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• Parser

Lex-sign-if-present

Lex a sign, if present.

Signature

(lex-sign-if-present parstate) 
  → 
(mv erp sign? last/next-pos new-parstate)

Arguments

parstate — Guard (parstatep parstate).

Returns

sign? — Type (sign-optionp sign?).

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

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

If a sign is found, the last/next-pos output is its position. Otherwise, it is the position where the suffix would be.

If there is no next character, there is no sign. Otherwise, we read the next character, and return a sign if appropriate, otherwise no sign and we put back the character.

Definitions and Theorems

Function: lex-sign-if-present

(defun lex-sign-if-present (parstate)
  (declare (xargs :stobjs (parstate)))
  (declare (xargs :guard (parstatep parstate)))
  (let ((__function__ 'lex-sign-if-present))
    (declare (ignorable __function__))
    (b* (((reterr) nil (irr-position) parstate)
         ((erp char pos parstate)
          (read-char parstate)))
      (cond ((not char) (retok nil pos parstate))
            ((= char (char-code #\+))
             (retok (sign-plus) pos parstate))
            ((= char (char-code #\-))
             (retok (sign-minus) pos parstate))
            (t (b* ((parstate (unread-char parstate)))
                 (retok nil pos parstate)))))))

Theorem: sign-optionp-of-lex-sign-if-present.sign?

(defthm sign-optionp-of-lex-sign-if-present.sign?
  (b* (((mv acl2::?erp
            ?sign? ?last/next-pos ?new-parstate)
        (lex-sign-if-present parstate)))
    (sign-optionp sign?))
  :rule-classes :rewrite)

Theorem: positionp-of-lex-sign-if-present.last/next-pos

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

Theorem: parstatep-of-lex-sign-if-present.new-parstate

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

Theorem: parsize-of-lex-sign-if-present-ucond

(defthm parsize-of-lex-sign-if-present-ucond
  (b* (((mv acl2::?erp
            ?sign? ?last/next-pos ?new-parstate)
        (lex-sign-if-present parstate)))
    (<= (parsize new-parstate)
        (parsize parstate)))
  :rule-classes :linear)

Theorem: parsize-of-lex-sign-if-present-cond

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