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Lexer

Lex-1*-decimal-digit

Lex a 1*decimal-digit.

Signature
(lex-1*-decimal-digit input) → (mv trees rest-input)
Arguments: input — Guard (nat-listp input).
Returns: trees — Type (abnf::tree-list-resultp trees).; rest-input — Type (nat-listp rest-input).

Definitions and Theorems

Function: lex-1*-decimal-digit

(defun lex-1*-decimal-digit (input)
  (declare (xargs :guard (nat-listp input)))
  (let ((__function__ 'lex-1*-decimal-digit))
    (declare (ignorable __function__))
    (b* (((mv tree input)
          (lex-decimal-digit input))
         ((when (reserrp tree))
          (mv (reserrf-push tree) input))
         ((mv trees input)
          (lex-*-decimal-digit input)))
      (mv (cons tree trees) input))))

Theorem: tree-list-resultp-of-lex-1*-decimal-digit.trees

(defthm tree-list-resultp-of-lex-1*-decimal-digit.trees
  (b* (((mv ?trees ?rest-input)
        (lex-1*-decimal-digit input)))
    (abnf::tree-list-resultp trees))
  :rule-classes :rewrite)

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

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

Theorem: len-of-lex-1*-decimal-digit-<=

(defthm len-of-lex-1*-decimal-digit-<=
  (b* (((mv ?trees ?rest-input)
        (lex-1*-decimal-digit input)))
    (<= (len rest-input) (len input)))
  :rule-classes :linear)

Theorem: len-of-lex-1*-decimal-digit-<

(defthm len-of-lex-1*-decimal-digit-<
  (b* (((mv ?trees ?rest-input)
        (lex-1*-decimal-digit input)))
    (implies (not (reserrp trees))
             (< (len rest-input) (len input))))
  :rule-classes :linear)

Theorem: lex-1*-decimal-digit-of-nat-list-fix-input

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

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

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