blob: 8e38395815ada1747ac27712f287919d49ebcbfa (
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
|
(in-package "ACL2")
(defun true-flistp (x)
(if (endp x)
(null x)
(and (consp x)
(true-flistp (car x)))))
(defun list-to-flist (x)
(if (endp x)
nil
(cons (list-to-flist (cdr x))
(car x))))
(defun flist-to-list (x)
(if (endp x)
nil
(cons (cdr x)
(flist-to-list (car x)))))
(defthm flist-to-list-to-flist
(implies (true-flistp x)
(equal (list-to-flist (flist-to-list x))
x)))
(defthm list-to-flist-to-list
(implies (true-listp x)
(equal (flist-to-list (list-to-flist x))
x)))
(defun fappend (x y)
(if (endp x)
y
(cons (fappend (car x) y)
(cdr x))))
(defthm assocativity-of-append
(equal (fappend (fappend x y) z)
(fappend x (fappend y z))))
(defthm fappend-append
(implies (and (true-listp x)
(true-listp y))
(equal (flist-to-list (fappend (list-to-flist x)
(list-to-flist y)))
(append x y))))
|
