		Search-engine friendly clone of the ACL2 documentation.

Decl

Decl-fix

Fixing function for decl structures.

Signature
(decl-fix x) → new-x
Arguments: x — Guard (decl-p x).
Returns: new-x — Type (decl-p new-x).

Definitions and Theorems

Function: decl-fix$inline

(defun decl-fix$inline (x)
  (declare (xargs :guard (decl-p x)))
  (let ((acl2::__function__ 'decl-fix))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((name (symbol-fix (cdr (std::da-nth 0 x))))
              (type (hint-pair-fix (cdr (std::da-nth 1 x)))))
           (let ((type (decl->type-reqfix type)))
             (list (cons 'name name)
                   (cons 'type type))))
         :exec x)))

Theorem: decl-p-of-decl-fix

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

Theorem: decl-fix-when-decl-p

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

Function: decl-equiv$inline

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

Theorem: decl-equiv-is-an-equivalence

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

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

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

Theorem: decl-fix-under-decl-equiv

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

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

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

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

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

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

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

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

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