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Hex-digit-char-p

Recognizer for hexadecimal digit characters: 0-9, A-F, a-f.

Signature
(hex-digit-char-p x) → bool

ACL2 provides digit-char-p which is more flexible and can recognize numeric characters in other bases. (hex-digit-char-p x) only recognizes base-16 digits, but is much faster, at least on CCL. Here is an experiment you can run in raw lisp, with times reported in CCL on an AMD FX-8350.

(defconstant *chars*
  (loop for i from 0 to 255 collect (code-char i)))

;; 19.216 seconds
(time (loop for i fixnum from 1 to 10000000 do
            (loop for c in *chars* do (digit-char-p c 16))))

;; 4.711 seconds
(time (loop for i fixnum from 1 to 10000000 do
            (loop for c in *chars* do (str::hex-digit-char-p c))))

Definitions and Theorems

Function: hex-digit-char-p$inline

(defun hex-digit-char-p$inline (x)
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'hex-digit-char-p))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (let ((code (char-code (char-fix x))))
           (or (and (<= (char-code #\0) code)
                    (<= code (char-code #\9)))
               (and (<= (char-code #\a) code)
                    (<= code (char-code #\f)))
               (and (<= (char-code #\A) code)
                    (<= code (char-code #\F)))))
         :exec (and (characterp x)
                    (b* (((the (unsigned-byte 8) code)
                          (char-code (the character x))))
                      (if (<= code 70)
                          (if (<= code 57)
                              (<= 48 code)
                            (<= 65 code))
                        (and (<= code 102) (<= 97 code))))))))

Theorem: ichareqv-implies-equal-hex-digit-char-p-1

(defthm ichareqv-implies-equal-hex-digit-char-p-1
  (implies (ichareqv x x-equiv)
           (equal (hex-digit-char-p x)
                  (hex-digit-char-p x-equiv)))
  :rule-classes (:congruence))

Theorem: characterp-when-hex-digit-char-p

(defthm characterp-when-hex-digit-char-p
  (implies (hex-digit-char-p char)
           (characterp char))
  :rule-classes :compound-recognizer)

Theorem: hex-digit-char-p-cases

(defthm hex-digit-char-p-cases
  (iff (hex-digit-char-p x)
       (member x
               '(#\0 #\1 #\2
                     #\3 #\4 #\5 #\6 #\7 #\8 #\9 #\a #\b #\c
                     #\d #\e #\f #\A #\B #\C #\D #\E #\F))))

Subtopics

Hex-digit-char: Fixtype of hexadecimal digit characters.