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• Api

Api-fix

Fixing function for api structures.

Signature

(api-fix x) → new-x

Arguments

x — Guard (apip x).

Returns

new-x — Type (apip new-x).

Definitions and Theorems

Function: api-fix$inline

(defun api-fix$inline (x)
 (declare (xargs :guard (apip x)))
 (let ((__function__ 'api-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (b* ((inputs (funparam-list-fix (cdr (std::da-nth 0 (cdr x)))))
          (output (type-fix (cdr (std::da-nth 1 (cdr x))))))
       (cons :api (list (cons 'inputs inputs)
                        (cons 'output output))))
     :exec x)))

Theorem: apip-of-api-fix

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

Theorem: api-fix-when-apip

(defthm api-fix-when-apip
  (implies (apip x)
           (equal (api-fix x) x)))

Function: api-equiv$inline

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

Theorem: api-equiv-is-an-equivalence

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

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

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

Theorem: api-fix-under-api-equiv

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

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

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

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

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

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

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

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

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