• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • Boolean-reasoning
  • Debugging
  • Projects
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
    • X86isa
      • Program-execution
      • Introduction
      • X86isa-build-instructions
      • Publications
      • Contributors
      • Machine
      • Implemented-opcodes
      • Proof-utilities
        • System-level-marking-view-proof-utilities
          • Rb-alt
          • Unwind-x86-interpreter-in-marking-view
          • Get-prefixes-alt
          • Get-prefixes-in-system-level-marking-view
          • Program-at-alt
          • Rb-in-system-level-marking-view
          • Xlate-equiv-memory-and-rml08
          • Reasoning-about-page-tables
            • Create-qword-address-list
            • Mult-8-qword-paddr-listp
            • Gather-paging-structures
              • Gather-all-paging-structure-qword-addresses
              • All-mem-except-paging-structures-equal
              • Gather-qword-addresses-corresponding-to-1-entry
              • Xlation-governing-entries-paddrs
              • Xlation-governing-entries-paddrs-for-page-dir-ptr-table
              • Xlate-equiv-structures
              • Xlation-governing-entries-paddrs-for-page-directory
              • All-xlation-governing-entries-paddrs
              • Xlation-governing-entries-paddrs-for-pml4-table
              • Gather-pml4-table-qword-addresses
              • Xlation-governing-entries-paddrs-for-page-table
              • Xlate-equiv-memory
              • Open-qword-paddr-list
            • Qword-paddr-listp
            • Find-l-addrs-from-disjoint-p$-of-two-las-to-pas-aux
            • Find-first-arg-of-disjoint-p$-candidates
            • Paging-basics
          • Las-to-pas-two-n-ind-hint
          • Find-l-addrs-from-disjoint-p-of-las-to-pas-1-aux
          • Replace-element
        • Non-marking-view-proof-utilities
        • App-view-proof-utilities
        • Subset-p
        • Disjoint-p
        • Pos
        • Member-p
        • No-duplicates-p
        • Common-system-level-utils
        • Debugging-code-proofs
        • General-memory-utils
        • X86-row-wow-thms
      • To-do
      • Concrete-simulation-examples
      • Model-validation
      • Utils
      • Debugging-code-proofs
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Gather-paging-structures

All-xlation-governing-entries-paddrs

Signature

(all-xlation-governing-entries-paddrs n lin-addr x86) → *

Arguments

n — Guard (natp n).

lin-addr — Guard (canonical-address-p lin-addr).

Definitions and Theorems

Function: all-xlation-governing-entries-paddrs

(defun all-xlation-governing-entries-paddrs (n lin-addr x86)
 (declare (xargs :stobjs (x86)))
 (declare (xargs :guard (and (natp n)
                             (canonical-address-p lin-addr))))
 (declare (xargs :guard (and (not (app-view x86))
                             (canonical-address-p (+ n lin-addr)))))
 (let ((__function__ 'all-xlation-governing-entries-paddrs))
   (declare (ignorable __function__))
   (if (zp n)
       nil
     (append (xlation-governing-entries-paddrs lin-addr x86)
             (all-xlation-governing-entries-paddrs (1- n)
                                                   (1+ lin-addr)
                                                   x86)))))

Theorem: all-xlation-governing-entries-paddrs-and-zero-bytes

(defthm all-xlation-governing-entries-paddrs-and-zero-bytes
  (equal (all-xlation-governing-entries-paddrs 0 lin-addr x86)
         nil))

Theorem: xlation-governing-entries-paddrs-subset-p-all-xlation-governing-entries-paddrs

(defthm
 xlation-governing-entries-paddrs-subset-p-all-xlation-governing-entries-paddrs
 (implies
   (and (<= addr a)
        (< a (+ n addr))
        (posp n)
        (integerp a)
        (integerp addr))
   (equal
        (subset-p (xlation-governing-entries-paddrs a x86)
                  (all-xlation-governing-entries-paddrs n addr x86))
        t)))

Theorem: all-xlation-governing-entries-paddrs-subset-p-all-xlation-governing-entries-paddrs

(defthm
 all-xlation-governing-entries-paddrs-subset-p-all-xlation-governing-entries-paddrs
 (implies
  (and (<= addr-2 addr-1)
       (<= (+ n-1 addr-1) (+ n-2 addr-2))
       (posp n-2)
       (integerp addr-1)
       (integerp addr-2))
  (equal
    (subset-p (all-xlation-governing-entries-paddrs n-1 addr-1 x86)
              (all-xlation-governing-entries-paddrs n-2 addr-2 x86))
    t)))

Theorem: all-xlation-governing-entries-paddrs-and-xw-not-mem

(defthm all-xlation-governing-entries-paddrs-and-xw-not-mem
  (implies (and (not (equal fld :mem))
                (not (equal fld :ctr))
                (not (equal fld :app-view)))
           (equal (all-xlation-governing-entries-paddrs
                       n addr (xw fld index value x86))
                  (all-xlation-governing-entries-paddrs
                       n addr (double-rewrite x86)))))

Theorem: all-xlation-governing-entries-paddrs-and-xw-mem-not-member

(defthm all-xlation-governing-entries-paddrs-and-xw-mem-not-member
  (implies (not (member-p index
                          (all-xlation-governing-entries-paddrs
                               n addr (double-rewrite x86))))
           (equal (all-xlation-governing-entries-paddrs
                       n addr (xw :mem index value x86))
                  (all-xlation-governing-entries-paddrs
                       n addr (double-rewrite x86)))))