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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 "misc/definline" :dir :system)
(include-book "strprefixp")
(include-book "std/lists/sublistp" :dir :system)
(include-book "std/basic/defs" :dir :system)
(local (include-book "arithmetic"))
(defsection strpos-fast
:parents (strpos)
:short "Fast implementation of @(see strpos)."
(defund strpos-fast (x y n xl yl)
(declare (type string x)
(type string y)
(type integer n)
(type integer xl)
(type integer 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 (prefixp (explode x)
(nthcdr n (explode y)))
:exec (strprefixp-impl (the string x)
(the string y)
(the integer 0)
(the integer n)
(the integer xl)
(the integer yl)))
(lnfix n))
((mbe :logic (zp (- (nfix yl) (nfix n)))
:exec (int= n yl))
nil)
(t
(strpos-fast (the string x)
(the string y)
(+ 1 (lnfix n))
(the integer xl)
(the integer yl)))))
(local (in-theory (enable strpos-fast)))
(local (defthm l0
(implies (sublistp x (cdr y))
(sublistp x y))
:hints(("Goal" :in-theory (enable sublistp)))))
(defthm strpos-fast-removal
(implies (and (force (stringp x))
(force (stringp y))
(force (natp n))
(force (equal xl (length x)))
(force (equal yl (length y))))
(equal (strpos-fast x y n xl yl)
(let ((idx (listpos (explode x)
(nthcdr n (explode y)))))
(and idx
(+ n idx)))))
:hints(("Goal"
:induct (strpos-fast x y n xl yl)
:do-not '(generalize fertilize eliminate-destructors)
:do-not-induct t
:in-theory (enable strpos-fast listpos)))))
(defsection strpos
:parents (substrings)
:short "Locate the first occurrence of a substring."
:long "<p>@(call strpos) searches through the string @('y') for the first
occurrence of the substring @('x'). If @('x') occurs somewhere in @('y'), it
returns the starting index of the first occurrence. Otherwise, it returns
@('nil') to indicate that @('x') never occurs in @('y').</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 strprefixp), rather than some better algorithm.</p>
<p>Corner case: we say that the empty string <b>is</b> a prefix of any other
string. That is, @('(strpos \"\" x)') is 0 for all @('x').</p>"
(definline strpos (x y)
(declare (type string x y))
(mbe :logic
(listpos (explode x)
(explode y))
:exec
(strpos-fast (the string x)
(the string y)
(the integer 0)
(the integer (length (the string x)))
(the integer (length (the string y))))))
(defcong streqv equal (strpos x y) 1)
(defcong streqv equal (strpos x y) 2))
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