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• Int-array

Int-array-fix

Fixing function for int-array structures.

Signature

(int-array-fix x) → new-x

Arguments

x — Guard (int-arrayp x).

Returns

new-x — Type (int-arrayp new-x).

Definitions and Theorems

Function: int-array-fix$inline

(defun int-array-fix$inline (x)
 (declare (xargs :guard (int-arrayp x)))
 (let ((__function__ 'int-array-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (b* ((components (int-value-list-fix (std::da-nth 0 (cdr x)))))
       (let ((components (if (< (len components) (expt 2 31))
                             components
                           nil)))
         (cons :int-array (list components))))
     :exec x)))

Theorem: int-arrayp-of-int-array-fix

(defthm int-arrayp-of-int-array-fix
  (b* ((new-x (int-array-fix$inline x)))
    (int-arrayp new-x))
  :rule-classes :rewrite)

Theorem: int-array-fix-when-int-arrayp

(defthm int-array-fix-when-int-arrayp
  (implies (int-arrayp x)
           (equal (int-array-fix x) x)))

Function: int-array-equiv$inline

(defun int-array-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (int-arrayp acl2::x)
                              (int-arrayp acl2::y))))
  (equal (int-array-fix acl2::x)
         (int-array-fix acl2::y)))

Theorem: int-array-equiv-is-an-equivalence

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

Theorem: int-array-equiv-implies-equal-int-array-fix-1

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

Theorem: int-array-fix-under-int-array-equiv

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

Theorem: equal-of-int-array-fix-1-forward-to-int-array-equiv

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

Theorem: equal-of-int-array-fix-2-forward-to-int-array-equiv

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

Theorem: int-array-equiv-of-int-array-fix-1-forward

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

Theorem: int-array-equiv-of-int-array-fix-2-forward

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