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Al->pat

(al->pat pat al default) builds a new data object that is compatible with pat, using the data from al and providing the default value for missing keys.

For instance,

(al->pat '((a (b c)) d)
         '((a . 1) (b . 2) (d . 4))
         'oops)
  -->
((1 (2 oops)) 4)

Note that al should be a fast alist.

Definitions and Theorems

Function: al->pat

(defun al->pat (pat al default)
  (declare (xargs :guard t))
  (if pat (if (atom pat)
              (let ((look (hons-get pat al)))
                (if look (cdr look) default))
            (cons (al->pat (car pat) al default)
                  (al->pat (cdr pat) al default)))
    nil))

Theorem: true-listp-al->pat

(defthm true-listp-al->pat
  (implies (true-listp pat)
           (true-listp (al->pat pat al default)))
  :rule-classes ((:rewrite) (:type-prescription)))

Theorem: len-al->pat

(defthm len-al->pat
  (implies (true-listp pat)
           (equal (len (al->pat pat al default))
                  (len pat))))