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Defstruct-info

Defstruct-info-fix

Fixing function for defstruct-info structures.

Signature
(defstruct-info-fix x) → new-x
Arguments: x — Guard (defstruct-infop x).
Returns: new-x — Type (defstruct-infop new-x).

Definitions and Theorems

Function: defstruct-info-fix$inline

(defun defstruct-info-fix$inline (x)
 (declare (xargs :guard (defstruct-infop x)))
 (let ((__function__ 'defstruct-info-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
     ((tag (ident-fix (cdr (std::da-nth 0 x))))
      (members
           (defstruct-member-info-list-fix (cdr (std::da-nth 1 x))))
      (flexiblep (acl2::bool-fix (cdr (std::da-nth 2 x))))
      (fixtype (symbol-fix (cdr (std::da-nth 3 x))))
      (recognizer (symbol-fix (cdr (std::da-nth 4 x))))
      (fixer (symbol-fix (cdr (std::da-nth 5 x))))
      (fixer-recognizer-thm (symbol-fix (cdr (std::da-nth 6 x))))
      (not-error-thm (symbol-fix (cdr (std::da-nth 7 x))))
      (valuep-thm (symbol-fix (cdr (std::da-nth 8 x))))
      (value-kind-thm (symbol-fix (cdr (std::da-nth 9 x))))
      (type-of-value-thm (symbol-fix (cdr (std::da-nth 10 x))))
      (flexiblep-thm (symbol-fix (cdr (std::da-nth 11 x))))
      (type-to-quoted-thm (symbol-fix (cdr (std::da-nth 12 x))))
      (pointer-type-to-quoted-thm
           (symbol-fix (cdr (std::da-nth 13 x))))
      (call (acl2::pseudo-event-form-fix (cdr (std::da-nth 14 x)))))
     (list (cons 'tag tag)
           (cons 'members members)
           (cons 'flexiblep flexiblep)
           (cons 'fixtype fixtype)
           (cons 'recognizer recognizer)
           (cons 'fixer fixer)
           (cons 'fixer-recognizer-thm
                 fixer-recognizer-thm)
           (cons 'not-error-thm not-error-thm)
           (cons 'valuep-thm valuep-thm)
           (cons 'value-kind-thm value-kind-thm)
           (cons 'type-of-value-thm
                 type-of-value-thm)
           (cons 'flexiblep-thm flexiblep-thm)
           (cons 'type-to-quoted-thm
                 type-to-quoted-thm)
           (cons 'pointer-type-to-quoted-thm
                 pointer-type-to-quoted-thm)
           (cons 'call call)))
    :exec x)))

Theorem: defstruct-infop-of-defstruct-info-fix

(defthm defstruct-infop-of-defstruct-info-fix
  (b* ((new-x (defstruct-info-fix$inline x)))
    (defstruct-infop new-x))
  :rule-classes :rewrite)

Theorem: defstruct-info-fix-when-defstruct-infop

(defthm defstruct-info-fix-when-defstruct-infop
  (implies (defstruct-infop x)
           (equal (defstruct-info-fix x) x)))

Function: defstruct-info-equiv$inline

(defun defstruct-info-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (defstruct-infop acl2::x)
                              (defstruct-infop acl2::y))))
  (equal (defstruct-info-fix acl2::x)
         (defstruct-info-fix acl2::y)))

Theorem: defstruct-info-equiv-is-an-equivalence

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

Theorem: defstruct-info-equiv-implies-equal-defstruct-info-fix-1

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

Theorem: defstruct-info-fix-under-defstruct-info-equiv

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

Theorem: equal-of-defstruct-info-fix-1-forward-to-defstruct-info-equiv

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

Theorem: equal-of-defstruct-info-fix-2-forward-to-defstruct-info-equiv

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

Theorem: defstruct-info-equiv-of-defstruct-info-fix-1-forward

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

Theorem: defstruct-info-equiv-of-defstruct-info-fix-2-forward

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