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• Grammar-parser-implementation

Parse-*digit

Parse a repetition of zero or more decimal digits.

Signature

(parse-*digit input) → (mv error? trees rest-input)

Arguments

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-*digit

(defun parse-*digit (input)
  (declare (xargs :guard (nat-listp input)))
  (seq-backtrack input
                 ((tree := (parse-digit input))
                  (trees := (parse-*digit input))
                  (return (cons tree trees)))
                 ((return-raw (mv nil nil (nat-list-fix input))))))

Theorem: not-of-parse-*digit.error?

(defthm not-of-parse-*digit.error?
  (b* (((mv ?error? ?trees ?rest-input)
        (parse-*digit input)))
    (not error?))
  :rule-classes :rewrite)

Theorem: tree-listp-of-parse-*digit.trees

(defthm tree-listp-of-parse-*digit.trees
  (b* (((mv ?error? ?trees ?rest-input)
        (parse-*digit input)))
    (tree-listp trees))
  :rule-classes :rewrite)

Theorem: nat-listp-of-parse-*digit.rest-input

(defthm nat-listp-of-parse-*digit.rest-input
  (b* (((mv ?error? ?trees ?rest-input)
        (parse-*digit input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

Theorem: len-of-parse-*digit-linear

(defthm len-of-parse-*digit-linear
  (b* (((mv ?error? ?trees ?rest-input)
        (parse-*digit input)))
    (<= (len rest-input) (len input)))
  :rule-classes :linear)

Theorem: parse-*digit-of-nat-list-fix-input

(defthm parse-*digit-of-nat-list-fix-input
  (equal (parse-*digit (nat-list-fix input))
         (parse-*digit input)))

Theorem: parse-*digit-nat-list-equiv-congruence-on-input

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