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• Attributes

Attributes-fix

(attributes-fix x) is an fty alist fixing function that follows the fix-keys strategy.

Signature

(attributes-fix x) → fty::newx

Arguments

x — Guard (attributes-p x).

Returns

fty::newx — Type (attributes-p fty::newx).

Note that in the execution this is just an inline identity function.

Definitions and Theorems

Function: attributes-fix$inline

(defun attributes-fix$inline (x)
  (declare (xargs :guard (attributes-p x)))
  (let ((__function__ 'attributes-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (if (consp (car x))
               (cons (cons (str-fix (caar x))
                           (maybe-svex-fix (cdar x)))
                     (attributes-fix (cdr x)))
             (attributes-fix (cdr x))))
         :exec x)))

Theorem: attributes-p-of-attributes-fix

(defthm attributes-p-of-attributes-fix
  (b* ((fty::newx (attributes-fix$inline x)))
    (attributes-p fty::newx))
  :rule-classes :rewrite)

Theorem: attributes-fix-when-attributes-p

(defthm attributes-fix-when-attributes-p
  (implies (attributes-p x)
           (equal (attributes-fix x) x)))

Function: attributes-equiv$inline

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

Theorem: attributes-equiv-is-an-equivalence

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

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

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

Theorem: attributes-fix-under-attributes-equiv

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

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

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

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

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

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

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

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

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

Theorem: cons-of-str-fix-k-under-attributes-equiv

(defthm cons-of-str-fix-k-under-attributes-equiv
  (attributes-equiv (cons (cons (str-fix acl2::k) acl2::v)
                          x)
                    (cons (cons acl2::k acl2::v) x)))

Theorem: cons-streqv-congruence-on-k-under-attributes-equiv

(defthm cons-streqv-congruence-on-k-under-attributes-equiv
  (implies (acl2::streqv acl2::k k-equiv)
           (attributes-equiv (cons (cons acl2::k acl2::v) x)
                             (cons (cons k-equiv acl2::v) x)))
  :rule-classes :congruence)

Theorem: cons-of-maybe-svex-fix-v-under-attributes-equiv

(defthm cons-of-maybe-svex-fix-v-under-attributes-equiv
  (attributes-equiv (cons (cons acl2::k (maybe-svex-fix acl2::v))
                          x)
                    (cons (cons acl2::k acl2::v) x)))

Theorem: cons-maybe-svex-equiv-congruence-on-v-under-attributes-equiv

(defthm cons-maybe-svex-equiv-congruence-on-v-under-attributes-equiv
  (implies (maybe-svex-equiv acl2::v v-equiv)
           (attributes-equiv (cons (cons acl2::k acl2::v) x)
                             (cons (cons acl2::k v-equiv) x)))
  :rule-classes :congruence)

Theorem: cons-of-attributes-fix-y-under-attributes-equiv

(defthm cons-of-attributes-fix-y-under-attributes-equiv
  (attributes-equiv (cons x (attributes-fix y))
                    (cons x y)))

Theorem: cons-attributes-equiv-congruence-on-y-under-attributes-equiv

(defthm cons-attributes-equiv-congruence-on-y-under-attributes-equiv
  (implies (attributes-equiv y y-equiv)
           (attributes-equiv (cons x y)
                             (cons x y-equiv)))
  :rule-classes :congruence)

Theorem: attributes-fix-of-acons

(defthm attributes-fix-of-acons
  (equal (attributes-fix (cons (cons acl2::a acl2::b) x))
         (cons (cons (str-fix acl2::a)
                     (maybe-svex-fix acl2::b))
               (attributes-fix x))))

Theorem: attributes-fix-of-append

(defthm attributes-fix-of-append
  (equal (attributes-fix (append std::a std::b))
         (append (attributes-fix std::a)
                 (attributes-fix std::b))))

Theorem: consp-car-of-attributes-fix

(defthm consp-car-of-attributes-fix
  (equal (consp (car (attributes-fix x)))
         (consp (attributes-fix x))))