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Integer-format

Integer-format-fix

Fixing function for integer-format structures.

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

Definitions and Theorems

Function: integer-format-fix$inline

(defun integer-format-fix$inline (x)
 (declare (xargs :guard (integer-formatp x)))
 (let ((__function__ 'integer-format-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((pair (uinteger+sinteger-format-fix (cdr (std::da-nth 0 x)))))
    (let
     ((pair
       (if (uinteger-sinteger-bit-roles-wfp
                (uinteger-format->bits
                     (uinteger+sinteger-format->unsigned pair))
                (sinteger-format->bits
                     (uinteger+sinteger-format->signed pair)))
           pair
        (make-uinteger+sinteger-format
             :unsigned (make-uinteger-format
                            :bits (list (uinteger-bit-role-value 0)
                                        (uinteger-bit-role-value 1))
                            :traps nil)
             :signed (make-sinteger-format
                          :bits (list (sinteger-bit-role-value 0)
                                      (sinteger-bit-role-sign))
                          :signed (signed-format-twos-complement)
                          :traps nil)))))
     (list (cons 'pair pair))))
   :exec x)))

Theorem: integer-formatp-of-integer-format-fix

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

Theorem: integer-format-fix-when-integer-formatp

(defthm integer-format-fix-when-integer-formatp
  (implies (integer-formatp x)
           (equal (integer-format-fix x) x)))

Function: integer-format-equiv$inline

(defun integer-format-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (integer-formatp acl2::x)
                              (integer-formatp acl2::y))))
  (equal (integer-format-fix acl2::x)
         (integer-format-fix acl2::y)))

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

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

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

(defthm integer-format-equiv-implies-equal-integer-format-fix-1
  (implies (integer-format-equiv acl2::x x-equiv)
           (equal (integer-format-fix acl2::x)
                  (integer-format-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: integer-format-fix-under-integer-format-equiv

(defthm integer-format-fix-under-integer-format-equiv
  (integer-format-equiv (integer-format-fix acl2::x)
                        acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

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

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

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

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

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

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

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

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