printtree-concat

(in-package "STR")

(include-book "printtree")

(local (include-book "printtree-fix"))

(defsection printable-empty-p
  (defund-inline printable-empty-p
    (x)
    (declare (xargs :guard (printable-p x)))
    (let ((x (printable-fix x)))
      (or (not x) (equal x ""))))
  (local (in-theory (enable printable-empty-p
        printable-fix
        printable-p
        printable->str)))
  (local (defthm character-listp-of-make-character-list
      (character-listp (make-character-list x))))
  (local (defthm coerce-inverse-better
      (equal (coerce (coerce x 'string) 'list)
        (make-character-list x))
      :hints (("goal" :use ((:instance completion-of-coerce
            (x x)
            (y 'string)))))))
  (local (defthm length-of-coerce-list-x
      (equal (length (coerce (list x) 'string)) 1)
      :rule-classes nil))
  (local (defthm char-to-list-not-empty
      (not (equal (coerce (list x) 'string) ""))
      :hints (("goal" :use ((:instance length-of-coerce-list-x))))))
  (defthm printable-empty-p-means-empty
    (equal (printable-empty-p x)
      (equal (printable->str x) ""))))

(defsection printtree-obviously-empty-p
  (local (in-theory (enable printtree->str printtree-p)))
  (defund-inline printtree-obviously-empty-p
    (x)
    (declare (xargs :guard (printtree-p x)))
    (and (atom x) (printable-empty-p x)))
  (local (in-theory (enable printtree-obviously-empty-p)))
  (defthmd printtree-obviously-empty-p-implies-empty
    (implies (printtree-obviously-empty-p x)
      (equal (printtree->str x) ""))))

(defsection printtree-concat
  (local (in-theory (enable printtree-obviously-empty-p-implies-empty)))
  (defund printtree-concat
    (x y)
    (declare (xargs :guard (and (printtree-p x) (printtree-p y))))
    (cond ((printtree-obviously-empty-p x) (printtree-fix y))
      ((printtree-obviously-empty-p y) (printtree-fix x))
      (t (cons (printtree-fix y)
          (printtree-fix x)))))
  (local (in-theory (enable printtree-concat)))
  (defthm printtree-p-of-printtree-concat
    (printtree-p (printtree-concat x y)))
  (defthm printtree->str-of-printtree-concat
    (equal (printtree->str (printtree-concat x y))
      (string-append (printtree->str x)
        (printtree->str y)))
    :hints (("Goal" :in-theory (enable printtree->str)))))

(defmacro printtree-rconcat
  (x y)
  `(printtree-concat ,STR::Y ,STR::X))

(defmacro pcat
  (&rest args)
  (xxxjoin 'printtree-rconcat (reverse args)))