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• Parstate$

Parstate$-fix

Fixing function for parstate$ structures.

Signature

(parstate$-fix x) → new-x

Arguments

x — Guard (parstate$-p x).

Returns

new-x — Type (parstate$-p new-x).

Definitions and Theorems

Function: parstate$-fix$inline

(defun parstate$-fix$inline (x)
 (declare (xargs :guard (parstate$-p x)))
 (mbe
    :logic
    (b* ((bytes (byte-list-fix (car (car x))))
         (position (position-fix (car (cdr (car x)))))
         (chars-read (char+position-list-fix (cdr (cdr (car x)))))
         (chars-unread (char+position-list-fix (car (car (cdr x)))))
         (tokens-read (token+span-list-fix (cdr (car (cdr x)))))
         (tokens-unread (token+span-list-fix (car (cdr (cdr x)))))
         (version (c::version-fix (cdr (cdr (cdr x))))))
      (cons (cons bytes (cons position chars-read))
            (cons (cons chars-unread tokens-read)
                  (cons tokens-unread version))))
    :exec x))

Theorem: parstate$-p-of-parstate$-fix

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

Theorem: parstate$-fix-when-parstate$-p

(defthm parstate$-fix-when-parstate$-p
  (implies (parstate$-p x)
           (equal (parstate$-fix x) x)))

Function: parstate$-equiv$inline

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

Theorem: parstate$-equiv-is-an-equivalence

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

Theorem: parstate$-equiv-implies-equal-parstate$-fix-1

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

Theorem: parstate$-fix-under-parstate$-equiv

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

Theorem: equal-of-parstate$-fix-1-forward-to-parstate$-equiv

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

Theorem: equal-of-parstate$-fix-2-forward-to-parstate$-equiv

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

Theorem: parstate$-equiv-of-parstate$-fix-1-forward

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

Theorem: parstate$-equiv-of-parstate$-fix-2-forward

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

Theorem: parstate$-fix$inline-of-parstate$-fix-x

(defthm parstate$-fix$inline-of-parstate$-fix-x
  (equal (parstate$-fix$inline (parstate$-fix x))
         (parstate$-fix$inline x)))

Theorem: parstate$-fix$inline-parstate$-equiv-congruence-on-x

(defthm parstate$-fix$inline-parstate$-equiv-congruence-on-x
  (implies (parstate$-equiv x x-equiv)
           (equal (parstate$-fix$inline x)
                  (parstate$-fix$inline x-equiv)))
  :rule-classes :congruence)