author | blanchet |
Sun, 22 May 2011 14:49:35 +0200 | |
changeset 42937 | cabb3a947894 |
parent 42761 | 8ea9c6fa8b53 |
child 42939 | 0134d6650092 |
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 format = UEQ | FOF | TFF |
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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 list * 'a | |
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Formula of string * formula_kind * ('a, 'a, '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_false : string |
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val tptp_true : string |
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val tptp_tff_type_of_types : string |
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val tptp_tff_bool_type : string |
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val tptp_tff_individual_type : string |
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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 is_atp_variable : string -> bool |
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val tptp_strings_for_atp_problem : format -> string problem -> string list |
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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 format = UEQ | FOF | TFF |
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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 list * 'a | |
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Formula of string * formula_kind * ('a, 'a, '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 = "$" |
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val tptp_false = "$false" |
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val tptp_true = "$true" |
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val tptp_tff_type_of_types = "$tType" |
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val tptp_tff_bool_type = "$o" |
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val tptp_tff_individual_type = "$i" |
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||
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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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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 string_for_term (ATerm (s, [])) = s |
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| string_for_term (ATerm ("equal", ts)) = |
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space_implode " = " (map string_for_term ts) |
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| string_for_term (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 ts) ^ "]" |
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| string_for_term (ATerm (s, ts)) = |
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s ^ "(" ^ commas (map string_for_term ts) ^ ")" |
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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 = "~" |
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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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| string_for_connective AIff = "<=>" |
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| string_for_connective ANotIff = "<~>" |
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fun string_for_bound_var TFF (s, ty) = |
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s ^ " : " ^ (ty |> the_default tptp_tff_individual_type) |
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| string_for_bound_var _ (s, _) = s |
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fun string_for_formula format (AQuant (q, xs, phi)) = |
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"(" ^ string_for_quantifier q ^ |
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"[" ^ commas (map (string_for_bound_var format) xs) ^ "] : " ^ |
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string_for_formula format phi ^ ")" |
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| string_for_formula _ (AConn (ANot, [AAtom (ATerm ("equal", ts))])) = |
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space_implode " != " (map string_for_term ts) |
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| string_for_formula format (AConn (c, [phi])) = |
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"(" ^ string_for_connective c ^ " " ^ string_for_formula format phi ^ ")" |
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| string_for_formula format (AConn (c, phis)) = |
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"(" ^ space_implode (" " ^ string_for_connective c ^ " ") |
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(map (string_for_formula format) phis) ^ ")" |
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| string_for_formula _ (AAtom tm) = string_for_term tm |
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fun string_for_symbol_type [] res_ty = res_ty |
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| string_for_symbol_type [arg_ty] res_ty = arg_ty ^ " > " ^ res_ty |
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| string_for_symbol_type arg_tys res_ty = |
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string_for_symbol_type ["(" ^ space_implode " * " arg_tys ^ ")"] res_ty |
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||
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val default_source = |
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ATerm ("inference", ATerm ("isabelle", []) :: replicate 2 (ATerm ("[]", []))) |
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fun string_for_problem_line _ (Decl (ident, sym, arg_tys, res_ty)) = |
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"tff(" ^ ident ^ ", type,\n " ^ sym ^ " : " ^ |
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string_for_symbol_type arg_tys res_ty ^ ").\n" |
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| string_for_problem_line format |
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(Formula (ident, kind, phi, source, useful_info)) = |
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(case format of UEQ => "cnf" | FOF => "fof" | TFF => "tff") ^ |
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"(" ^ ident ^ ", " ^ string_for_kind kind ^ ",\n (" ^ |
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string_for_formula format phi ^ ")" ^ |
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(case (source, useful_info) of |
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(NONE, NONE) => "" |
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| (SOME tm, NONE) => ", " ^ string_for_term tm |
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| (_, SOME tm) => |
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", " ^ string_for_term (source |> the_default default_source) ^ |
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", " ^ string_for_term tm) ^ ").\n" |
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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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\% " ^ timestamp () ^ "\n" :: |
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maps (fn (_, []) => [] |
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| (heading, lines) => |
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"\n% " ^ heading ^ " (" ^ string_of_int (length lines) ^ ")\n" :: |
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allow each prover to specify its own formula kind for symbols occurring in the conjecture
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map (string_for_problem_line format) lines) |
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prefer TPTP "conjecture" tag to "hypothesis" on ATPs where this is possible;
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problem |
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151 |
|
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fun is_atp_variable s = Char.isUpper (String.sub (s, 0)) |
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153 |
|
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154 |
|
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(** Nice names **) |
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156 |
|
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fun empty_name_pool readable_names = |
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if readable_names then SOME (Symtab.empty, Symtab.empty) else NONE |
37624 | 159 |
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fun pool_fold f xs z = pair z #> fold_rev (fn x => uncurry (f x)) xs |
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fun pool_map f xs = |
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pool_fold (fn x => fn ys => fn pool => f x pool |>> (fn y => y :: ys)) xs [] |
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||
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val no_qualifiers = |
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let |
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fun skip [] = [] |
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| skip (#"." :: cs) = skip cs |
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| skip (c :: cs) = if Char.isAlphaNum c then skip cs else c :: keep cs |
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and keep [] = [] |
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| keep (#"." :: cs) = skip cs |
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| keep (c :: cs) = c :: keep cs |
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in String.explode #> rev #> keep #> rev #> String.implode end |
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173 |
|
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fixed several bugs in Isar proof reconstruction, in particular w.r.t. mangled types and hAPP
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(* Long names can slow down the ATPs. *) |
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added "max_mono_instances" option to Sledgehammer and renamed old "monomorphize_limit" option
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val max_readable_name_size = 20 |
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176 |
|
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(* "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. *) |
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val reserved_nice_names = ["op", "equal", "eq"] |
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fun readable_name full_name s = |
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if s = full_name then |
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s |
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else |
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s |> no_qualifiers |
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|> Name.desymbolize (Char.isUpper (String.sub (full_name, 0))) |
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187 |
(* SNARK doesn't like sort (type) names that end with digits. We make |
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an effort to avoid this here. *) |
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|> (fn s => if Char.isDigit (String.sub (s, size s - 1)) then s ^ "_" |
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else s) |
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191 |
|> (fn s => |
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if size s > max_readable_name_size then |
193 |
String.substring (s, 0, max_readable_name_size div 2 - 4) ^ |
|
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Word.toString (hashw_string (full_name, 0w0)) ^ |
42659 | 195 |
String.extract (s, size s - max_readable_name_size div 2 + 4, |
196 |
NONE) |
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197 |
else |
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198 |
s) |
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|> (fn s => if member (op =) reserved_nice_names s then full_name else s) |
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|
201 |
fun nice_name (full_name, _) NONE = (full_name, NONE) |
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| nice_name (full_name, desired_name) (SOME the_pool) = |
|
39384 | 203 |
if String.isPrefix "$" full_name then |
204 |
(full_name, SOME the_pool) |
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205 |
else case Symtab.lookup (fst the_pool) full_name of |
|
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SOME nice_name => (nice_name, SOME the_pool) |
207 |
| NONE => |
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208 |
let |
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209 |
val nice_prefix = readable_name full_name desired_name |
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fun add j = |
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211 |
let |
|
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(* The trailing "_" is for SNARK (cf. comment above). *) |
213 |
val nice_name = |
|
214 |
nice_prefix ^ (if j = 0 then "" else "_" ^ string_of_int j ^ "_") |
|
37624 | 215 |
in |
216 |
case Symtab.lookup (snd the_pool) nice_name of |
|
217 |
SOME full_name' => |
|
218 |
if full_name = full_name' then (nice_name, the_pool) |
|
219 |
else add (j + 1) |
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220 |
| NONE => |
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221 |
(nice_name, |
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(Symtab.update_new (full_name, nice_name) (fst the_pool), |
|
223 |
Symtab.update_new (nice_name, full_name) (snd the_pool))) |
|
224 |
end |
|
225 |
in add 0 |> apsnd SOME end |
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226 |
||
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fun nice_term (ATerm (name, ts)) = |
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nice_name name ##>> pool_map nice_term ts #>> ATerm |
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fun nice_formula (AQuant (q, xs, phi)) = |
42526 | 230 |
pool_map nice_name (map fst xs) |
231 |
##>> pool_map (fn NONE => pair NONE |
|
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232 |
| SOME ty => nice_name ty #>> SOME) (map snd xs) |
42526 | 233 |
##>> nice_formula phi |
234 |
#>> (fn ((ss, ts), phi) => AQuant (q, ss ~~ ts, phi)) |
|
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| nice_formula (AConn (c, phis)) = |
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pool_map nice_formula phis #>> curry AConn c |
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| nice_formula (AAtom tm) = nice_term tm #>> AAtom |
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fun nice_problem_line (Decl (ident, sym, arg_tys, res_ty)) = |
42528 | 239 |
nice_name sym |
240 |
##>> pool_map nice_name arg_tys |
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241 |
##>> nice_name res_ty |
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#>> (fn ((sym, arg_tys), res_ty) => Decl (ident, sym, arg_tys, res_ty)) |
42577
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243 |
| nice_problem_line (Formula (ident, kind, phi, source, useful_info)) = |
42529
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added "useful_info" argument to ATP formulas -- this will probably be useful later to specify intro, simp, elim to SPASS
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244 |
nice_formula phi |
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#>> (fn phi => Formula (ident, kind, phi, source, useful_info)) |
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fun nice_problem problem = |
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247 |
pool_map (fn (heading, lines) => |
37931 | 248 |
pool_map nice_problem_line lines #>> pair heading) problem |
39452 | 249 |
fun nice_atp_problem readable_names problem = |
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250 |
nice_problem problem (empty_name_pool readable_names) |
37509
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251 |
|
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252 |
end; |