		Search-engine friendly clone of the ACL2 documentation.

Value

Value-fix

Fixing function for value structures.

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

Definitions and Theorems

Function: value-fix$inline

(defun value-fix$inline (x)
 (declare (xargs :guard (valuep x)))
 (let ((__function__ 'value-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (value-kind x)
    (:number (b* ((get (fix (std::da-nth 0 (cdr x)))))
               (cons :number (list get))))
    (:character (b* ((get (acl2::char-fix (std::da-nth 0 (cdr x)))))
                  (cons :character (list get))))
    (:string (b* ((get (str-fix (std::da-nth 0 (cdr x)))))
               (cons :string (list get))))
    (:symbol (b* ((get (symbol-value-fix (std::da-nth 0 (cdr x)))))
               (cons :symbol (list get))))
    (:cons (b* ((car (value-fix (std::da-nth 0 (cdr x))))
                (cdr (value-fix (std::da-nth 1 (cdr x)))))
             (cons :cons (list car cdr)))))
   :exec x)))

Theorem: valuep-of-value-fix

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

Theorem: value-fix-when-valuep

(defthm value-fix-when-valuep
  (implies (valuep x)
           (equal (value-fix x) x)))

Function: value-equiv$inline

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

Theorem: value-equiv-is-an-equivalence

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

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

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

Theorem: value-fix-under-value-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-value-fix

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