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Parser

Lex-transition

Parse a transition.

Signature
(lex-transition 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-transition

(defun lex-transition (abnf::input)
 (declare (xargs :guard (nat-listp abnf::input)))
 (let ((__function__ 'lex-transition))
  (declare (ignorable __function__))
  (b*
   (((mv abnf::treess abnf::input)
     (b*
      (((mv abnf::treess1 abnf::input1)
        (b*
         (((mv abnf::tree abnf::input)
           (lex-cws abnf::input))
          ((when (reserrp abnf::tree))
           (mv (reserrf-push abnf::tree)
               abnf::input))
          (abnf::trees1 (list abnf::tree))
          ((mv abnf::tree abnf::input)
           (abnf::parse-schars "transition" abnf::input))
          ((when (reserrp abnf::tree))
           (mv (reserrf-push abnf::tree)
               abnf::input))
          (abnf::trees2 (list abnf::tree))
          ((mv abnf::tree abnf::input)
           (lex-ws abnf::input))
          ((when (reserrp abnf::tree))
           (mv (reserrf-push abnf::tree)
               abnf::input))
          (abnf::trees3 (list abnf::tree))
          ((mv abnf::tree abnf::input)
           (lex-identifier 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)
           (abnf::parse-ichars ":" abnf::input))
          ((when (reserrp abnf::tree))
           (mv (reserrf-push abnf::tree)
               abnf::input))
          (abnf::trees6 (list abnf::tree))
          ((mv abnf::trees7 abnf::input)
           (lex-repetition-*-transition-input abnf::input))
          ((when (reserrp abnf::trees7))
           (mv (reserrf-push abnf::trees7)
               abnf::input))
          ((mv abnf::trees8 abnf::input)
           (lex-repetition-*-instruction abnf::input))
          ((when (reserrp abnf::trees8))
           (mv (reserrf-push abnf::trees8)
               abnf::input))
          ((mv abnf::trees9 abnf::input)
           (lex-repetition-*-transition-output abnf::input))
          ((when (reserrp abnf::trees9))
           (mv (reserrf-push abnf::trees9)
               abnf::input))
          ((mv abnf::tree abnf::input)
           (lex-optional-transition-finalize abnf::input))
          ((when (reserrp abnf::tree))
           (mv (reserrf-push abnf::tree)
               abnf::input))
          (abnf::trees10 (list abnf::tree))
          (abnf::treess (list abnf::trees1 abnf::trees2
                              abnf::trees3 abnf::trees4 abnf::trees5
                              abnf::trees6 abnf::trees7 abnf::trees8
                              abnf::trees9 abnf::trees10)))
         (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 "cws")))
            (:repetition (:repeat 1 (:finite 1))
                         (:char-val (:sensitive "transition")))
            (:repetition (:repeat 1 (:finite 1))
                         (:rulename (:rulename "ws")))
            (:repetition (:repeat 1 (:finite 1))
                         (:rulename (:rulename "identifier")))
            (:repetition (:repeat 1 (:finite 1))
                         (:rulename (:rulename "ws")))
            (:repetition (:repeat 1 (:finite 1))
                         (:char-val (:insensitive nil ":")))
            (:repetition (:repeat 0 (:infinity))
                         (:rulename (:rulename "transition-input")))
            (:repetition (:repeat 0 (:infinity))
                         (:rulename (:rulename "instruction")))
            (:repetition
                 (:repeat 0 (:infinity))
                 (:rulename (:rulename "transition-output")))
            (:repetition
             (:repeat 1 (:finite 1))
             (:option
                  (((:repetition
                         (:repeat 1 (:finite 1))
                         (:rulename (:rulename "finalize-command")))
                    (:repetition
                         (:repeat 1 (:finite 1))
                         (:rulename (:rulename "finalize")))))))))))
       abnf::input)))
    ((when (reserrp abnf::treess))
     (mv (reserrf-push abnf::treess)
         (nat-list-fix abnf::input))))
   (mv (abnf::make-tree-nonleaf
            :rulename? (abnf::rulename "transition")
            :branches abnf::treess)
       abnf::input))))

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

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

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

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

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

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

Theorem: len-of-lex-transition-<

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

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

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

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

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