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• Gather-all-paging-structure-qword-addresses

Gather-qword-addresses-corresponding-to-entries

Returns a list --- with no duplicates --- of qword addresses of inferior paging structures referred by the entries located at addresses superior-structure-paddrs of a given superior structure

Signature

(gather-qword-addresses-corresponding-to-entries 
     superior-structure-paddrs x86) 
 
  → 
list-of-addresses

Returns

list-of-addresses — Type (qword-paddr-listp list-of-addresses).

Definitions and Theorems

Function: gather-qword-addresses-corresponding-to-entries

(defun gather-qword-addresses-corresponding-to-entries
       (superior-structure-paddrs x86)
 (declare (xargs :stobjs (x86)))
 (declare
   (xargs
        :guard (and (not (app-view x86))
                    (qword-paddr-listp superior-structure-paddrs))))
 (let
  ((__function__ 'gather-qword-addresses-corresponding-to-entries))
  (declare (ignorable __function__))
  (remove-duplicates-equal (gather-qword-addresses-corresponding-to-entries-aux
                                superior-structure-paddrs x86))))

Theorem: qword-paddr-listp-of-gather-qword-addresses-corresponding-to-entries

(defthm
 qword-paddr-listp-of-gather-qword-addresses-corresponding-to-entries
 (b* ((list-of-addresses (gather-qword-addresses-corresponding-to-entries
                              superior-structure-paddrs x86)))
   (qword-paddr-listp list-of-addresses))
 :rule-classes :rewrite)

Theorem: true-listp-of-gather-qword-addresses-corresponding-to-entries

(defthm
      true-listp-of-gather-qword-addresses-corresponding-to-entries
  (b* ((list-of-addresses (gather-qword-addresses-corresponding-to-entries
                               superior-structure-paddrs x86)))
    (true-listp list-of-addresses))
  :rule-classes :rewrite)

Theorem: mult-8-qword-paddr-listp-gather-qword-addresses-corresponding-to-entries

(defthm
 mult-8-qword-paddr-listp-gather-qword-addresses-corresponding-to-entries
 (implies
  (mult-8-qword-paddr-listp addrs)
  (mult-8-qword-paddr-listp
      (gather-qword-addresses-corresponding-to-entries addrs x86))))

Theorem: no-duplicates-p-gather-qword-addresses-corresponding-to-entries

(defthm
    no-duplicates-p-gather-qword-addresses-corresponding-to-entries
  (no-duplicates-p
       (gather-qword-addresses-corresponding-to-entries addrs x86)))

Theorem: gather-qword-addresses-corresponding-to-entries-xw-fld!=mem

(defthm gather-qword-addresses-corresponding-to-entries-xw-fld!=mem
 (implies
  (and (not (equal fld :mem))
       (not (equal fld :app-view)))
  (equal
      (gather-qword-addresses-corresponding-to-entries
           addrs (xw fld index val x86))
      (gather-qword-addresses-corresponding-to-entries addrs x86))))

Theorem: gather-qword-addresses-corresponding-to-entries-xw-fld=mem-disjoint

(defthm
 gather-qword-addresses-corresponding-to-entries-xw-fld=mem-disjoint
 (implies
  (and (not (member-p index (open-qword-paddr-list addrs)))
       (physical-address-p index))
  (equal
      (gather-qword-addresses-corresponding-to-entries
           addrs (xw :mem index val x86))
      (gather-qword-addresses-corresponding-to-entries addrs x86))))

Theorem: gather-qword-addresses-corresponding-to-entries-wm-low-64-disjoint

(defthm
 gather-qword-addresses-corresponding-to-entries-wm-low-64-disjoint
 (implies
  (disjoint-p (addr-range 8 index)
              (open-qword-paddr-list addrs))
  (equal
      (gather-qword-addresses-corresponding-to-entries
           addrs (wm-low-64 index val x86))
      (gather-qword-addresses-corresponding-to-entries addrs x86))))

Theorem: gather-qword-addresses-corresponding-to-entries-wm-low-64-superior-entry-addr

(defthm
 gather-qword-addresses-corresponding-to-entries-wm-low-64-superior-entry-addr
 (implies
  (and (member-p index addrs)
       (mult-8-qword-paddr-listp addrs)
       (no-duplicates-p addrs)
       (xlate-equiv-entries (double-rewrite val)
                            (rm-low-64 index x86))
       (unsigned-byte-p 64 val)
       (not (xr :app-view nil x86)))
  (equal
      (gather-qword-addresses-corresponding-to-entries
           addrs (wm-low-64 index val x86))
      (gather-qword-addresses-corresponding-to-entries addrs x86))))

Theorem: gather-qword-addresses-corresponding-to-entries-wm-low-64-with-different-x86-disjoint

(defthm
 gather-qword-addresses-corresponding-to-entries-wm-low-64-with-different-x86-disjoint
 (implies
  (and
   (equal
        (gather-qword-addresses-corresponding-to-entries
             addrs x86-equiv)
        (gather-qword-addresses-corresponding-to-entries addrs x86))
   (disjoint-p (addr-range 8 index)
               (open-qword-paddr-list addrs)))
  (equal
      (gather-qword-addresses-corresponding-to-entries
           addrs (wm-low-64 index val x86-equiv))
      (gather-qword-addresses-corresponding-to-entries addrs x86))))

Theorem: gather-qword-addresses-corresponding-to-entries-wm-low-64-with-different-x86

(defthm
 gather-qword-addresses-corresponding-to-entries-wm-low-64-with-different-x86
 (implies
  (and
   (equal
        (gather-qword-addresses-corresponding-to-entries
             addrs x86-equiv)
        (gather-qword-addresses-corresponding-to-entries addrs x86))
   (member-p index addrs)
   (mult-8-qword-paddr-listp addrs)
   (no-duplicates-p addrs)
   (xlate-equiv-entries (double-rewrite val)
                        (rm-low-64 index x86-equiv))
   (unsigned-byte-p 64 val)
   (not (xr :app-view nil x86-equiv)))
  (equal
      (gather-qword-addresses-corresponding-to-entries
           addrs (wm-low-64 index val x86-equiv))
      (gather-qword-addresses-corresponding-to-entries addrs x86))))

Theorem: gather-qword-addresses-corresponding-to-entries-and-wm-low-64-subset-and-superset-general

(defthm
 gather-qword-addresses-corresponding-to-entries-and-wm-low-64-subset-and-superset-general
 (implies
  (and (subset-p sub super)
       (equal (page-size value) 1)
       (mult-8-qword-paddr-listp super)
       (physical-address-p index)
       (equal (loghead 3 index) 0)
       (not (app-view x86))
       (unsigned-byte-p 64 value))
  (subset-p
      (gather-qword-addresses-corresponding-to-entries
           sub (wm-low-64 index value x86))
      (gather-qword-addresses-corresponding-to-entries super x86))))

Subtopics

Gather-qword-addresses-corresponding-to-entries-aux

Returns a list of qword addresses of inferior paging structures referred by the entries located at addresses superior-structure-paddrs of a given superior structure