(* 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
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
datatype tptp_polymorphism = TPTP_Monomorphic | TPTP_Polymorphic
datatype tptp_explicitness = TPTP_Implicit | TPTP_Explicit
datatype thf_flavor = THF_Without_Choice | THF_With_Choice
datatype atp_format =
CNF |
CNF_UEQ |
FOF |
TFF of tptp_polymorphism * tptp_explicitness |
THF of tptp_polymorphism * tptp_explicitness * thf_flavor |
DFG_Sorted
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 option
type 'a problem = (string * 'a problem_line list) list
val isabelle_info_prefix : string
val isabelle_info : atp_format -> string -> (string, 'a) ho_term option
val introN : string
val elimN : string
val simpN : string
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 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_format_thf : atp_format -> bool
val is_format_typed : atp_format -> bool
val lines_for_atp_problem : atp_format -> 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 declare_undeclared_syms_in_atp_problem :
string -> string -> (string * string) problem -> (string * string) problem
val nice_atp_problem :
bool -> ('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
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
datatype tptp_polymorphism = TPTP_Monomorphic | TPTP_Polymorphic
datatype tptp_explicitness = TPTP_Implicit | TPTP_Explicit
datatype thf_flavor = THF_Without_Choice | THF_With_Choice
datatype atp_format =
CNF |
CNF_UEQ |
FOF |
TFF of tptp_polymorphism * tptp_explicitness |
THF of tptp_polymorphism * tptp_explicitness * thf_flavor |
DFG_Sorted
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 option
type 'a problem = (string * 'a problem_line list) list
val isabelle_info_prefix = "isabelle_"
(* Currently, only SPASS supports Isabelle metainformation. *)
fun isabelle_info DFG_Sorted s =
SOME (ATerm ("[]", [ATerm (isabelle_info_prefix ^ s, [])]))
| isabelle_info _ _ = NONE
val introN = "intro"
val elimN = "elim"
val simpN = "simp"
fun is_isabelle_info suffix (SOME (ATerm ("[]", [ATerm (s, [])]))) =
s = isabelle_info_prefix ^ suffix
| is_isabelle_info _ _ = false
(* 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 = "[]"
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_format_thf (THF _) = true
| is_format_thf _ = false
fun is_format_typed (TFF _) = true
| is_format_typed (THF _) = true
| is_format_typed (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_thf 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"
fun str_for_type format ty =
let
val dfg = (format = DFG_Sorted)
fun str _ (AType (s, [])) =
if dfg andalso s = tptp_individual_type then "Top" 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_thf 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)]) =>
(* There is code in "ATP_Translate" to ensure that "Eps" is always
applied to an abstraction. *)
tptp_choice ^ "[" ^ s' ^ " : " ^ string_for_type format ty ^ "]: " ^
tptp_string_for_term format tm ^ ""
|> enclose "(" ")"
| _ => tptp_string_for_app format s (map (tptp_string_for_term format) ts))
| tptp_string_for_term (format as THF _) (AAbs ((s, ty), tm)) =
"(^[" ^ s ^ " : " ^ string_for_type format ty ^ "]: " ^
tptp_string_for_term format tm ^ ")"
| 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_thf format ? enclose "(" ")"
| tptp_string_for_formula format (AConn (c, [phi])) =
tptp_string_for_connective c ^ " " ^
(tptp_string_for_formula format phi
|> is_format_thf 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 the_source (SOME source) = source
| the_source NONE =
ATerm ("inference",
ATerm ("isabelle", []) :: replicate 2 (ATerm ("[]", [])))
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_Sorted = 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, info)) =
tptp_string_for_format format ^ "(" ^ ident ^ ", " ^
tptp_string_for_kind kind ^ ",\n (" ^
tptp_string_for_formula format phi ^ ")" ^
(case (source, info) of
(NONE, NONE) => ""
| (SOME tm, NONE) => ", " ^ tptp_string_for_term format tm
| (_, SOME tm) =>
", " ^ tptp_string_for_term format (the_source source) ^
", " ^ tptp_string_for_term format tm) ^ ").\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 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 dfg_string_for_formula info =
let
fun str_for_term simp (ATerm (s, tms)) =
(if is_tptp_equal s then "equal" |> simp ? suffix ":lr"
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 simp AIff = "equiv" |> simp ? suffix ":lr"
fun str_for_formula simp (AQuant (q, xs, phi)) =
str_for_quant q ^ "(" ^ "[" ^
commas (map (string_for_bound_var DFG_Sorted) xs) ^ "], " ^
str_for_formula simp phi ^ ")"
| str_for_formula simp (AConn (c, phis)) =
str_for_conn simp c ^ "(" ^
commas (map (str_for_formula false) phis) ^ ")"
| str_for_formula simp (AAtom tm) = str_for_term simp tm
in str_for_formula (is_isabelle_info simpN info) end
fun dfg_lines problem =
let
fun ary sym ty =
"(" ^ sym ^ ", " ^ string_of_int (arity_of_type ty) ^ ")"
fun fun_typ sym ty =
"function(" ^ sym ^ ", " ^ string_for_type DFG_Sorted ty ^ ")."
fun pred_typ sym ty =
"predicate(" ^
commas (sym :: map (string_for_type DFG_Sorted) (binder_atypes ty)) ^ ")."
fun formula pred (Formula (ident, kind, phi, _, info)) =
if pred kind then
SOME ("formula(" ^ dfg_string_for_formula info phi ^ ", " ^ ident ^
").")
else
NONE
| formula _ _ = NONE
fun filt f = problem |> map (map_filter f o snd) |> flat
val func_aries =
filt (fn Decl (_, sym, ty) =>
if is_function_type ty then SOME (ary sym ty) else NONE
| _ => NONE)
|> commas |> enclose "functions [" "]."
val pred_aries =
filt (fn Decl (_, sym, ty) =>
if is_predicate_type ty then SOME (ary sym ty) else NONE
| _ => NONE)
|> commas |> enclose "predicates [" "]."
val sorts =
filt (fn Decl (_, sym, AType (s, [])) =>
if s = tptp_type_of_types then SOME sym else NONE
| _ => NONE)
|> commas |> enclose "sorts [" "]."
val func_sigs =
filt (fn Decl (_, sym, ty) =>
if is_function_type ty then SOME (fun_typ sym ty) else NONE
| _ => NONE)
val pred_sigs =
filt (fn Decl (_, sym, ty) =>
if is_predicate_type ty then SOME (pred_typ sym ty) else NONE
| _ => NONE)
val axioms = filt (formula (curry (op <>) Conjecture))
val conjs = filt (formula (curry (op =) Conjecture))
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" [func_aries, pred_aries, sorts] @
list_of "declarations" (func_sigs @ pred_sigs) @
list_of "formulae(axioms)" axioms @
list_of "formulae(conjectures)" conjs @
["end_problem.\n"]
end
fun lines_for_atp_problem format problem =
"% This file was generated by Isabelle (most likely Sledgehammer)\n\
\% " ^ timestamp () ^ "\n" ::
(if format = DFG_Sorted then dfg_lines else 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 **)
(* TFF allows implicit declarations of types, function symbols, and predicate
symbols (with "$i" as the type of individuals), but some provers (e.g.,
SNARK) require explicit declarations. The situation is similar for THF. *)
fun default_type pred_sym =
let
fun typ 0 = if pred_sym then bool_atype else individual_atype
| typ ary = AFun (individual_atype, typ (ary - 1))
in typ end
fun add_declared_syms_in_problem_line (Decl (_, sym, _)) = insert (op =) 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 []
fun nary_type_constr_type n =
funpow n (curry AFun atype_of_types) atype_of_types
fun undeclared_syms_in_problem declared problem =
let
fun do_sym name ty =
if member (op =) declared name then I else AList.default (op =) (name, ty)
fun do_type (AType (name as (s, _), tys)) =
is_tptp_user_symbol s
? do_sym name (fn _ => nary_type_constr_type (length tys))
#> fold do_type tys
| do_type (AFun (ty1, ty2)) = do_type ty1 #> do_type ty2
| do_type (ATyAbs (_, ty)) = do_type ty
fun do_term pred_sym (ATerm (name as (s, _), tms)) =
is_tptp_user_symbol s
? do_sym name (fn _ => default_type pred_sym (length tms))
#> fold (do_term false) tms
| do_term _ (AAbs ((_, ty), tm)) = do_type ty #> do_term false tm
fun do_formula (AQuant (_, xs, phi)) =
fold do_type (map_filter snd xs) #> do_formula phi
| do_formula (AConn (_, phis)) = fold do_formula phis
| do_formula (AAtom tm) = do_term true tm
fun do_problem_line (Decl (_, _, ty)) = do_type ty
| do_problem_line (Formula (_, _, phi, _, _)) = do_formula phi
in
fold (fold do_problem_line o snd) problem []
|> filter_out (is_built_in_tptp_symbol o fst o fst)
end
fun declare_undeclared_syms_in_atp_problem prefix heading problem =
let
fun decl_line (x as (s, _), ty) = Decl (prefix ^ s, x, ty ())
val declared = problem |> declared_syms_in_problem
val decls =
problem |> undeclared_syms_in_problem declared
|> sort_wrt (fst o fst)
|> map decl_line
in (heading, decls) :: problem end
(** Nice names **)
fun empty_name_pool readable_names =
if readable_names then SOME (Symtab.empty, Symtab.empty) else NONE
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 spass_reserved_nice_names =
["forall", "exists", "le", "ls", "ge", "gs", "plus", "minus", "mult", "fract",
"equal", "true", "false", "or", "and", "not", "implies", "implied", "equiv",
"lr", "def"]
val reserved_nice_names =
[tptp_old_equal, "op", "eq"] @ spass_reserved_nice_names
fun readable_name 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 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)
fun nice_name (full_name, _) NONE = (full_name, NONE)
| nice_name (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 full_name desired_name
fun add j =
let
val nice_name =
nice_prefix ^ (if j = 0 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 0 |> apsnd SOME end
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)) =
nice_name name ##>> nice_type ty ##>> nice_term tm #>> 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
fun nice_atp_problem readable_names problem =
nice_problem problem (empty_name_pool readable_names)
end;