extend ATP data structure to avoid having to perform ((non-)capture avoiding) beta reduction -- fixes a bug in the THF translation of "is_measure.simps"
(* 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) ho_term =
ATerm of 'a * ('a, 'b) ho_term list |
AAbs of (('a * 'b) * ('a, 'b) ho_term) * ('a, 'b) ho_term list
datatype quantifier = AForall | AExists
datatype connective = ANot | AAnd | AOr | AImplies | AIff
datatype ('a, 'b, 'c) formula =
AQuant of quantifier * ('a * 'b option) list * ('a, 'b, 'c) formula |
AConn of connective * ('a, 'b, 'c) formula list |
AAtom of 'c
datatype 'a ho_type =
AType of 'a * 'a ho_type list |
AFun of 'a ho_type * 'a ho_type |
ATyAbs of 'a list * 'a ho_type
type term_order =
{is_lpo : bool,
gen_weights : bool,
gen_prec : bool,
gen_simp : bool}
datatype tptp_polymorphism = TPTP_Monomorphic | TPTP_Polymorphic
datatype tptp_explicitness = TPTP_Implicit | TPTP_Explicit
datatype thf_flavor = THF_Without_Choice | THF_With_Choice
datatype dfg_flavor = DFG_Unsorted | DFG_Sorted
datatype atp_format =
CNF |
CNF_UEQ |
FOF |
TFF of tptp_polymorphism * tptp_explicitness |
THF of tptp_polymorphism * tptp_explicitness * thf_flavor |
DFG of dfg_flavor
datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture
datatype 'a problem_line =
Decl of string * 'a * 'a ho_type |
Formula of string * formula_kind
* ('a, 'a ho_type, ('a, 'a ho_type) ho_term) formula
* (string, string ho_type) ho_term option
* (string, string ho_type) ho_term list
type 'a problem = (string * 'a 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_not : string
val tptp_and : string
val tptp_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_old_equal : string
val tptp_false : string
val tptp_true : string
val tptp_empty_list : string
val isabelle_info_prefix : string
val isabelle_info : string -> int -> (string, 'a) ho_term list
val extract_isabelle_status : (string, 'a) ho_term list -> string option
val extract_isabelle_rank : (string, 'a) ho_term list -> int
val introN : string
val inductiveN : string
val elimN : string
val simpN : string
val 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 atype_of_types : (string * string) ho_type
val bool_atype : (string * string) ho_type
val individual_atype : (string * string) ho_type
val mk_anot : ('a, 'b, 'c) formula -> ('a, 'b, 'c) formula
val mk_aconn :
connective -> ('a, 'b, 'c) formula -> ('a, 'b, 'c) formula
-> ('a, 'b, 'c) formula
val aconn_fold :
bool option -> (bool option -> 'a -> 'b -> 'b) -> connective * 'a list
-> 'b -> 'b
val aconn_map :
bool option -> (bool option -> 'a -> ('b, 'c, 'd) formula)
-> connective * 'a list -> ('b, 'c, 'd) formula
val formula_fold :
bool option -> (bool option -> 'c -> 'd -> 'd) -> ('a, 'b, 'c) formula
-> 'd -> 'd
val formula_map : ('c -> 'd) -> ('a, 'b, 'c) formula -> ('a, 'b, 'd) formula
val is_function_type : string ho_type -> bool
val is_predicate_type : string ho_type -> bool
val is_format_higher_order : atp_format -> bool
val lines_for_atp_problem :
atp_format -> term_order -> (unit -> (string * int) list) -> string problem
-> string list
val ensure_cnf_problem :
(string * string) problem -> (string * string) problem
val filter_cnf_ueq_problem :
(string * string) problem -> (string * string) problem
val declared_syms_in_problem : 'a problem -> 'a list
val nice_atp_problem :
bool -> atp_format -> ('a * (string * string) problem_line list) list
-> ('a * string problem_line list) list
* (string Symtab.table * string Symtab.table) option
end;
structure ATP_Problem : ATP_PROBLEM =
struct
open ATP_Util
(** ATP problem **)
datatype ('a, 'b) ho_term =
ATerm of 'a * ('a, 'b) ho_term list |
AAbs of (('a * 'b) * ('a, 'b) ho_term) * ('a, 'b) ho_term list
datatype quantifier = AForall | AExists
datatype connective = ANot | AAnd | AOr | AImplies | AIff
datatype ('a, 'b, 'c) formula =
AQuant of quantifier * ('a * 'b option) list * ('a, 'b, 'c) formula |
AConn of connective * ('a, 'b, 'c) formula list |
AAtom of 'c
datatype 'a ho_type =
AType of 'a * 'a ho_type list |
AFun of 'a ho_type * 'a ho_type |
ATyAbs of 'a list * 'a ho_type
type term_order =
{is_lpo : bool,
gen_weights : bool,
gen_prec : bool,
gen_simp : bool}
datatype tptp_polymorphism = TPTP_Monomorphic | TPTP_Polymorphic
datatype tptp_explicitness = TPTP_Implicit | TPTP_Explicit
datatype thf_flavor = THF_Without_Choice | THF_With_Choice
datatype dfg_flavor = DFG_Unsorted | DFG_Sorted
datatype atp_format =
CNF |
CNF_UEQ |
FOF |
TFF of tptp_polymorphism * tptp_explicitness |
THF of tptp_polymorphism * tptp_explicitness * thf_flavor |
DFG of dfg_flavor
datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture
datatype 'a problem_line =
Decl of string * 'a * 'a ho_type |
Formula of string * formula_kind
* ('a, 'a ho_type, ('a, 'a ho_type) ho_term) formula
* (string, string ho_type) ho_term option
* (string, string ho_type) ho_term list
type 'a problem = (string * 'a 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 = "$i"
val tptp_fun_type = ">"
val tptp_product_type = "*"
val tptp_forall = "!"
val tptp_ho_forall = "!!"
val tptp_pi_binder = "!>"
val tptp_exists = "?"
val tptp_ho_exists = "??"
val tptp_choice = "@+"
val tptp_not = "~"
val tptp_and = "&"
val tptp_or = "|"
val tptp_implies = "=>"
val tptp_if = "<="
val tptp_iff = "<=>"
val tptp_not_iff = "<~>"
val tptp_app = "@"
val tptp_not_infix = "!"
val tptp_equal = "="
val tptp_old_equal = "equal"
val tptp_false = "$false"
val tptp_true = "$true"
val tptp_empty_list = "[]"
val isabelle_info_prefix = "isabelle_"
val introN = "intro"
val inductiveN = "inductive"
val elimN = "elim"
val simpN = "simp"
val defN = "def"
val rankN = "rank"
val minimum_rank = 0
val default_rank = 1000
val default_term_order_weight = 1
(* Currently, only newer versions of SPASS, with sorted DFG format support, can
process Isabelle metainformation. *)
fun isabelle_info status rank =
[] |> rank <> default_rank
? cons (ATerm (isabelle_info_prefix ^ rankN,
[ATerm (string_of_int rank, [])]))
|> status <> "" ? cons (ATerm (isabelle_info_prefix ^ status, []))
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 = Char.isUpper (String.sub (s, 0))
val is_tptp_user_symbol = not o (is_tptp_variable orf is_built_in_tptp_symbol)
val atype_of_types = AType (`I tptp_type_of_types, [])
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 ? pairself (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 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 (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 (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
| formula_map f (AAtom tm) = AAtom (f tm)
fun is_function_type (AFun (_, ty)) = is_function_type ty
| is_function_type (AType (s, _)) =
s <> tptp_type_of_types andalso s <> tptp_bool_type
| is_function_type _ = false
fun is_predicate_type (AFun (_, ty)) = is_predicate_type ty
| is_predicate_type (AType (s, _)) = (s = tptp_bool_type)
| is_predicate_type _ = false
fun is_nontrivial_predicate_type (AFun (_, ty)) = is_predicate_type ty
| is_nontrivial_predicate_type _ = false
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 DFG_Sorted) = true
| is_format_typed _ = false
fun tptp_string_for_kind Axiom = "axiom"
| tptp_string_for_kind Definition = "definition"
| tptp_string_for_kind Lemma = "lemma"
| tptp_string_for_kind Hypothesis = "hypothesis"
| tptp_string_for_kind Conjecture = "conjecture"
fun tptp_string_for_app format func args =
if is_format_higher_order format then
"(" ^ space_implode (" " ^ tptp_app ^ " ") (func :: args) ^ ")"
else
func ^ "(" ^ commas args ^ ")"
fun flatten_type (ATyAbs (tys, ty)) = ATyAbs (tys, flatten_type ty)
| flatten_type (ty as AFun (ty1 as AType _, ty2)) =
(case flatten_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)
| flatten_type (ty as AType _) = ty
| flatten_type _ =
raise Fail "unexpected higher-order type in first-order format"
val dfg_individual_type = "iii" (* cannot clash *)
fun str_for_type format ty =
let
val dfg = (format = DFG DFG_Sorted)
fun str _ (AType (s, [])) =
if dfg andalso s = tptp_individual_type then dfg_individual_type else s
| str _ (AType (s, tys)) =
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) ? enclose "(" ")"
else
tptp_string_for_app format s ss
end
| str rhs (AFun (ty1, ty2)) =
(str false ty1 |> dfg ? enclose "(" ")") ^ " " ^
(if dfg then "" else tptp_fun_type ^ " ") ^ str true ty2
|> not rhs ? enclose "(" ")"
| str _ (ATyAbs (ss, ty)) =
tptp_pi_binder ^ "[" ^
commas (map (suffix (" " ^ tptp_has_type ^ " " ^ tptp_type_of_types))
ss) ^ "]: " ^ str false ty
in str true ty end
fun string_for_type (format as THF _) ty = str_for_type format ty
| string_for_type format ty = str_for_type format (flatten_type ty)
fun tptp_string_for_quantifier AForall = tptp_forall
| tptp_string_for_quantifier AExists = tptp_exists
fun tptp_string_for_connective ANot = tptp_not
| tptp_string_for_connective AAnd = tptp_and
| tptp_string_for_connective AOr = tptp_or
| tptp_string_for_connective AImplies = tptp_implies
| tptp_string_for_connective AIff = tptp_iff
fun string_for_bound_var format (s, ty) =
s ^
(if is_format_typed format then
" " ^ tptp_has_type ^ " " ^
(ty |> the_default (AType (tptp_individual_type, []))
|> string_for_type format)
else
"")
fun is_format_with_choice (THF (_, _, THF_With_Choice)) = true
| is_format_with_choice _ = false
fun tptp_string_for_term _ (ATerm (s, [])) = s
| tptp_string_for_term format (ATerm (s, ts)) =
(if s = tptp_empty_list then
(* used for lists in the optional "source" field of a derivation *)
"[" ^ commas (map (tptp_string_for_term format) ts) ^ "]"
else if is_tptp_equal s then
space_implode (" " ^ tptp_equal ^ " ")
(map (tptp_string_for_term format) ts)
|> is_format_higher_order format ? enclose "(" ")"
else case (s = tptp_ho_forall orelse s = tptp_ho_exists,
s = tptp_choice andalso is_format_with_choice format, ts) of
(true, _, [AAbs (((s', ty), tm), [])]) =>
(* Use syntactic sugar "!" and "?" instead of "!!" and "??" whenever
possible, to work around LEO-II 1.2.8 parser limitation. *)
tptp_string_for_formula format
(AQuant (if s = tptp_ho_forall then AForall else AExists,
[(s', SOME ty)], AAtom tm))
| (_, true, [AAbs (((s', ty), tm), args)]) =>
(* There is code in "ATP_Problem_Generate" to ensure that "Eps" is always
applied to an abstraction. *)
tptp_string_for_app format
(tptp_choice ^ "[" ^ s' ^ " : " ^ string_for_type format ty ^ "]: " ^
tptp_string_for_term format tm ^ ""
|> enclose "(" ")")
(map (tptp_string_for_term format) args)
| _ => tptp_string_for_app format s (map (tptp_string_for_term format) ts))
| tptp_string_for_term (format as THF _) (AAbs (((s, ty), tm), args)) =
tptp_string_for_app format
("(^[" ^ s ^ " : " ^ string_for_type format ty ^ "]: " ^
tptp_string_for_term format tm ^ ")")
(map (tptp_string_for_term format) args)
| tptp_string_for_term _ _ =
raise Fail "unexpected term in first-order format"
and tptp_string_for_formula format (AQuant (q, xs, phi)) =
tptp_string_for_quantifier q ^
"[" ^ commas (map (string_for_bound_var format) xs) ^ "]: " ^
tptp_string_for_formula format phi
|> enclose "(" ")"
| tptp_string_for_formula format
(AConn (ANot, [AAtom (ATerm ("=" (* tptp_equal *), ts))])) =
space_implode (" " ^ tptp_not_infix ^ tptp_equal ^ " ")
(map (tptp_string_for_term format) ts)
|> is_format_higher_order format ? enclose "(" ")"
| tptp_string_for_formula format (AConn (c, [phi])) =
tptp_string_for_connective c ^ " " ^
(tptp_string_for_formula format phi
|> is_format_higher_order format ? enclose "(" ")")
|> enclose "(" ")"
| tptp_string_for_formula format (AConn (c, phis)) =
space_implode (" " ^ tptp_string_for_connective c ^ " ")
(map (tptp_string_for_formula format) phis)
|> enclose "(" ")"
| tptp_string_for_formula format (AAtom tm) = tptp_string_for_term format tm
fun tptp_string_for_format CNF = tptp_cnf
| tptp_string_for_format CNF_UEQ = tptp_cnf
| tptp_string_for_format FOF = tptp_fof
| tptp_string_for_format (TFF _) = tptp_tff
| tptp_string_for_format (THF _) = tptp_thf
| tptp_string_for_format (DFG _) = raise Fail "non-TPTP format"
fun tptp_string_for_problem_line format (Decl (ident, sym, ty)) =
tptp_string_for_format format ^ "(" ^ ident ^ ", type,\n " ^ sym ^
" : " ^ string_for_type format ty ^ ").\n"
| tptp_string_for_problem_line format
(Formula (ident, kind, phi, source, _)) =
tptp_string_for_format format ^ "(" ^ ident ^ ", " ^
tptp_string_for_kind kind ^ ",\n (" ^
tptp_string_for_formula format phi ^ ")" ^
(case source of
SOME tm => ", " ^ tptp_string_for_term format tm
| NONE => "") ^ ").\n"
fun tptp_lines format =
maps (fn (_, []) => []
| (heading, lines) =>
"\n% " ^ heading ^ " (" ^ string_of_int (length lines) ^ ")\n" ::
map (tptp_string_for_problem_line format) lines)
fun arity_of_type (AFun (_, ty)) = 1 + arity_of_type ty
| arity_of_type _ = 0
fun binder_atypes (AFun (ty1, ty2)) = ty1 :: binder_atypes ty2
| binder_atypes _ = []
fun dfg_string_for_formula gen_simp flavor info =
let
fun suffix_tag top_level s =
if flavor = DFG_Sorted andalso top_level then
case extract_isabelle_status info of
SOME s' => if s' = defN then s ^ ":lt"
else if s' = simpN andalso gen_simp then s ^ ":lr"
else s
| NONE => s
else
s
fun str_for_term top_level (ATerm (s, tms)) =
(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) ^
(if null tms then ""
else "(" ^ commas (map (str_for_term false) tms) ^ ")")
| str_for_term _ _ = raise Fail "unexpected term in first-order format"
fun str_for_quant AForall = "forall"
| str_for_quant AExists = "exists"
fun str_for_conn _ ANot = "not"
| str_for_conn _ AAnd = "and"
| str_for_conn _ AOr = "or"
| str_for_conn _ AImplies = "implies"
| str_for_conn top_level AIff = "equiv" |> suffix_tag top_level
fun str_for_formula top_level (AQuant (q, xs, phi)) =
str_for_quant q ^ "(" ^ "[" ^
commas (map (string_for_bound_var (DFG flavor)) xs) ^ "], " ^
str_for_formula top_level phi ^ ")"
| str_for_formula top_level (AConn (c, phis)) =
str_for_conn top_level c ^ "(" ^
commas (map (str_for_formula false) phis) ^ ")"
| str_for_formula top_level (AAtom tm) = str_for_term top_level tm
in str_for_formula true end
fun maybe_enclose bef aft "" = "% " ^ bef ^ aft
| maybe_enclose bef aft s = bef ^ s ^ aft
fun dfg_lines flavor {is_lpo, gen_weights, gen_prec, gen_simp} ord_info
problem =
let
val sorted = (flavor = DFG_Sorted)
val format = DFG flavor
fun spair (sym, k) = "(" ^ sym ^ ", " ^ string_of_int k ^ ")"
fun ary sym = curry spair sym o arity_of_type
fun fun_typ sym ty =
"function(" ^ sym ^ ", " ^ string_for_type format ty ^ ")."
fun pred_typ sym ty =
"predicate(" ^
commas (sym :: map (string_for_type format) (binder_atypes ty)) ^ ")."
fun formula pred (Formula (ident, kind, phi, _, info)) =
if pred kind then
let
val rank =
if flavor = DFG_Sorted then extract_isabelle_rank info
else default_rank
in
"formula(" ^ dfg_string_for_formula gen_simp flavor info phi ^
", " ^ ident ^
(if rank = default_rank then "" else ", " ^ string_of_int rank) ^
")." |> SOME
end
else
NONE
| formula _ _ = NONE
fun filt f = problem |> map (map_filter f o snd) |> filter_out null
val func_aries =
filt (fn Decl (_, sym, ty) =>
if is_function_type ty then SOME (ary sym ty) else NONE
| _ => NONE)
|> flat |> commas |> maybe_enclose "functions [" "]."
val pred_aries =
filt (fn Decl (_, sym, ty) =>
if is_predicate_type ty then SOME (ary sym ty) else NONE
| _ => NONE)
|> flat |> commas |> maybe_enclose "predicates [" "]."
fun sorts () =
filt (fn Decl (_, sym, AType (s, [])) =>
if s = tptp_type_of_types then SOME sym else NONE
| _ => NONE) @ [[dfg_individual_type]]
|> flat |> commas |> maybe_enclose "sorts [" "]."
val ord_info =
if sorted andalso (gen_weights orelse gen_prec) then ord_info () else []
fun do_term_order_weights () =
(if gen_weights then ord_info else [])
|> map spair |> commas |> maybe_enclose "weights [" "]."
val syms =
[func_aries, pred_aries] @
(if sorted then [do_term_order_weights (), sorts ()] else [])
fun func_sigs () =
filt (fn Decl (_, sym, ty) =>
if is_function_type ty then SOME (fun_typ sym ty) else NONE
| _ => NONE)
|> flat
fun pred_sigs () =
filt (fn Decl (_, sym, ty) =>
if is_nontrivial_predicate_type ty then SOME (pred_typ sym ty)
else NONE
| _ => NONE)
|> flat
val decls = if sorted then func_sigs () @ pred_sigs () else []
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_for_atp_problem format ord ord_info problem =
"% This file was generated by Isabelle (most likely Sledgehammer)\n\
\% " ^ timestamp () ^ "\n" ::
(case format of
DFG flavor => dfg_lines flavor ord ord_info
| _ => tptp_lines format) problem
(** CNF (Metis) and CNF UEQ (Waldmeister) **)
fun is_problem_line_negated (Formula (_, _, AConn (ANot, _), _, _)) = true
| is_problem_line_negated _ = false
fun is_problem_line_cnf_ueq (Formula (_, _, AAtom (ATerm ((s, _), _)), _, _)) =
is_tptp_equal s
| is_problem_line_cnf_ueq _ = false
fun open_conjecture_term (ATerm ((s, s'), tms)) =
ATerm (if is_tptp_variable s then (s |> Name.desymbolize false, s')
else (s, s'), 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) |> pairself (clausify_formula true)
|> uncurry (map_product (mk_aconn AOr))
| clausify_formula false (AConn (AAnd, [phi1, phi2])) =
(phi1, phi2) |> pairself (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, 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", kind, phi, source,
info))
phis (1 upto n)
end
| clausify_formula_line _ = []
fun ensure_cnf_problem_line line =
line |> open_formula_line |> negate_conjecture_line |> clausify_formula_line
fun ensure_cnf_problem problem =
problem |> map (apsnd (maps ensure_cnf_problem_line))
fun filter_cnf_ueq_problem problem =
problem
|> map (apsnd (map open_formula_line
#> filter is_problem_line_cnf_ueq
#> map negate_conjecture_line))
|> (fn problem =>
let
val lines = problem |> maps snd
val conjs = lines |> filter is_problem_line_negated
in if length conjs = 1 andalso conjs <> lines then problem else [] end)
(** Symbol declarations **)
fun add_declared_syms_in_problem_line (Decl (_, sym, _)) = cons sym
| add_declared_syms_in_problem_line _ = I
fun declared_syms_in_problem problem =
fold (fold add_declared_syms_in_problem_line o snd) problem []
(** Nice names **)
fun pool_fold f xs z = pair z #> fold_rev (fn x => uncurry (f x)) xs
fun pool_map f xs =
pool_fold (fn x => fn ys => fn pool => f x pool |>> (fn y => y :: ys)) xs []
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
|> perhaps (try (unprefix "'"))
|> Name.desymbolize (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_alt_ergo_type_vars s =
if is_tptp_variable s then s else s ^ "_"
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
(* "DL" appears to be a SPASS 3.7 keyword *)
if s = "DL" then s ^ "_" else 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
TFF (TPTP_Polymorphic, _) => avoid_clash_with_alt_ergo_type_vars
| DFG _ => avoid_clash_with_dfg_keywords
| _ => I
val nice_name = nice_name avoid_clash
fun nice_type (AType (name, tys)) =
nice_name name ##>> pool_map nice_type tys #>> AType
| nice_type (AFun (ty1, ty2)) = nice_type ty1 ##>> nice_type ty2 #>> AFun
| nice_type (ATyAbs (names, ty)) =
pool_map nice_name names ##>> nice_type ty #>> ATyAbs
fun nice_term (ATerm (name, ts)) =
nice_name name ##>> pool_map nice_term ts #>> ATerm
| nice_term (AAbs (((name, ty), tm), args)) =
nice_name name ##>> nice_type ty ##>> nice_term tm
##>> pool_map nice_term args #>> AAbs
fun nice_formula (AQuant (q, xs, phi)) =
pool_map nice_name (map fst xs)
##>> pool_map (fn NONE => pair NONE
| SOME ty => nice_type ty #>> SOME) (map snd xs)
##>> nice_formula phi
#>> (fn ((ss, ts), phi) => AQuant (q, ss ~~ ts, phi))
| nice_formula (AConn (c, phis)) =
pool_map nice_formula phis #>> curry AConn c
| nice_formula (AAtom tm) = nice_term tm #>> AAtom
fun nice_problem_line (Decl (ident, sym, ty)) =
nice_name sym ##>> nice_type ty #>> (fn (sym, ty) => Decl (ident, sym, ty))
| nice_problem_line (Formula (ident, kind, phi, source, info)) =
nice_formula phi #>> (fn phi => Formula (ident, kind, phi, source, info))
fun nice_problem problem =
pool_map (fn (heading, lines) =>
pool_map nice_problem_line lines #>> pair heading) problem
in nice_problem problem empty_pool end
end;