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Integer-result

Integer-result-fix

Fixing function for integer-result structures.

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

Definitions and Theorems

Function: integer-result-fix$inline

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

Theorem: integer-resultp-of-integer-result-fix

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

Theorem: integer-result-fix-when-integer-resultp

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

Function: integer-result-equiv$inline

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

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

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

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

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

Theorem: integer-result-fix-under-integer-result-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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