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• Gather-paging-structures

Xlate-equiv-memory

Signature

(xlate-equiv-memory x86-1 x86-2) → *

Definitions and Theorems

Function: xlate-equiv-memory

(defun xlate-equiv-memory (x86-1 x86-2)
 (declare (xargs :guard (and (x86p x86-1) (x86p x86-2))
                 :non-executable t))
 (prog2$
    (acl2::throw-nonexec-error 'xlate-equiv-memory
                               (list x86-1 x86-2))
    (let ((__function__ 'xlate-equiv-memory))
      (declare (ignorable __function__))
      (if (and (equal (xr :app-view nil x86-1) nil)
               (equal (xr :app-view nil x86-2) nil)
               (64-bit-modep x86-1)
               (64-bit-modep x86-2))
          (and (xlate-equiv-structures x86-1 x86-2)
               (all-mem-except-paging-structures-equal x86-1 x86-2))
        (equal x86-1 x86-2)))))

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

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

Theorem: xlate-equiv-memory-refines-xlate-equiv-structures

(defthm xlate-equiv-memory-refines-xlate-equiv-structures
  (implies (xlate-equiv-memory x86-1 x86-2)
           (xlate-equiv-structures x86-1 x86-2))
  :rule-classes :refinement)

Theorem: xlate-equiv-memory-refines-all-mem-except-paging-structures-equal

(defthm
  xlate-equiv-memory-refines-all-mem-except-paging-structures-equal
  (implies (xlate-equiv-memory x86-1 x86-2)
           (all-mem-except-paging-structures-equal x86-1 x86-2))
  :rule-classes :refinement)

Theorem: xlate-equiv-memory-implies-equal-64-bit-modep-1

(defthm xlate-equiv-memory-implies-equal-64-bit-modep-1
  (implies (xlate-equiv-memory x86 x86-equiv)
           (equal (64-bit-modep x86)
                  (64-bit-modep x86-equiv)))
  :rule-classes (:congruence))

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

(defthm xlate-equiv-memory-and-xw-rflags
  (implies (and (equal (rflagsbits->ac val)
                       (rflagsbits->ac (xr :rflags nil x86)))
                (64-bit-modep x86)
                (not (app-view x86)))
           (xlate-equiv-memory (xw :rflags nil val x86)
                               (double-rewrite x86))))