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Concatenation

Append-chars

Append a string's characters onto a list.

Signature
(append-chars x y) → *

(append-chars x y) takes the characters from the string x and appends them onto y.

Its logical definition is nothing more than (append (explode x) y).

In the execution, we traverse the string x using char to avoid the overhead of coerce-ing it into a character list before performing the append. This reduces the overhead from 2n conses to n conses, where n is the length of x.

Definitions and Theorems

Function: append-chars-aux

(defun append-chars-aux (x n y)
  "Appends the characters from x[0:n] onto y"
  (declare (type string x)
           (type (integer 0 *) n)
           (xargs :guard (< n (length x))))
  (if (zp n)
      (cons (char x 0) y)
    (append-chars-aux x (the (integer 0 *) (- n 1))
                      (cons (char x n) y))))

Theorem: append-chars-aux-correct

(defthm append-chars-aux-correct
  (implies (and (stringp x)
                (natp n)
                (< n (length x)))
           (equal (append-chars-aux x n y)
                  (append (take (+ 1 n) (explode x)) y))))

Function: append-chars$inline

(defun append-chars$inline (x y)
  (declare (type string x))
  (let ((acl2::__function__ 'append-chars))
    (declare (ignorable acl2::__function__))
    (mbe :logic (append (explode x) y)
         :exec
         (b* (((the (integer 0 *) xl) (length x))
              ((when (eql xl 0)) y)
              ((the (integer 0 *) n) (- xl 1)))
           (append-chars-aux x n y)))))

Theorem: character-listp-of-append-chars

(defthm character-listp-of-append-chars
  (equal (character-listp (append-chars x y))
         (character-listp y)))

Theorem: streqv-implies-equal-append-chars-1

(defthm streqv-implies-equal-append-chars-1
  (implies (streqv x x-equiv)
           (equal (append-chars x y)
                  (append-chars x-equiv y)))
  :rule-classes (:congruence))

Theorem: istreqv-implies-icharlisteqv-append-chars-1

(defthm istreqv-implies-icharlisteqv-append-chars-1
  (implies (istreqv x x-equiv)
           (icharlisteqv (append-chars x y)
                         (append-chars x-equiv y)))
  :rule-classes (:congruence))

Theorem: list-equiv-implies-list-equiv-append-chars-2

(defthm list-equiv-implies-list-equiv-append-chars-2
  (implies (list-equiv y y-equiv)
           (list-equiv (append-chars x y)
                       (append-chars x y-equiv)))
  :rule-classes (:congruence))

Theorem: charlisteqv-implies-charlisteqv-append-chars-2

(defthm charlisteqv-implies-charlisteqv-append-chars-2
  (implies (charlisteqv y y-equiv)
           (charlisteqv (append-chars x y)
                        (append-chars x y-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-append-chars-2

(defthm icharlisteqv-implies-icharlisteqv-append-chars-2
  (implies (icharlisteqv y y-equiv)
           (icharlisteqv (append-chars x y)
                         (append-chars x y-equiv)))
  :rule-classes (:congruence))