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• Concatenation

Prefix-strings

Concatenates a prefix onto every string in a list of strings.

Signature

(prefix-strings prefix x) → *

Arguments

prefix — Guard (stringp prefix).

x — Guard (string-listp x).

(prefix-strings prefix x) produces a new string list by concatenating prefix onto every member of x.

Definitions and Theorems

Function: prefix-strings

(defun prefix-strings (prefix x)
  (declare (xargs :guard (and (stringp prefix)
                              (string-listp x))))
  (let ((acl2::__function__ 'prefix-strings))
    (declare (ignorable acl2::__function__))
    (if (atom x)
        nil
      (cons (cat prefix (car x))
            (prefix-strings prefix (cdr x))))))

Theorem: prefix-strings-when-atom

(defthm prefix-strings-when-atom
  (implies (atom x)
           (equal (prefix-strings prefix x) nil)))

Theorem: prefix-strings-of-cons

(defthm prefix-strings-of-cons
  (equal (prefix-strings prefix (cons a x))
         (cons (cat prefix a)
               (prefix-strings prefix x))))

Theorem: string-listp-of-prefix-strings

(defthm string-listp-of-prefix-strings
  (string-listp (prefix-strings prefix x)))

Theorem: len-of-prefix-strings

(defthm len-of-prefix-strings
  (equal (len (prefix-strings prefix x))
         (len x)))

Theorem: streqv-implies-equal-prefix-strings-1

(defthm streqv-implies-equal-prefix-strings-1
  (implies (streqv prefix prefix-equiv)
           (equal (prefix-strings prefix x)
                  (prefix-strings prefix-equiv x)))
  :rule-classes (:congruence))

Theorem: list-equiv-implies-equal-prefix-strings-2

(defthm list-equiv-implies-equal-prefix-strings-2
  (implies (list-equiv x x-equiv)
           (equal (prefix-strings prefix x)
                  (prefix-strings prefix x-equiv)))
  :rule-classes (:congruence))