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) formula =
14 AQuant of quantifier * ('a * 'a option) list * ('a, 'b) formula |
15 AConn of connective * ('a, 'b) formula list |
17 type 'a uniform_formula = ('a, 'a fo_term) formula
19 datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture
20 datatype 'a problem_line =
21 Type_Decl of string * 'a * 'a list * 'a |
22 Formula of string * formula_kind * ('a, 'a fo_term) formula
23 * string fo_term option
24 type 'a problem = (string * 'a problem_line list) list
26 val timestamp : unit -> string
27 val is_atp_variable : string -> bool
28 val tptp_strings_for_atp_problem :
29 bool -> (string * string problem_line list) list -> string list
30 val nice_atp_problem :
31 bool -> ('a * (string * string) problem_line list) list
32 -> ('a * string problem_line list) list
33 * (string Symtab.table * string Symtab.table) option
36 structure ATP_Problem : ATP_PROBLEM =
41 datatype 'a fo_term = ATerm of 'a * 'a fo_term list
42 datatype quantifier = AForall | AExists
43 datatype connective = ANot | AAnd | AOr | AImplies | AIf | AIff | ANotIff
44 datatype ('a, 'b) formula =
45 AQuant of quantifier * ('a * 'a option) list * ('a, 'b) formula |
46 AConn of connective * ('a, 'b) formula list |
48 type 'a uniform_formula = ('a, 'a fo_term) formula
50 datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture
51 datatype 'a problem_line =
52 Type_Decl of string * 'a * 'a list * 'a |
53 Formula of string * formula_kind * ('a, 'a fo_term) formula
54 * string fo_term option
55 type 'a problem = (string * 'a problem_line list) list
57 val timestamp = Date.fmt "%Y-%m-%d %H:%M:%S" o Date.fromTimeLocal o Time.now
59 fun string_for_kind Axiom = "axiom"
60 | string_for_kind Definition = "definition"
61 | string_for_kind Lemma = "lemma"
62 | string_for_kind Hypothesis = "hypothesis"
63 | string_for_kind Conjecture = "conjecture"
65 fun string_for_term (ATerm (s, [])) = s
66 | string_for_term (ATerm ("equal", ts)) =
67 space_implode " = " (map string_for_term ts)
68 | string_for_term (ATerm ("[]", ts)) =
69 (* used for lists in the optional "source" field of a derivation *)
70 "[" ^ commas (map string_for_term ts) ^ "]"
71 | string_for_term (ATerm (s, ts)) =
72 s ^ "(" ^ commas (map string_for_term ts) ^ ")"
73 fun string_for_quantifier AForall = "!"
74 | string_for_quantifier AExists = "?"
75 fun string_for_connective ANot = "~"
76 | string_for_connective AAnd = "&"
77 | string_for_connective AOr = "|"
78 | string_for_connective AImplies = "=>"
79 | string_for_connective AIf = "<="
80 | string_for_connective AIff = "<=>"
81 | string_for_connective ANotIff = "<~>"
82 fun string_for_bound_var (s, NONE) = s
83 | string_for_bound_var (s, SOME t) = s ^ " : " ^ t
84 fun string_for_formula (AQuant (q, xs, phi)) =
85 "(" ^ string_for_quantifier q ^
86 "[" ^ commas (map string_for_bound_var xs) ^ "] : " ^
87 string_for_formula phi ^ ")"
88 | string_for_formula (AConn (ANot, [AAtom (ATerm ("equal", ts))])) =
89 space_implode " != " (map string_for_term ts)
90 | string_for_formula (AConn (c, [phi])) =
91 "(" ^ string_for_connective c ^ " " ^ string_for_formula phi ^ ")"
92 | string_for_formula (AConn (c, phis)) =
93 "(" ^ space_implode (" " ^ string_for_connective c ^ " ")
94 (map string_for_formula phis) ^ ")"
95 | string_for_formula (AAtom tm) = string_for_term tm
97 fun formula_needs_typed_logic (AQuant (_, xs, phi)) =
98 exists (is_some o snd) xs orelse formula_needs_typed_logic phi
99 | formula_needs_typed_logic (AConn (_, phis)) =
100 exists formula_needs_typed_logic phis
101 | formula_needs_typed_logic (AAtom _) = false
103 fun string_for_symbol_type [] res_ty = res_ty
104 | string_for_symbol_type [arg_ty] res_ty = arg_ty ^ " > " ^ res_ty
105 | string_for_symbol_type arg_tys res_ty =
106 string_for_symbol_type ["(" ^ space_implode " * " arg_tys ^ ")"] res_ty
108 fun string_for_problem_line _ (Type_Decl (ident, sym, arg_tys, res_ty)) =
109 "tff(" ^ ident ^ ", type, " ^ sym ^ " : " ^
110 string_for_symbol_type arg_tys res_ty ^ ").\n"
111 | string_for_problem_line use_conjecture_for_hypotheses
112 (Formula (ident, kind, phi, source)) =
115 if kind = Hypothesis andalso use_conjecture_for_hypotheses then
116 (Conjecture, AConn (ANot, [phi]))
120 (if formula_needs_typed_logic phi then "tff" else "fof") ^
121 "(" ^ ident ^ ", " ^ string_for_kind kind ^ ",\n (" ^
122 string_for_formula phi ^ ")" ^
124 SOME tm => ", " ^ string_for_term tm
125 | NONE => "") ^ ").\n"
127 fun tptp_strings_for_atp_problem use_conjecture_for_hypotheses problem =
128 "% This file was generated by Isabelle (most likely Sledgehammer)\n\
129 \% " ^ timestamp () ^ "\n" ::
130 maps (fn (_, []) => []
131 | (heading, lines) =>
132 "\n% " ^ heading ^ " (" ^ string_of_int (length lines) ^ ")\n" ::
133 map (string_for_problem_line use_conjecture_for_hypotheses) lines)
136 fun is_atp_variable s = Char.isUpper (String.sub (s, 0))
141 fun empty_name_pool readable_names =
142 if readable_names then SOME (Symtab.empty, Symtab.empty) else NONE
144 fun pool_fold f xs z = pair z #> fold_rev (fn x => uncurry (f x)) xs
146 pool_fold (fn x => fn ys => fn pool => f x pool |>> (fn y => y :: ys)) xs []
151 | skip (#"." :: cs) = skip cs
152 | skip (c :: cs) = if Char.isAlphaNum c then skip cs else c :: keep cs
154 | keep (#"." :: cs) = skip cs
155 | keep (c :: cs) = c :: keep cs
156 in String.explode #> rev #> keep #> rev #> String.implode end
158 (* "op" is also reserved, to avoid the unreadable "op_1", "op_2", etc., in the
159 problem files. "equal" is reserved by some ATPs. "eq" is reserved to ensure
160 that "HOL.eq" is correctly mapped to equality. *)
161 val reserved_nice_names = ["op", "equal", "eq"]
162 fun readable_name full_name s =
163 if s = full_name then
167 val s = s |> no_qualifiers
168 |> Name.desymbolize (Char.isUpper (String.sub (full_name, 0)))
169 in if member (op =) reserved_nice_names s then full_name else s end
171 fun nice_name (full_name, _) NONE = (full_name, NONE)
172 | nice_name (full_name, desired_name) (SOME the_pool) =
173 if String.isPrefix "$" full_name then
174 (full_name, SOME the_pool)
175 else case Symtab.lookup (fst the_pool) full_name of
176 SOME nice_name => (nice_name, SOME the_pool)
179 val nice_prefix = readable_name full_name desired_name
182 val nice_name = nice_prefix ^
183 (if j = 0 then "" else "_" ^ string_of_int j)
185 case Symtab.lookup (snd the_pool) nice_name of
187 if full_name = full_name' then (nice_name, the_pool)
191 (Symtab.update_new (full_name, nice_name) (fst the_pool),
192 Symtab.update_new (nice_name, full_name) (snd the_pool)))
194 in add 0 |> apsnd SOME end
196 fun nice_term (ATerm (name, ts)) =
197 nice_name name ##>> pool_map nice_term ts #>> ATerm
198 fun nice_formula (AQuant (q, xs, phi)) =
199 pool_map nice_name (map fst xs)
200 ##>> pool_map (fn NONE => pair NONE
201 | SOME s => nice_name s #>> SOME) (map snd xs)
202 ##>> nice_formula phi
203 #>> (fn ((ss, ts), phi) => AQuant (q, ss ~~ ts, phi))
204 | nice_formula (AConn (c, phis)) =
205 pool_map nice_formula phis #>> curry AConn c
206 | nice_formula (AAtom tm) = nice_term tm #>> AAtom
207 fun nice_problem_line (Type_Decl (ident, sym, arg_tys, res_ty)) =
209 ##>> pool_map nice_name arg_tys
210 ##>> nice_name res_ty
211 #>> (fn ((sym, arg_tys), res_ty) => Type_Decl (ident, sym, arg_tys, res_ty))
212 | nice_problem_line (Formula (ident, kind, phi, source)) =
213 nice_formula phi #>> (fn phi => Formula (ident, kind, phi, source))
214 fun nice_problem problem =
215 pool_map (fn (heading, lines) =>
216 pool_map nice_problem_line lines #>> pair heading) problem
217 fun nice_atp_problem readable_names problem =
218 nice_problem problem (empty_name_pool readable_names)