-
Notifications
You must be signed in to change notification settings - Fork 85
/
Copy pathWord8ProgScript.sml
155 lines (123 loc) · 4.08 KB
/
Word8ProgScript.sml
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
(*
Module about the built-in word8 type.
*)
open preamble ml_translatorLib ml_progLib basisFunctionsLib
Word64ProgTheory
val _ = new_theory "Word8Prog";
val _ = translation_extends "Word64Prog";
(* Word8 module -- translated *)
val _ = ml_prog_update (add_dec
``Dtabbrev unknown_loc [] "byte" (Atapp [] (Short "word8"))`` I);
val _ = ml_prog_update (open_module "Word8");
val () = generate_sigs := true;
val _ = ml_prog_update (add_dec
``Dtabbrev unknown_loc [] "word" (Atapp [] (Short "word8"))`` I);
(* to/from int *)
val _ = trans "fromInt" ``n2w:num->word8``;
val _ = trans "toInt" ``w2n:word8->num``;
val _ = trans "toIntSigned" ``w2i:word8->int``;
(* bitwise operations *)
val _ = trans "andb" ``word_and:word8->word8->word8``;
val _ = trans "orb" ``word_or:word8->word8->word8``;
val _ = trans "xorb" ``word_xor:word8->word8->word8``;
val word_1comp_eq = prove(
``word_1comp w = word_xor w 0xFFw:word8``,
fs []);
val _ = (next_ml_names := ["notb"]);
val _ = translate word_1comp_eq
(* arithmetic *)
val _ = trans "+" ``word_add:word8->word8->word8``;
val _ = trans "-" ``word_sub:word8->word8->word8``;
(* shifts *)
Definition var_word_lsl_def:
var_word_lsl (w:word8) (n:num) =
if n < 8 then
if n < 4 then
if n < 2 then if n < 1 then w else w << 1
else if n < 3 then w << 2
else w << 3
else if n < 6 then if n < 5 then w << 4 else w << 5
else if n < 7 then w << 6
else w << 7 else 0w
End
Theorem var_word_lsl_thm[simp]:
var_word_lsl w n = word_lsl w n
Proof
ntac 32 (
Cases_on `n` \\ fs [ADD1] THEN1 (EVAL_TAC \\ fs [LSL_ADD])
\\ Cases_on `n'` \\ fs [ADD1] THEN1 (EVAL_TAC \\ fs [LSL_ADD]))
\\ ntac 9 (once_rewrite_tac [var_word_lsl_def] \\ fs [])
QED
Definition var_word_lsr_def:
var_word_lsr (w:word8) (n:num) =
if n < 8 then
if n < 4 then
if n < 2 then if n < 1 then w else w >>> 1
else if n < 3 then w >>> 2
else w >>> 3
else if n < 6 then if n < 5 then w >>> 4 else w >>> 5
else if n < 7 then w >>> 6
else w >>> 7 else 0w
End
Theorem var_word_lsr_thm[simp]:
var_word_lsr w n = word_lsr w n
Proof
ntac 32 (
Cases_on `n` \\ fs [ADD1] THEN1 (EVAL_TAC \\ fs [LSR_ADD])
\\ Cases_on `n'` \\ fs [ADD1] THEN1 (EVAL_TAC \\ fs [LSR_ADD]))
\\ ntac 9 (once_rewrite_tac [var_word_lsr_def] \\ fs [])
QED
Definition var_word_asr_def:
var_word_asr (w:word8) (n:num) =
if n < 8 then
if n < 4 then
if n < 2 then if n < 1 then w else w >> 1
else if n < 3 then w >> 2
else w >> 3
else if n < 6 then if n < 5 then w >> 4 else w >> 5
else if n < 7 then w >> 6
else w >> 7 else w >> 8
End
Theorem var_word_asr_thm[simp]:
var_word_asr w n = word_asr w n
Proof
ntac 32 (
Cases_on `n` \\ fs [ADD1] THEN1 (EVAL_TAC \\ fs [ASR_ADD])
\\ Cases_on `n'` \\ fs [ADD1] THEN1 (EVAL_TAC \\ fs [ASR_ADD]))
\\ ntac 9 (once_rewrite_tac [var_word_asr_def] \\ fs [])
QED
val _ = (next_ml_names := ["<<"]);
val _ = translate var_word_lsl_def;
val _ = (next_ml_names := [">>"]);
val _ = translate var_word_lsr_def;
val _ = (next_ml_names := ["~>>"]);
val _ = translate var_word_asr_def;
val sigs = module_signatures ["fromInt", "toInt", "andb",
"orb", "xorb", "notb", "+", "-", "<<", ">>", "~>>"];
val _ = ml_prog_update (close_module (SOME sigs));
(* if any more theorems get added here, probably should create Word8ProofTheory *)
open ml_translatorTheory
Theorem WORD_UNICITY_R[xlet_auto_match]:
!f fv fv'. WORD (f :word8) fv ==> (WORD f fv' <=> fv' = fv)
Proof
fs[WORD_def]
QED
Theorem WORD_UNICITY_L[xlet_auto_match]:
!f f' fv. WORD (f :word8) fv ==> (WORD f' fv <=> f = f')
Proof
fs[WORD_def]
QED
Theorem n2w_UNICITY[xlet_auto_match]:
!n1 n2.n1 <= 255 ==> ((n2w n1 :word8 = n2w n2 /\ n2 <= 255) <=> n1 = n2)
Proof
rw[] >> eq_tac >> fs[]
QED
Theorem WORD_n2w_UNICITY_L[xlet_auto_match]:
!n1 n2 f. n1 <= 255 /\ WORD (n2w n1 :word8) f ==>
(WORD (n2w n2 :word8) f /\ n2 <= 255 <=> n1 = n2)
Proof
rw[] >> eq_tac >> rw[] >> imp_res_tac WORD_UNICITY_L >>
`n1 MOD 256 = n1` by fs[] >> `n2 MOD 256 = n2` by fs[] >> fs[]
QED
Overload WORD8 = ``WORD:word8 -> v -> bool``
val _ = export_theory()