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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)