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
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
|
;; Copyright (C) 2017, Regents of the University of Texas
;; Written by Cuong Chau (derived from the FM9001 work of Brock and Hunt)
;; License: A 3-clause BSD license. See the LICENSE file distributed with
;; ACL2.
;; The ACL2 source code for the FM9001 work is available at
;; https://github.com/acl2/acl2/tree/master/books/projects/fm9001.
;; Cuong Chau <ckcuong@cs.utexas.edu>
;; January 2019
;; Automatic definition and proofs for simple linear vector modules of
;; primitives or other modules. VECTOR-MODULE is defined in
;; "vector-macros.lisp".
(in-package "ADE")
(include-book "unbound")
(include-book "vector-macros")
;; ======================================================================
;; VECTOR-MODULE-INDUCTION
;; The induction scheme for vector modules.
(defun vector-module-induction (body m n wire-alist st-alist netlist)
(if (zp n)
(list body m wire-alist st-alist netlist)
(vector-module-induction
(cdr body)
(1+ m)
(1- n)
(se-occ-bindings 1 body wire-alist st-alist netlist)
st-alist
netlist)))
;; V-BUF
;; V-NOT
;; V-AND
;; V-OR
;; V-XOR
;; V-PULLUP
;; VFT-WIRE
(vector-module v-buf (g (y) b-buf (a)) ((v-threefix a)))
(vector-module v-not (g (y) b-not (a)) ((fv-not a)) :enable (fv-not))
(vector-module v-and (g (y) b-and (a b)) ((fv-and a b)) :enable (fv-and))
(vector-module v-or (g (y) b-or (a b)) ((fv-or a b)) :enable (fv-or))
(vector-module v-xor (g (y) b-xor (a b)) ((fv-xor a b)) :enable (fv-xor))
(vector-module v-pullup (g (y) pullup (a)) ((v-pullup a)) :enable (v-pullup))
(vector-module vft-wire (g (y) t-wire (a b)) ((vft-wire a b))
:enable (vft-wire))
;; V-WIRE
(defun v-wire-body (m n)
(declare (xargs :guard (and (natp m) (natp n))))
(if (zp n)
nil
(cons (list (si 'g m)
(list (si 'y m))
'wire
(list (si 'a m)))
(v-wire-body (1+ m) (1- n)))))
(module-generator
v-wire* (n)
(si 'v-wire n)
(sis 'a 0 n)
(sis 'y 0 n)
nil
(v-wire-body 0 n)
(declare (xargs :guard (natp n))))
(defund v-wire& (netlist n)
(declare (xargs :guard (and (alistp netlist) (natp n))))
(equal (assoc (si 'v-wire n) netlist)
(v-wire* n)))
(defund v-wire$netlist (n)
(declare (xargs :guard (natp n)))
(list (v-wire* n)))
(local
(defthm v-wire$unbound-in-body
(implies (and (natp l) (natp m) (< l m))
(unbound-in-body (si 'y l)
(v-wire-body m n)))
:hints (("Goal" :in-theory (enable occ-outs)))))
(local
(defthm v-wire-body$value
(implies
(and (natp m)
(equal body (v-wire-body m n)))
(equal (assoc-eq-values (sis 'y m n)
(se-occ body wire-alist st-alist netlist))
(assoc-eq-values (sis 'a m n)
wire-alist)))
:hints (("Goal"
:induct (vector-module-induction
body m n wire-alist st-alist netlist)
:in-theory (enable de-rules sis)))))
(defthm v-wire$value
(implies (and (v-wire& netlist n)
(true-listp a)
(equal (len a) n))
(equal (se (si 'v-wire n) a st netlist)
a))
:hints (("Goal"
:expand (:free (n)
(se (si 'v-wire n) a st netlist))
:in-theory (enable de-rules v-wire& v-wire*$destructure))))
;; V-IF
(defun v-if-body (m n)
(declare (xargs :guard (and (natp m) (natp n))))
(if (zp n)
nil
(cons (list (si 'g m)
(list (si 'y m))
'b-if
(list 'c (si 'a m) (si 'b m)))
(v-if-body (1+ m) (1- n)))))
(module-generator
v-if* (n)
(si 'v-if n)
(cons 'c
(append (sis 'a 0 n) (sis 'b 0 n)))
(sis 'y 0 n)
nil
(v-if-body 0 n)
(declare (xargs :guard (natp n))))
(defund v-if& (netlist n)
(declare (xargs :guard (and (alistp netlist) (natp n))))
(equal (assoc (si 'v-if n) netlist)
(v-if* n)))
(defund v-if$netlist (n)
(declare (xargs :guard (natp n)))
(list (v-if* n)))
(local
(defthm v-if$unbound-in-body
(implies (and (natp l) (natp m) (< l m))
(unbound-in-body (si 'y l)
(v-if-body m n)))
:hints (("Goal" :in-theory (enable occ-outs)))))
(local
(defthm v-if-body$value
(implies
(and (natp m)
(equal body (v-if-body m n)))
(equal (assoc-eq-values (sis 'y m n)
(se-occ body wire-alist st-alist netlist))
(fv-if (assoc-eq-value 'c wire-alist)
(assoc-eq-values (sis 'a m n) wire-alist)
(assoc-eq-values (sis 'b m n) wire-alist))))
:hints (("Goal"
:induct (vector-module-induction
body m n wire-alist st-alist netlist)
:in-theory (enable de-rules sis fv-if)))))
(defthm v-if$value
(implies (and (v-if& netlist n)
(true-listp a) (equal (len a) n)
(true-listp b) (equal (len b) n))
(equal (se (si 'v-if n) (cons c (append a b)) st netlist)
(fv-if c a b)))
:hints (("Goal"
:expand (:free (inputs n)
(se (si 'v-if n) inputs st netlist))
:in-theory (enable de-rules v-if& v-if*$destructure))))
|
