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• Vl-echarlist-unsigned-value

Vl-echarlist-unsigned-value-aux

Signature

(vl-echarlist-unsigned-value-aux x radix n) → *

Arguments

x — Guard (vl-echarlist-p x).

radix — Guard (natp radix).

n — Guard (equal n (len x)).

Definitions and Theorems

Function: vl-echarlist-unsigned-value-aux

(defun vl-echarlist-unsigned-value-aux (x radix n)
  (declare (xargs :guard (and (vl-echarlist-p x)
                              (natp radix)
                              (equal n (len x)))))
  (declare (xargs :guard (and (<= 2 radix) (<= radix 36))))
  (let ((__function__ 'vl-echarlist-unsigned-value-aux))
    (declare (ignorable __function__))
    (b* (((when (atom x)) 0)
         (car-digit (vl-echar-digit-value (car x) radix))
         ((unless car-digit) nil)
         (cdr-value (vl-echarlist-unsigned-value-aux (cdr x)
                                                     radix (1- n)))
         ((unless cdr-value) nil))
      (+ (* (expt (lnfix radix) (1- n))
            car-digit)
         cdr-value))))

Theorem: vl-echarlist-unsigned-value-aux-of-vl-echarlist-fix-x

(defthm vl-echarlist-unsigned-value-aux-of-vl-echarlist-fix-x
  (equal (vl-echarlist-unsigned-value-aux (vl-echarlist-fix x)
                                          radix n)
         (vl-echarlist-unsigned-value-aux x radix n)))

Theorem: vl-echarlist-unsigned-value-aux-vl-echarlist-equiv-congruence-on-x

(defthm
 vl-echarlist-unsigned-value-aux-vl-echarlist-equiv-congruence-on-x
 (implies (vl-echarlist-equiv x x-equiv)
          (equal (vl-echarlist-unsigned-value-aux x radix n)
                 (vl-echarlist-unsigned-value-aux x-equiv radix n)))
 :rule-classes :congruence)

Theorem: vl-echarlist-unsigned-value-aux-of-nfix-radix

(defthm vl-echarlist-unsigned-value-aux-of-nfix-radix
  (equal (vl-echarlist-unsigned-value-aux x (nfix radix)
                                          n)
         (vl-echarlist-unsigned-value-aux x radix n)))

Theorem: vl-echarlist-unsigned-value-aux-nat-equiv-congruence-on-radix

(defthm
      vl-echarlist-unsigned-value-aux-nat-equiv-congruence-on-radix
 (implies (acl2::nat-equiv radix radix-equiv)
          (equal (vl-echarlist-unsigned-value-aux x radix n)
                 (vl-echarlist-unsigned-value-aux x radix-equiv n)))
 :rule-classes :congruence)