/usr/share/acl2-4.3/books/str/substrp.lisp is in acl2-books-source 4.3-3.
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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 | ; ACL2 String Library
; Copyright (C) 2009-2010 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 "strpos")
(local (include-book "arithmetic"))
(defund substrp (x y)
":Doc-Section Str
Case-sensitive test for the existence of a substring~/
~c[(substrp x y)] determines if x ever occurs as a substring of y. The test is
case-sensitive.~/
~l[str::isubstrp], and ~pl[str::strpos]"
(declare (type string x)
(type string y))
(if (strpos x y)
t
nil))
(defthm prefixp-when-substrp
(implies (and (substrp x y)
(force (stringp x))
(force (stringp y)))
(prefixp (coerce x 'list)
(nthcdr (strpos x y) (coerce y 'list))))
:hints(("Goal" :in-theory (enable substrp))))
(defthm completeness-of-substrp
(implies (and (prefixp (coerce x 'list)
(nthcdr m (coerce y 'list)))
(force (natp m))
(force (stringp x))
(force (stringp y)))
(substrp x y))
:hints(("Goal"
:in-theory (e/d (substrp)
(completeness-of-strpos))
:use ((:instance completeness-of-strpos)))))
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