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Double-array

Double-array-fix

Fixing function for double-array structures.

Signature
(double-array-fix x) → new-x
Arguments: x — Guard (double-arrayp x).
Returns: new-x — Type (double-arrayp new-x).

Definitions and Theorems

Function: double-array-fix$inline

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

Theorem: double-arrayp-of-double-array-fix

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

Theorem: double-array-fix-when-double-arrayp

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

Function: double-array-equiv$inline

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

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

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

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

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

Theorem: double-array-fix-under-double-array-equiv

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

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

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

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

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

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

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

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

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