
(case format of
DFG _ => avoid_clash_with_dfg_keywords
| _ => I)
val nice_name = nice_name avoid_clash
fun nice_bound_tvars xs =
fold_map (nice_name o fst) xs
##>> fold_map (fold_map nice_name o snd) xs
#>> op ~~
fun nice_type (AType ((name, clss), tys)) =
nice_name name ##>> fold_map nice_name clss ##>> fold_map nice_type tys #>> AType
| nice_type (AFun (ty1, ty2)) = nice_type ty1 ##>> nice_type ty2 #>> AFun
| nice_type (APi (names, ty)) = fold_map nice_name names ##>> nice_type ty #>> APi
fun nice_term (ATerm ((name, tys), ts)) =
nice_name name ##>> fold_map nice_type tys ##>> fold_map nice_term ts #>> ATerm
| nice_term (AAbs (((name, ty), tm), args)) =
nice_name name ##>> nice_type ty ##>> nice_term tm ##>> fold_map nice_term args #>> AAbs
fun nice_formula (ATyQuant (q, xs, phi)) =
fold_map (nice_type o fst) xs
##>> fold_map (fold_map nice_name o snd) xs
##>> nice_formula phi
#>> (fn ((tys, cls), phi) => ATyQuant (q, tys ~~ cls, phi))
| nice_formula (AQuant (q, xs, phi)) =
fold_map (nice_name o fst) xs
##>> fold_map (fn (_, NONE) => pair NONE
| (_, SOME ty) => nice_type ty #>> SOME) xs
##>> nice_formula phi
#>> (fn ((ss, ts), phi) => AQuant (q, ss ~~ ts, phi))
| nice_formula (AConn (c, phis)) =
fold_map nice_formula phis #>> curry AConn c
| nice_formula (AAtom tm) = nice_term tm #>> AAtom
fun nice_line (Class_Decl (ident, cl, cls)) =
nice_name cl ##>> fold_map nice_name cls
#>> (fn (cl, cls) => Class_Decl (ident, cl, cls))
| nice_line (Type_Decl (ident, ty, ary)) =
nice_name ty #>> (fn ty => Type_Decl (ident, ty, ary))
| nice_line (Sym_Decl (ident, sym, ty)) =
nice_name sym ##>> nice_type ty #>> (fn (sym, ty) => Sym_Decl (ident, sym, ty))
| nice_line (Datatype_Decl (ident, xs, ty, tms, exhaust)) =
nice_bound_tvars xs ##>> nice_type ty ##>> fold_map nice_term tms
#>> (fn ((xs, ty), tms) => Datatype_Decl (ident, xs, ty, tms, exhaust))
| nice_line (Class_Memb (ident, xs, ty, cl)) =
nice_bound_tvars xs ##>> nice_type ty ##>> nice_name cl
#>> (fn ((xs, ty), cl) => Class_Memb (ident, xs, ty, cl))
| nice_line (Formula (ident, kind, phi, source, info)) =
nice_formula phi #>> (fn phi => Formula (ident, kind, phi, source, info))
fun nice_problem problem =
fold_map (fn (heading, lines) => fold_map nice_line lines #>> pair heading) problem
in
nice_problem problem empty_pool
end
end;
¤ Dauer der Verarbeitung: 0.86 Sekunden
(vorverarbeitet)
¤
|
Haftungshinweis
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
|
