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• Std/alists

Hons-remove-assoc

Remove a particular key from a "modern" alist.

The hons- here just refers to our observation of the "modern" atom-skipping convention as in hons-assoc-equal, etc. There is nothing fast or hons-specific here.

Definitions and Theorems

Theorem: hons-remove-assoc-of-cons

(defthm hons-remove-assoc-of-cons
  (equal (hons-remove-assoc k (cons x y))
         (if (and (consp x) (not (equal (car x) k)))
             (cons x (hons-remove-assoc k y))
           (hons-remove-assoc k y))))

Theorem: hons-remove-assoc-of-atom

(defthm hons-remove-assoc-of-atom
  (implies (not (consp x))
           (equal (hons-remove-assoc k x) nil))
  :rule-classes ((:rewrite :backchain-limit-lst 0)))

Theorem: hons-remove-assoc-commutes

(defthm hons-remove-assoc-commutes
  (equal (hons-remove-assoc k (hons-remove-assoc j x))
         (hons-remove-assoc j (hons-remove-assoc k x)))
  :rule-classes ((:rewrite :loop-stopper ((j k)))))

Theorem: hons-assoc-equal-remove-assoc

(defthm hons-assoc-equal-remove-assoc
  (equal (hons-assoc-equal k (hons-remove-assoc j x))
         (and (not (equal k j))
              (hons-assoc-equal k x))))

Theorem: hons-remove-assoc-of-fast-alist-fork

(defthm hons-remove-assoc-of-fast-alist-fork
  (equal (hons-remove-assoc k (fast-alist-fork x y))
         (fast-alist-fork (hons-remove-assoc k x)
                          (hons-remove-assoc k y))))

Theorem: hons-remove-assoc-of-append

(defthm hons-remove-assoc-of-append
  (equal (hons-remove-assoc k (append x y))
         (append (hons-remove-assoc k x)
                 (hons-remove-assoc k y))))

Theorem: hons-remove-assoc-when-not-hons-assoc-equal

(defthm hons-remove-assoc-when-not-hons-assoc-equal
  (implies (not (hons-assoc-equal k x))
           (equal (hons-remove-assoc k x)
                  (alist-fix x))))

Theorem: alistp-of-hons-remove-assoc

(defthm alistp-of-hons-remove-assoc
  (alistp (hons-remove-assoc k x)))

Theorem: hons-remove-assoc-of-alist-fix

(defthm hons-remove-assoc-of-alist-fix
  (equal (hons-remove-assoc k (alist-fix x))
         (hons-remove-assoc k x)))