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• Utilities

Remove-from-alist

(remove-from-alist key alist) removes all bindings for key from alist.

Signature

(remove-from-alist key alist) → ans

Arguments

alist — Guard (alistp alist).

Returns

ans — Type (alistp ans), given the guard.

Definitions and Theorems

Function: remove-from-alist

(defun remove-from-alist (key alist)
  (declare (xargs :guard (alistp alist)))
  (let ((__function__ 'remove-from-alist))
    (declare (ignorable __function__))
    (cond ((atom alist) nil)
          ((equal key (caar alist))
           (remove-from-alist key (cdr alist)))
          (t (cons (car alist)
                   (remove-from-alist key (cdr alist)))))))

Theorem: alistp-of-remove-from-alist

(defthm alistp-of-remove-from-alist
  (implies (and (force (alistp alist)))
           (b* ((ans (remove-from-alist key alist)))
             (alistp ans)))
  :rule-classes :rewrite)

Theorem: remove-from-alist-when-not-consp

(defthm remove-from-alist-when-not-consp
  (implies (not (consp alist))
           (equal (remove-from-alist key alist)
                  nil)))

Theorem: remove-from-alist-of-cons

(defthm remove-from-alist-of-cons
  (equal (remove-from-alist key (cons a x))
         (if (equal key (car a))
             (remove-from-alist key x)
           (cons a (remove-from-alist key x)))))