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Snippet-mismatch

Snippet-mismatch-fix

Fixing function for snippet-mismatch structures.

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

Definitions and Theorems

Function: snippet-mismatch-fix$inline

(defun snippet-mismatch-fix$inline (x)
 (declare (xargs :guard (snippet-mismatch-p x)))
 (let ((__function__ 'snippet-mismatch-fix))
  (declare (ignorable __function__))
  (mbe :logic
       (b* ((input-bytes (byte-list-fix (cdr (std::da-nth 0 x))))
            (expected-bytes (byte-list-fix (cdr (std::da-nth 1 x))))
            (actual-bytes (byte-list-fix (cdr (std::da-nth 2 x)))))
         (list (cons 'input-bytes input-bytes)
               (cons 'expected-bytes expected-bytes)
               (cons 'actual-bytes actual-bytes)))
       :exec x)))

Theorem: snippet-mismatch-p-of-snippet-mismatch-fix

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

Theorem: snippet-mismatch-fix-when-snippet-mismatch-p

(defthm snippet-mismatch-fix-when-snippet-mismatch-p
  (implies (snippet-mismatch-p x)
           (equal (snippet-mismatch-fix x) x)))

Function: snippet-mismatch-equiv$inline

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

Theorem: snippet-mismatch-equiv-is-an-equivalence

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

Theorem: snippet-mismatch-equiv-implies-equal-snippet-mismatch-fix-1

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

Theorem: snippet-mismatch-fix-under-snippet-mismatch-equiv

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

Theorem: equal-of-snippet-mismatch-fix-1-forward-to-snippet-mismatch-equiv

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

Theorem: equal-of-snippet-mismatch-fix-2-forward-to-snippet-mismatch-equiv

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

Theorem: snippet-mismatch-equiv-of-snippet-mismatch-fix-1-forward

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

Theorem: snippet-mismatch-equiv-of-snippet-mismatch-fix-2-forward

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