(* 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 fo_term = ATerm of 'a * 'a fo_term list
datatype quantifier = AForall | AExists
datatype connective = ANot | AAnd | AOr | AImplies | AIf | AIff | ANotIff
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 format = CNF_UEQ | FOF | TFF
datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture
datatype 'a problem_line =
Decl of string * 'a * 'a list * 'a |
Formula of string * formula_kind * ('a, 'a, 'a fo_term) formula
* string fo_term option * string fo_term option
type 'a problem = (string * 'a problem_line list) list
(* official TPTP syntax *)
val tptp_special_prefix : string
val tptp_false : string
val tptp_true : string
val tptp_tff_type_of_types : string
val tptp_tff_bool_type : string
val tptp_tff_individual_type : string
val is_atp_variable : string -> bool
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 formula_map : ('c -> 'd) -> ('a, 'b, 'c) formula -> ('a, 'b, 'd) formula
val timestamp : unit -> string
val hashw : word * word -> word
val hashw_string : string * word -> word
val tptp_strings_for_atp_problem : format -> string problem -> string list
val filter_cnf_ueq_problem :
(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
(** ATP problem **)
datatype 'a fo_term = ATerm of 'a * 'a fo_term list
datatype quantifier = AForall | AExists
datatype connective = ANot | AAnd | AOr | AImplies | AIf | AIff | ANotIff
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 format = CNF_UEQ | FOF | TFF
datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture
datatype 'a problem_line =
Decl of string * 'a * 'a list * 'a |
Formula of string * formula_kind * ('a, 'a, 'a fo_term) formula
* string fo_term option * string fo_term option
type 'a problem = (string * 'a problem_line list) list
(* official TPTP syntax *)
val tptp_special_prefix = "$"
val tptp_false = "$false"
val tptp_true = "$true"
val tptp_tff_type_of_types = "$tType"
val tptp_tff_bool_type = "$o"
val tptp_tff_individual_type = "$i"
fun is_atp_variable s = Char.isUpper (String.sub (s, 0))
fun mk_anot (AConn (ANot, [phi])) = phi
| mk_anot phi = AConn (ANot, [phi])
fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
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)
val timestamp = Date.fmt "%Y-%m-%d %H:%M:%S" o Date.fromTimeLocal o Time.now
(* This hash function is recommended in Compilers: Principles, Techniques, and
Tools, by Aho, Sethi, and Ullman. The "hashpjw" function, which they
particularly recommend, triggers a bug in versions of Poly/ML up to 4.2.0. *)
fun hashw (u, w) = Word.+ (u, Word.* (0w65599, w))
fun hashw_char (c, w) = hashw (Word.fromInt (Char.ord c), w)
fun hashw_string (s : string, w) = CharVector.foldl hashw_char w s
fun string_for_kind Axiom = "axiom"
| string_for_kind Definition = "definition"
| string_for_kind Lemma = "lemma"
| string_for_kind Hypothesis = "hypothesis"
| string_for_kind Conjecture = "conjecture"
fun string_for_term (ATerm (s, [])) = s
| string_for_term (ATerm ("equal", ts)) =
space_implode " = " (map string_for_term ts)
| string_for_term (ATerm ("[]", ts)) =
(* used for lists in the optional "source" field of a derivation *)
"[" ^ commas (map string_for_term ts) ^ "]"
| string_for_term (ATerm (s, ts)) =
s ^ "(" ^ commas (map string_for_term ts) ^ ")"
fun string_for_quantifier AForall = "!"
| string_for_quantifier AExists = "?"
fun string_for_connective ANot = "~"
| string_for_connective AAnd = "&"
| string_for_connective AOr = "|"
| string_for_connective AImplies = "=>"
| string_for_connective AIf = "<="
| string_for_connective AIff = "<=>"
| string_for_connective ANotIff = "<~>"
fun string_for_bound_var TFF (s, ty) =
s ^ " : " ^ (ty |> the_default tptp_tff_individual_type)
| string_for_bound_var _ (s, _) = s
fun string_for_formula format (AQuant (q, xs, phi)) =
"(" ^ string_for_quantifier q ^
"[" ^ commas (map (string_for_bound_var format) xs) ^ "] : " ^
string_for_formula format phi ^ ")"
| string_for_formula _ (AConn (ANot, [AAtom (ATerm ("equal", ts))])) =
space_implode " != " (map string_for_term ts)
| string_for_formula format (AConn (c, [phi])) =
"(" ^ string_for_connective c ^ " " ^ string_for_formula format phi ^ ")"
| string_for_formula format (AConn (c, phis)) =
"(" ^ space_implode (" " ^ string_for_connective c ^ " ")
(map (string_for_formula format) phis) ^ ")"
| string_for_formula _ (AAtom tm) = string_for_term tm
fun string_for_symbol_type [] res_ty = res_ty
| string_for_symbol_type [arg_ty] res_ty = arg_ty ^ " > " ^ res_ty
| string_for_symbol_type arg_tys res_ty =
string_for_symbol_type ["(" ^ space_implode " * " arg_tys ^ ")"] res_ty
val default_source =
ATerm ("inference", ATerm ("isabelle", []) :: replicate 2 (ATerm ("[]", [])))
fun string_for_problem_line _ (Decl (ident, sym, arg_tys, res_ty)) =
"tff(" ^ ident ^ ", type,\n " ^ sym ^ " : " ^
string_for_symbol_type arg_tys res_ty ^ ").\n"
| string_for_problem_line format (Formula (ident, kind, phi, source, info)) =
(case format of CNF_UEQ => "cnf" | FOF => "fof" | TFF => "tff") ^
"(" ^ ident ^ ", " ^ string_for_kind kind ^ ",\n (" ^
string_for_formula format phi ^ ")" ^
(case (source, info) of
(NONE, NONE) => ""
| (SOME tm, NONE) => ", " ^ string_for_term tm
| (_, SOME tm) =>
", " ^ string_for_term (source |> the_default default_source) ^
", " ^ string_for_term tm) ^ ").\n"
fun tptp_strings_for_atp_problem format problem =
"% This file was generated by Isabelle (most likely Sledgehammer)\n\
\% " ^ timestamp () ^ "\n" ::
maps (fn (_, []) => []
| (heading, lines) =>
"\n% " ^ heading ^ " (" ^ string_of_int (length lines) ^ ")\n" ::
map (string_for_problem_line format) lines)
problem
(** CNF UEQ (Waldmeister) **)
exception LOST_CONJECTURE of unit
fun is_problem_line_negated (Formula (_, _, AConn (ANot, _), _, _)) = true
| is_problem_line_negated _ = false
fun is_problem_line_cnf_ueq
(Formula (_, _, AAtom (ATerm (("equal", _), _)), _, _)) = true
| is_problem_line_cnf_ueq _ = false
fun open_conjecture_term (ATerm ((s, s'), tms)) =
ATerm (s |> is_atp_variable s ? Name.desymbolize false |> `I,
tms |> map open_conjecture_term)
fun open_formula conj (AQuant (AForall, _, phi)) = open_formula conj phi
| open_formula true (AAtom t) = AAtom (open_conjecture_term t)
| open_formula _ phi = phi
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
val filter_cnf_ueq_problem =
map (apsnd (map open_formula_line
#> filter is_problem_line_cnf_ueq
#> map negate_conjecture_line))
#> (fn problem =>
let
val conjs = problem |> maps snd |> filter is_problem_line_negated
in if length conjs = 1 then problem else [] 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
(* "op" is also reserved, to avoid the unreadable "op_1", "op_2", etc., in the
problem files. "equal" is reserved by some ATPs. "eq" is reserved to ensure
that "HOL.eq" is correctly mapped to equality. *)
val reserved_nice_names = ["op", "equal", "eq"]
fun readable_name full_name s =
if s = full_name then
s
else
s |> no_qualifiers
|> 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) ^
Word.toString (hashw_string (full_name, 0w0)) ^
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 String.isPrefix "$" 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_term (ATerm (name, ts)) =
nice_name name ##>> pool_map nice_term ts #>> ATerm
fun nice_formula (AQuant (q, xs, phi)) =
pool_map nice_name (map fst xs)
##>> pool_map (fn NONE => pair NONE
| SOME ty => nice_name 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, arg_tys, res_ty)) =
nice_name sym
##>> pool_map nice_name arg_tys
##>> nice_name res_ty
#>> (fn ((sym, arg_tys), res_ty) => Decl (ident, sym, arg_tys, res_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;