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• Sv::vl-expr.lisp

Svex-concat-list-aux

Signature

(svex-concat-list-aux widths x acc) → concat

Arguments

widths — the widths of the expressions remaining in x.
    Guard (nat-listp widths).

x — the less-significant expressions, most-significant first.
    Guard (sv::svexlist-p x).

acc — the final svex for the more-significant part.
    Guard (sv::svex-p acc).

Returns

concat — Type (sv::svex-p concat).

Definitions and Theorems

Function: svex-concat-list-aux

(defun svex-concat-list-aux (widths x acc)
  (declare (xargs :guard (and (nat-listp widths)
                              (sv::svexlist-p x)
                              (sv::svex-p acc))))
  (declare (xargs :guard (eql (len widths) (len x))))
  (let ((__function__ 'svex-concat-list-aux))
    (declare (ignorable __function__))
    (if (atom x)
        (sv::svex-fix acc)
      (svex-concat-list-aux (cdr widths)
                            (cdr x)
                            (sv::svex-concat (car widths)
                                             (car x)
                                             acc)))))

Theorem: svex-p-of-svex-concat-list-aux

(defthm svex-p-of-svex-concat-list-aux
  (b* ((concat (svex-concat-list-aux widths x acc)))
    (sv::svex-p concat))
  :rule-classes :rewrite)

Theorem: vars-of-svex-concat-list-aux

(defthm vars-of-svex-concat-list-aux
 (implies
  (and (not (member v (sv::svexlist-vars x)))
       (not (member v (sv::svex-vars acc))))
  (not
     (member v
             (sv::svex-vars (svex-concat-list-aux widths x acc))))))

Theorem: svex-concat-list-aux-of-svexlist-fix-x

(defthm svex-concat-list-aux-of-svexlist-fix-x
  (equal (svex-concat-list-aux widths (sv::svexlist-fix x)
                               acc)
         (svex-concat-list-aux widths x acc)))

Theorem: svex-concat-list-aux-svexlist-equiv-congruence-on-x

(defthm svex-concat-list-aux-svexlist-equiv-congruence-on-x
  (implies (sv::svexlist-equiv x x-equiv)
           (equal (svex-concat-list-aux widths x acc)
                  (svex-concat-list-aux widths x-equiv acc)))
  :rule-classes :congruence)

Theorem: svex-concat-list-aux-of-svex-fix-acc

(defthm svex-concat-list-aux-of-svex-fix-acc
  (equal (svex-concat-list-aux widths x (sv::svex-fix acc))
         (svex-concat-list-aux widths x acc)))

Theorem: svex-concat-list-aux-svex-equiv-congruence-on-acc

(defthm svex-concat-list-aux-svex-equiv-congruence-on-acc
  (implies (sv::svex-equiv acc acc-equiv)
           (equal (svex-concat-list-aux widths x acc)
                  (svex-concat-list-aux widths x acc-equiv)))
  :rule-classes :congruence)