(* Title: HOL/Tools/numeral_syntax.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
Concrete syntax for generic numerals. Assumes consts and syntax of
theory HOL/Numeral.
*)
signature NUMERAL_SYNTAX =
sig
val dest_bin : term -> int
val mk_bin : int -> term
val setup : (theory -> theory) list
end;
structure NumeralSyntax: NUMERAL_SYNTAX =
struct
(* bits *)
fun mk_bit 0 = Syntax.const "False"
| mk_bit 1 = Syntax.const "True"
| mk_bit _ = sys_error "mk_bit";
fun dest_bit (Const ("False", _)) = 0
| dest_bit (Const ("True", _)) = 1
| dest_bit _ = raise Match;
(* bit strings *) (*we try to handle superfluous leading digits nicely*)
fun prefix_len _ [] = 0
| prefix_len pred (x :: xs) =
if pred x then 1 + prefix_len pred xs else 0;
fun mk_bin n =
let
fun bin_of 0 = []
| bin_of ~1 = [~1]
| bin_of n = (n mod 2) :: bin_of (n div 2);
fun term_of [] = Syntax.const "Numeral.bin.Pls"
| term_of [~1] = Syntax.const "Numeral.bin.Min"
| term_of (b :: bs) = Syntax.const "Numeral.bin.Bit" $ term_of bs
$ mk_bit b;
in term_of (bin_of n) end;
fun bin_of_string str =
let
val (sign, digs) =
(case Symbol.explode str of
"#" :: "-" :: cs => (~1, cs)
| "#" :: cs => (1, cs)
| _ => raise ERROR);
in mk_bin (sign * (#1 (Term.read_int digs))) end;
(*we consider all "spellings"; Min is likely to be declared elsewhere*)
fun bin_of (Const ("Pls", _)) = []
| bin_of (Const ("bin.Pls", _)) = []
| bin_of (Const ("Numeral.bin.Pls", _)) = []
| bin_of (Const ("Min", _)) = [~1]
| bin_of (Const ("bin.Min", _)) = [~1]
| bin_of (Const ("Numeral.bin.Min", _)) = [~1]
| bin_of (Const ("Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
| bin_of (Const ("bin.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
| bin_of (Const ("Numeral.bin.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
| bin_of _ = raise Match;
fun int_of [] = 0
| int_of (b :: bs) = b + 2 * int_of bs;
val dest_bin = int_of o bin_of;
fun dest_bin_str tm =
let
val rev_digs = bin_of tm;
val (sign, zs) =
(case rev rev_digs of
~1 :: bs => ("-", prefix_len (equal 1) bs)
| bs => ("", prefix_len (equal 0) bs));
val num = string_of_int (abs (int_of rev_digs));
in "#" ^ sign ^ implode (replicate zs "0") ^ num end;
(* translation of integer numeral tokens to and from bitstrings *)
fun numeral_tr (*"_Numeral"*) [t as Free (str, _)] =
(Syntax.const "Numeral.number_of" $
(bin_of_string str handle ERROR => raise TERM ("numeral_tr", [t])))
| numeral_tr (*"_Numeral"*) ts = raise TERM ("numeral_tr", ts);
fun numeral_tr' show_sorts (*"number_of"*) (Type ("fun", [_, T])) (t :: ts) =
let val t' = Syntax.const "_Numeral" $ (Syntax.const "_xnum" $ Syntax.free (dest_bin_str t)) in
if can Term.dest_Type T then t'
else Syntax.const Syntax.constrainC $ t' $ Syntax.term_of_typ show_sorts T
end
| numeral_tr' _ (*"number_of"*) _ _ = raise Match;
(* theory setup *)
val setup =
[Theory.add_trfuns ([], [("_Numeral", numeral_tr)], [], []),
Theory.add_trfunsT [("number_of", numeral_tr'), ("Numeral.number_of", numeral_tr')]];
end;