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Representation-of-integers

Uint-from-integer-mod

Reduce modularly ACL2 integers to values of type unsigned int.

Signature
(uint-from-integer-mod x) → result
Arguments: x — Guard (integerp x).
Returns: result — Type (uintp result).

Definitions and Theorems

Function: uint-from-integer-mod

(defun uint-from-integer-mod (x)
  (declare (xargs :guard (integerp x)))
  (let ((__function__ 'uint-from-integer-mod))
    (declare (ignorable __function__))
    (uint-from-integer (mod (ifix x) (1+ (uint-max))))))

Theorem: uintp-of-uint-from-integer-mod

(defthm uintp-of-uint-from-integer-mod
  (b* ((result (uint-from-integer-mod x)))
    (uintp result))
  :rule-classes :rewrite)

Theorem: uint-from-integer-mod-of-ifix-x

(defthm uint-from-integer-mod-of-ifix-x
  (equal (uint-from-integer-mod (ifix x))
         (uint-from-integer-mod x)))

Theorem: uint-from-integer-mod-int-equiv-congruence-on-x

(defthm uint-from-integer-mod-int-equiv-congruence-on-x
  (implies (acl2::int-equiv x x-equiv)
           (equal (uint-from-integer-mod x)
                  (uint-from-integer-mod x-equiv)))
  :rule-classes :congruence)