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Parser

Lex-binary

Parse a binary.

Signature
(lex-binary 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-binary

(defun lex-binary (abnf::input)
 (declare (xargs :guard (nat-listp abnf::input)))
 (let ((__function__ 'lex-binary))
  (declare (ignorable __function__))
  (b*
   (((mv abnf::treess abnf::input)
     (b*
      (((mv abnf::treess1 abnf::input1)
        (b*
         (((mv abnf::tree abnf::input)
           (lex-binary-op abnf::input))
          ((when (reserrp abnf::tree))
           (mv (reserrf-push abnf::tree)
               abnf::input))
          (abnf::trees1 (list abnf::tree))
          ((mv abnf::tree abnf::input)
           (lex-ws abnf::input))
          ((when (reserrp abnf::tree))
           (mv (reserrf-push abnf::tree)
               abnf::input))
          (abnf::trees2 (list abnf::tree))
          ((mv abnf::trees3 abnf::input)
           (lex-repetition-2-operands abnf::input))
          ((when (reserrp abnf::trees3))
           (mv (reserrf-push abnf::trees3)
               abnf::input))
          ((mv abnf::tree abnf::input)
           (abnf::parse-schars "into" abnf::input))
          ((when (reserrp abnf::tree))
           (mv (reserrf-push abnf::tree)
               abnf::input))
          (abnf::trees4 (list abnf::tree))
          ((mv abnf::tree abnf::input)
           (lex-ws abnf::input))
          ((when (reserrp abnf::tree))
           (mv (reserrf-push abnf::tree)
               abnf::input))
          (abnf::trees5 (list abnf::tree))
          ((mv abnf::tree abnf::input)
           (lex-register abnf::input))
          ((when (reserrp abnf::tree))
           (mv (reserrf-push abnf::tree)
               abnf::input))
          (abnf::trees6 (list abnf::tree))
          (abnf::treess (list abnf::trees1
                              abnf::trees2 abnf::trees3 abnf::trees4
                              abnf::trees5 abnf::trees6)))
         (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))
                         (:rulename (:rulename "binary-op")))
            (:repetition (:repeat 1 (:finite 1))
                         (:rulename (:rulename "ws")))
            (:repetition
              (:repeat 2 (:finite 2))
              (:group
                   (((:repetition (:repeat 1 (:finite 1))
                                  (:rulename (:rulename "operand")))
                     (:repetition (:repeat 1 (:finite 1))
                                  (:rulename (:rulename "ws")))))))
            (:repetition (:repeat 1 (:finite 1))
                         (:char-val (:sensitive "into")))
            (:repetition (:repeat 1 (:finite 1))
                         (:rulename (:rulename "ws")))
            (:repetition (:repeat 1 (:finite 1))
                         (:rulename (:rulename "register")))))))
       abnf::input)))
    ((when (reserrp abnf::treess))
     (mv (reserrf-push abnf::treess)
         (nat-list-fix abnf::input))))
   (mv (abnf::make-tree-nonleaf :rulename? (abnf::rulename "binary")
                                :branches abnf::treess)
       abnf::input))))

Theorem: tree-resultp-of-lex-binary.tree

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

Theorem: nat-listp-of-lex-binary.rest-input

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

Theorem: len-of-lex-binary-<=

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

Theorem: len-of-lex-binary-<

(defthm len-of-lex-binary-<
  (b* (((mv abnf::?tree abnf::?rest-input)
        (lex-binary abnf::input)))
    (implies (not (reserrp abnf::tree))
             (< (len abnf::rest-input)
                (len abnf::input))))
  :rule-classes :linear)

Theorem: lex-binary-of-nat-list-fix-input

(defthm lex-binary-of-nat-list-fix-input
  (equal (lex-binary (nat-list-fix abnf::input))
         (lex-binary abnf::input)))

Theorem: lex-binary-nat-list-equiv-congruence-on-input

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