blob: 9c27b61b82fcd86abdd17e5e56da60f52f71edcd (
plain)
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
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
|
;; File: routing_main.lisp
;; Proof of the main theorem of Route
;; August 15th 2005
;; proof of compliance with GeNoC
(in-package "ACL2")
;; we import the definition of route and lemmas that prove its
;; correctness
(include-book "routing_local_lemmas")
;; 1. Correction of function Route
;; ------------------------------
;; we group the main properties of Route in one theorem
(local
(defthm consp_len_>_0
(implies (consp x)
(< 0 (len x)))))
(defthm CORRECTNESS_OF_ROUTE
(implies (and (natp from) (< from (* 4 n))
(natp to) (< to (* 4 n))
(not (equal from to))
(< 0 n) (integerp n))
(and ;; Route contains at least two nodes
(<= 2 (len (route from to n)))
;; it is a consp
(consp (route from to n))
;; every node is an integer
(OctagonNodeSetp (route from to n))
;; every node is less than the maximum of nodes
(all_inf_np (route from to n) (* 4 n))
;; the first node is the starting node
(equal (car (route from to n)) from)
;; the last node is the final node
(equal (car (last (route from to n))) to))))
;; we load the book about the generic routing
;; it also imports the types and misc. of GeNoC
(include-book "../../../generic-modules/GeNoC-routing")
;; 2. Definition of OctagonRouting
;; -------------------------------
(defun octagon-routing (Missives Bound)
(if (endp Missives)
nil
(let* ((miss (car Missives))
(Id (IdM miss))
(frm (FrmM miss))
(origin (OrgM miss))
(destination (DestM miss)))
(cons (list Id frm (list
(route origin destination
(/ Bound 4))))
(octagon-routing (cdr Missives) Bound)))))
;; 3. Matching the hyps
;; --------------------
;; in order to use the theorem CORRECTNESS_OF_ROUTE
;; we need to go from GeNoC hyps to the Octagon hyps
(defthm member-of-naturals-hyp
(implies (and (member-equal e (naturals N))
(natp N))
(and (natp e) (< e (+ 1 N)))))
(defthm len-naturalsp
(implies (natp N)
(equal (len (naturals N)) (+ 1 N))))
(defthm V-ids-M-ids-octagon-routing
;; this is the same lemma as for the witness
(equal (V-ids (octagon-routing Missives NodeSet))
(M-ids Missives)))
(defthm len->=-2-=>-consp-cdr
(implies (<= 2 (len x))
(consp (cdr x))))
;; the next theorem does not go through ... but should !!
;; check what's wrong ...
(defthm trlstp-octagon-routing
;; octagon-routing returns a TrLstp
;; the hints are very ugly.
;; They are all the same, but the proof does not go through
;; if I put the :use at the goal Subgoal *1/2.
(let ((NodeSet (OctagonNodeSetGenerator Bound)))
(implies (and (Missivesp M NodeSet)
; (equal NodeSet (Octagonnodesetgenerator Bound))
(OctagonValidParamsp Bound))
(TrLstp (octagon-routing M (* 4 bound)))))
:otf-flg t
:hints (("GOAL"
:induct (octagon-routing M (len (OctagonNodeSetGenerator Bound)))
:do-not-induct t
:in-theory (disable len))
("Subgoal *1/2.2"
:use ((:instance member-of-naturals-hyp
(e (cadar M))
(N (+ -1 (* 4 Bound))))
(:instance member-of-naturals-hyp
(e (cadddr (car M)))
(N (+ -1 (* 4 Bound)))))
:in-theory (disable member-of-naturals-hyp))
("Subgoal *1/2.1"
:use ((:instance member-of-naturals-hyp
(e (cadar M))
(N (+ -1 (* 4 Bound))))
(:instance member-of-naturals-hyp
(e (cadddr (car M)))
(N (+ -1 (* 4 Bound)))))
:in-theory (disable member-of-naturals-hyp))))
(defthm naturals_member
(implies (and (<= a b) (natp a) (natp b))
(member-equal a (naturals b))))
(defthm naturals_subset_all_inf
(implies (and (all_inf_np L n1)
(natp n1) (OctagonNodeSetp L))
(subsetp L (naturals (1- n1)))))
(defthm subsetp-route-valid-nodes
(implies (and (natp from) (< from (* 4 n))
(natp to) (< to (* 4 n))
(not (equal from to))
(integerp n) (< 0 n))
(let ((route (route from to n)))
(subsetp route (naturals (1- (* 4 n)))))))
(defthm CorrectRoutesp-Octagon-Routing
(let ((NodeSet (Naturals (+ -1 (* 4 N)))))
(implies (and (Missivesp M NodeSet)
; (equal NodeSet (Naturals (+ -1 (* 4 N))))
(OctagonValidParamsp N))
(CorrectRoutesp (octagon-routing M (* 4 n))
M NodeSet)))
:otf-flg t
:hints (("GOAL"
:do-not '(eliminate-destructors generalize fertilize)
:induct (true-listp M)
:do-not-induct t)
("Subgoal *1/1"
:use ((:instance member-of-naturals-hyp
(N (+ -1 (* 4 N)))
(e (nth 1 (car M))))
(:instance member-of-naturals-hyp
(N (+ -1 (* 4 N)))
(e (nth 3 (car M)))))
:in-theory (disable member-of-naturals-hyp))))
(defthm ToMissives-octagon-routing
(let ((NodeSet (Naturals (+ -1 (* 4 N)))))
(implies (and (Missivesp M NodeSet)
(OctagonValidParamsp N))
; (equal NodeSet (Naturals (+ -1 (* 4 N)))))
(equal (ToMissives (octagon-routing M
(* 4 N)))
M)))
:otf-flg t
:hints (("GOAL"
:do-not '(eliminate-destructors generalize fertilize)
:induct (true-listp M)
; [Removed by Matt K. to handle changes to member, assoc, etc. after ACL2 4.2.]
; :in-theory (disable no-duplicatesp->no-duplicatesp-equal)
:do-not-induct t)
("Subgoal *1/1"
:use ((:instance member-of-naturals-hyp
(N (+ -1 (* 4 N)))
(e (nth 1 (car M))))
(:instance member-of-naturals-hyp
(N (+ -1 (* 4 N)))
(e (nth 3 (car M)))))
:in-theory (disable member-of-naturals-hyp))))
(defun OctagonRouting (M NodeSet)
;; definition that is conform to GeNoC-routing
(octagon-routing M (len NodeSet)))
(defthm check-octagonrouting-compliance
t
:rule-classes nil
:otf-flg t
:hints (("GOAL"
:do-not-induct t
:use (:instance
(:functional-instance
trlstp-routing
(NodeSetGenerator OctagonNodeSetGenerator)
(NodeSetp OctagonNodeSetp)
(ValidParamsp OctagonValidParamsp)
(routing OctagonRouting)))
:in-theory (disable trlstp-routing
trlstp missivesp))))
|
