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; 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 "istrpos")
(local (include-book "arithmetic"))
(defsection isubstrp
:parents (substrings)
:short "Case-insensitively test for the existence of a substring."
:long "<p>@(call isubstrp) determines if x ever occurs as a case-insensitive
substring of y.</p>
<p>See also @(see substrp) for a case-sensitive version.</p>
<p>See also @(see istrpos) for an alternative that reports the position of the
matched substring.</p>"
(definlined isubstrp (x y)
(declare (type string x y))
(if (istrpos x y)
t
nil))
(local (in-theory (enable isubstrp)))
(defthm iprefixp-when-isubstrp
(implies (isubstrp x y)
(iprefixp (explode x)
(nthcdr (istrpos x y) (explode y)))))
(defthm completeness-of-isubstrp
(implies (and (iprefixp (explode x)
(nthcdr m (explode y)))
(force (natp m)))
(isubstrp x y))
:hints(("Goal"
:in-theory (disable completeness-of-istrpos)
:use ((:instance completeness-of-istrpos)))))
(local (in-theory (disable istreqv)))
(defcong istreqv equal (isubstrp x y) 1)
(defcong istreqv equal (isubstrp x y) 2))
(defsection collect-strs-with-isubstr
:parents (substrings)
:short "Gather strings that have some (case-insensitive) substring."
:long "<p>@(call collect-strs-with-isubstr) returns a list of all the strings
in the list @('x') that have @('a') as a case-insensitve substring. The
substring tests are carried out with @(see isubstrp).</p>
<p>See also @(see collect-syms-with-isubstr), which is similar but for symbol
lists instead of string lists.</p>"
(defund collect-strs-with-isubstr (a x)
(declare (xargs :guard (and (stringp a)
(string-listp x))))
(cond ((atom x)
nil)
((str::isubstrp a (car x))
(cons (car x) (collect-strs-with-isubstr a (cdr x))))
(t
(collect-strs-with-isubstr a (cdr x)))))
(local (in-theory (enable collect-strs-with-isubstr)))
(defcong istreqv equal (collect-strs-with-isubstr a x) 1
:hints(("Goal" :in-theory (disable istreqv))))
(defthm collect-strs-with-isubstr-when-atom
(implies (atom x)
(equal (collect-strs-with-isubstr a x)
nil)))
(defthm collect-strs-with-isubstr-of-cons
(equal (collect-strs-with-isubstr a (cons b x))
(if (str::isubstrp a b)
(cons b (collect-strs-with-isubstr a x))
(collect-strs-with-isubstr a x))))
(defthm member-equal-collect-strs-with-isubstr
(iff (member-equal b (collect-strs-with-isubstr a x))
(and (member-equal b x)
(str::isubstrp a b))))
(defthm subsetp-equal-of-collect-strs-with-isubstr
(implies (subsetp-equal x y)
(subsetp-equal (collect-strs-with-isubstr a x) y)))
(defthm subsetp-equal-collect-strs-with-isubstr-self
(subsetp-equal (collect-strs-with-isubstr a x) x)))
(defsection collect-syms-with-isubstr
:parents (substrings)
:short "Gather symbols whose names have some (case-insensitive) substring."
:long "<p>@(call collect-syms-with-isubstr) returns a list of all the symbols
in the list @('x') that have @('a') as a case-insensitve substring of their
@(see symbol-name). The substring tests are carried out with @(see
isubstrp).</p>
<p>See also @(see collect-strs-with-isubstr), which is similar but for string
lists instead of symbol lists.</p>"
(defund collect-syms-with-isubstr (a x)
(declare (xargs :guard (and (stringp a)
(symbol-listp x))))
(cond ((atom x)
nil)
((str::isubstrp a (symbol-name (car x)))
(cons (car x) (collect-syms-with-isubstr a (cdr x))))
(t
(collect-syms-with-isubstr a (cdr x)))))
(local (in-theory (enable collect-syms-with-isubstr)))
(defcong istreqv equal (collect-syms-with-isubstr a x) 1
:hints(("Goal" :in-theory (disable istreqv))))
(defthm collect-syms-with-isubstr-when-atom
(implies (atom x)
(equal (collect-syms-with-isubstr a x)
nil)))
(defthm collect-syms-with-isubstr-of-cons
(equal (collect-syms-with-isubstr a (cons b x))
(if (str::isubstrp a (symbol-name b))
(cons b (collect-syms-with-isubstr a x))
(collect-syms-with-isubstr a x))))
(defthm member-equal-collect-syms-with-isubstr
(iff (member-equal b (collect-syms-with-isubstr a x))
(and (member-equal b x)
(str::isubstrp a (symbol-name b)))))
(defthm subsetp-equal-of-collect-syms-with-isubstr
(implies (subsetp-equal x y)
(subsetp-equal (collect-syms-with-isubstr a x) y)))
(defthm subsetp-equal-collect-syms-with-isubstr-self
(subsetp-equal (collect-syms-with-isubstr a x) x)))
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