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Firstn-chars

Efficient way to take leading characters from a string.

(firstn-chars n x) is logically equal to:

(take (min n (length x)) (explode x))

But it is implemented more efficiently, via char.

Definitions and Theorems

Function: firstn-chars-aux

(defun firstn-chars-aux (x n acc)
  (declare (xargs :guard (and (stringp x)
                              (natp n)
                              (< n (length x))))
           (type string x)
           (type (integer 0 *) n))
  (if (zp n)
      (cons (char x 0) acc)
    (firstn-chars-aux x (the (integer 0 *) (- n 1))
                      (cons (char x n) acc))))

Function: firstn-chars

(defun firstn-chars (n x)
  (declare (xargs :guard (and (stringp x) (natp n)))
           (type string x)
           (type (integer 0 *) n))
  (mbe :logic
       (take (min (nfix n) (len (explode x)))
             (explode x))
       :exec
       (let ((n (min n (length x))))
         (if (zp n)
             nil
           (firstn-chars-aux x (the (integer 0 *) (- n 1))
                             nil)))))

Theorem: firstn-chars-aux-removal

(defthm firstn-chars-aux-removal
  (implies (and (stringp x)
                (natp n)
                (< n (length x)))
           (equal (firstn-chars-aux x n acc)
                  (append (take (+ n 1) (coerce x 'list))
                          acc))))

Theorem: character-listp-of-firstn-chars

(defthm character-listp-of-firstn-chars
  (character-listp (firstn-chars n x)))

Theorem: streqv-implies-equal-firstn-chars-2

(defthm streqv-implies-equal-firstn-chars-2
  (implies (streqv x x-equiv)
           (equal (firstn-chars n x)
                  (firstn-chars n x-equiv)))
  :rule-classes (:congruence))

Theorem: istreqv-implies-icharlisteqv-firstn-chars-2

(defthm istreqv-implies-icharlisteqv-firstn-chars-2
  (implies (istreqv x x-equiv)
           (icharlisteqv (firstn-chars n x)
                         (firstn-chars n x-equiv)))
  :rule-classes (:congruence))