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• Svar

Svar-fix

Fixing function for svar structures.

Signature

(svar-fix x) → new-x

Arguments

x — Guard (svar-p x).

Returns

new-x — Type (svar-p new-x).

Definitions and Theorems

Function: svar-fix$inline

(defun svar-fix$inline (x)
 (declare (xargs :guard (svar-p x)))
 (let ((__function__ 'svar-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b* ((name (if (atom x) x (cadr x)))
        (delay (nfix (if (atom x)
                         0
                       (b* ((rest (cddr x))
                            ((when (integerp rest))
                             (loghead 4 rest))
                            ((when (integerp (first rest)))
                             (first rest)))
                         (cdr (first rest))))))
        (bits (ifix (if (atom x)
                        0
                      (b* ((rest (cddr x))
                           ((when (integerp rest))
                            (logtail 4 rest))
                           ((when (integerp (first rest)))
                            (cdr rest)))
                        (cdr (second rest))))))
        (props (svar-proplist-fix
                    (if (atom x)
                        nil
                      (b* ((rest (cddr x))
                           ((when (integerp rest)) nil)
                           ((when (integerp (first rest))) nil))
                        (cddr rest))))))
    (cond
      (props
           (hons :var (hons name
                            (hons (hons :delay delay)
                                  (hons (hons :bits bits) props)))))
      ((>= delay 16)
       (hons :var (hons name (hons delay bits))))
      ((and (or (stringp name)
                (and (symbolp name)
                     (not (booleanp name))))
            (eql delay 0)
            (eql bits 0))
       name)
      (t (hons :var (hons name (logapp 4 delay bits))))))
   :exec x)))

Theorem: svar-p-of-svar-fix

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

Theorem: svar-fix-when-svar-p

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

Function: svar-equiv$inline

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

Theorem: svar-equiv-is-an-equivalence

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

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

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

Theorem: svar-fix-under-svar-equiv

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

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

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

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

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

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

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

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

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