6905
|
1 |
(* Title: HOL/Tools/numeral_syntax.ML
|
|
2 |
ID: $Id$
|
|
3 |
Author: Markus Wenzel, TU Muenchen
|
|
4 |
|
|
5 |
Concrete syntax for generic numerals. Assumes consts and syntax of
|
|
6 |
theory HOL/Numeral.
|
|
7 |
*)
|
|
8 |
|
|
9 |
signature NUMERAL_SYNTAX =
|
|
10 |
sig
|
7055
|
11 |
val dest_bin : term -> int
|
|
12 |
val mk_bin : int -> term
|
|
13 |
val setup : (theory -> theory) list
|
6905
|
14 |
end;
|
|
15 |
|
|
16 |
structure NumeralSyntax: NUMERAL_SYNTAX =
|
|
17 |
struct
|
|
18 |
|
|
19 |
|
|
20 |
(* bits *)
|
|
21 |
|
7078
|
22 |
fun mk_bit 0 = HOLogic.false_const
|
|
23 |
| mk_bit 1 = HOLogic.true_const
|
6905
|
24 |
| mk_bit _ = sys_error "mk_bit";
|
|
25 |
|
|
26 |
fun dest_bit (Const ("False", _)) = 0
|
|
27 |
| dest_bit (Const ("True", _)) = 1
|
|
28 |
| dest_bit _ = raise Match;
|
|
29 |
|
|
30 |
|
|
31 |
(* bit strings *) (*we try to handle superfluous leading digits nicely*)
|
|
32 |
|
|
33 |
fun prefix_len _ [] = 0
|
|
34 |
| prefix_len pred (x :: xs) =
|
|
35 |
if pred x then 1 + prefix_len pred xs else 0;
|
|
36 |
|
7055
|
37 |
fun mk_bin n =
|
|
38 |
let
|
|
39 |
fun bin_of 0 = []
|
|
40 |
| bin_of ~1 = [~1]
|
|
41 |
| bin_of n = (n mod 2) :: bin_of (n div 2);
|
|
42 |
|
7078
|
43 |
fun term_of [] = HOLogic.pls_const
|
|
44 |
| term_of [~1] = HOLogic.min_const
|
|
45 |
| term_of (b :: bs) = HOLogic.bit_const $ term_of bs $ mk_bit b;
|
7055
|
46 |
in term_of (bin_of n) end;
|
|
47 |
|
|
48 |
fun bin_of_string str =
|
6905
|
49 |
let
|
|
50 |
val (sign, digs) =
|
|
51 |
(case Symbol.explode str of
|
|
52 |
"#" :: "-" :: cs => (~1, cs)
|
|
53 |
| "#" :: cs => (1, cs)
|
|
54 |
| _ => raise ERROR);
|
7055
|
55 |
in mk_bin (sign * (#1 (Term.read_int digs))) end;
|
6905
|
56 |
|
|
57 |
(*we consider all "spellings"; Min is likely to be declared elsewhere*)
|
|
58 |
fun bin_of (Const ("Pls", _)) = []
|
|
59 |
| bin_of (Const ("bin.Pls", _)) = []
|
|
60 |
| bin_of (Const ("Numeral.bin.Pls", _)) = []
|
|
61 |
| bin_of (Const ("Min", _)) = [~1]
|
|
62 |
| bin_of (Const ("bin.Min", _)) = [~1]
|
|
63 |
| bin_of (Const ("Numeral.bin.Min", _)) = [~1]
|
|
64 |
| bin_of (Const ("Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
|
|
65 |
| bin_of (Const ("bin.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
|
|
66 |
| bin_of (Const ("Numeral.bin.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
|
|
67 |
| bin_of _ = raise Match;
|
|
68 |
|
|
69 |
fun int_of [] = 0
|
|
70 |
| int_of (b :: bs) = b + 2 * int_of bs;
|
|
71 |
|
|
72 |
val dest_bin = int_of o bin_of;
|
|
73 |
|
|
74 |
fun dest_bin_str tm =
|
|
75 |
let
|
|
76 |
val rev_digs = bin_of tm;
|
|
77 |
val (sign, zs) =
|
|
78 |
(case rev rev_digs of
|
|
79 |
~1 :: bs => ("-", prefix_len (equal 1) bs)
|
|
80 |
| bs => ("", prefix_len (equal 0) bs));
|
|
81 |
val num = string_of_int (abs (int_of rev_digs));
|
|
82 |
in "#" ^ sign ^ implode (replicate zs "0") ^ num end;
|
|
83 |
|
|
84 |
|
|
85 |
(* translation of integer numeral tokens to and from bitstrings *)
|
|
86 |
|
|
87 |
fun numeral_tr (*"_Numeral"*) [t as Free (str, _)] =
|
|
88 |
(Syntax.const "Numeral.number_of" $
|
7055
|
89 |
(bin_of_string str handle ERROR => raise TERM ("numeral_tr", [t])))
|
6905
|
90 |
| numeral_tr (*"_Numeral"*) ts = raise TERM ("numeral_tr", ts);
|
|
91 |
|
|
92 |
fun numeral_tr' show_sorts (*"number_of"*) (Type ("fun", [_, T])) (t :: ts) =
|
|
93 |
let val t' = Syntax.const "_Numeral" $ (Syntax.const "_xnum" $ Syntax.free (dest_bin_str t)) in
|
|
94 |
if can Term.dest_Type T then t'
|
|
95 |
else Syntax.const Syntax.constrainC $ t' $ Syntax.term_of_typ show_sorts T
|
|
96 |
end
|
|
97 |
| numeral_tr' _ (*"number_of"*) _ _ = raise Match;
|
|
98 |
|
|
99 |
|
|
100 |
(* theory setup *)
|
|
101 |
|
|
102 |
val setup =
|
|
103 |
[Theory.add_trfuns ([], [("_Numeral", numeral_tr)], [], []),
|
|
104 |
Theory.add_trfunsT [("number_of", numeral_tr'), ("Numeral.number_of", numeral_tr')]];
|
|
105 |
|
|
106 |
|
|
107 |
end;
|