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; Defsort - Defines a stable sort when given a comparison function
; Copyright (C) 2008 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 "ACL2")
(include-book "defsort")
(include-book "misc/total-order" :dir :system)
(include-book "std/util/define" :dir :system)
(defsort :compare< <<
:prefix <<)
(define no-adjacent-duplicates-p (x)
:parents (uniquep)
(cond ((atom x)
t)
((atom (cdr x))
t)
(t
(and (not (equal (car x) (cadr x)))
(no-adjacent-duplicates-p (cdr x))))))
(define uniquep (x)
:parents (no-duplicatesp)
:short "Sometimes better than @(see no-duplicatesp): first sorts the list and
then looks for adjacent duplicates."
:long "<p>@(call uniquep) is provably equal to @('(no-duplicatesp x)'), but
has different performance characteristics. It operates by sorting its argument
and then scanning for adjacent duplicates.</p>
<p>Note: we leave this function enabled. You should never write a theorem
about @('uniquep'). Reason about @(see no-duplicatesp) instead.</p>
<p>Since we use a mergesort, the complexity of @('uniquep') is @('O(n log n)').
By comparison, @('no-duplicatesp') is @('O(n^2)').</p>
<p>It is not always better to use @('uniquep') than @('no-duplicatesp'):</p>
<ul>
<li>It uses far more memory than @('no-duplicatesp') because it sorts the
list.</li>
<li>On a list with lots of duplicates, @('no-duplicatesp') may find a duplicate
very quickly and stop early, but @('uniquep') has to sort the whole list before
it looks for any duplicates.</li>
</ul>
<p>However, if your lists are sometimes long with few duplicates, @('uniquep')
is probably a much better function to use.</p>"
:inline t
:enabled t
(mbe :logic (no-duplicatesp x)
:exec (no-adjacent-duplicates-p (<<-sort x)))
:prepwork
((local (defthm lemma
(implies (<<-ordered-p x)
(equal (no-adjacent-duplicates-p x)
(no-duplicatesp x)))
:hints(("Goal" :in-theory (enable no-duplicatesp
no-adjacent-duplicates-p
<<-ordered-p)))))))
#||
Below is only performance-test stuff. Tested on CCL on Lisp2.
:q
(ccl::set-lisp-heap-gc-threshold (expt 2 30))
(defparameter *integers1*
;; A test vector of 10,000 integers with many duplicates
(loop for j from 1 to 10
nconc
(loop for i from 1 to 1000 collect i)))
(defparameter *integers2*
;; A test vector of 10,000 integers with no duplicates
(loop for i from 1 to 10000 collect i)))
;; In certain cases, no-duplicatesp-equal is much faster because a duplicate is
;; found right away. For instance, on *integers1*, which contains lots of
;; duplicates, we only have to scan a little to find a match.
;; 0.0 seconds, no allocation
(prog2$ (ccl::gc)
(time (loop for i fixnum from 1 to 1000
do
(let ((result (no-duplicatesp-equal *integers1*)))
(declare (ignore result))
nil))))
;; 4.2 seconds, 1.5 GB allocated
(prog2$ (ccl::gc)
(time (loop for i fixnum from 1 to 1000
do
(let ((result (uniquep *integers1*)))
(declare (ignore result))
nil))))
;; In other cases, uniquep is much faster because it is O(n log n) instead of
;; O(n^2).
;; 27.4 seconds, no allocation.
(prog2$ (ccl::gc)
(time (loop for i fixnum from 1 to 100
do
(let ((result (no-duplicatesp-equal *integers2*)))
(declare (ignore result))
nil))))
;; 0.2 seconds, 120 MB allocated
(prog2$ (ccl::gc)
(time (loop for i fixnum from 1 to 100
do
(let ((result (uniquep *integers2*)))
(declare (ignore result))
nil))))
||#
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