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Const

Const-fix

Fixing function for const structures.

Signature
(const-fix x) → new-x
Arguments: x — Guard (constp x).
Returns: new-x — Type (constp new-x).

Definitions and Theorems

Function: const-fix$inline

(defun const-fix$inline (x)
  (declare (xargs :guard (constp x)))
  (let ((__function__ 'const-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (const-kind x)
           (:int (b* ((get (iconst-fix (std::da-nth 0 (cdr x)))))
                   (cons :int (list get))))
           (:float (cons :float (list)))
           (:enum (b* ((get (ident-fix (std::da-nth 0 (cdr x)))))
                    (cons :enum (list get))))
           (:char (cons :char (list))))
         :exec x)))

Theorem: constp-of-const-fix

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

Theorem: const-fix-when-constp

(defthm const-fix-when-constp
  (implies (constp x)
           (equal (const-fix x) x)))

Function: const-equiv$inline

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

Theorem: const-equiv-is-an-equivalence

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

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

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

Theorem: const-fix-under-const-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-const-fix

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