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Svstmt-compile.lisp

Svstack-fork

Signature
(svstack-fork x) → new-x
Arguments: x — Guard (svstack-p x).
Returns: new-x — Type (svstack-p new-x).

Definitions and Theorems

Function: svstack-fork

(defun svstack-fork (x)
  (declare (xargs :guard (svstack-p x)))
  (let ((__function__ 'svstack-fork))
    (declare (ignorable __function__))
    (if (atom x)
        nil
      (cons (fast-alist-fork (svex-alist-fix (car x))
                             nil)
            (svstack-fork (cdr x))))))

Theorem: svstack-p-of-svstack-fork

(defthm svstack-p-of-svstack-fork
  (b* ((new-x (svstack-fork x)))
    (svstack-p new-x))
  :rule-classes :rewrite)

Theorem: len-of-svstack-fork

(defthm len-of-svstack-fork
  (b* ((?new-x (svstack-fork x)))
    (equal (len new-x) (len x))))

Theorem: lookup-in-svstack-fork

(defthm lookup-in-svstack-fork
  (b* ((?new-x (svstack-fork x)))
    (equal (svex-lookup v (svstack-to-svex-alist new-x))
           (svex-lookup v (svstack-to-svex-alist x)))))

Theorem: vars-of-svstack-fork

(defthm vars-of-svstack-fork
 (b* ((?new-x (svstack-fork x)))
  (implies
   (not (member v
                (svex-alist-vars (svstack-to-svex-alist x))))
   (not (member v
                (svex-alist-vars (svstack-to-svex-alist new-x)))))))

Theorem: consp-of-svstack-fork

(defthm consp-of-svstack-fork
  (b* ((?new-x (svstack-fork x)))
    (equal (consp new-x) (consp x))))

Theorem: svstack-fork-of-svstack-fix-x

(defthm svstack-fork-of-svstack-fix-x
  (equal (svstack-fork (svstack-fix x))
         (svstack-fork x)))

Theorem: svstack-fork-svstack-equiv-congruence-on-x

(defthm svstack-fork-svstack-equiv-congruence-on-x
  (implies (svstack-equiv x x-equiv)
           (equal (svstack-fork x)
                  (svstack-fork x-equiv)))
  :rule-classes :congruence)