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Lexer

Lex-letter

Parse a letter.

Signature
(lex-letter 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-letter

(defun lex-letter (abnf::input)
 (declare (xargs :guard (nat-listp abnf::input)))
 (let ((__function__ 'lex-letter))
  (declare (ignorable __function__))
  (b*
   (((mv abnf::treess abnf::input)
     (b* (((mv abnf::treess1 abnf::input1)
           (b* (((mv abnf::tree abnf::input)
                 (lex-uppercase-letter abnf::input))
                ((when (reserrp abnf::tree))
                 (mv (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 abnf::treess2 abnf::input1)
           (b* (((mv abnf::tree abnf::input)
                 (lex-lowercase-letter abnf::input))
                ((when (reserrp abnf::tree))
                 (mv (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::treess2)))
           (mv abnf::treess2 abnf::input1)))
      (mv
       (reserrf
        (list
             :found (list abnf::treess1 abnf::treess2)
             :required
             '(((:repetition
                     (:repeat 1 (:finite 1))
                     (:rulename (:rulename "uppercase-letter"))))
               ((:repetition
                     (:repeat 1 (:finite 1))
                     (:rulename (:rulename "lowercase-letter")))))))
       abnf::input)))
    ((when (reserrp abnf::treess))
     (mv (reserrf-push abnf::treess)
         (nat-list-fix abnf::input))))
   (mv (abnf::make-tree-nonleaf :rulename? (abnf::rulename "letter")
                                :branches abnf::treess)
       abnf::input))))

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

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

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

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

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

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

Theorem: len-of-lex-letter-<

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

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

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

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

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