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S4vecs

S4vec-lsh

Signature
(s4vec-lsh amt x) → res
Arguments: amt — Guard (s4vec-p amt).; x — Guard (s4vec-p x).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s4vec-lsh

(defun s4vec-lsh (amt x)
  (declare (xargs :guard (and (s4vec-p amt) (s4vec-p x))))
  (let ((__function__ 's4vec-lsh))
    (declare (ignorable __function__))
    (b* (((unless (s4vec-2vec-p amt)) (s4vec-x))
         (amtval (s4vec-sparseint-val (s4vec->upper amt))))
      (s4vec-shift-core amtval x))))

Theorem: s4vec-p-of-s4vec-lsh

(defthm s4vec-p-of-s4vec-lsh
  (b* ((res (s4vec-lsh amt x)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s4vec-lsh-correct

(defthm s4vec-lsh-correct
  (b* ((?res (s4vec-lsh amt x)))
    (equal (s4vec->4vec res)
           (4vec-lsh (s4vec->4vec amt)
                     (s4vec->4vec x)))))

Theorem: s4vec-lsh-of-s4vec-fix-amt

(defthm s4vec-lsh-of-s4vec-fix-amt
  (equal (s4vec-lsh (s4vec-fix amt) x)
         (s4vec-lsh amt x)))

Theorem: s4vec-lsh-s4vec-equiv-congruence-on-amt

(defthm s4vec-lsh-s4vec-equiv-congruence-on-amt
  (implies (s4vec-equiv amt amt-equiv)
           (equal (s4vec-lsh amt x)
                  (s4vec-lsh amt-equiv x)))
  :rule-classes :congruence)

Theorem: s4vec-lsh-of-s4vec-fix-x

(defthm s4vec-lsh-of-s4vec-fix-x
  (equal (s4vec-lsh amt (s4vec-fix x))
         (s4vec-lsh amt x)))

Theorem: s4vec-lsh-s4vec-equiv-congruence-on-x

(defthm s4vec-lsh-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s4vec-lsh amt x)
                  (s4vec-lsh amt x-equiv)))
  :rule-classes :congruence)