• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
    • Vwsim
    • Fgl
    • Vl
      • Syntax
      • Loader
      • Warnings
      • Getting-started
      • Utilities
        • Name-database
        • Vl-gc
        • Symbol-list-names
        • Ints-from
        • Nats-from
        • Make-lookup-alist
        • Redundant-mergesort
        • Longest-common-prefix
        • Vl-remove-keys
        • Vl-plural-p
        • Vl-merge-contiguous-indices
        • Sum-nats
        • Vl-edition-p
        • Vl-maybe-integer-listp
        • Fast-memberp
        • Nat-listp
        • Max-nats
        • Longest-common-prefix-list
        • Character-list-listp
        • Vl-character-list-list-values-p
        • Remove-from-alist
        • Prefix-of-eachp
        • Vl-string-keys-p
        • Vl-maybe-nat-listp
        • Vl-string-list-values-p
        • String-list-listp
        • Vl-string-values-p
        • Explode-list
        • True-list-listp
        • Symbol-list-listp
        • All-have-len
        • Pos-listp
        • Min-nats
        • Debuggable-and
        • Vl-starname
        • Remove-equal-without-guard
        • String-fix
        • Anyp
        • Vl-maybe-string-list
        • Longer-than-p
        • Fast-alist-free-each-alist-val
        • Not*
        • Free-list-of-fast-alists
        • *nls*
      • Printer
      • Kit
      • Mlib
      • Transforms
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Testing-utilities
  • Math

• Utilities

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)))