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Transform

Transform-fix

Fixing function for transform structures.

Signature
(transform-fix x) → new-x
Arguments: x — Guard (transformp x).
Returns: new-x — Type (transformp new-x).

Definitions and Theorems

Function: transform-fix$inline

(defun transform-fix$inline (x)
 (declare (xargs :guard (transformp x)))
 (let ((__function__ 'transform-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b* ((new-function-name (identifier-fix (cdr (std::da-nth 0 x))))
        (old-function-name (identifier-fix (cdr (std::da-nth 1 x))))
        (transform-name (str-fix (cdr (std::da-nth 2 x))))
        (arguments
             (transform-argument-list-fix (cdr (std::da-nth 3 x)))))
     (list (cons 'new-function-name
                 new-function-name)
           (cons 'old-function-name
                 old-function-name)
           (cons 'transform-name transform-name)
           (cons 'arguments arguments)))
   :exec x)))

Theorem: transformp-of-transform-fix

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

Theorem: transform-fix-when-transformp

(defthm transform-fix-when-transformp
  (implies (transformp x)
           (equal (transform-fix x) x)))

Function: transform-equiv$inline

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

Theorem: transform-equiv-is-an-equivalence

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

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

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

Theorem: transform-fix-under-transform-equiv

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

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

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

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

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

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

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

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

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