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Instructions

Op-imm-32-funct

Fixtype of names of non-shift instructions with the OP-IMM-32 opcode [ISA:4.2.1].

This is analogous to op-imm-funct, but for the OP-IMM-32 opcode.

Ideally we would like to use a fty::deftagsum here, even though there is just one summand, for uniformity with other fixtypes that have at least two summands. However, doing so triggers a (broader) issue in XDOC. Until that issue is resolved, we ``manually'' define this fixtype.

Definitions and Theorems

Function: op-imm-32-funct-p

(defun op-imm-32-funct-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'op-imm-32-funct-p))
    (declare (ignorable __function__))
    (and (true-listp x)
         (= (len x) 1)
         (eq (car x) :addiw))))

Theorem: booleanp-of-op-imm-32-funct-p

(defthm booleanp-of-op-imm-32-funct-p
  (b* ((yes/no (op-imm-32-funct-p x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Function: op-imm-32-funct-addiw

(defun op-imm-32-funct-addiw nil
  (declare (xargs :guard t))
  (let ((__function__ 'op-imm-32-funct-addiw))
    (declare (ignorable __function__))
    '(:addiw)))

Theorem: op-imm-32-funct-p-of-op-imm-32-funct-addiw

(defthm op-imm-32-funct-p-of-op-imm-32-funct-addiw
  (b* ((x (op-imm-32-funct-addiw)))
    (op-imm-32-funct-p x))
  :rule-classes :rewrite)

Function: op-imm-32-funct-fix

(defun op-imm-32-funct-fix (x)
  (declare (xargs :guard (op-imm-32-funct-p x)))
  (mbe :logic
       (if (op-imm-32-funct-p x)
           x
         (op-imm-32-funct-addiw))
       :exec x))

Theorem: op-imm-32-funct-p-of-op-imm-32-funct-fix

(defthm op-imm-32-funct-p-of-op-imm-32-funct-fix
  (b* ((fixed-x (op-imm-32-funct-fix x)))
    (op-imm-32-funct-p fixed-x))
  :rule-classes :rewrite)

Theorem: op-imm-32-funct-fix-when-op-imm-32-funct-p

(defthm op-imm-32-funct-fix-when-op-imm-32-funct-p
  (implies (op-imm-32-funct-p x)
           (equal (op-imm-32-funct-fix x) x)))

Function: op-imm-32-funct-equiv$inline

(defun op-imm-32-funct-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (op-imm-32-funct-p acl2::x)
                              (op-imm-32-funct-p acl2::y))))
  (equal (op-imm-32-funct-fix acl2::x)
         (op-imm-32-funct-fix acl2::y)))

Theorem: op-imm-32-funct-equiv-is-an-equivalence

(defthm op-imm-32-funct-equiv-is-an-equivalence
  (and (booleanp (op-imm-32-funct-equiv x y))
       (op-imm-32-funct-equiv x x)
       (implies (op-imm-32-funct-equiv x y)
                (op-imm-32-funct-equiv y x))
       (implies (and (op-imm-32-funct-equiv x y)
                     (op-imm-32-funct-equiv y z))
                (op-imm-32-funct-equiv x z)))
  :rule-classes (:equivalence))

Theorem: op-imm-32-funct-equiv-implies-equal-op-imm-32-funct-fix-1

(defthm op-imm-32-funct-equiv-implies-equal-op-imm-32-funct-fix-1
  (implies (op-imm-32-funct-equiv acl2::x x-equiv)
           (equal (op-imm-32-funct-fix acl2::x)
                  (op-imm-32-funct-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: op-imm-32-funct-fix-under-op-imm-32-funct-equiv

(defthm op-imm-32-funct-fix-under-op-imm-32-funct-equiv
  (op-imm-32-funct-equiv (op-imm-32-funct-fix acl2::x)
                         acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-op-imm-32-funct-fix-1-forward-to-op-imm-32-funct-equiv

(defthm
    equal-of-op-imm-32-funct-fix-1-forward-to-op-imm-32-funct-equiv
  (implies (equal (op-imm-32-funct-fix acl2::x)
                  acl2::y)
           (op-imm-32-funct-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-op-imm-32-funct-fix-2-forward-to-op-imm-32-funct-equiv

(defthm
    equal-of-op-imm-32-funct-fix-2-forward-to-op-imm-32-funct-equiv
  (implies (equal acl2::x (op-imm-32-funct-fix acl2::y))
           (op-imm-32-funct-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: op-imm-32-funct-equiv-of-op-imm-32-funct-fix-1-forward

(defthm op-imm-32-funct-equiv-of-op-imm-32-funct-fix-1-forward
  (implies (op-imm-32-funct-equiv (op-imm-32-funct-fix acl2::x)
                                  acl2::y)
           (op-imm-32-funct-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: op-imm-32-funct-equiv-of-op-imm-32-funct-fix-2-forward

(defthm op-imm-32-funct-equiv-of-op-imm-32-funct-fix-2-forward
  (implies
       (op-imm-32-funct-equiv acl2::x (op-imm-32-funct-fix acl2::y))
       (op-imm-32-funct-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)