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Lexer

Lex-optional-underbar

Parse a [ "_" ].

Signature
(lex-optional-underbar abnf::input) → (mv abnf::tree abnf::rest-input)
Arguments: abnf::input — Guard (nat-listp abnf::input).
Returns: abnf::tree — Type (abnf::tree-resultp abnf::tree).; abnf::rest-input — Type (nat-listp abnf::rest-input).

Definitions and Theorems

Function: lex-optional-underbar

(defun lex-optional-underbar (abnf::input)
 (declare (xargs :guard (nat-listp abnf::input)))
 (let ((__function__ 'lex-optional-underbar))
  (declare (ignorable __function__))
  (b*
   (((mv abnf::treess abnf::input)
     (b* (((mv abnf::treess1 abnf::input1)
           (b* (((mv abnf::tree abnf::input)
                 (abnf::parse-ichars "_" abnf::input))
                ((when (reserrp abnf::tree))
                 (mv (fty::reserrf-push abnf::tree)
                     abnf::input))
                (abnf::trees1 (list abnf::tree))
                (abnf::treess (list abnf::trees1)))
             (mv abnf::treess abnf::input)))
          ((when (not (reserrp abnf::treess1)))
           (mv abnf::treess1 abnf::input1)))
      (mv
       (reserrf
        (list
             :found (list abnf::treess1)
             :required
             '(((:repetition (:repeat 1 (:finite 1))
                             (:char-val (:insensitive nil "_")))))))
       abnf::input)))
    ((when (reserrp abnf::treess))
     (mv (abnf::make-tree-nonleaf :rulename? nil
                                  :branches nil)
         (acl2::nat-list-fix abnf::input))))
   (mv (abnf::make-tree-nonleaf :rulename? nil
                                :branches abnf::treess)
       abnf::input))))

Theorem: tree-resultp-of-lex-optional-underbar.tree

(defthm tree-resultp-of-lex-optional-underbar.tree
  (b* (((mv abnf::?tree abnf::?rest-input)
        (lex-optional-underbar abnf::input)))
    (abnf::tree-resultp abnf::tree))
  :rule-classes :rewrite)

Theorem: nat-listp-of-lex-optional-underbar.rest-input

(defthm nat-listp-of-lex-optional-underbar.rest-input
  (b* (((mv abnf::?tree abnf::?rest-input)
        (lex-optional-underbar abnf::input)))
    (nat-listp abnf::rest-input))
  :rule-classes :rewrite)

Theorem: len-of-lex-optional-underbar-<=

(defthm len-of-lex-optional-underbar-<=
  (b* (((mv abnf::?tree abnf::?rest-input)
        (lex-optional-underbar abnf::input)))
    (<= (len abnf::rest-input)
        (len abnf::input)))
  :rule-classes :linear)

Theorem: lex-optional-underbar-of-nat-list-fix-input

(defthm lex-optional-underbar-of-nat-list-fix-input
  (equal (lex-optional-underbar (acl2::nat-list-fix abnf::input))
         (lex-optional-underbar abnf::input)))

Theorem: lex-optional-underbar-nat-list-equiv-congruence-on-input

(defthm lex-optional-underbar-nat-list-equiv-congruence-on-input
  (implies (acl2::nat-list-equiv abnf::input input-equiv)
           (equal (lex-optional-underbar abnf::input)
                  (lex-optional-underbar input-equiv)))
  :rule-classes :congruence)