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States64

Xregfile64

Fixtype of the x register file [ISA:2.1].

There are 32 registers, each of which consists of 64 bits. We model the content of each register as an unsigned 64-bit integer, which can be interpreted in different ways (see operations on states).

The x0 register is always 0; writing to it is a no-op. We build this invariant into this fixtype by only modeling 31 registers, namely x1 to x31, and leaving x0 implicit.

Definitions and Theorems

Function: xregfile64-equiv$inline

(defun xregfile64-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (xregfile64p acl2::x)
                              (xregfile64p acl2::y))))
  (equal (xregfile64-fix acl2::x)
         (xregfile64-fix acl2::y)))

Theorem: xregfile64-equiv-is-an-equivalence

(defthm xregfile64-equiv-is-an-equivalence
  (and (booleanp (xregfile64-equiv x y))
       (xregfile64-equiv x x)
       (implies (xregfile64-equiv x y)
                (xregfile64-equiv y x))
       (implies (and (xregfile64-equiv x y)
                     (xregfile64-equiv y z))
                (xregfile64-equiv x z)))
  :rule-classes (:equivalence))

Theorem: xregfile64-equiv-implies-equal-xregfile64-fix-1

(defthm xregfile64-equiv-implies-equal-xregfile64-fix-1
  (implies (xregfile64-equiv acl2::x x-equiv)
           (equal (xregfile64-fix acl2::x)
                  (xregfile64-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: xregfile64-fix-under-xregfile64-equiv

(defthm xregfile64-fix-under-xregfile64-equiv
  (xregfile64-equiv (xregfile64-fix acl2::x)
                    acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-xregfile64-fix-1-forward-to-xregfile64-equiv

(defthm equal-of-xregfile64-fix-1-forward-to-xregfile64-equiv
  (implies (equal (xregfile64-fix acl2::x) acl2::y)
           (xregfile64-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-xregfile64-fix-2-forward-to-xregfile64-equiv

(defthm equal-of-xregfile64-fix-2-forward-to-xregfile64-equiv
  (implies (equal acl2::x (xregfile64-fix acl2::y))
           (xregfile64-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: xregfile64-equiv-of-xregfile64-fix-1-forward

(defthm xregfile64-equiv-of-xregfile64-fix-1-forward
  (implies (xregfile64-equiv (xregfile64-fix acl2::x)
                             acl2::y)
           (xregfile64-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: xregfile64-equiv-of-xregfile64-fix-2-forward

(defthm xregfile64-equiv-of-xregfile64-fix-2-forward
  (implies (xregfile64-equiv acl2::x (xregfile64-fix acl2::y))
           (xregfile64-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Subtopics

Xregfile64p: Recognizer for xregfile64.
Xregfile64-fix: Fixer for xregfile64.