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• Parsing-primitives-defresult

Parse-direct

Parse a direct numeric value consisting of given natural numbers.

Signature

(parse-direct nats input) → (mv tree rest-input)

Arguments

nats — Guard (nat-listp nats).

input — Guard (nat-listp input).

Returns

tree — Type (tree-resultp tree).

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

Definitions and Theorems

Function: parse-direct-aux

(defun parse-direct-aux (nats input)
  (declare (xargs :guard (and (nat-listp nats)
                              (nat-listp input))))
  (let ((__function__ 'parse-direct-aux))
    (declare (ignorable __function__))
    (b* (((when (endp nats))
          (mv nil (nat-list-fix input)))
         ((mv nat? input1) (parse-next input))
         ((when (reserrp nat?))
          (mv (reserrf-push nat?)
              (nat-list-fix input)))
         (nat nat?)
         ((unless (equal nat (lnfix (car nats))))
          (mv (reserrf (list :found nat
                             :required (lnfix (car nats))))
              (nat-list-fix input)))
         ((mv nats? input2)
          (parse-direct-aux (cdr nats) input1))
         ((when (reserrp nats?))
          (mv (reserrf-push nats?) input1))
         (nats nats?))
      (mv (cons nat nats) input2))))

Theorem: nat-list-resultp-of-parse-direct-aux.nats1

(defthm nat-list-resultp-of-parse-direct-aux.nats1
  (b* (((mv ?nats1 ?rest-input)
        (parse-direct-aux nats input)))
    (nat-list-resultp nats1))
  :rule-classes :rewrite)

Theorem: nat-listp-of-parse-direct-aux.rest-input

(defthm nat-listp-of-parse-direct-aux.rest-input
  (b* (((mv ?nats1 ?rest-input)
        (parse-direct-aux nats input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

Theorem: len-of-parse-direct-aux-<=

(defthm len-of-parse-direct-aux-<=
  (b* (((mv ?nats1 ?rest-input)
        (parse-direct-aux nats input)))
    (<= (len rest-input) (len input)))
  :rule-classes :linear)

Theorem: len-of-parse-direct-aux-<

(defthm len-of-parse-direct-aux-<
  (b* (((mv ?nats1 ?rest-input)
        (parse-direct-aux nats input)))
    (implies (and (not (reserrp nats1)) (consp nats))
             (< (len rest-input) (len input))))
  :rule-classes :linear)

Theorem: parse-direct-aux-of-nat-list-fix-nats

(defthm parse-direct-aux-of-nat-list-fix-nats
  (equal (parse-direct-aux (nat-list-fix nats)
                           input)
         (parse-direct-aux nats input)))

Theorem: parse-direct-aux-nat-list-equiv-congruence-on-nats

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

Theorem: parse-direct-aux-of-nat-list-fix-input

(defthm parse-direct-aux-of-nat-list-fix-input
  (equal (parse-direct-aux nats (nat-list-fix input))
         (parse-direct-aux nats input)))

Theorem: parse-direct-aux-nat-list-equiv-congruence-on-input

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

Function: parse-direct

(defun parse-direct (nats input)
  (declare (xargs :guard (and (nat-listp nats)
                              (nat-listp input))))
  (let ((__function__ 'parse-direct))
    (declare (ignorable __function__))
    (b* (((mv nats input)
          (parse-direct-aux nats input))
         ((when (reserrp nats))
          (mv (reserrf-push nats) input)))
      (mv (tree-leafterm nats) input))))

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

(defthm tree-resultp-of-parse-direct.tree
  (b* (((mv ?tree ?rest-input)
        (parse-direct nats input)))
    (tree-resultp tree))
  :rule-classes :rewrite)

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

(defthm nat-listp-of-parse-direct.rest-input
  (b* (((mv ?tree ?rest-input)
        (parse-direct nats input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

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

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

Theorem: len-of-parse-direct-<

(defthm len-of-parse-direct-<
  (b* (((mv ?tree ?rest-input)
        (parse-direct nats input)))
    (implies (and (not (reserrp tree)) (consp nats))
             (< (len rest-input) (len input))))
  :rule-classes :linear)

Theorem: parse-direct-of-nat-list-fix-nats

(defthm parse-direct-of-nat-list-fix-nats
  (equal (parse-direct (nat-list-fix nats) input)
         (parse-direct nats input)))

Theorem: parse-direct-nat-list-equiv-congruence-on-nats

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

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

(defthm parse-direct-of-nat-list-fix-input
  (equal (parse-direct nats (nat-list-fix input))
         (parse-direct nats input)))

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

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