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Svex-alist

Svex-alist-keys

Like alist-keys but with proper fty-discipline for svex-alists.

Signature
(svex-alist-keys x) → keys
Arguments: x — Guard (svex-alist-p x).
Returns: keys — Type (svarlist-p keys).

Definitions and Theorems

Function: svex-alist-keys

(defun svex-alist-keys (x)
  (declare (xargs :guard (svex-alist-p x)))
  (let ((__function__ 'svex-alist-keys))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (if (mbt (and (consp (car x)) (svar-p (caar x))))
               (cons (caar x)
                     (svex-alist-keys (cdr x)))
             (svex-alist-keys (cdr x))))
         :exec (strip-cars x))))

Theorem: svarlist-p-of-svex-alist-keys

(defthm svarlist-p-of-svex-alist-keys
  (b* ((keys (svex-alist-keys x)))
    (svarlist-p keys))
  :rule-classes :rewrite)

Theorem: svex-alist-keys-of-svex-alist-fix-x

(defthm svex-alist-keys-of-svex-alist-fix-x
  (equal (svex-alist-keys (svex-alist-fix x))
         (svex-alist-keys x)))

Theorem: svex-alist-keys-svex-alist-equiv-congruence-on-x

(defthm svex-alist-keys-svex-alist-equiv-congruence-on-x
  (implies (svex-alist-equiv x x-equiv)
           (equal (svex-alist-keys x)
                  (svex-alist-keys x-equiv)))
  :rule-classes :congruence)

Theorem: member-svex-alist-keys

(defthm member-svex-alist-keys
  (iff (member k (svex-alist-keys x))
       (and (svar-p k) (svex-lookup k x))))

Theorem: svex-alist-keys-of-svex-acons

(defthm svex-alist-keys-of-svex-acons
  (equal (svex-alist-keys (svex-acons k v x))
         (cons (svar-fix k)
               (svex-alist-keys x))))

Theorem: svex-alist-keys-of-pairlis$

(defthm svex-alist-keys-of-pairlis$
  (equal (svex-alist-keys (pairlis$ x y))
         (svarlist-filter x)))