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• Extended-characters

Vl-echar-digit-value

(vl-echar-digit-value x radix) interprets the extended character x as a base-radix digit, or returns nil if x is not a valid digit in this base.

Signature

(vl-echar-digit-value x radix) → *

Arguments

x — Guard (vl-echar-p x).

radix — Guard (natp radix).

Definitions and Theorems

Function: vl-echar-digit-value

(defun vl-echar-digit-value (x radix)
  (declare (xargs :guard (and (vl-echar-p x) (natp radix))))
  (declare (xargs :guard (and (<= 2 radix) (<= radix 36))))
  (let ((__function__ 'vl-echar-digit-value))
    (declare (ignorable __function__))
    (digit-char-p (vl-echar->char x)
                  (lnfix radix))))

Theorem: natp-of-vl-echar-digit-value

(defthm natp-of-vl-echar-digit-value
 (let ((ret (vl-echar-digit-value x radix)))
   (implies ret
            (and (natp ret)
                 (integerp ret)
                 (<= 0 ret))))
 :rule-classes
 ((:rewrite)
  (:type-prescription
      :corollary (or (not (vl-echar-digit-value x radix))
                     (and (integerp (vl-echar-digit-value x radix))
                          (<= 0 (vl-echar-digit-value x radix)))))))

Theorem: vl-echar-digit-value-of-vl-echar-fix-x

(defthm vl-echar-digit-value-of-vl-echar-fix-x
  (equal (vl-echar-digit-value (vl-echar-fix x)
                               radix)
         (vl-echar-digit-value x radix)))

Theorem: vl-echar-digit-value-vl-echar-raw-equiv-congruence-on-x

(defthm vl-echar-digit-value-vl-echar-raw-equiv-congruence-on-x
  (implies (vl-echar-raw-equiv x x-equiv)
           (equal (vl-echar-digit-value x radix)
                  (vl-echar-digit-value x-equiv radix)))
  :rule-classes :congruence)

Theorem: vl-echar-digit-value-of-nfix-radix

(defthm vl-echar-digit-value-of-nfix-radix
  (equal (vl-echar-digit-value x (nfix radix))
         (vl-echar-digit-value x radix)))

Theorem: vl-echar-digit-value-nat-equiv-congruence-on-radix

(defthm vl-echar-digit-value-nat-equiv-congruence-on-radix
  (implies (acl2::nat-equiv radix radix-equiv)
           (equal (vl-echar-digit-value x radix)
                  (vl-echar-digit-value x radix-equiv)))
  :rule-classes :congruence)