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Rv32im-le-states

Memory

Fixtype of memories fo RV32IM little endian.

This is a list of 2^{32} unsigned 8-bit integers, according to riscv::stat and riscv::stat-validp. Recall that we do not model restrictions on the address space yet.

Definitions and Theorems

Function: memory-equiv$inline

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

Theorem: memory-equiv-is-an-equivalence

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

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

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

Theorem: memory-fix-under-memory-equiv

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

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

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

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

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

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

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

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

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

Subtopics

Memoryp: Recognizer for memory.
Memory-fix: Fixer for memory.