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
|
; 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 "ieqv")
(include-book "std/lists/prefixp" :dir :system)
(local (include-book "arithmetic"))
(defsection iprefixp
:parents (substrings)
:short "Case-insensitive character-list prefix test."
:long "<p>@(call iprefixp) determines whether one character list is a prefix
of another, where each character is tested using @(see ichareqv).</p>"
(defund iprefixp (x y)
(declare (xargs :guard (and (character-listp x)
(character-listp y))))
(if (consp x)
(and (consp y)
(ichareqv (car x) (car y))
(iprefixp (cdr x) (cdr y)))
t))
(local (in-theory (enable iprefixp)))
(defthm iprefixp-when-not-consp-left
(implies (not (consp x))
(iprefixp x y)))
(defthm iprefixp-of-cons-left
(equal (iprefixp (cons a x) y)
(and (consp y)
(ichareqv a (car y))
(iprefixp x (cdr y)))))
(defthm iprefixp-when-not-consp-right
(implies (not (consp y))
(equal (iprefixp x y)
(not (consp x))))
:hints(("Goal" :induct (len x))))
(defthm iprefixp-of-cons-right
(equal (iprefixp x (cons a y))
(if (consp x)
(and (ichareqv (car x) a)
(iprefixp (cdr x) y))
t)))
(defthm iprefixp-of-list-fix-left
(equal (iprefixp (list-fix x) y)
(iprefixp x y)))
(defthm iprefixp-of-list-fix-right
(equal (iprefixp x (list-fix y))
(iprefixp x y)))
(defcong icharlisteqv equal (iprefixp x y) 1)
(defcong icharlisteqv equal (iprefixp x y) 2)
(defthm iprefixp-when-prefixp
(implies (prefixp x y) (iprefixp x y))))
|
