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Longest-common-prefix

(longest-common-prefix x y) returns the longest list, p, such that p is a prefix of both x and y, in the sense of prefixp.

Signature

(longest-common-prefix x y) → *

See also longest-common-prefix-list, which extends this function to a list of lists.

Definitions and Theorems

Function: longest-common-prefix

(defun longest-common-prefix (x y)
  (declare (xargs :guard t))
  (let ((__function__ 'longest-common-prefix))
    (declare (ignorable __function__))
    (cond ((or (atom x) (atom y)) nil)
          ((equal (car x) (car y))
           (cons (car x)
                 (longest-common-prefix (cdr x)
                                        (cdr y))))
          (t nil))))

Theorem: true-listp-of-longest-common-prefix

(defthm true-listp-of-longest-common-prefix
  (true-listp (longest-common-prefix x y))
  :rule-classes :type-prescription)

Theorem: string-listp-of-longest-common-prefix

(defthm string-listp-of-longest-common-prefix
  (implies (and (string-listp x) (string-listp y))
           (string-listp (longest-common-prefix x y))))

Theorem: longest-common-prefix-of-list-fix-left

(defthm longest-common-prefix-of-list-fix-left
  (equal (longest-common-prefix (list-fix x) y)
         (longest-common-prefix x y)))

Theorem: longest-common-prefix-of-list-fix-right

(defthm longest-common-prefix-of-list-fix-right
  (equal (longest-common-prefix x (list-fix y))
         (longest-common-prefix x y)))

Theorem: prefixp-of-longest-common-prefix-left

(defthm prefixp-of-longest-common-prefix-left
  (prefixp (longest-common-prefix x y) x))

Theorem: prefixp-of-longest-common-prefix-right

(defthm prefixp-of-longest-common-prefix-right
  (prefixp (longest-common-prefix x y) y))

Theorem: longest-common-prefix-preserves-prefixp

(defthm longest-common-prefix-preserves-prefixp
  (implies (prefixp p a)
           (prefixp (longest-common-prefix p b)
                    a)))