1 (* Title: HOL/Tools/ATP/atp_problem.ML
2 Author: Jia Meng, Cambridge University Computer Laboratory and NICTA
3 Author: Jasmin Blanchette, TU Muenchen
5 Abstract representation of ATP problems and TPTP syntax.
8 signature ATP_PROBLEM =
10 datatype 'a fo_term = ATerm of 'a * 'a fo_term list
11 datatype quantifier = AForall | AExists
12 datatype connective = ANot | AAnd | AOr | AImplies | AIf | AIff | ANotIff
13 datatype ('a, 'b, 'c) formula =
14 AQuant of quantifier * ('a * 'b option) list * ('a, 'b, 'c) formula |
15 AConn of connective * ('a, 'b, 'c) formula list |
18 datatype format = UEQ | FOF | TFF
19 datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture
20 datatype 'a problem_line =
21 Decl of string * 'a * 'a list * 'a |
22 Formula of string * formula_kind * ('a, 'a, 'a fo_term) formula
23 * string fo_term option * string fo_term option
24 type 'a problem = (string * 'a problem_line list) list
26 (* official TPTP syntax *)
27 val tptp_special_prefix : string
28 val tptp_false : string
29 val tptp_true : string
30 val tptp_tff_type_of_types : string
31 val tptp_tff_bool_type : string
32 val tptp_tff_individual_type : string
33 val timestamp : unit -> string
34 val hashw : word * word -> word
35 val hashw_string : string * word -> word
36 val is_atp_variable : string -> bool
37 val tptp_strings_for_atp_problem : format -> string problem -> string list
38 val nice_atp_problem :
39 bool -> ('a * (string * string) problem_line list) list
40 -> ('a * string problem_line list) list
41 * (string Symtab.table * string Symtab.table) option
44 structure ATP_Problem : ATP_PROBLEM =
49 datatype 'a fo_term = ATerm of 'a * 'a fo_term list
50 datatype quantifier = AForall | AExists
51 datatype connective = ANot | AAnd | AOr | AImplies | AIf | AIff | ANotIff
52 datatype ('a, 'b, 'c) formula =
53 AQuant of quantifier * ('a * 'b option) list * ('a, 'b, 'c) formula |
54 AConn of connective * ('a, 'b, 'c) formula list |
57 datatype format = UEQ | FOF | TFF
58 datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture
59 datatype 'a problem_line =
60 Decl of string * 'a * 'a list * 'a |
61 Formula of string * formula_kind * ('a, 'a, 'a fo_term) formula
62 * string fo_term option * string fo_term option
63 type 'a problem = (string * 'a problem_line list) list
65 (* official TPTP syntax *)
66 val tptp_special_prefix = "$"
67 val tptp_false = "$false"
68 val tptp_true = "$true"
69 val tptp_tff_type_of_types = "$tType"
70 val tptp_tff_bool_type = "$o"
71 val tptp_tff_individual_type = "$i"
73 val timestamp = Date.fmt "%Y-%m-%d %H:%M:%S" o Date.fromTimeLocal o Time.now
75 (* This hash function is recommended in Compilers: Principles, Techniques, and
76 Tools, by Aho, Sethi, and Ullman. The "hashpjw" function, which they
77 particularly recommend, triggers a bug in versions of Poly/ML up to 4.2.0. *)
78 fun hashw (u, w) = Word.+ (u, Word.* (0w65599, w))
79 fun hashw_char (c, w) = hashw (Word.fromInt (Char.ord c), w)
80 fun hashw_string (s : string, w) = CharVector.foldl hashw_char w s
82 fun string_for_kind Axiom = "axiom"
83 | string_for_kind Definition = "definition"
84 | string_for_kind Lemma = "lemma"
85 | string_for_kind Hypothesis = "hypothesis"
86 | string_for_kind Conjecture = "conjecture"
88 fun string_for_term (ATerm (s, [])) = s
89 | string_for_term (ATerm ("equal", ts)) =
90 space_implode " = " (map string_for_term ts)
91 | string_for_term (ATerm ("[]", ts)) =
92 (* used for lists in the optional "source" field of a derivation *)
93 "[" ^ commas (map string_for_term ts) ^ "]"
94 | string_for_term (ATerm (s, ts)) =
95 s ^ "(" ^ commas (map string_for_term ts) ^ ")"
96 fun string_for_quantifier AForall = "!"
97 | string_for_quantifier AExists = "?"
98 fun string_for_connective ANot = "~"
99 | string_for_connective AAnd = "&"
100 | string_for_connective AOr = "|"
101 | string_for_connective AImplies = "=>"
102 | string_for_connective AIf = "<="
103 | string_for_connective AIff = "<=>"
104 | string_for_connective ANotIff = "<~>"
105 fun string_for_bound_var TFF (s, ty) =
106 s ^ " : " ^ (ty |> the_default tptp_tff_individual_type)
107 | string_for_bound_var _ (s, _) = s
108 fun string_for_formula format (AQuant (q, xs, phi)) =
109 "(" ^ string_for_quantifier q ^
110 "[" ^ commas (map (string_for_bound_var format) xs) ^ "] : " ^
111 string_for_formula format phi ^ ")"
112 | string_for_formula _ (AConn (ANot, [AAtom (ATerm ("equal", ts))])) =
113 space_implode " != " (map string_for_term ts)
114 | string_for_formula format (AConn (c, [phi])) =
115 "(" ^ string_for_connective c ^ " " ^ string_for_formula format phi ^ ")"
116 | string_for_formula format (AConn (c, phis)) =
117 "(" ^ space_implode (" " ^ string_for_connective c ^ " ")
118 (map (string_for_formula format) phis) ^ ")"
119 | string_for_formula _ (AAtom tm) = string_for_term tm
121 fun string_for_symbol_type [] res_ty = res_ty
122 | string_for_symbol_type [arg_ty] res_ty = arg_ty ^ " > " ^ res_ty
123 | string_for_symbol_type arg_tys res_ty =
124 string_for_symbol_type ["(" ^ space_implode " * " arg_tys ^ ")"] res_ty
127 ATerm ("inference", ATerm ("isabelle", []) :: replicate 2 (ATerm ("[]", [])))
129 fun string_for_problem_line _ (Decl (ident, sym, arg_tys, res_ty)) =
130 "tff(" ^ ident ^ ", type,\n " ^ sym ^ " : " ^
131 string_for_symbol_type arg_tys res_ty ^ ").\n"
132 | string_for_problem_line format
133 (Formula (ident, kind, phi, source, useful_info)) =
134 (case format of UEQ => "cnf" | FOF => "fof" | TFF => "tff") ^
135 "(" ^ ident ^ ", " ^ string_for_kind kind ^ ",\n (" ^
136 string_for_formula format phi ^ ")" ^
137 (case (source, useful_info) of
139 | (SOME tm, NONE) => ", " ^ string_for_term tm
141 ", " ^ string_for_term (source |> the_default default_source) ^
142 ", " ^ string_for_term tm) ^ ").\n"
143 fun tptp_strings_for_atp_problem format problem =
144 "% This file was generated by Isabelle (most likely Sledgehammer)\n\
145 \% " ^ timestamp () ^ "\n" ::
146 maps (fn (_, []) => []
147 | (heading, lines) =>
148 "\n% " ^ heading ^ " (" ^ string_of_int (length lines) ^ ")\n" ::
149 map (string_for_problem_line format) lines)
152 fun is_atp_variable s = Char.isUpper (String.sub (s, 0))
157 fun empty_name_pool readable_names =
158 if readable_names then SOME (Symtab.empty, Symtab.empty) else NONE
160 fun pool_fold f xs z = pair z #> fold_rev (fn x => uncurry (f x)) xs
162 pool_fold (fn x => fn ys => fn pool => f x pool |>> (fn y => y :: ys)) xs []
167 | skip (#"." :: cs) = skip cs
168 | skip (c :: cs) = if Char.isAlphaNum c then skip cs else c :: keep cs
170 | keep (#"." :: cs) = skip cs
171 | keep (c :: cs) = c :: keep cs
172 in String.explode #> rev #> keep #> rev #> String.implode end
174 (* Long names can slow down the ATPs. *)
175 val max_readable_name_size = 20
177 (* "op" is also reserved, to avoid the unreadable "op_1", "op_2", etc., in the
178 problem files. "equal" is reserved by some ATPs. "eq" is reserved to ensure
179 that "HOL.eq" is correctly mapped to equality. *)
180 val reserved_nice_names = ["op", "equal", "eq"]
181 fun readable_name full_name s =
182 if s = full_name then
186 |> Name.desymbolize (Char.isUpper (String.sub (full_name, 0)))
187 (* SNARK doesn't like sort (type) names that end with digits. We make
188 an effort to avoid this here. *)
189 |> (fn s => if Char.isDigit (String.sub (s, size s - 1)) then s ^ "_"
192 if size s > max_readable_name_size then
193 String.substring (s, 0, max_readable_name_size div 2 - 4) ^
194 Word.toString (hashw_string (full_name, 0w0)) ^
195 String.extract (s, size s - max_readable_name_size div 2 + 4,
199 |> (fn s => if member (op =) reserved_nice_names s then full_name else s)
201 fun nice_name (full_name, _) NONE = (full_name, NONE)
202 | nice_name (full_name, desired_name) (SOME the_pool) =
203 if String.isPrefix "$" full_name then
204 (full_name, SOME the_pool)
205 else case Symtab.lookup (fst the_pool) full_name of
206 SOME nice_name => (nice_name, SOME the_pool)
209 val nice_prefix = readable_name full_name desired_name
212 (* The trailing "_" is for SNARK (cf. comment above). *)
214 nice_prefix ^ (if j = 0 then "" else "_" ^ string_of_int j ^ "_")
216 case Symtab.lookup (snd the_pool) nice_name of
218 if full_name = full_name' then (nice_name, the_pool)
222 (Symtab.update_new (full_name, nice_name) (fst the_pool),
223 Symtab.update_new (nice_name, full_name) (snd the_pool)))
225 in add 0 |> apsnd SOME end
227 fun nice_term (ATerm (name, ts)) =
228 nice_name name ##>> pool_map nice_term ts #>> ATerm
229 fun nice_formula (AQuant (q, xs, phi)) =
230 pool_map nice_name (map fst xs)
231 ##>> pool_map (fn NONE => pair NONE
232 | SOME ty => nice_name ty #>> SOME) (map snd xs)
233 ##>> nice_formula phi
234 #>> (fn ((ss, ts), phi) => AQuant (q, ss ~~ ts, phi))
235 | nice_formula (AConn (c, phis)) =
236 pool_map nice_formula phis #>> curry AConn c
237 | nice_formula (AAtom tm) = nice_term tm #>> AAtom
238 fun nice_problem_line (Decl (ident, sym, arg_tys, res_ty)) =
240 ##>> pool_map nice_name arg_tys
241 ##>> nice_name res_ty
242 #>> (fn ((sym, arg_tys), res_ty) => Decl (ident, sym, arg_tys, res_ty))
243 | nice_problem_line (Formula (ident, kind, phi, source, useful_info)) =
245 #>> (fn phi => Formula (ident, kind, phi, source, useful_info))
246 fun nice_problem problem =
247 pool_map (fn (heading, lines) =>
248 pool_map nice_problem_line lines #>> pair heading) problem
249 fun nice_atp_problem readable_names problem =
250 nice_problem problem (empty_name_pool readable_names)