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• Parsing-primitives-defresult

Parse-next

Obtain the next natural number from the input.

Signature

(parse-next input) → (mv nat rest-input)

Arguments

input — Guard (nat-listp input).

Returns

nat — Type (nat-resultp nat).

rest-input — Type (nat-listp rest-input).

Definitions and Theorems

Function: parse-next

(defun parse-next (input)
  (declare (xargs :guard (nat-listp input)))
  (let ((__function__ 'parse-next))
    (declare (ignorable __function__))
    (if (consp input)
        (mv (lnfix (car input))
            (nat-list-fix (cdr input)))
      (mv (reserrf :end-of-input) nil))))

Theorem: nat-resultp-of-parse-next.nat

(defthm nat-resultp-of-parse-next.nat
  (b* (((mv acl2::?nat ?rest-input)
        (parse-next input)))
    (nat-resultp nat))
  :rule-classes :rewrite)

Theorem: nat-listp-of-parse-next.rest-input

(defthm nat-listp-of-parse-next.rest-input
  (b* (((mv acl2::?nat ?rest-input)
        (parse-next input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

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

(defthm len-of-parse-next-<=
  (b* (((mv acl2::?nat ?rest-input)
        (parse-next input)))
    (<= (len rest-input) (len input)))
  :rule-classes :linear)

Theorem: len-of-parse-next-<

(defthm len-of-parse-next-<
  (b* (((mv acl2::?nat ?rest-input)
        (parse-next input)))
    (implies (not (reserrp nat))
             (< (len rest-input) (len input))))
  :rule-classes :linear)

Theorem: parse-next-of-nat-list-fix-input

(defthm parse-next-of-nat-list-fix-input
  (equal (parse-next (nat-list-fix input))
         (parse-next input)))

Theorem: parse-next-nat-list-equiv-congruence-on-input

(defthm parse-next-nat-list-equiv-congruence-on-input
  (implies (acl2::nat-list-equiv input input-equiv)
           (equal (parse-next input)
                  (parse-next input-equiv)))
  :rule-classes :congruence)