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
|
; ACL2 String Library
; Copyright (C) 2009-2013 Centaur Technology
;
; Contact:
; Centaur Technology Formal Verification Group
; 7600-C N. Capital of Texas Highway, Suite 300, Austin, TX 78731, USA.
; http://www.centtech.com/
;
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
;
; Original author: Jared Davis <jared@centtech.com>
(in-package "STR")
(include-book "strprefixp")
(local (include-book "std/lists/nthcdr" :dir :system))
(local (include-book "arithmetic/top" :dir :system))
(local (in-theory (disable acl2::prefixp-when-equal-lengths)))
(local (defthm crock
(implies (and (equal (len x) (len y))
(true-listp x)
(true-listp y))
(equal (prefixp x y)
(equal x y)))
:hints(("Goal" :in-theory (enable prefixp)))))
(defsection strsuffixp
:parents (substrings)
:short "Case-sensitive string suffix test."
:long "<p>@(call strsuffixp) determines if the string @('x') is a suffix of
the string @('y'), in a case-sensitive manner.</p>
<p>Logically, we ask whether @('|x| < |y|'), and whether</p>
@({
(equal (nthcdr (- |y| |x|) (explode x))
(explode y))
})
<p>But we use a more efficient implementation that avoids coercing the strings
into lists; basically we ask if the last @('|x|') characters of @('y') are
equal to @('x').</p>
<p>Corner case: we regard the empty string as a suffix of every other string.
That is, @('(strsuffixp \"\" x)') is always true.</p>"
(definlined strsuffixp (x y)
(declare (type string x y))
(mbe :logic
(let* ((xchars (explode x))
(ychars (explode y))
;; note that using, e.g., (len (explode x)) instead of (length
;; x)) gives better congruence behavior
(xlen (len xchars))
(ylen (len ychars)))
(and (<= xlen ylen)
(equal (nthcdr (- ylen xlen) (explode y))
(explode x))))
:exec
(let* ((xlen (length x))
(ylen (length y)))
(and (<= xlen ylen)
(strprefixp-impl x y 0 (- ylen xlen) xlen ylen)))))
(local (in-theory (enable strsuffixp)))
(local (defthm c0
(implies (and (natp n)
(<= (len x) n)
(true-listp x))
(equal (nthcdr n x) nil))))
(local (defthm c1
(implies (true-listp x)
(not (nthcdr (len x) x)))))
(defthm strsuffixp-of-empty
(strsuffixp "" y))
(defcong streqv equal (strsuffixp x y) 1)
(defcong streqv equal (strsuffixp x y) 2))
|
