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Input-parser

Parse-input-title

Parse an input-title.

Signature
(parse-input-title token input) → (mv tree next-token rest-input)
Arguments: token — Guard (abnf::tree-optionp token).; input — Guard (abnf::tree-listp input).
Returns: tree — Type (abnf::tree-resultp tree).; next-token — Type (abnf::tree-optionp next-token).; rest-input — Type (abnf::tree-listp rest-input).

Definitions and Theorems

Function: parse-input-title

(defun parse-input-title (token input)
  (declare (xargs :guard (and (abnf::tree-optionp token)
                              (abnf::tree-listp input))))
  (let ((__function__ 'parse-input-title))
    (declare (ignorable __function__))
    (b* (((pok tree1)
          (parse-symbol "[" token input))
         ((pok tree2)
          (parse-public/private/constants/constant/const/main/registers
               token input))
         ((pok tree3)
          (parse-symbol "]" token input)))
      (mv (abnf::make-tree-nonleaf
               :rulename? (abnf::rulename "input-title")
               :branches (list (list tree1)
                               (list tree2)
                               (list tree3)))
          token input))))

Theorem: tree-resultp-of-parse-input-title.tree

(defthm tree-resultp-of-parse-input-title.tree
  (b* (((mv ?tree ?next-token ?rest-input)
        (parse-input-title token input)))
    (abnf::tree-resultp tree))
  :rule-classes :rewrite)

Theorem: tree-optionp-of-parse-input-title.next-token

(defthm tree-optionp-of-parse-input-title.next-token
  (b* (((mv ?tree ?next-token ?rest-input)
        (parse-input-title token input)))
    (abnf::tree-optionp next-token))
  :rule-classes :rewrite)

Theorem: tree-listp-of-parse-input-title.rest-input

(defthm tree-listp-of-parse-input-title.rest-input
  (b* (((mv ?tree ?next-token ?rest-input)
        (parse-input-title token input)))
    (abnf::tree-listp rest-input))
  :rule-classes :rewrite)

Theorem: parsize-of-parse-input-title-<=

(defthm parsize-of-parse-input-title-<=
  (b* (((mv ?tree ?next-token ?rest-input)
        (parse-input-title token input)))
    (<= (parsize next-token rest-input)
        (parsize token input)))
  :rule-classes :linear)

Theorem: parsize-of-parse-input-title-<

(defthm parsize-of-parse-input-title-<
  (b* (((mv ?tree ?next-token ?rest-input)
        (parse-input-title token input)))
    (implies (not (reserrp tree))
             (< (parsize next-token rest-input)
                (parsize token input))))
  :rule-classes :linear)

Theorem: parse-input-title-of-tree-option-fix-token

(defthm parse-input-title-of-tree-option-fix-token
  (equal (parse-input-title (abnf::tree-option-fix token)
                            input)
         (parse-input-title token input)))

Theorem: parse-input-title-tree-option-equiv-congruence-on-token

(defthm parse-input-title-tree-option-equiv-congruence-on-token
  (implies (abnf::tree-option-equiv token token-equiv)
           (equal (parse-input-title token input)
                  (parse-input-title token-equiv input)))
  :rule-classes :congruence)

Theorem: parse-input-title-of-tree-list-fix-input

(defthm parse-input-title-of-tree-list-fix-input
  (equal (parse-input-title token (abnf::tree-list-fix input))
         (parse-input-title token input)))

Theorem: parse-input-title-tree-list-equiv-congruence-on-input

(defthm parse-input-title-tree-list-equiv-congruence-on-input
  (implies (abnf::tree-list-equiv input input-equiv)
           (equal (parse-input-title token input)
                  (parse-input-title token input-equiv)))
  :rule-classes :congruence)