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• Parsing-primitives-seq

Parse-in-range

Parse a natural number in a given range into a tree that matches a range numeric value notation that consists of that range.

Signature

(parse-in-range min max input) → (mv error? tree? rest-input)

Arguments

min — Guard (natp min).

max — Guard (natp max).

input — Guard (nat-listp input).

Returns

error? — Type (maybe-msgp error?).

tree? — Type (and (tree-optionp tree?) (implies (not error?) (treep tree?)) (implies error? (not tree?))) .

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

Definitions and Theorems

Function: parse-in-range

(defun parse-in-range (min max input)
 (declare (xargs :guard (and (natp min)
                             (natp max)
                             (nat-listp input))))
 (declare (xargs :guard (<= min max)))
 (b*
  ((min (lnfix min))
   (max (lnfix max))
   ((mv error? nat input)
    (parse-any input))
   ((when error?) (mv error? nil input))
   ((unless (and (<= min nat) (<= nat max)))
    (mv
     (msg
      "Failed to parse a number between ~x0 and ~x1; ~
                  found ~x2 instead."
      min max nat)
     nil (cons nat input))))
  (mv nil (tree-leafterm (list nat))
      input)))

Theorem: maybe-msgp-of-parse-in-range.error?

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

Theorem: return-type-of-parse-in-range.tree?

(defthm return-type-of-parse-in-range.tree?
  (b* (((mv ?error? ?tree? ?rest-input)
        (parse-in-range min max input)))
    (and (tree-optionp tree?)
         (implies (not error?) (treep tree?))
         (implies error? (not tree?))))
  :rule-classes :rewrite)

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

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

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

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

Theorem: len-of-parse-in-range-linear-<

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

Theorem: parse-in-range-of-nfix-min

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

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

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

Theorem: parse-in-range-of-nfix-max

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

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

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

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

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

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

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