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• Lexer

Lex-?-exponent-part

Lex a decimal exponent, if present.

Signature

(lex-?-exponent-part parstate) 
  → 
(mv erp expo? last/next-pos new-parstate)

Arguments

parstate — Guard (parstatep parstate).

Returns

expo? — Type (dexpo-optionp expo?).

last/next-pos — Type (positionp last/next-pos).

new-parstate — Type (parstatep new-parstate), given (parstatep parstate).

If an exponent is found, the last/next-pos output is the position of its last character. Otherwise, it is the first position where the exponent would start.

If there is no next character, there is no exponent. If the next character is not e or E, there is no exponent. Otherwise, we read a sign (if present), and then we read zero or more digits. If there are no digits, there is no exponent: we put back the sign character (if it was present), and we put back the e or E. If there are digits, we return an appropriate exponent.

Definitions and Theorems

Function: lex-?-exponent-part

(defun lex-?-exponent-part (parstate)
  (declare (xargs :stobjs (parstate)))
  (declare (xargs :guard (parstatep parstate)))
  (let ((__function__ 'lex-?-exponent-part))
    (declare (ignorable __function__))
    (b* (((reterr) nil (irr-position) parstate)
         ((erp char pos parstate)
          (read-char parstate)))
      (cond ((not char) (retok nil pos parstate))
            ((or (utf8-= char (char-code #\e))
                 (utf8-= char (char-code #\E)))
             (b* ((prefix (if (utf8-= char (char-code #\e))
                              (dexprefix-locase-e)
                            (dexprefix-upcase-e)))
                  ((erp sign? sign-pos parstate)
                   (lex-?-sign parstate))
                  (pos-so-far (if sign? sign-pos pos))
                  ((erp digits last-pos & parstate)
                   (lex-*-digit pos-so-far parstate))
                  ((unless digits)
                   (b* ((parstate (if sign? (unread-char parstate)
                                    parstate))
                        (parstate (unread-char parstate)))
                     (retok nil pos parstate))))
               (retok (make-dexpo :prefix prefix
                                  :sign? sign?
                                  :digits digits)
                      last-pos parstate)))
            (t (b* ((parstate (unread-char parstate)))
                 (retok nil pos parstate)))))))

Theorem: dexpo-optionp-of-lex-?-exponent-part.expo?

(defthm dexpo-optionp-of-lex-?-exponent-part.expo?
  (b* (((mv acl2::?erp
            ?expo? ?last/next-pos ?new-parstate)
        (lex-?-exponent-part parstate)))
    (dexpo-optionp expo?))
  :rule-classes :rewrite)

Theorem: positionp-of-lex-?-exponent-part.last/next-pos

(defthm positionp-of-lex-?-exponent-part.last/next-pos
  (b* (((mv acl2::?erp
            ?expo? ?last/next-pos ?new-parstate)
        (lex-?-exponent-part parstate)))
    (positionp last/next-pos))
  :rule-classes :rewrite)

Theorem: parstatep-of-lex-?-exponent-part.new-parstate

(defthm parstatep-of-lex-?-exponent-part.new-parstate
  (implies (parstatep parstate)
           (b* (((mv acl2::?erp
                     ?expo? ?last/next-pos ?new-parstate)
                 (lex-?-exponent-part parstate)))
             (parstatep new-parstate)))
  :rule-classes :rewrite)

Theorem: parsize-of-lex-?-exponent-part-uncond

(defthm parsize-of-lex-?-exponent-part-uncond
  (b* (((mv acl2::?erp
            ?expo? ?last/next-pos ?new-parstate)
        (lex-?-exponent-part parstate)))
    (<= (parsize new-parstate)
        (parsize parstate)))
  :rule-classes :linear)

Theorem: parsize-of-lex-?-exponent-part-cond

(defthm parsize-of-lex-?-exponent-part-cond
  (b* (((mv acl2::?erp
            ?expo? ?last/next-pos ?new-parstate)
        (lex-?-exponent-part parstate)))
    (implies (and (not erp) expo?)
             (<= (parsize new-parstate)
                 (1- (parsize parstate)))))
  :rule-classes :linear)