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Parser

Parse-numeral

Parse a numeral token.

Signature
(parse-numeral 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-numeral

(defun parse-numeral (token input)
  (declare (xargs :guard (and (abnf::tree-optionp token)
                              (abnf::tree-listp input))))
  (let ((__function__ 'parse-numeral))
    (declare (ignorable __function__))
    (b* ((tree (check-token-root "numeral" token))
         ((when (reserrp tree))
          (perr (reserrf-push tree)))
         ((mv token input) (parse-token input)))
      (mv tree token input))))

Theorem: tree-resultp-of-parse-numeral.tree

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

Theorem: tree-optionp-of-parse-numeral.next-token

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

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

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

Theorem: parsize-of-parse-numeral-<=

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

Theorem: parsize-of-parse-numeral-<

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

Theorem: len-of-parse-numeral-<=

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

Theorem: len-of-parse-numeral-<

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

Theorem: parse-numeral-of-tree-option-fix-token

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

Theorem: parse-numeral-tree-option-equiv-congruence-on-token

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

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

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

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

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