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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))))