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Parse-*-in-either-range

Parse zero or more natural numbers, each of which in one of two given ranges, into a list of trees that matches the repetition of zero or more alternations of the corresponding range numeric value notations.

Signature

(parse-*-in-either-range min1 max1 min2 max2 input) 
  → 
(mv error? trees rest-input)

Arguments

min1 — Guard (natp min1).

max1 — Guard (natp max1).

min2 — Guard (natp min2).

max2 — Guard (natp max2).

input — Guard (nat-listp input).

Returns

error? — Type (not error?).

trees — Type (tree-listp trees).

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

Definitions and Theorems

Function: parse-*-in-either-range

(defun parse-*-in-either-range (min1 max1 min2 max2 input)
 (declare (xargs :guard (and (natp min1)
                             (natp max1)
                             (natp min2)
                             (natp max2)
                             (nat-listp input))))
 (declare (xargs :guard (and (<= min1 max1)
                             (< max1 min2)
                             (<= min2 max2))))
 (seq-backtrack
     input
     ((tree := (parse-in-either-range min1 max1 min2 max2 input))
      (trees := (parse-*-in-either-range min1 max1 min2 max2 input))
      (return (cons tree trees)))
     ((return-raw (mv nil nil (nat-list-fix input))))))

Theorem: not-of-parse-*-in-either-range.error?

(defthm not-of-parse-*-in-either-range.error?
  (b* (((mv ?error? ?trees ?rest-input)
        (parse-*-in-either-range min1 max1 min2 max2 input)))
    (not error?))
  :rule-classes :rewrite)

Theorem: tree-listp-of-parse-*-in-either-range.trees

(defthm tree-listp-of-parse-*-in-either-range.trees
  (b* (((mv ?error? ?trees ?rest-input)
        (parse-*-in-either-range min1 max1 min2 max2 input)))
    (tree-listp trees))
  :rule-classes :rewrite)

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

(defthm nat-listp-of-parse-*-in-either-range.rest-input
  (b* (((mv ?error? ?trees ?rest-input)
        (parse-*-in-either-range min1 max1 min2 max2 input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

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

(defthm parse-*-in-either-range-of-nat-list-fix-input
  (equal
       (parse-*-in-either-range min1
                                max1 min2 max2 (nat-list-fix input))
       (parse-*-in-either-range min1 max1 min2 max2 input)))

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

(defthm parse-*-in-either-range-nat-list-equiv-congruence-on-input
 (implies
  (acl2::nat-list-equiv input input-equiv)
  (equal (parse-*-in-either-range min1 max1 min2 max2 input)
         (parse-*-in-either-range min1 max1 min2 max2 input-equiv)))
 :rule-classes :congruence)

Theorem: len-of-parse-*-in-either-range-linear

(defthm len-of-parse-*-in-either-range-linear
  (b* (((mv ?error? ?trees ?rest-input)
        (parse-*-in-either-range min1 max1 min2 max2 input)))
    (<= (len rest-input) (len input)))
  :rule-classes :linear)