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Assigns-compose

Signature

(assigns-compose x alist) → new-x

Arguments

x — Guard (assigns-p x).

alist — Guard (svex-alist-p alist).

Returns

new-x — Type (assigns-p new-x).

Definitions and Theorems

Function: assigns-compose

(defun assigns-compose (x alist)
 (declare (xargs :guard (and (assigns-p x)
                             (svex-alist-p alist))))
 (let ((__function__ 'assigns-compose))
  (declare (ignorable __function__))
  (b* ((x (assigns-fix x))
       ((when (atom x)) nil)
       ((cons key (driver dr)) (car x)))
   (cons (cons key
               (change-driver dr
                              :value (svex-compose dr.value alist)))
         (assigns-compose (cdr x) alist)))))

Theorem: assigns-p-of-assigns-compose

(defthm assigns-p-of-assigns-compose
  (b* ((new-x (assigns-compose x alist)))
    (assigns-p new-x))
  :rule-classes :rewrite)

Theorem: vars-of-assigns-compose

(defthm vars-of-assigns-compose
  (b* ((?new-x (assigns-compose x alist)))
    (implies (and (not (member v (assigns-vars x)))
                  (not (member v (svex-alist-vars alist))))
             (not (member v (assigns-vars new-x))))))

Theorem: assigns-compose-of-assigns-fix-x

(defthm assigns-compose-of-assigns-fix-x
  (equal (assigns-compose (assigns-fix x) alist)
         (assigns-compose x alist)))

Theorem: assigns-compose-assigns-equiv-congruence-on-x

(defthm assigns-compose-assigns-equiv-congruence-on-x
  (implies (assigns-equiv x x-equiv)
           (equal (assigns-compose x alist)
                  (assigns-compose x-equiv alist)))
  :rule-classes :congruence)

Theorem: assigns-compose-of-svex-alist-fix-alist

(defthm assigns-compose-of-svex-alist-fix-alist
  (equal (assigns-compose x (svex-alist-fix alist))
         (assigns-compose x alist)))

Theorem: assigns-compose-svex-alist-equiv-congruence-on-alist

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