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• Bitsets

Bitset-intersectp

(bitset-intersectp x y) efficiently determines if X and Y have any common members.

Signature

(bitset-intersectp x y) → intersectp

Arguments

x — Guard (natp x).

y — Guard (natp y).

Returns

intersectp — Type (booleanp intersectp).

This is efficient because, unlike bitset-intersect, we don't actually construct the intersection.

Definitions and Theorems

Function: bitset-intersectp$inline

(defun acl2::bitset-intersectp$inline (x y)
  (declare (type unsigned-byte x)
           (type unsigned-byte y))
  (declare (xargs :guard (and (natp x) (natp y))))
  (declare (xargs :split-types t))
  (let ((__function__ 'bitset-intersectp))
    (declare (ignorable __function__))
    (logtest (the unsigned-byte (lnfix x))
             (the unsigned-byte (lnfix y)))))

Theorem: booleanp-of-bitset-intersectp

(defthm acl2::booleanp-of-bitset-intersectp
  (b* ((intersectp (acl2::bitset-intersectp$inline x y)))
    (booleanp intersectp))
  :rule-classes :type-prescription)

Theorem: bitset-intersectp-when-not-natp-left

(defthm bitset-intersectp-when-not-natp-left
  (implies (not (natp x))
           (equal (bitset-intersectp x y) nil)))

Theorem: bitset-intersectp-when-not-natp-right

(defthm bitset-intersectp-when-not-natp-right
  (implies (not (natp y))
           (equal (bitset-intersectp x y) nil)))

Theorem: bitset-intersectp-of-nfix-left

(defthm bitset-intersectp-of-nfix-left
  (equal (bitset-intersectp (nfix x) y)
         (bitset-intersectp x y)))

Theorem: bitset-intersectp-of-nfix-right

(defthm bitset-intersectp-of-nfix-right
  (equal (bitset-intersectp x (nfix y))
         (bitset-intersectp x y)))

Theorem: bitset-intersectp-removal

(defthm bitset-intersectp-removal
  (implies (bitset-intersectp x y)
           (intersect (bitset-members x)
                      (bitset-members y))))