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• Decimal

Dec-digit-char-p

Recognizer for numeric characters (0-9).

Signature

(dec-digit-char-p x) → bool

ACL2 provides digit-char-p which is more flexible and can recognize numeric characters in other bases. (dec-digit-char-p x) only recognizes base-10 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 256 collect (code-char i)))

;; 17.130 seconds, no garbage
(time (loop for i fixnum from 1 to 10000000 do
            (loop for c in *chars* do (digit-char-p c))))

;; 3.772 seconds, no garbage
(time (loop for i fixnum from 1 to 10000000 do
            (loop for c in *chars* do (str::dec-digit-char-p c))))

Definitions and Theorems

Function: dec-digit-char-p$inline

(defun dec-digit-char-p$inline (x)
 (declare (xargs :guard t))
 (let ((acl2::__function__ 'dec-digit-char-p))
   (declare (ignorable acl2::__function__))
   (mbe :logic
        (let ((code (char-code (char-fix x))))
          (and (<= (char-code #\0) code)
               (<= code (char-code #\9))))
        :exec (and (characterp x)
                   (let ((code (the (unsigned-byte 8)
                                    (char-code (the character x)))))
                     (declare (type (unsigned-byte 8) code))
                     (and (<= (the (unsigned-byte 8) code)
                              (the (unsigned-byte 8) 57))
                          (<= (the (unsigned-byte 8) 48)
                              (the (unsigned-byte 8) code))))))))

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

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

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

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

Subtopics

Dec-digit-char

Fixtype of decimal digit characters.