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Parsing-primitives-defresult

Parse-range

Parse a range numeric value consisting of given minimum and maximum.

Signature
(parse-range min max input) → (mv tree rest-input)
Arguments: min — Guard (natp min).; max — Guard (natp max).; input — Guard (nat-listp input).
Returns: tree — Type (tree-resultp tree).; rest-input — Type (nat-listp rest-input).

Definitions and Theorems

Function: parse-range

(defun parse-range (min max input)
  (declare (xargs :guard (and (natp min)
                              (natp max)
                              (nat-listp input))))
  (declare (xargs :guard (<= min max)))
  (let ((__function__ 'parse-range))
    (declare (ignorable __function__))
    (b* (((mv nat? input1) (parse-next input))
         ((when (reserrp nat?))
          (mv (reserrf-push nat?)
              (nat-list-fix input)))
         (nat nat?)
         ((unless (and (<= (lnfix min) nat)
                       (<= nat (lnfix max))))
          (mv (reserrf (list :found nat :required (lnfix min)
                             (lnfix max)))
              (nat-list-fix input))))
      (mv (tree-leafterm (list nat))
          input1))))

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

(defthm tree-resultp-of-parse-range.tree
  (b* (((mv ?tree ?rest-input)
        (parse-range min max input)))
    (tree-resultp tree))
  :rule-classes :rewrite)

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

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

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

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

Theorem: len-of-parse-range-<

(defthm len-of-parse-range-<
  (b* (((mv ?tree ?rest-input)
        (parse-range min max input)))
    (implies (not (reserrp tree))
             (< (len rest-input) (len input))))
  :rule-classes :linear)

Theorem: parse-range-of-nfix-min

(defthm parse-range-of-nfix-min
  (equal (parse-range (nfix min) max input)
         (parse-range min max input)))

Theorem: parse-range-nat-equiv-congruence-on-min

(defthm parse-range-nat-equiv-congruence-on-min
  (implies (acl2::nat-equiv min min-equiv)
           (equal (parse-range min max input)
                  (parse-range min-equiv max input)))
  :rule-classes :congruence)

Theorem: parse-range-of-nfix-max

(defthm parse-range-of-nfix-max
  (equal (parse-range min (nfix max) input)
         (parse-range min max input)))

Theorem: parse-range-nat-equiv-congruence-on-max

(defthm parse-range-nat-equiv-congruence-on-max
  (implies (acl2::nat-equiv max max-equiv)
           (equal (parse-range min max input)
                  (parse-range min max-equiv input)))
  :rule-classes :congruence)

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

(defthm parse-range-of-nat-list-fix-input
  (equal (parse-range min max (nat-list-fix input))
         (parse-range min max input)))

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

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