/usr/share/acl2-7.2dfsg/books/system/random.lisp is in acl2-books-source 7.2dfsg-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 | ; Random$ function
; Copyright (C) 2012 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 authors: Jared Davis <jared@centtech.com>
; Sol Swords <sswords@centtech.com>
(in-package "ACL2")
(include-book "xdoc/top" :dir :system)
(include-book "std/util/bstar" :dir :system)
(local (include-book "tools/mv-nth" :dir :system))
(set-state-ok t)
(defsection random$-lemmas
:parents (random$)
:short "Lemmas about random$ available in the system/random book."
(local (in-theory (enable random$)))
(defthm natp-random$-better
(natp (mv-nth 0 (random$ limit state)))
:rule-classes :type-prescription)
(defthm random$-linear-better
(and (<= 0 (mv-nth 0 (random$ n state)))
(implies (posp n)
(< (mv-nth 0 (random$ n state)) n)))
:hints(("Goal"
:in-theory (enable mv-nth)
:use ((:instance acl2::random$-linear (acl2::n n))))))
(defthm state-p1-of-random
(implies (force (state-p1 state))
(state-p1 (mv-nth 1 (random$ limit state))))
:hints(("Goal" :in-theory (enable random$ read-acl2-oracle)))))
(defsection random-list-aux
:parents (random$)
:short "Add random numbers onto an accumulator."
(defund random-list-aux (n limit acc state)
(declare (xargs :guard (and (natp n)
(posp limit))))
(if (zp n)
(mv acc state)
(b* (((mv x1 state) (random$ limit state)))
(random-list-aux (- n 1) limit (cons x1 acc) state))))
(local (in-theory (enable random-list-aux)))
(defthm nat-listp-of-random-list-aux
(equal (nat-listp (mv-nth 0 (random-list-aux n limit acc state)))
(nat-listp acc)))
(defthm state-p1-of-random-list-aux
(implies (force (state-p1 state))
(state-p1 (mv-nth 1 (random-list-aux n limit acc state))))))
(defsection random-list
:parents (random$)
:short "Generate a list of random numbers in [0, limit)."
(defund random-list (n limit state)
(declare (xargs :guard (and (natp n)
(posp limit))))
(random-list-aux n limit nil state))
(local (in-theory (enable random-list)))
(defthm nat-listp-of-random-list
(nat-listp (mv-nth 0 (random-list n limit state))))
(defthm state-p1-of-random-list
(implies (force (state-p1 state))
(state-p1 (mv-nth 1 (random-list n limit state))))))
|