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• Gather-paging-structures

Xlate-equiv-structures

Signature

(xlate-equiv-structures x86-1 x86-2) → *

Two x86 states are xlate-equiv-structures if their paging structures are equal, modulo the accessed and dirty bits (See xlate-equiv-entries).

Definitions and Theorems

Function: xlate-equiv-structures

(defun xlate-equiv-structures (x86-1 x86-2)
 (declare (xargs :non-executable t
                 :guard (and (x86p x86-1) (x86p x86-2))))
 (prog2$
  (acl2::throw-nonexec-error 'xlate-equiv-structures
                             (list x86-1 x86-2))
  (let ((__function__ 'xlate-equiv-structures))
   (declare (ignorable __function__))
   (if
    (and (equal (xr :app-view nil x86-1) nil)
         (equal (xr :app-view nil x86-2) nil))
    (let*
        ((paging-qword-addresses-1
              (gather-all-paging-structure-qword-addresses x86-1))
         (paging-qword-addresses-2
              (gather-all-paging-structure-qword-addresses x86-2)))
     (and
       (equal (segment-selectorbits->rpl (seg-visiblei *cs* x86-1))
              (segment-selectorbits->rpl (seg-visiblei *cs* x86-2)))
       (equal (cr0bits->wp (n32 (ctri *cr0* x86-1)))
              (cr0bits->wp (n32 (ctri *cr0* x86-2))))
       (equal (cr3bits->pdb (ctri *cr3* x86-1))
              (cr3bits->pdb (ctri *cr3* x86-2)))
       (equal (cr4bits->smep (loghead 22 (ctri *cr4* x86-1)))
              (cr4bits->smep (loghead 22 (ctri *cr4* x86-2))))
       (equal (cr4bits->smap (loghead 22 (ctri *cr4* x86-1)))
              (cr4bits->smap (loghead 22 (ctri *cr4* x86-2))))
       (equal
            (ia32_eferbits->nxe (n12 (msri *ia32_efer-idx* x86-1)))
            (ia32_eferbits->nxe (n12 (msri *ia32_efer-idx* x86-2))))
       (equal (rflagsbits->ac (rflags x86-1))
              (rflagsbits->ac (rflags x86-2)))
       (equal (xr :marking-view nil x86-1)
              (xr :marking-view nil x86-2))
       (equal paging-qword-addresses-1
              paging-qword-addresses-2)
       (equal (implicit-supervisor-access x86-1)
              (implicit-supervisor-access x86-2))
       (xlate-equiv-entries-at-qword-addresses
            paging-qword-addresses-1
            paging-qword-addresses-2 x86-1 x86-2)))
    (and (equal (xr :app-view nil x86-2)
                (xr :app-view nil x86-1)))))))

Theorem: xlate-equiv-structures-is-an-equivalence

(defthm xlate-equiv-structures-is-an-equivalence
  (and (booleanp (xlate-equiv-structures x y))
       (xlate-equiv-structures x x)
       (implies (xlate-equiv-structures x y)
                (xlate-equiv-structures y x))
       (implies (and (xlate-equiv-structures x y)
                     (xlate-equiv-structures y z))
                (xlate-equiv-structures x z)))
  :rule-classes (:equivalence))

Theorem: xlate-equiv-structures-and-xw

(defthm xlate-equiv-structures-and-xw
  (implies (and (not (equal fld :mem))
                (not (equal fld :seg-visible))
                (not (equal fld :msr))
                (not (equal fld :ctr))
                (not (equal fld :rflags))
                (not (equal fld :app-view))
                (not (equal fld :marking-view))
                (not (equal fld :implicit-supervisor-access)))
           (xlate-equiv-structures (xw fld index val x86)
                                   (double-rewrite x86))))

Theorem: xlate-equiv-structures-and-xw-rflags

(defthm xlate-equiv-structures-and-xw-rflags
  (implies (equal (rflagsbits->ac val)
                  (rflagsbits->ac (xr :rflags nil x86)))
           (xlate-equiv-structures (xw :rflags nil val x86)
                                   (double-rewrite x86))))

Theorem: xlate-equiv-structures-and-app-view-cong

(defthm xlate-equiv-structures-and-app-view-cong
  (implies (xlate-equiv-structures x86-1 x86-2)
           (equal (xr :app-view nil x86-1)
                  (xr :app-view nil x86-2)))
  :rule-classes :congruence)

Subtopics

Xlate-equiv-entries

Xlate-equiv-entries-at-qword-addresses