(* 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) formula =
AQuant of quantifier * ('a * 'a option) list * ('a, 'b) formula |
AConn of connective * ('a, 'b) formula list |
AAtom of 'b
type 'a uniform_formula = ('a, 'a fo_term) formula
datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture
datatype 'a problem_line =
Type_Decl of string * 'a * 'a list * 'a |
Formula of string * formula_kind * ('a, 'a fo_term) formula
* string fo_term option
type 'a problem = (string * 'a problem_line list) list
val timestamp : unit -> string
val is_atp_variable : string -> bool
val tptp_strings_for_atp_problem :
bool -> (string * string problem_line list) list -> string list
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) formula =
AQuant of quantifier * ('a * 'a option) list * ('a, 'b) formula |
AConn of connective * ('a, 'b) formula list |
AAtom of 'b
type 'a uniform_formula = ('a, 'a fo_term) formula
datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture
datatype 'a problem_line =
Type_Decl of string * 'a * 'a list * 'a |
Formula of string * formula_kind * ('a, 'a fo_term) formula
* string fo_term option
type 'a problem = (string * 'a problem_line list) list
val timestamp = Date.fmt "%Y-%m-%d %H:%M:%S" o Date.fromTimeLocal o Time.now
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 (s, NONE) = s
| string_for_bound_var (s, SOME t) = s ^ " : " ^ t
fun string_for_formula (AQuant (q, xs, phi)) =
"(" ^ string_for_quantifier q ^
"[" ^ commas (map string_for_bound_var xs) ^ "] : " ^
string_for_formula phi ^ ")"
| string_for_formula (AConn (ANot, [AAtom (ATerm ("equal", ts))])) =
space_implode " != " (map string_for_term ts)
| string_for_formula (AConn (c, [phi])) =
"(" ^ string_for_connective c ^ " " ^ string_for_formula phi ^ ")"
| string_for_formula (AConn (c, phis)) =
"(" ^ space_implode (" " ^ string_for_connective c ^ " ")
(map string_for_formula phis) ^ ")"
| string_for_formula (AAtom tm) = string_for_term tm
fun formula_needs_typed_logic (AQuant (_, xs, phi)) =
exists (is_some o snd) xs orelse formula_needs_typed_logic phi
| formula_needs_typed_logic (AConn (_, phis)) =
exists formula_needs_typed_logic phis
| formula_needs_typed_logic (AAtom _) = false
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
fun string_for_problem_line _ (Type_Decl (ident, sym, arg_tys, res_ty)) =
"tff(" ^ ident ^ ", type, " ^ sym ^ " : " ^
string_for_symbol_type arg_tys res_ty ^ ").\n"
| string_for_problem_line use_conjecture_for_hypotheses
(Formula (ident, kind, phi, source)) =
let
val (kind, phi) =
if kind = Hypothesis andalso use_conjecture_for_hypotheses then
(Conjecture, AConn (ANot, [phi]))
else
(kind, phi)
in
(if formula_needs_typed_logic phi then "tff" else "fof") ^
"(" ^ ident ^ ", " ^ string_for_kind kind ^ ",\n (" ^
string_for_formula phi ^ ")" ^
(case source of
SOME tm => ", " ^ string_for_term tm
| NONE => "") ^ ").\n"
end
fun tptp_strings_for_atp_problem use_conjecture_for_hypotheses 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 use_conjecture_for_hypotheses) lines)
problem
fun is_atp_variable s = Char.isUpper (String.sub (s, 0))
(** 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
(* "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
let
val s = s |> no_qualifiers
|> Name.desymbolize (Char.isUpper (String.sub (full_name, 0)))
in if member (op =) reserved_nice_names s then full_name else s end
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 s => nice_name s #>> 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 (Type_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) => Type_Decl (ident, sym, arg_tys, res_ty))
| nice_problem_line (Formula (ident, kind, phi, source)) =
nice_formula phi #>> (fn phi => Formula (ident, kind, phi, source))
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;