author | blanchet |
Tue, 24 May 2011 10:01:00 +0200 | |
changeset 42967 | 13cb8895f538 |
parent 42966 | 4e2d6c1e5392 |
child 42968 | 74415622d293 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/ATP/atp_problem.ML |
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Author: Jia Meng, Cambridge University Computer Laboratory and NICTA |
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Author: Jasmin Blanchette, TU Muenchen |
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Abstract representation of ATP problems and TPTP syntax. |
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*) |
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signature ATP_PROBLEM = |
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sig |
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datatype 'a fo_term = ATerm of 'a * 'a fo_term list |
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datatype quantifier = AForall | AExists |
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datatype connective = ANot | AAnd | AOr | AImplies | AIf | AIff | ANotIff |
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datatype ('a, 'b, 'c) formula = |
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AQuant of quantifier * ('a * 'b option) list * ('a, 'b, 'c) formula | |
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AConn of connective * ('a, 'b, 'c) formula list | |
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AAtom of 'c |
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datatype 'a ho_type = AType of 'a | AFun of 'a ho_type * 'a ho_type |
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||
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datatype format = CNF_UEQ | FOF | TFF | THF |
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datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture |
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datatype 'a problem_line = |
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Decl of string * 'a * 'a ho_type | |
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Formula of string * formula_kind * ('a, 'a ho_type, 'a fo_term) formula |
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* string fo_term option * string fo_term option |
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type 'a problem = (string * 'a problem_line list) list |
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(* official TPTP syntax *) |
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val tptp_special_prefix : string |
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val tptp_has_type : string |
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val tptp_type_of_types : string |
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val tptp_bool_type : string |
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val tptp_individual_type : string |
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val tptp_fun_type : string |
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val tptp_false : string |
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val tptp_true : string |
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val tptp_not : string |
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val tptp_app : string |
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val is_atp_variable : string -> bool |
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val mk_anot : ('a, 'b, 'c) formula -> ('a, 'b, 'c) formula |
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val mk_aconn : |
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connective -> ('a, 'b, 'c) formula -> ('a, 'b, 'c) formula |
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-> ('a, 'b, 'c) formula |
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val formula_map : ('c -> 'd) -> ('a, 'b, 'c) formula -> ('a, 'b, 'd) formula |
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val timestamp : unit -> string |
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val hashw : word * word -> word |
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val hashw_string : string * word -> word |
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val tptp_strings_for_atp_problem : format -> string problem -> string list |
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val filter_cnf_ueq_problem : |
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(string * string) problem -> (string * string) problem |
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val nice_atp_problem : |
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bool -> ('a * (string * string) problem_line list) list |
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-> ('a * string problem_line list) list |
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* (string Symtab.table * string Symtab.table) option |
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end; |
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structure ATP_Problem : ATP_PROBLEM = |
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struct |
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(** ATP problem **) |
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datatype 'a fo_term = ATerm of 'a * 'a fo_term list |
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datatype quantifier = AForall | AExists |
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datatype connective = ANot | AAnd | AOr | AImplies | AIf | AIff | ANotIff |
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datatype ('a, 'b, 'c) formula = |
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AQuant of quantifier * ('a * 'b option) list * ('a, 'b, 'c) formula | |
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AConn of connective * ('a, 'b, 'c) formula list | |
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AAtom of 'c |
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datatype 'a ho_type = AType of 'a | AFun of 'a ho_type * 'a ho_type |
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datatype format = CNF_UEQ | FOF | TFF | THF |
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datatype formula_kind = Axiom | Definition | Lemma | Hypothesis | Conjecture |
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datatype 'a problem_line = |
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Decl of string * 'a * 'a ho_type | |
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Formula of string * formula_kind * ('a, 'a ho_type, 'a fo_term) formula |
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* string fo_term option * string fo_term option |
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type 'a problem = (string * 'a problem_line list) list |
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(* official TPTP syntax *) |
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val tptp_special_prefix = "$" |
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val tptp_has_type = ":" |
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val tptp_type_of_types = "$tType" |
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val tptp_bool_type = "$o" |
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val tptp_individual_type = "$i" |
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val tptp_fun_type = ">" |
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val tptp_false = "$false" |
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val tptp_true = "$true" |
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val tptp_not = "~" |
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val tptp_app = "@" |
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fun is_atp_variable s = Char.isUpper (String.sub (s, 0)) |
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fun mk_anot (AConn (ANot, [phi])) = phi |
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| mk_anot phi = AConn (ANot, [phi]) |
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fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2]) |
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fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi) |
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| formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis) |
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| formula_map f (AAtom tm) = AAtom (f tm) |
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val timestamp = Date.fmt "%Y-%m-%d %H:%M:%S" o Date.fromTimeLocal o Time.now |
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(* This hash function is recommended in "Compilers: Principles, Techniques, and |
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Tools" by Aho, Sethi, and Ullman. The "hashpjw" function, which they |
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particularly recommend, triggers a bug in versions of Poly/ML up to 4.2.0. *) |
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fun hashw (u, w) = Word.+ (u, Word.* (0w65599, w)) |
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fun hashw_char (c, w) = hashw (Word.fromInt (Char.ord c), w) |
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fun hashw_string (s : string, w) = CharVector.foldl hashw_char w s |
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110 |
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fun string_for_kind Axiom = "axiom" |
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| string_for_kind Definition = "definition" |
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| string_for_kind Lemma = "lemma" |
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| string_for_kind Hypothesis = "hypothesis" |
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| string_for_kind Conjecture = "conjecture" |
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fun strip_tff_type (AFun (AType s, ty)) = strip_tff_type ty |>> cons s |
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| strip_tff_type (AFun (AFun _, _)) = |
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raise Fail "unexpected higher-order type in first-order format" |
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| strip_tff_type (AType s) = ([], s) |
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||
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fun string_for_type THF ty = |
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let |
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fun aux _ (AType s) = s |
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| aux rhs (AFun (ty1, ty2)) = |
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aux false ty1 ^ " " ^ tptp_fun_type ^ " " ^ aux true ty2 |
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|> not rhs ? enclose "(" ")" |
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in aux true ty end |
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| string_for_type TFF ty = |
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(case strip_tff_type ty of |
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([], s) => s |
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| ([s'], s) => s' ^ " " ^ tptp_fun_type ^ " " ^ s |
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| (ss, s) => "(" ^ space_implode " * " ss ^ ") " ^ tptp_fun_type ^ " " ^ s) |
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| string_for_type _ _ = raise Fail "unexpected type in untyped format" |
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fun string_for_term _ (ATerm (s, [])) = s |
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| string_for_term format (ATerm ("equal", ts)) = |
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space_implode " = " (map (string_for_term format) ts) |
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|> format = THF ? enclose "(" ")" |
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| string_for_term format (ATerm ("[]", ts)) = |
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(* used for lists in the optional "source" field of a derivation *) |
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"[" ^ commas (map (string_for_term format) ts) ^ "]" |
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| string_for_term format (ATerm (s, ts)) = |
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let val ss = map (string_for_term format) ts in |
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if format = THF then "(" ^ space_implode " @ " (s :: ss) ^ ")" |
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else s ^ "(" ^ commas ss ^ ")" |
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end |
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fun string_for_quantifier AForall = "!" |
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| string_for_quantifier AExists = "?" |
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fun string_for_connective ANot = tptp_not |
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| string_for_connective AAnd = "&" |
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| string_for_connective AOr = "|" |
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| string_for_connective AImplies = "=>" |
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| string_for_connective AIf = "<=" |
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157 |
| string_for_connective AIff = "<=>" |
37992 | 158 |
| string_for_connective ANotIff = "<~>" |
42963 | 159 |
|
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160 |
fun string_for_bound_var format (s, ty) = |
42963 | 161 |
s ^ (if format = TFF orelse format = THF then |
162 |
" : " ^ |
|
163 |
string_for_type format (ty |> the_default (AType tptp_individual_type)) |
|
164 |
else |
|
165 |
"") |
|
166 |
||
42722 | 167 |
fun string_for_formula format (AQuant (q, xs, phi)) = |
42526 | 168 |
"(" ^ string_for_quantifier q ^ |
42722 | 169 |
"[" ^ commas (map (string_for_bound_var format) xs) ^ "] : " ^ |
170 |
string_for_formula format phi ^ ")" |
|
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|
171 |
| string_for_formula format (AConn (ANot, [AAtom (ATerm ("equal", ts))])) = |
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space_implode " != " (map (string_for_term format) ts) |
42963 | 173 |
|> format = THF ? enclose "(" ")" |
42722 | 174 |
| string_for_formula format (AConn (c, [phi])) = |
175 |
"(" ^ string_for_connective c ^ " " ^ string_for_formula format phi ^ ")" |
|
176 |
| string_for_formula format (AConn (c, phis)) = |
|
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"(" ^ space_implode (" " ^ string_for_connective c ^ " ") |
42722 | 178 |
(map (string_for_formula format) phis) ^ ")" |
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179 |
| string_for_formula format (AAtom tm) = string_for_term format tm |
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180 |
|
42639 | 181 |
val default_source = |
182 |
ATerm ("inference", ATerm ("isabelle", []) :: replicate 2 (ATerm ("[]", []))) |
|
183 |
||
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184 |
fun string_for_format CNF_UEQ = "cnf" |
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|
185 |
| string_for_format FOF = "fof" |
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|
186 |
| string_for_format TFF = "tff" |
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|
187 |
| string_for_format THF = "thf" |
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|
188 |
|
42963 | 189 |
fun string_for_problem_line format (Decl (ident, sym, ty)) = |
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190 |
string_for_format format ^ "(" ^ ident ^ ", type,\n " ^ sym ^ " : " ^ |
42963 | 191 |
string_for_type format ty ^ ").\n" |
42939 | 192 |
| string_for_problem_line format (Formula (ident, kind, phi, source, info)) = |
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string_for_format format ^ "(" ^ ident ^ ", " ^ string_for_kind kind ^ |
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|
194 |
",\n (" ^ string_for_formula format phi ^ ")" ^ |
42939 | 195 |
(case (source, info) of |
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(NONE, NONE) => "" |
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|
197 |
| (SOME tm, NONE) => ", " ^ string_for_term format tm |
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| (_, SOME tm) => |
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", " ^ string_for_term format (source |> the_default default_source) ^ |
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", " ^ string_for_term format tm) ^ ").\n" |
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|
201 |
fun tptp_strings_for_atp_problem format problem = |
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"% This file was generated by Isabelle (most likely Sledgehammer)\n\ |
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|
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\% " ^ timestamp () ^ "\n" :: |
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|
204 |
maps (fn (_, []) => [] |
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205 |
| (heading, lines) => |
41491 | 206 |
"\n% " ^ heading ^ " (" ^ string_of_int (length lines) ^ ")\n" :: |
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|
207 |
map (string_for_problem_line format) lines) |
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|
208 |
problem |
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|
209 |
|
42939 | 210 |
|
211 |
(** CNF UEQ (Waldmeister) **) |
|
212 |
||
213 |
fun is_problem_line_negated (Formula (_, _, AConn (ANot, _), _, _)) = true |
|
214 |
| is_problem_line_negated _ = false |
|
215 |
||
216 |
fun is_problem_line_cnf_ueq |
|
217 |
(Formula (_, _, AAtom (ATerm (("equal", _), _)), _, _)) = true |
|
218 |
| is_problem_line_cnf_ueq _ = false |
|
219 |
||
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|
220 |
fun open_conjecture_term (ATerm ((s, s'), tms)) = |
42961 | 221 |
ATerm (if is_atp_variable s then (s |> Name.desymbolize false, s') |
222 |
else (s, s'), tms |> map open_conjecture_term) |
|
42944
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|
223 |
fun open_formula conj (AQuant (AForall, _, phi)) = open_formula conj phi |
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|
224 |
| open_formula true (AAtom t) = AAtom (open_conjecture_term t) |
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|
225 |
| open_formula _ phi = phi |
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|
226 |
fun open_formula_line (Formula (ident, kind, phi, source, info)) = |
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|
227 |
Formula (ident, kind, open_formula (kind = Conjecture) phi, source, info) |
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|
228 |
| open_formula_line line = line |
42939 | 229 |
|
230 |
fun negate_conjecture_line (Formula (ident, Conjecture, phi, source, info)) = |
|
42942 | 231 |
Formula (ident, Hypothesis, mk_anot phi, source, info) |
42939 | 232 |
| negate_conjecture_line line = line |
233 |
||
42962
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|
234 |
fun filter_cnf_ueq_problem problem = |
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|
235 |
problem |
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|
236 |
|> map (apsnd (map open_formula_line |
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|
237 |
#> filter is_problem_line_cnf_ueq |
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|
238 |
#> map negate_conjecture_line)) |
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|
239 |
|> (fn problem => |
42939 | 240 |
let |
241 |
val conjs = problem |> maps snd |> filter is_problem_line_negated |
|
242 |
in if length conjs = 1 then problem else [] end) |
|
38017
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changeset
|
243 |
|
37643
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changeset
|
244 |
|
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|
245 |
(** Nice names **) |
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|
246 |
|
37624 | 247 |
fun empty_name_pool readable_names = |
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|
248 |
if readable_names then SOME (Symtab.empty, Symtab.empty) else NONE |
37624 | 249 |
|
250 |
fun pool_fold f xs z = pair z #> fold_rev (fn x => uncurry (f x)) xs |
|
251 |
fun pool_map f xs = |
|
252 |
pool_fold (fn x => fn ys => fn pool => f x pool |>> (fn y => y :: ys)) xs [] |
|
253 |
||
42227
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|
254 |
val no_qualifiers = |
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|
255 |
let |
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|
256 |
fun skip [] = [] |
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|
257 |
| skip (#"." :: cs) = skip cs |
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changeset
|
258 |
| skip (c :: cs) = if Char.isAlphaNum c then skip cs else c :: keep cs |
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|
259 |
and keep [] = [] |
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changeset
|
260 |
| keep (#"." :: cs) = skip cs |
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changeset
|
261 |
| keep (c :: cs) = c :: keep cs |
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changeset
|
262 |
in String.explode #> rev #> keep #> rev #> String.implode end |
662b50b7126f
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changeset
|
263 |
|
42761
8ea9c6fa8b53
fixed several bugs in Isar proof reconstruction, in particular w.r.t. mangled types and hAPP
blanchet
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42752
diff
changeset
|
264 |
(* Long names can slow down the ATPs. *) |
42724
4d6bcf846759
added "max_mono_instances" option to Sledgehammer and renamed old "monomorphize_limit" option
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42722
diff
changeset
|
265 |
val max_readable_name_size = 20 |
42567
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diff
changeset
|
266 |
|
39109 | 267 |
(* "op" is also reserved, to avoid the unreadable "op_1", "op_2", etc., in the |
268 |
problem files. "equal" is reserved by some ATPs. "eq" is reserved to ensure |
|
269 |
that "HOL.eq" is correctly mapped to equality. *) |
|
270 |
val reserved_nice_names = ["op", "equal", "eq"] |
|
42939 | 271 |
|
37624 | 272 |
fun readable_name full_name s = |
37643
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changeset
|
273 |
if s = full_name then |
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changeset
|
274 |
s |
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changeset
|
275 |
else |
42567
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changeset
|
276 |
s |> no_qualifiers |
d012947edd36
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changeset
|
277 |
|> Name.desymbolize (Char.isUpper (String.sub (full_name, 0))) |
42583
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changeset
|
278 |
|> (fn s => |
42659 | 279 |
if size s > max_readable_name_size then |
280 |
String.substring (s, 0, max_readable_name_size div 2 - 4) ^ |
|
42583
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diff
changeset
|
281 |
Word.toString (hashw_string (full_name, 0w0)) ^ |
42659 | 282 |
String.extract (s, size s - max_readable_name_size div 2 + 4, |
283 |
NONE) |
|
42583
84b134118616
avoid trailing digits for SNARK (type) names -- grr...
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42577
diff
changeset
|
284 |
else |
84b134118616
avoid trailing digits for SNARK (type) names -- grr...
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42577
diff
changeset
|
285 |
s) |
42567
d012947edd36
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42543
diff
changeset
|
286 |
|> (fn s => if member (op =) reserved_nice_names s then full_name else s) |
37624 | 287 |
|
288 |
fun nice_name (full_name, _) NONE = (full_name, NONE) |
|
289 |
| nice_name (full_name, desired_name) (SOME the_pool) = |
|
42962
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diff
changeset
|
290 |
if String.isPrefix tptp_special_prefix full_name then |
39384 | 291 |
(full_name, SOME the_pool) |
292 |
else case Symtab.lookup (fst the_pool) full_name of |
|
37624 | 293 |
SOME nice_name => (nice_name, SOME the_pool) |
294 |
| NONE => |
|
295 |
let |
|
296 |
val nice_prefix = readable_name full_name desired_name |
|
297 |
fun add j = |
|
298 |
let |
|
42644 | 299 |
val nice_name = |
42942 | 300 |
nice_prefix ^ (if j = 0 then "" else "_" ^ string_of_int j) |
37624 | 301 |
in |
302 |
case Symtab.lookup (snd the_pool) nice_name of |
|
303 |
SOME full_name' => |
|
304 |
if full_name = full_name' then (nice_name, the_pool) |
|
305 |
else add (j + 1) |
|
306 |
| NONE => |
|
307 |
(nice_name, |
|
308 |
(Symtab.update_new (full_name, nice_name) (fst the_pool), |
|
309 |
Symtab.update_new (nice_name, full_name) (snd the_pool))) |
|
310 |
end |
|
311 |
in add 0 |> apsnd SOME end |
|
312 |
||
37961
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first step in using "fof" rather than "cnf" in TPTP problems
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37931
diff
changeset
|
313 |
fun nice_term (ATerm (name, ts)) = |
6a48c85a211a
first step in using "fof" rather than "cnf" in TPTP problems
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parents:
37931
diff
changeset
|
314 |
nice_name name ##>> pool_map nice_term ts #>> ATerm |
42963 | 315 |
fun nice_type (AType name) = nice_name name #>> AType |
316 |
| nice_type (AFun (ty1, ty2)) = nice_type ty1 ##>> nice_type ty2 #>> AFun |
|
37961
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37931
diff
changeset
|
317 |
fun nice_formula (AQuant (q, xs, phi)) = |
42526 | 318 |
pool_map nice_name (map fst xs) |
319 |
##>> pool_map (fn NONE => pair NONE |
|
42963 | 320 |
| SOME ty => nice_type ty #>> SOME) (map snd xs) |
42526 | 321 |
##>> nice_formula phi |
322 |
#>> (fn ((ss, ts), phi) => AQuant (q, ss ~~ ts, phi)) |
|
37961
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first step in using "fof" rather than "cnf" in TPTP problems
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37931
diff
changeset
|
323 |
| nice_formula (AConn (c, phis)) = |
6a48c85a211a
first step in using "fof" rather than "cnf" in TPTP problems
blanchet
parents:
37931
diff
changeset
|
324 |
pool_map nice_formula phis #>> curry AConn c |
38034 | 325 |
| nice_formula (AAtom tm) = nice_term tm #>> AAtom |
42963 | 326 |
fun nice_problem_line (Decl (ident, sym, ty)) = |
327 |
nice_name sym ##>> nice_type ty |
|
328 |
#>> (fn (sym, ty) => Decl (ident, sym, ty)) |
|
42939 | 329 |
| nice_problem_line (Formula (ident, kind, phi, source, info)) = |
330 |
nice_formula phi #>> (fn phi => Formula (ident, kind, phi, source, info)) |
|
37931 | 331 |
fun nice_problem problem = |
37643
f576af716aa6
rewrote the TPTP problem generation code more or less from scratch;
blanchet
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37642
diff
changeset
|
332 |
pool_map (fn (heading, lines) => |
37931 | 333 |
pool_map nice_problem_line lines #>> pair heading) problem |
39452 | 334 |
fun nice_atp_problem readable_names problem = |
38017
3ad3e3ca2451
move Sledgehammer-specific code out of "Sledgehammer_TPTP_Format"
blanchet
parents:
38014
diff
changeset
|
335 |
nice_problem problem (empty_name_pool readable_names) |
37509
f39464d971c4
factor out TPTP format output into file of its own, to facilitate further changes
blanchet
parents:
diff
changeset
|
336 |
|
f39464d971c4
factor out TPTP format output into file of its own, to facilitate further changes
blanchet
parents:
diff
changeset
|
337 |
end; |