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|
; X86ISA Library
; Note: The license below is based on the template at:
; http://opensource.org/licenses/BSD-3-Clause
; Copyright (C) 2015, Regents of the University of Texas
; All rights reserved.
; Redistribution and use in source and binary forms, with or without
; modification, are permitted provided that the following conditions are
; met:
; o Redistributions of source code must retain the above copyright
; notice, this list of conditions and the following disclaimer.
; o Redistributions in binary form must reproduce the above copyright
; notice, this list of conditions and the following disclaimer in the
; documentation and/or other materials provided with the distribution.
; o Neither the name of the copyright holders nor the names of its
; contributors may be used to endorse or promote products derived
; from this software without specific prior written permission.
; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
; "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
; LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
; A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
; HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
; SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
; LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
; DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
; THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
; (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
; OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
; Original Author(s):
; Shilpi Goel <shigoel@cs.utexas.edu>
(in-package "X86ISA")
(include-book "pml4-table-lemmas" :ttags :all)
(include-book "gather-paging-structures-thms" :ttags :all)
(local (include-book "centaur/bitops/ihs-extensions" :dir :system))
(local (include-book "centaur/bitops/signed-byte-p" :dir :system))
(local (in-theory (e/d () (unsigned-byte-p signed-byte-p))))
;; ======================================================================
(defthm xlate-equiv-memory-and-cr0Bits->wp
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (cr0Bits->wp (loghead 32 (xr :ctr *cr0* x86-1)))
(cr0Bits->wp (loghead 32 (xr :ctr *cr0* x86-2)))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-cr0-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (bool->bit (logbitp 16 (xr :ctr *cr0* x86-1)))
(bool->bit (logbitp 16 (xr :ctr *cr0* x86-2)))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures
cr0bits->wp)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-cr3Bits->pdb
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (cr3Bits->pdb (xr :ctr *cr3* x86-1))
(cr3Bits->pdb (xr :ctr *cr3* x86-2))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-cr3-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (loghead 40 (logtail 12 (xr :ctr *cr3* x86-1)))
(loghead 40 (logtail 12 (xr :ctr *cr3* x86-2)))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures
cr3bits->pdb)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-cr4Bits->smep
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (cr4Bits->smep (loghead 22 (xr :ctr *cr4* x86-1)))
(cr4Bits->smep (loghead 22 (xr :ctr *cr4* x86-2)))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-cr4Bits->smap
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (cr4Bits->smap (loghead 22 (xr :ctr *cr4* x86-1)))
(cr4Bits->smap (loghead 22 (xr :ctr *cr4* x86-2)))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-cr4-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (bool->bit (logbitp 20 (xr :ctr *cr4* x86-1)))
(bool->bit (logbitp 20 (xr :ctr *cr4* x86-2)))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures
cr4bits->smap
cr4bits->smep)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-ia32_eferbits->nxe
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (ia32_eferbits->nxe (loghead 12 (xr :msr *ia32_efer-idx* x86-1)))
(ia32_eferbits->nxe (loghead 12 (xr :msr *ia32_efer-idx* x86-2)))))
:hints (("goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-msr-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (bool->bit (logbitp 11 (xr :msr *ia32_efer-idx* x86-1)))
(bool->bit (logbitp 11 (xr :msr *ia32_efer-idx* x86-2)))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures
ia32_eferbits->nxe)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-rflagsbits->ac
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (rflagsbits->ac (xr :rflags nil x86-1))
(rflagsbits->ac (xr :rflags nil x86-2))))
:hints (("goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-rflags-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (bool->bit (logbitp 18 (xr :rflags nil x86-1)))
(bool->bit (logbitp 18 (xr :rflags nil x86-2)))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures
rflagsbits->ac)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-segment-selectorbits->rpl
(implies (xlate-equiv-memory x86-1 x86-2)
(equal
(segment-selectorbits->rpl (xr :seg-visible 1 x86-1))
(segment-selectorbits->rpl (xr :seg-visible 1 x86-2))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-seg-visible-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (loghead 2 (xr :seg-visible 1 x86-1))
(loghead 2 (xr :seg-visible 1 x86-2))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory
xlate-equiv-structures
segment-selectorbits->rpl)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-marking-view-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (xr :marking-view nil x86-1)
(xr :marking-view nil x86-2)))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory xlate-equiv-structures)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-app-view-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (xr :app-view nil x86-1)
(xr :app-view nil x86-2)))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory xlate-equiv-structures)
())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-in-app-view-implies-equal-states
(implies (and (xlate-equiv-memory x86-1 x86-2)
(app-view x86-1))
(equal x86-1 x86-2))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory) ())))
:rule-classes nil)
;; ======================================================================
;; Lemmas about ia32e-la-to-pa:
(defthm ia32e-la-to-pa-in-app-view
(implies (app-view x86)
(equal (ia32e-la-to-pa lin-addr r-w-x x86)
(mv t 0 x86)))
:hints (("Goal" :in-theory (e/d* (ia32e-la-to-pa) ()))))
(defthmd xlate-equiv-memory-and-ia32e-la-to-pa
(implies (xlate-equiv-memory (double-rewrite x86-1) x86-2)
(and
(equal (mv-nth 0 (ia32e-la-to-pa lin-addr r-w-x x86-1))
(mv-nth 0 (ia32e-la-to-pa lin-addr r-w-x x86-2)))
(equal (mv-nth 1 (ia32e-la-to-pa lin-addr r-w-x x86-1))
(mv-nth 1 (ia32e-la-to-pa lin-addr r-w-x x86-2)))))
:hints (("Goal" :in-theory (e/d* (ia32e-la-to-pa)
()))))
(defthm xlate-equiv-memory-and-mv-nth-0-ia32e-la-to-pa-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (mv-nth 0 (ia32e-la-to-pa lin-addr r-w-x x86-1))
(mv-nth 0 (ia32e-la-to-pa lin-addr r-w-x x86-2))))
:hints (("Goal" :use ((:instance xlate-equiv-memory-and-ia32e-la-to-pa))))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-mv-nth-1-ia32e-la-to-pa-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (mv-nth 1 (ia32e-la-to-pa lin-addr r-w-x x86-1))
(mv-nth 1 (ia32e-la-to-pa lin-addr r-w-x x86-2))))
:hints (("Goal" :use ((:instance xlate-equiv-memory-and-ia32e-la-to-pa))))
:rule-classes :congruence)
(defthm xlate-equiv-structures-and-mv-nth-2-ia32e-la-to-pa
(xlate-equiv-structures (mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86))
(double-rewrite x86))
:hints (("Goal" :in-theory (e/d* (ia32e-la-to-pa) (force (force))))))
(defthm xlate-equiv-structures-and-two-mv-nth-2-ia32e-la-to-pa-cong
(implies (xlate-equiv-structures x86-1 x86-2)
(xlate-equiv-structures (mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86-1))
(mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86-2))))
:rule-classes :congruence)
(local
(encapsulate
()
(local (in-theory (e/d* ()
(loghead-of-non-integerp
acl2::ash-0
(:t bitops::logtail-natp)
unsigned-byte-p-of-logtail))))
(defthm all-mem-except-paging-structures-equal-with-mv-nth-2-ia32e-la-to-pa-1G-pages
(implies
(and
;; (equal (page-present
;; (rm-low-64 (pml4-table-entry-addr (logext 48 lin-addr) (pml4-table-base-addr x86)) x86))
;; 1)
(equal
(page-size (rm-low-64
(pml4-table-entry-addr (logext 48 lin-addr) (pml4-table-base-addr x86)) x86))
0)
(equal
(page-size
(rm-low-64 (page-dir-ptr-table-entry-addr (logext 48 lin-addr) (page-dir-ptr-table-base-addr (logext 48 lin-addr) x86))
x86))
1))
(all-mem-except-paging-structures-equal
(mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86))
x86))
:hints (("Goal"
:in-theory (e/d* (ia32e-la-to-pa
ia32e-la-to-pa-pml4-table
ia32e-la-to-pa-page-dir-ptr-table
ia32e-pml4ebits->pdpt
cr3bits->pdb)
(bitops::logand-with-negated-bitmask
accessed-bit
dirty-bit
force (force)
not)))))
(defthm all-mem-except-paging-structures-equal-with-mv-nth-2-ia32e-la-to-pa-2M-and-4K-pages
(implies
(and
;; (equal
;; (page-present
;; (rm-low-64 (pml4-table-entry-addr (logext 48 lin-addr) (pml4-table-base-addr x86)) x86))
;; 1)
(equal
(page-size
(rm-low-64 (pml4-table-entry-addr (logext 48 lin-addr) (pml4-table-base-addr x86)) x86))
0)
;; (equal
;; (page-present
;; (rm-low-64 (page-dir-ptr-table-entry-addr (logext 48 lin-addr) (page-dir-ptr-table-base-addr (logext 48 lin-addr) x86)) x86))
;; 1)
;; (equal
;; (page-present
;; (rm-low-64 (page-directory-entry-addr (logext 48 lin-addr) (page-directory-base-addr (logext 48 lin-addr) x86)) x86))
;; 1)
)
(all-mem-except-paging-structures-equal
(mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86))
x86))
:hints (("Goal"
:in-theory (e/d* (ia32e-la-to-pa
ia32e-la-to-pa-pml4-table
ia32e-la-to-pa-page-dir-ptr-table
ia32e-pml4ebits->pdpt
cr3bits->pdb
ia32e-pdpte-pg-dirbits->pd)
(bitops::logand-with-negated-bitmask
accessed-bit
dirty-bit
force (force)
not)))))
(defthm all-mem-except-paging-structures-equal-with-mv-nth-2-ia32e-la-to-pa-pml4-page-size=1
(implies
(equal (page-size
(rm-low-64 (pml4-table-entry-addr (logext 48 lin-addr) (pml4-table-base-addr x86)) x86))
1)
(all-mem-except-paging-structures-equal
(mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86))
x86))
:hints (("Goal"
:in-theory (e/d* (ia32e-la-to-pa
ia32e-la-to-pa-pml4-table
paging-entry-no-page-fault-p
page-fault-exception
cr3bits->pdb)
(bitops::logand-with-negated-bitmask
accessed-bit
dirty-bit
force (force)
not)))))))
(defthm all-mem-except-paging-structures-equal-with-mv-nth-2-ia32e-la-to-pa
(all-mem-except-paging-structures-equal
(mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86))
(double-rewrite x86))
:hints (("Goal"
:cases ((and
;; (equal (page-present
;; (rm-low-64 (pml4-table-entry-addr (logext 48 lin-addr) (pml4-table-base-addr x86)) x86))
;; 1)
(equal
(page-size (rm-low-64
(pml4-table-entry-addr (logext 48 lin-addr) (pml4-table-base-addr x86)) x86))
0)
(equal
(page-size
(rm-low-64 (page-dir-ptr-table-entry-addr (logext 48 lin-addr) (page-dir-ptr-table-base-addr (logext 48 lin-addr) x86))
x86))
1))
(and
;; (equal
;; (page-present
;; (rm-low-64 (pml4-table-entry-addr (logext 48 lin-addr) (pml4-table-base-addr x86)) x86))
;; 1)
(equal
(page-size
(rm-low-64 (pml4-table-entry-addr (logext 48 lin-addr) (pml4-table-base-addr x86)) x86))
0)
;; (equal
;; (page-present
;; (rm-low-64 (page-dir-ptr-table-entry-addr (logext 48 lin-addr) (page-dir-ptr-table-base-addr (logext 48 lin-addr) x86)) x86))
;; 1)
;; (equal
;; (page-present
;; (rm-low-64 (page-directory-entry-addr (logext 48 lin-addr) (page-directory-base-addr (logext 48 lin-addr) x86)) x86))
;; 1)
))
:in-theory (e/d* ()
(bitops::logand-with-negated-bitmask
accessed-bit
dirty-bit
force (force)
not)))))
(defthm all-mem-except-paging-structures-equal-with-two-mv-nth-2-ia32e-la-to-pa-cong
(implies (all-mem-except-paging-structures-equal x86-1 x86-2)
(all-mem-except-paging-structures-equal
(mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86-1))
(mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86-2))))
:rule-classes :congruence)
(defthm xlate-equiv-memory-with-mv-nth-2-ia32e-la-to-pa
;; without the 64-bit mode hyp, this theorem is not true,
;; because ia32e-la-to-pa may mark bits in the state
(implies (64-bit-modep x86)
(xlate-equiv-memory
(mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86))
(double-rewrite x86)))
:hints (("Goal" :do-not '(preprocess)
:in-theory (e/d* (xlate-equiv-memory)
(bitops::logand-with-negated-bitmask
accessed-bit
dirty-bit
not)))))
(defthm xlate-equiv-memory-with-two-mv-nth-2-ia32e-la-to-pa-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(xlate-equiv-memory
(mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86-1))
(mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86-2))))
:rule-classes :congruence
;; add the following after adding 64-bit mode hyp to previous theorem:
:hints (("Goal" :in-theory (enable xlate-equiv-memory))))
(defthm two-page-walks-ia32e-la-to-pa
(implies
;; the 64-bit mode hyp makes the proof of this theorem easy
;; (via xlate-equiv-memory-with-mv-nth-2-ia32e-la-to-pa above),
;; but could this hyp be removed from here?
(64-bit-modep x86)
(and
(equal
(mv-nth 0 (ia32e-la-to-pa lin-addr-1 r-w-x-1
(mv-nth 2 (ia32e-la-to-pa lin-addr-2 r-w-x-2 x86))))
(mv-nth 0 (ia32e-la-to-pa lin-addr-1 r-w-x-1 x86)))
(equal
(mv-nth 1 (ia32e-la-to-pa lin-addr-1 r-w-x-1
(mv-nth 2 (ia32e-la-to-pa lin-addr-2 r-w-x-2 x86))))
(mv-nth 1 (ia32e-la-to-pa lin-addr-1 r-w-x-1 x86)))))
:hints (("Goal" :in-theory (e/d* () (ia32e-la-to-pa)))))
(in-theory (e/d* () (ia32e-la-to-pa)))
;; ======================================================================
(defthm gather-all-paging-structure-qword-addresses-mv-nth-2-ia32e-la-to-pa
(equal (gather-all-paging-structure-qword-addresses
(mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86)))
(gather-all-paging-structure-qword-addresses x86))
:hints (("Goal"
:use ((:instance
gather-all-paging-structure-qword-addresses-with-xlate-equiv-structures
(x86-equiv (mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86))))))))
(defthm xlate-equiv-entries-at-qword-addresses-mv-nth-2-ia32e-la-to-pa
(implies (equal addrs (gather-all-paging-structure-qword-addresses x86))
(equal (xlate-equiv-entries-at-qword-addresses
addrs addrs
x86
(mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86)))
(xlate-equiv-entries-at-qword-addresses addrs addrs x86 x86)))
:hints (("Goal" :in-theory (e/d* ()
(xlate-equiv-structures-and-xlate-equiv-entries-at-qword-addresses
booleanp-of-xlate-equiv-entries-at-qword-addresses))
:use ((:instance xlate-equiv-structures-and-xlate-equiv-entries-at-qword-addresses
(addrs (gather-all-paging-structure-qword-addresses x86))
(x86 x86)
(x86-equiv (mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86))))
(:instance booleanp-of-xlate-equiv-entries-at-qword-addresses
(addrs (gather-all-paging-structure-qword-addresses x86))
(x x86)
(y x86))
(:instance booleanp-of-xlate-equiv-entries-at-qword-addresses
(addrs (gather-all-paging-structure-qword-addresses x86))
(x x86)
(y (mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86))))))))
;; ======================================================================
;; Lemmas about las-to-pas:
(defthmd xlate-equiv-memory-and-las-to-pas
(implies (xlate-equiv-memory (double-rewrite x86-1) x86-2)
(and
(equal (mv-nth 0 (las-to-pas n lin-addr r-w-x x86-1))
(mv-nth 0 (las-to-pas n lin-addr r-w-x x86-2)))
(equal (mv-nth 1 (las-to-pas n lin-addr r-w-x x86-1))
(mv-nth 1 (las-to-pas n lin-addr r-w-x x86-2)))))
:hints (("Goal"
:induct (cons (las-to-pas n lin-addr r-w-x x86-1)
(las-to-pas n lin-addr r-w-x x86-2)))))
(defthm xlate-equiv-memory-and-mv-nth-0-las-to-pas-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (mv-nth 0 (las-to-pas n lin-addr r-w-x x86-1))
(mv-nth 0 (las-to-pas n lin-addr r-w-x x86-2))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory-and-las-to-pas) ())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-and-mv-nth-1-las-to-pas-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(equal (mv-nth 1 (las-to-pas n lin-addr r-w-x x86-1))
(mv-nth 1 (las-to-pas n lin-addr r-w-x x86-2))))
:hints (("Goal" :in-theory (e/d* (xlate-equiv-memory-and-las-to-pas) ())))
:rule-classes :congruence)
(defthm xlate-equiv-memory-with-mv-nth-2-las-to-pas
;; the 64-bit mode hyp makes the proof of this theorem easy
;; (via xlate-equiv-memory-with-mv-nth-2-ia32e-la-to-pa),
;; but could this hyp be removed from here?
(implies (64-bit-modep (double-rewrite x86))
(xlate-equiv-memory
(mv-nth 2 (las-to-pas n lin-addr r-w-x x86))
(double-rewrite x86)))
:hints (("Goal" :induct (las-to-pas n lin-addr r-w-x x86))))
(defthm xlate-equiv-memory-with-two-mv-nth-2-las-to-pas-cong
(implies (xlate-equiv-memory x86-1 x86-2)
(xlate-equiv-memory
(mv-nth 2 (las-to-pas n lin-addr r-w-x x86-1))
(mv-nth 2 (las-to-pas n lin-addr r-w-x x86-2))))
:hints (("Goal"
:induct (cons (las-to-pas n lin-addr r-w-x x86-1)
(las-to-pas n lin-addr r-w-x x86-2))))
:rule-classes :congruence)
;; ======================================================================
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