/usr/share/acl2-6.3/books/str/istrpos.lisp is in acl2-books-source 6.3-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 | ; 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/
;
; This program is free software; you can redistribute it and/or modify it under
; the terms of the GNU General Public License as published by the Free Software
; Foundation; either version 2 of the License, or (at your option) any later
; version. This program is distributed in the hope that it will be useful but
; WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
; FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
; more details. You should have received a copy of the GNU General Public
; License along with this program; if not, write to the Free Software
; Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA.
;
; Original author: Jared Davis <jared@centtech.com>
(in-package "STR")
(include-book "iprefixp")
(include-book "istrprefixp")
(local (include-book "arithmetic"))
(defsection istrpos
:parents (substrings)
:short "Case-insensitivly locate the first occurrence of a substring."
:long "<p>@(call istrpos) is like @(see strpos), but the comparisons are done
in a case insensitive manner. It returns @('nil') if @('x') never occurs in
@('y'), or returns the index of the first character of the first occurrence
otherwise.</p>
<p>The function is \"efficient\" in the sense that it does not coerce its
arguments into lists, but rather traverses both strings with @(see char). On
the other hand, it is a naive string search which operates by repeatedly
calling @(see istrprefixp) rather than some better algorithm.</p>
<p>The \"soundness\" and \"completness\" of strpos are established in the
theorems @('iprefixp-of-istrpos') and @('completeness-of-istrpos').</p>"
(defund istrpos-impl (x y n xl yl)
(declare (type string x y)
(type (integer 0 *) n xl yl)
(xargs :guard (and (stringp x)
(stringp y)
(natp xl)
(natp yl)
(natp n)
(<= n (length y))
(= xl (length x))
(= yl (length y)))
:measure (nfix (- (nfix yl) (nfix n)))))
(cond ((mbe :logic (iprefixp (explode x)
(nthcdr n (explode y)))
:exec (istrprefixp-impl (the string x)
(the string y)
(the (integer 0 *) 0)
(the (integer 0 *) n)
(the (integer 0 *) xl)
(the (integer 0 *) yl)))
(lnfix n))
((mbe :logic (zp (- (nfix yl) (nfix n)))
:exec (int= n yl))
nil)
(t
(istrpos-impl (the string x)
(the string y)
(the (integer 0 *) (+ 1 (the (integer 0 *) (lnfix n))))
(the (integer 0 *) xl)
(the (integer 0 *) yl)))))
(definlined istrpos (x y)
(declare (type string x y))
(let* ((xl (mbe :logic (len (explode x))
:exec (length (the string x))))
(yl (mbe :logic (len (explode y))
:exec (length (the string y)))))
(declare (type (integer 0 *) xl yl))
(istrpos-impl (the string x)
(the string y)
(the (integer 0 *) 0)
xl
yl)))
(local (in-theory (enable istrpos istrpos-impl)))
(defthm istrpos-type
(or (and (integerp (istrpos x y))
(<= 0 (istrpos x y)))
(not (istrpos x y)))
:rule-classes :type-prescription)
(encapsulate
()
(local (defthm lemma
(implies (and (istrpos-impl x y n xl yl)
(natp xl)
(natp yl)
(natp n)
(<= n (len (explode y)))
(= xl (len (explode x)))
(= yl (len (explode y))))
(iprefixp (explode x)
(nthcdr (istrpos-impl x y n xl yl)
(explode y))))
:hints(("Goal" :induct (istrpos-impl x y n xl yl)))))
(defthm iprefixp-of-istrpos
(implies (istrpos x y)
(iprefixp (explode x)
(nthcdr (istrpos x y) (explode y))))))
(encapsulate
()
(local (defun my-induction (x y n m xl yl)
(declare (xargs :measure (nfix (- (nfix yl) (nfix n)))))
(cond ((iprefixp (explode x)
(nthcdr n (explode y)))
nil)
((zp (- (nfix yl) (nfix n)))
(list x y n m xl yl))
(t
(my-induction x y
(+ (nfix n) 1)
(if (= (nfix n) (nfix m))
(+ (nfix m) 1)
(nfix m))
xl yl)))))
(local (defthm lemma
(implies (and (iprefixp (explode x)
(nthcdr m (explode y)))
(natp xl)
(natp yl)
(natp n)
(natp m)
(<= n (nfix m))
(<= n (len (explode y)))
(= xl (len (explode x)))
(= yl (len (explode y))))
(and (natp (istrpos-impl x y n xl yl))
(<= (istrpos-impl x y n xl yl) m)))
:hints(("Goal"
:induct (my-induction x y n m xl yl)
:do-not '(generalize fertilize)))))
(defthm completeness-of-istrpos
(implies (and (iprefixp (explode x)
(nthcdr m (explode y)))
(force (natp m)))
(and (natp (istrpos x y))
(<= (istrpos x y) m)))))
(defcong istreqv equal (istrpos-impl x y n xl yl) 1)
(defcong istreqv equal (istrpos-impl x y n xl yl) 2)
(local (in-theory (disable istreqv)))
(defcong istreqv equal (istrpos x y) 1)
(defcong istreqv equal (istrpos x y) 2))
|