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• Substitution

Strsubst-list

Carry out a strsubst replacement throughout a list of strings.

(strsubst-list old new x) replaces every occurrence of old with new throughout x. Here, old and new are strings, but x is a list of strings. A new list of strings is returned.

Example:

(strsubst-list "Sun"
               "Moon"
               '("Sun Roof" "Hello Sun" "Sunny Sunshades"))
  -->
("Moon Roof" "Hello Moon" "Moonny Moonshades")

Definitions and Theorems

Function: strsubst-list

(defun strsubst-list (old new x)
  (declare (xargs :guard (and (stringp old)
                              (stringp new)
                              (string-listp x))))
  (if (atom x)
      nil
    (cons (strsubst old new (car x))
          (strsubst-list old new (cdr x)))))

Theorem: strsubst-list-when-atom

(defthm strsubst-list-when-atom
  (implies (atom x)
           (equal (strsubst-list old new x) nil)))

Theorem: strsubst-list-of-cons

(defthm strsubst-list-of-cons
  (equal (strsubst-list old new (cons a x))
         (cons (strsubst old new a)
               (strsubst-list old new x))))

Theorem: string-listp-of-strsubst-list

(defthm string-listp-of-strsubst-list
  (string-listp (strsubst-list old new x)))

Theorem: list-equiv-implies-equal-strsubst-list-3

(defthm list-equiv-implies-equal-strsubst-list-3
  (implies (list-equiv x x-equiv)
           (equal (strsubst-list old new x)
                  (strsubst-list old new x-equiv)))
  :rule-classes (:congruence))

Theorem: strsubst-list-of-append

(defthm strsubst-list-of-append
  (equal (strsubst-list old new (append x y))
         (append (strsubst-list old new x)
                 (strsubst-list old new y))))

Theorem: strsubst-list-of-revappend

(defthm strsubst-list-of-revappend
  (equal (strsubst-list old new (revappend x y))
         (revappend (strsubst-list old new x)
                    (strsubst-list old new y))))

Theorem: strsubst-list-of-rev

(defthm strsubst-list-of-rev
  (equal (strsubst-list old new (rev x))
         (rev (strsubst-list old new x))))