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Data-value

Data-value-fix

Fixing function for data-value structures.

Signature
(data-value-fix x) → new-x
Arguments: x — Guard (data-value-p x).
Returns: new-x — Type (data-value-p new-x).

Definitions and Theorems

Function: data-value-fix$inline

(defun data-value-fix$inline (x)
 (declare (xargs :guard (data-value-p x)))
 (let ((__function__ 'data-value-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (case (data-value-kind x)
      (:hex (b* ((get (hex-string-fix (std::da-nth 0 (cdr x)))))
              (cons :hex (list get))))
      (:plain (b* ((get (plain-string-fix (std::da-nth 0 (cdr x)))))
                (cons :plain (list get)))))
    :exec x)))

Theorem: data-value-p-of-data-value-fix

(defthm data-value-p-of-data-value-fix
  (b* ((new-x (data-value-fix$inline x)))
    (data-value-p new-x))
  :rule-classes :rewrite)

Theorem: data-value-fix-when-data-value-p

(defthm data-value-fix-when-data-value-p
  (implies (data-value-p x)
           (equal (data-value-fix x) x)))

Function: data-value-equiv$inline

(defun data-value-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (data-value-p acl2::x)
                              (data-value-p acl2::y))))
  (equal (data-value-fix acl2::x)
         (data-value-fix acl2::y)))

Theorem: data-value-equiv-is-an-equivalence

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

Theorem: data-value-equiv-implies-equal-data-value-fix-1

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

Theorem: data-value-fix-under-data-value-equiv

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

Theorem: equal-of-data-value-fix-1-forward-to-data-value-equiv

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

Theorem: equal-of-data-value-fix-2-forward-to-data-value-equiv

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

Theorem: data-value-equiv-of-data-value-fix-1-forward

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

Theorem: data-value-equiv-of-data-value-fix-2-forward

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

Theorem: data-value-kind$inline-of-data-value-fix-x

(defthm data-value-kind$inline-of-data-value-fix-x
  (equal (data-value-kind$inline (data-value-fix x))
         (data-value-kind$inline x)))

Theorem: data-value-kind$inline-data-value-equiv-congruence-on-x

(defthm data-value-kind$inline-data-value-equiv-congruence-on-x
  (implies (data-value-equiv x x-equiv)
           (equal (data-value-kind$inline x)
                  (data-value-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-data-value-fix

(defthm consp-of-data-value-fix
  (consp (data-value-fix x))
  :rule-classes :type-prescription)