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; Centaur Bitops Library
; Copyright (C) 2010-2013 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 "BITOPS")
(include-book "xdoc/top" :dir :system)
(include-book "ihs/basic-definitions" :dir :system)
(local (include-book "ihsext-basics"))
(local (in-theory (enable* arith-equiv-forwarding)))
(defxdoc bitops/defaults
:parents (bitops)
:short "(semi-deprecated) Basic theorems about the \"default\" behavior of
bit-vector operations when their inputs are ill-formed (e.g., not integers, not
naturals)."
:long "<p>We tend not to include this any more, because it should mostly be
subsumed by the @('nat-equiv') and @('int-equiv') congruence reasoning.</p>")
(defsection logbitp-defaults
:parents (bitops/defaults logbitp)
:short "Behavior of @(see logbitp) on bad inputs."
(defthm logbitp-default-1
(implies (not (natp a))
(equal (logbitp a x)
(logbitp 0 x)))
:hints(("Goal" :in-theory (enable logbitp**)))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm logbitp-default-2
(implies (not (integerp x))
(equal (logbitp a x)
nil))
:hints(("Goal" :in-theory (enable logbitp**)))
:rule-classes ((:rewrite :backchain-limit-lst 0))))
(defsection lognot-default
:parents (bitops/defaults lognot)
:short "Behavior of @(see lognot) on bad inputs."
(defthm lognot-default
(implies (not (integerp x))
(equal (lognot x)
-1))
:hints(("Goal" :in-theory (enable lognot**)))
:rule-classes ((:rewrite :backchain-limit-lst 0))))
(defsection logand-defaults
:parents (bitops/defaults logand)
:short "Behavior of @(see logand) on bad inputs."
(defthm logand-default-1
(implies (not (integerp x))
(equal (logand x y)
(logand 0 y)))
:hints(("Goal" :in-theory (enable logand**)))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm logand-default-2
(implies (not (integerp y))
(equal (logand x y)
(logand x 0)))
:hints(("Goal" :in-theory (e/d (logand**))))
:rule-classes ((:rewrite :backchain-limit-lst 0))))
(defsection logior-defaults
:parents (bitops/defaults logior)
:short "Behavior of @(see logior) on bad inputs."
(defthm logior-default-1
(implies (not (integerp x))
(equal (logior x y)
(logior 0 y)))
:hints(("Goal" :in-theory (enable logior**)))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm logior-default-2
(implies (not (integerp y))
(equal (logior x y)
(logior x 0)))
:hints(("Goal" :in-theory (enable logior**)))
:rule-classes ((:rewrite :backchain-limit-lst 0))))
(defsection logcar-default
:parents (bitops/defaults logcar)
:short "Behavior of @(see logcar) on bad inputs."
(defthm logcar-default
(implies (not (integerp x))
(equal (logcar x)
0))
:rule-classes ((:rewrite :backchain-limit-lst 0))))
(defsection logcdr-default
:parents (bitops/defaults logcdr)
:short "Behavior of @(see logcdr) on bad inputs."
(defthm logcdr-default
(implies (not (integerp x))
(equal (logcdr x)
0))
:rule-classes ((:rewrite :backchain-limit-lst 0))))
(defsection integer-length-default
:parents (bitops/defaults integer-length)
:short "Behavior of @(see integer-length) on bad inputs."
(defthm integer-length-default
(implies (not (integerp x))
(equal (integer-length x)
0))
:rule-classes ((:rewrite :backchain-limit-lst 0))))
(defsection ash-defaults
:parents (bitops/defaults ash)
:short "Behavior of @(see ash) on bad inputs."
(defthm ash-default-1
(implies (not (integerp x))
(equal (ash x y)
0))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm ash-default-2
(implies (not (integerp y))
(equal (ash x y)
(ifix x)))
:hints(("Goal" :in-theory (enable ash**)))
:rule-classes ((:rewrite :backchain-limit-lst 0))))
(defsection logxor-defaults
:parents (bitops/defaults logxor)
:short "Behavior of @(see logxor) on bad inputs."
(defthm logxor-default-1
(implies (not (integerp x))
(equal (logxor x y)
(logxor 0 y)))
:hints(("Goal" :in-theory (enable logxor**)))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm logxor-default-2
(implies (not (integerp y))
(equal (logxor x y)
(logxor x 0)))
:hints(("Goal" :in-theory (enable logxor**)))
:rule-classes ((:rewrite :backchain-limit-lst 0))))
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