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Prefixes

!prefixes->adr

Update the |X86ISA|::|ADR| field of a prefixes bit structure.

Signature
(!prefixes->adr adr x) → new-x
Arguments: adr — Guard (8bits-p adr).; x — Guard (prefixes-p x).
Returns: new-x — Type (prefixes-p new-x).

Definitions and Theorems

Function: !prefixes->adr$inline

(defun !prefixes->adr$inline (adr x)
 (declare (xargs :guard (and (8bits-p adr) (prefixes-p x))))
 (mbe
  :logic
  (b* ((adr (mbe :logic (8bits-fix adr) :exec adr))
       (x (prefixes-fix x)))
    (part-install adr x :width 8 :low 36))
  :exec
  (the (unsigned-byte 52)
       (logior (the (unsigned-byte 52)
                    (logand (the (unsigned-byte 52) x)
                            (the (signed-byte 45) -17523466567681)))
               (the (unsigned-byte 44)
                    (ash (the (unsigned-byte 8) adr)
                         36))))))

Theorem: prefixes-p-of-!prefixes->adr

(defthm prefixes-p-of-!prefixes->adr
  (b* ((new-x (!prefixes->adr$inline adr x)))
    (prefixes-p new-x))
  :rule-classes :rewrite)

Theorem: !prefixes->adr$inline-of-8bits-fix-adr

(defthm !prefixes->adr$inline-of-8bits-fix-adr
  (equal (!prefixes->adr$inline (8bits-fix adr)
                                x)
         (!prefixes->adr$inline adr x)))

Theorem: !prefixes->adr$inline-8bits-equiv-congruence-on-adr

(defthm !prefixes->adr$inline-8bits-equiv-congruence-on-adr
  (implies (8bits-equiv adr adr-equiv)
           (equal (!prefixes->adr$inline adr x)
                  (!prefixes->adr$inline adr-equiv x)))
  :rule-classes :congruence)

Theorem: !prefixes->adr$inline-of-prefixes-fix-x

(defthm !prefixes->adr$inline-of-prefixes-fix-x
  (equal (!prefixes->adr$inline adr (prefixes-fix x))
         (!prefixes->adr$inline adr x)))

Theorem: !prefixes->adr$inline-prefixes-equiv-congruence-on-x

(defthm !prefixes->adr$inline-prefixes-equiv-congruence-on-x
  (implies (prefixes-equiv x x-equiv)
           (equal (!prefixes->adr$inline adr x)
                  (!prefixes->adr$inline adr x-equiv)))
  :rule-classes :congruence)

Theorem: !prefixes->adr-is-prefixes

(defthm !prefixes->adr-is-prefixes
  (equal (!prefixes->adr adr x)
         (change-prefixes x :adr adr)))

Theorem: prefixes->adr-of-!prefixes->adr

(defthm prefixes->adr-of-!prefixes->adr
  (b* ((?new-x (!prefixes->adr$inline adr x)))
    (equal (prefixes->adr new-x)
           (8bits-fix adr))))

Theorem: !prefixes->adr-equiv-under-mask

(defthm !prefixes->adr-equiv-under-mask
  (b* ((?new-x (!prefixes->adr$inline adr x)))
    (prefixes-equiv-under-mask new-x x -17523466567681)))