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• Grammar-parser-implementation

Parse-1*digit

Parse a repetition of one or more decimal digits.

Signature

(parse-1*digit input) → (mv error? trees rest-input)

Arguments

input — Guard (nat-listp input).

Returns

error? — Type (maybe-msgp error?).

trees — Type (and (tree-listp trees) (implies error? (not trees))).

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

Definitions and Theorems

Function: parse-1*digit

(defun parse-1*digit (input)
  (declare (xargs :guard (nat-listp input)))
  (seq input (tree := (parse-digit input))
       (trees := (parse-*digit input))
       (return (cons tree trees))))

Theorem: maybe-msgp-of-parse-1*digit.error?

(defthm maybe-msgp-of-parse-1*digit.error?
  (b* (((mv ?error? ?trees ?rest-input)
        (parse-1*digit input)))
    (maybe-msgp error?))
  :rule-classes :rewrite)

Theorem: return-type-of-parse-1*digit.trees

(defthm return-type-of-parse-1*digit.trees
  (b* (((mv ?error? ?trees ?rest-input)
        (parse-1*digit input)))
    (and (tree-listp trees)
         (implies error? (not trees))))
  :rule-classes :rewrite)

Theorem: nat-listp-of-parse-1*digit.rest-input

(defthm nat-listp-of-parse-1*digit.rest-input
  (b* (((mv ?error? ?trees ?rest-input)
        (parse-1*digit input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

Theorem: len-of-parse-1*digit-linear

(defthm len-of-parse-1*digit-linear
  (b* (((mv ?error? ?trees ?rest-input)
        (parse-1*digit input)))
    (and (<= (len rest-input) (len input))
         (implies (not error?)
                  (< (len rest-input) (len input)))))
  :rule-classes :linear)

Theorem: parse-1*digit-of-nat-list-fix-input

(defthm parse-1*digit-of-nat-list-fix-input
  (equal (parse-1*digit (nat-list-fix input))
         (parse-1*digit input)))

Theorem: parse-1*digit-nat-list-equiv-congruence-on-input

(defthm parse-1*digit-nat-list-equiv-congruence-on-input
  (implies (acl2::nat-list-equiv input input-equiv)
           (equal (parse-1*digit input)
                  (parse-1*digit input-equiv)))
  :rule-classes :congruence)