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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 "eqv")
(include-book "std/lists/prefixp" :dir :system)
(include-book "misc/definline" :dir :system) ;; bozo
(local (include-book "std/lists/nthcdr" :dir :system))
(local (include-book "arithmetic"))
(local (defthm prefixp-lemma-1
(implies (and (natp xn)
(natp yn)
(< xn (len x))
(< yn (len y))
(not (equal (nth xn x) (nth yn y))))
(not (prefixp (nthcdr xn x) (nthcdr yn y))))
:hints(("Goal" :in-theory (enable nthcdr nth prefixp)))))
(local (defthm prefixp-lemma-2
(implies (and (natp xn)
(natp yn)
(< xn (len x))
(< yn (len y))
(equal (nth xn x) (nth yn y)))
(equal (prefixp (nthcdr xn x) (nthcdr yn y))
(prefixp (cdr (nthcdr xn x)) (cdr (nthcdr yn y)))))
:hints(("Goal" :in-theory (enable prefixp nth nthcdr)))))
(defsection strprefixp-impl
:parents (strprefixp)
:short "Fast implementation of @(see strprefixp)."
(defund strprefixp-impl (x y xn yn xl yl)
(declare (type string x)
(type string y)
(type integer xn)
(type integer yn)
(type integer xl)
(type integer yl)
(xargs :guard (and (stringp x)
(stringp y)
(natp xn)
(natp yn)
(natp xl)
(natp yl)
(= xl (length x))
(= yl (length y))
(<= xn (length x))
(<= yn (length y)))
:measure (min (nfix (- (nfix xl) (nfix xn)))
(nfix (- (nfix yl) (nfix yn))))))
(cond ((mbe :logic (zp (- (nfix xl) (nfix xn)))
:exec (int= xn xl))
t)
((mbe :logic (zp (- (nfix yl) (nfix yn)))
:exec (int= yn yl))
nil)
((eql (the character (char x xn))
(the character (char y yn)))
(mbe :logic (strprefixp-impl x y
(+ (nfix xn) 1)
(+ (nfix yn) 1)
xl yl)
:exec (strprefixp-impl (the string x)
(the string y)
(the integer (+ (the integer xn) 1))
(the integer (+ (the integer yn) 1))
(the integer xl)
(the integer yl))))
(t
nil)))
(local (in-theory (enable strprefixp-impl)))
(defthm strprefixp-impl-elim
(implies (and (force (stringp x))
(force (stringp y))
(force (natp xn))
(force (natp yn))
(force (= xl (length x)))
(force (= yl (length y))))
(equal (strprefixp-impl x y xn yn xl yl)
(prefixp (nthcdr xn (explode x))
(nthcdr yn (explode y)))))))
(defsection strprefixp
:parents (substrings)
:short "Case-sensitive string prefix test."
:long "<p>@(call strprefixp) determines if the string @('x') is a prefix of
the string @('y'), in a case-sensitive manner.</p>
<p>Logically, this is identical to</p>
@({
(prefixp (explode x) (explode y))
})
<p>But we use a more efficient implementation which avoids coercing the strings
into character lists.</p>"
(definline strprefixp (x y)
(declare (type string x)
(type string y))
(mbe :logic (prefixp (explode x)
(explode y))
:exec (strprefixp-impl (the string x)
(the string y)
(the integer 0)
(the integer 0)
(the integer (length (the string x)))
(the integer (length (the string y))))))
(defcong streqv equal (strprefixp x y) 1)
(defcong streqv equal (strprefixp x y) 2))
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