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String-result

String-result-fix

Fixing function for string-result structures.

Signature
(string-result-fix x) → new-x
Arguments: x — Guard (string-resultp x).
Returns: new-x — Type (string-resultp new-x).

Definitions and Theorems

Function: string-result-fix$inline

(defun string-result-fix$inline (x)
  (declare (xargs :guard (string-resultp x)))
  (let ((__function__ 'string-result-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (string-result-kind x)
           (:ok (b* ((get (str-fix x))) get))
           (:err (b* ((get (fty::reserr-fix x))) get)))
         :exec x)))

Theorem: string-resultp-of-string-result-fix

(defthm string-resultp-of-string-result-fix
  (b* ((new-x (string-result-fix$inline x)))
    (string-resultp new-x))
  :rule-classes :rewrite)

Theorem: string-result-fix-when-string-resultp

(defthm string-result-fix-when-string-resultp
  (implies (string-resultp x)
           (equal (string-result-fix x) x)))

Function: string-result-equiv$inline

(defun string-result-equiv$inline (x y)
  (declare (xargs :guard (and (string-resultp x)
                              (string-resultp y))))
  (equal (string-result-fix x)
         (string-result-fix y)))

Theorem: string-result-equiv-is-an-equivalence

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

Theorem: string-result-equiv-implies-equal-string-result-fix-1

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

Theorem: string-result-fix-under-string-result-equiv

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

Theorem: equal-of-string-result-fix-1-forward-to-string-result-equiv

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

Theorem: equal-of-string-result-fix-2-forward-to-string-result-equiv

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

Theorem: string-result-equiv-of-string-result-fix-1-forward

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

Theorem: string-result-equiv-of-string-result-fix-2-forward

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

Theorem: string-result-kind$inline-of-string-result-fix-x

(defthm string-result-kind$inline-of-string-result-fix-x
  (equal (string-result-kind$inline (string-result-fix x))
         (string-result-kind$inline x)))

Theorem: string-result-kind$inline-string-result-equiv-congruence-on-x

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