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• Vl-merge-contiguous-indices

Vl-match-contiguous-indices

Identify one strictly increasing segment of a vl-maybe-integer-listp.

Signature

(vl-match-contiguous-indices n x) → (mv range-end rest)

Arguments

n — Index to try to count up from.
    Guard (maybe-integerp n).

x — List whose elements we are to collect.
    Guard (vl-maybe-integer-listp x).

Returns

range-end — Type (maybe-integerp range-end), given the guard.

rest — Type (vl-maybe-integer-listp rest), given the guard.

We try to consume the leading portion of x if it counts up from n. For example:

(vl-match-contiguous-indices 1 '(2 3 4 5 10 11 12))
  -->
(mv 5 (10 11 12))

Definitions and Theorems

Function: vl-match-contiguous-indices

(defun vl-match-contiguous-indices (n x)
  (declare (xargs :guard (and (maybe-integerp n)
                              (vl-maybe-integer-listp x))))
  (let ((__function__ 'vl-match-contiguous-indices))
    (declare (ignorable __function__))
    (if (or (not (integerp n))
            (atom x)
            (not (equal (car x) (+ n 1))))
        (mv n x)
      (vl-match-contiguous-indices (+ n 1)
                                   (cdr x)))))

Theorem: maybe-integerp-of-vl-match-contiguous-indices.range-end

(defthm maybe-integerp-of-vl-match-contiguous-indices.range-end
  (implies (and (force (acl2::maybe-integerp$inline n))
                (force (vl-maybe-integer-listp x)))
           (b* (((mv ?range-end common-lisp::?rest)
                 (vl-match-contiguous-indices n x)))
             (maybe-integerp range-end)))
  :rule-classes :rewrite)

Theorem: vl-maybe-integer-listp-of-vl-match-contiguous-indices.rest

(defthm vl-maybe-integer-listp-of-vl-match-contiguous-indices.rest
  (implies (and (force (acl2::maybe-integerp$inline n))
                (force (vl-maybe-integer-listp x)))
           (b* (((mv ?range-end common-lisp::?rest)
                 (vl-match-contiguous-indices n x)))
             (vl-maybe-integer-listp rest)))
  :rule-classes :rewrite)

Theorem: len-of-vl-match-contiguous-indices

(defthm len-of-vl-match-contiguous-indices
 (implies (not (equal n
                      (mv-nth 0 (vl-match-contiguous-indices n x))))
          (< (len (mv-nth 1 (vl-match-contiguous-indices n x)))
             (len x)))
 :rule-classes ((:rewrite) (:linear)))

Theorem: vl-match-contiguous-indices-fails-on-nil

(defthm vl-match-contiguous-indices-fails-on-nil
  (equal (mv-nth 0 (vl-match-contiguous-indices nil x))
         nil))

Theorem: vl-match-contiguous-indices-monotonic-on-success

(defthm vl-match-contiguous-indices-monotonic-on-success
 (implies
     (and (not (equal n
                      (mv-nth 0 (vl-match-contiguous-indices n x))))
          (force (maybe-integerp n))
          (force (vl-maybe-integer-listp x)))
     (< n
        (mv-nth 0 (vl-match-contiguous-indices n x))))
 :rule-classes ((:rewrite) (:linear)))

Theorem: vl-match-contiguous-indices-exists-on-success

(defthm vl-match-contiguous-indices-exists-on-success
 (implies
     (and (not (equal n
                      (mv-nth 0 (vl-match-contiguous-indices n x))))
          (force (maybe-integerp n))
          (force (vl-maybe-integer-listp x)))
     (integerp (mv-nth 0 (vl-match-contiguous-indices n x)))))