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Jexpr-rank

Jexpr-rank-fix

Fixing function for jexpr-rank structures.

Signature
(jexpr-rank-fix x) → new-x
Arguments: x — Guard (jexpr-rankp x).
Returns: new-x — Type (jexpr-rankp new-x).

Definitions and Theorems

Function: jexpr-rank-fix$inline

(defun jexpr-rank-fix$inline (x)
  (declare (xargs :guard (jexpr-rankp x)))
  (let ((__function__ 'jexpr-rank-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (jexpr-rank-kind x)
           (:expression (cons :expression (list)))
           (:assignment (cons :assignment (list)))
           (:conditional (cons :conditional (list)))
           (:conditional-or (cons :conditional-or (list)))
           (:conditional-and (cons :conditional-and (list)))
           (:inclusive-or (cons :inclusive-or (list)))
           (:exclusive-or (cons :exclusive-or (list)))
           (:and (cons :and (list)))
           (:equality (cons :equality (list)))
           (:relational (cons :relational (list)))
           (:shift (cons :shift (list)))
           (:additive (cons :additive (list)))
           (:multiplicative (cons :multiplicative (list)))
           (:unary (cons :unary (list)))
           (:postfix (cons :postfix (list)))
           (:primary (cons :primary (list))))
         :exec x)))

Theorem: jexpr-rankp-of-jexpr-rank-fix

(defthm jexpr-rankp-of-jexpr-rank-fix
  (b* ((new-x (jexpr-rank-fix$inline x)))
    (jexpr-rankp new-x))
  :rule-classes :rewrite)

Theorem: jexpr-rank-fix-when-jexpr-rankp

(defthm jexpr-rank-fix-when-jexpr-rankp
  (implies (jexpr-rankp x)
           (equal (jexpr-rank-fix x) x)))

Function: jexpr-rank-equiv$inline

(defun jexpr-rank-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (jexpr-rankp acl2::x)
                              (jexpr-rankp acl2::y))))
  (equal (jexpr-rank-fix acl2::x)
         (jexpr-rank-fix acl2::y)))

Theorem: jexpr-rank-equiv-is-an-equivalence

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

Theorem: jexpr-rank-equiv-implies-equal-jexpr-rank-fix-1

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

Theorem: jexpr-rank-fix-under-jexpr-rank-equiv

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

Theorem: equal-of-jexpr-rank-fix-1-forward-to-jexpr-rank-equiv

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

Theorem: equal-of-jexpr-rank-fix-2-forward-to-jexpr-rank-equiv

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

Theorem: jexpr-rank-equiv-of-jexpr-rank-fix-1-forward

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

Theorem: jexpr-rank-equiv-of-jexpr-rank-fix-2-forward

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

Theorem: jexpr-rank-kind$inline-of-jexpr-rank-fix-x

(defthm jexpr-rank-kind$inline-of-jexpr-rank-fix-x
  (equal (jexpr-rank-kind$inline (jexpr-rank-fix x))
         (jexpr-rank-kind$inline x)))

Theorem: jexpr-rank-kind$inline-jexpr-rank-equiv-congruence-on-x

(defthm jexpr-rank-kind$inline-jexpr-rank-equiv-congruence-on-x
  (implies (jexpr-rank-equiv x x-equiv)
           (equal (jexpr-rank-kind$inline x)
                  (jexpr-rank-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-jexpr-rank-fix

(defthm consp-of-jexpr-rank-fix
  (consp (jexpr-rank-fix x))
  :rule-classes :type-prescription)