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Parser

Lex-repetition-*-underbar

Lex zero or more underbars.

Signature
(lex-repetition-*-underbar input) → (mv trees rest-input)
Arguments: input — Guard (nat-listp input).
Returns: trees — Type (abnf::tree-listp trees).; rest-input — Type (nat-listp rest-input).

Definitions and Theorems

Function: lex-repetition-*-underbar

(defun lex-repetition-*-underbar (input)
  (declare (xargs :guard (nat-listp input)))
  (let ((__function__ 'lex-repetition-*-underbar))
    (declare (ignorable __function__))
    (b* (((mv tree-underbar1 input-after-underbar1)
          (abnf::parse-ichars "_" input))
         ((when (reserrp tree-underbar1))
          (mv nil (nat-list-fix input)))
         ((mv trees-rest input-after-rest)
          (lex-repetition-*-underbar input-after-underbar1)))
      (mv (cons tree-underbar1 trees-rest)
          input-after-rest))))

Theorem: tree-listp-of-lex-repetition-*-underbar.trees

(defthm tree-listp-of-lex-repetition-*-underbar.trees
  (b* (((mv ?trees ?rest-input)
        (lex-repetition-*-underbar input)))
    (abnf::tree-listp trees))
  :rule-classes :rewrite)

Theorem: nat-listp-of-lex-repetition-*-underbar.rest-input

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

Theorem: len-of-lex-repetition-*-underbar

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

Theorem: lex-repetition-*-underbar-of-nat-list-fix-input

(defthm lex-repetition-*-underbar-of-nat-list-fix-input
  (equal (lex-repetition-*-underbar (nat-list-fix input))
         (lex-repetition-*-underbar input)))

Theorem: lex-repetition-*-underbar-nat-list-equiv-congruence-on-input

(defthm lex-repetition-*-underbar-nat-list-equiv-congruence-on-input
  (implies (acl2::nat-list-equiv input input-equiv)
           (equal (lex-repetition-*-underbar input)
                  (lex-repetition-*-underbar input-equiv)))
  :rule-classes :congruence)