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• Reasoning-about-memory-reads-and-writes

Las-to-pas

Signature

(las-to-pas n lin-addr r-w-x x86) → (mv flg p-addrs x86)

Arguments

n — Number of bytes to be read.
    Guard (natp n).

lin-addr — First linear address.
    Guard (integerp lin-addr).

r-w-x — Type of memory access: read, write, or execute.

Returns

p-addrs — Type (true-listp p-addrs).

x86 — Type (x86p x86), given (x86p x86).

Definitions and Theorems

Function: las-to-pas

(defun las-to-pas (n lin-addr r-w-x x86)
  (declare (xargs :stobjs (x86)))
  (declare (type (member :r :w :x) r-w-x))
  (declare (xargs :guard (and (natp n) (integerp lin-addr))))
  (declare (xargs :guard (not (app-view x86))))
  (let ((__function__ 'las-to-pas))
    (declare (ignorable __function__))
    (if (zp n)
        (mv nil nil x86)
      (b* (((unless (canonical-address-p lin-addr))
            (mv t nil x86))
           ((mv flg p-addr x86)
            (ia32e-la-to-pa lin-addr r-w-x x86))
           ((when flg) (mv flg nil x86))
           ((mv flg p-addrs x86)
            (las-to-pas (1- n)
                        (1+ lin-addr)
                        r-w-x x86)))
        (mv flg (if flg nil (cons p-addr p-addrs))
            x86)))))

Theorem: true-listp-of-las-to-pas.p-addrs

(defthm true-listp-of-las-to-pas.p-addrs
  (b* (((mv ?flg ?p-addrs ?x86)
        (las-to-pas n lin-addr r-w-x x86)))
    (true-listp p-addrs))
  :rule-classes (:rewrite :type-prescription))

Theorem: x86p-of-las-to-pas.x86

(defthm x86p-of-las-to-pas.x86
  (implies (x86p x86)
           (b* (((mv ?flg ?p-addrs ?x86)
                 (las-to-pas n lin-addr r-w-x x86)))
             (x86p x86)))
  :rule-classes :rewrite)

Theorem: consp-mv-nth-1-las-to-pas

(defthm consp-mv-nth-1-las-to-pas
  (implies (and (not (mv-nth 0 (las-to-pas n lin-addr r-w-x x86)))
                (not (zp n)))
           (consp (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))
  :rule-classes (:rewrite :type-prescription))

Theorem: car-mv-nth-1-las-to-pas

(defthm car-mv-nth-1-las-to-pas
  (implies (and (not (mv-nth 0 (las-to-pas n lin-addr r-w-x x86)))
                (not (zp n)))
           (equal (car (mv-nth 1 (las-to-pas n lin-addr r-w-x x86)))
                  (mv-nth 1
                          (ia32e-la-to-pa lin-addr r-w-x x86)))))

Theorem: physical-address-listp-mv-nth-1-las-to-pas

(defthm physical-address-listp-mv-nth-1-las-to-pas
  (physical-address-listp
       (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: las-to-pas-n=0

(defthm las-to-pas-n=0
  (and (equal (mv-nth 0 (las-to-pas 0 lin-addr r-w-x x86))
              nil)
       (equal (mv-nth 1 (las-to-pas 0 lin-addr r-w-x x86))
              nil)
       (equal (mv-nth 2 (las-to-pas 0 lin-addr r-w-x x86))
              x86)))

Theorem: xr-las-to-pas

(defthm xr-las-to-pas
  (implies (and (not (equal fld :tlb))
                (not (equal fld :mem))
                (not (equal fld :fault)))
           (equal (xr fld index
                      (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
                  (xr fld index x86))))

Theorem: xr-rflags-las-to-pas

(defthm xr-rflags-las-to-pas
 (implies
   (not (mv-nth 0
                (las-to-pas n lin-addr r-w-x (double-rewrite x86))))
   (equal (xr :rflags nil
              (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
          (xr :rflags nil (double-rewrite x86)))))

Theorem: xr-fault-las-to-pas

(defthm xr-fault-las-to-pas
 (implies
   (not (mv-nth 0
                (las-to-pas n lin-addr r-w-x (double-rewrite x86))))
   (equal (xr :fault nil
              (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
          (xr :fault nil (double-rewrite x86)))))

Theorem: las-to-pas-xw-values

(defthm las-to-pas-xw-values
 (implies
  (and (not (equal fld :mem))
       (not (equal fld :rflags))
       (not (equal fld :fault))
       (not (equal fld :ctr))
       (not (equal fld :msr))
       (not (equal fld :app-view))
       (not (equal fld :marking-view))
       (not (equal fld :seg-visible))
       (not (equal fld :tlb))
       (not (equal fld :implicit-supervisor-access)))
  (and
    (equal
         (mv-nth 0
                 (las-to-pas n
                             lin-addr r-w-x (xw fld index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86)))
    (equal
         (mv-nth 1
                 (las-to-pas n
                             lin-addr r-w-x (xw fld index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))))

Theorem: 64-bit-modep-of-las-to-pas

(defthm 64-bit-modep-of-las-to-pas
  (equal (64-bit-modep (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (64-bit-modep x86)))

Theorem: x86-operation-mode-of-las-to-pas

(defthm x86-operation-mode-of-las-to-pas
 (equal
   (x86-operation-mode (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
   (x86-operation-mode x86)))

Theorem: las-to-pas-xw-state

(defthm las-to-pas-xw-state
 (implies
  (and (not (equal fld :mem))
       (not (equal fld :rflags))
       (not (equal fld :fault))
       (not (equal fld :ctr))
       (not (equal fld :msr))
       (not (equal fld :app-view))
       (not (equal fld :marking-view))
       (not (equal fld :seg-visible))
       (not (equal fld :tlb))
       (not (equal fld :implicit-supervisor-access)))
  (equal (mv-nth 2
                 (las-to-pas n
                             lin-addr r-w-x (xw fld index val x86)))
         (xw fld index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86))))))

Theorem: las-to-pas-xw-rflags-not-ac

(defthm las-to-pas-xw-rflags-not-ac
 (implies
  (equal (rflagsbits->ac value)
         (rflagsbits->ac (rflags (double-rewrite x86))))
  (and
   (equal
        (mv-nth 0
                (las-to-pas n lin-addr
                            r-w-x (xw :rflags nil value x86)))
        (mv-nth 0
                (las-to-pas n lin-addr r-w-x (double-rewrite x86))))
   (equal (mv-nth 1
                  (las-to-pas n lin-addr
                              r-w-x (xw :rflags nil value x86)))
          (mv-nth 1
                  (las-to-pas n lin-addr
                              r-w-x (double-rewrite x86)))))))

Theorem: las-to-pas-xw-rflags-state-not-ac

(defthm las-to-pas-xw-rflags-state-not-ac
  (implies
       (equal (rflagsbits->ac value)
              (rflagsbits->ac (rflags x86)))
       (equal (mv-nth 2
                      (las-to-pas n lin-addr
                                  r-w-x (xw :rflags nil value x86)))
              (xw :rflags nil value
                  (mv-nth 2 (las-to-pas n lin-addr r-w-x x86))))))

Theorem: len-of-mv-nth-1-las-to-pas

(defthm len-of-mv-nth-1-las-to-pas
  (implies (not (mv-nth 0 (las-to-pas n lin-addr r-w-x x86)))
           (equal (len (mv-nth 1 (las-to-pas n lin-addr r-w-x x86)))
                  (nfix n))))