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Lexer

Lex-*-lexeme

Parse a *lexeme.

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

Definitions and Theorems

Function: lex-*-lexeme

(defun lex-*-lexeme (abnf::input)
  (declare (xargs :guard (nat-listp abnf::input)))
  (let ((__function__ 'lex-*-lexeme))
    (declare (ignorable __function__))
    (b* (((mv abnf::tree abnf::input)
          (lex-lexeme abnf::input))
         ((when (reserrp abnf::tree))
          (mv nil abnf::input))
         ((mv abnf::trees abnf::input)
          (lex-*-lexeme abnf::input)))
      (mv (cons abnf::tree abnf::trees)
          abnf::input))))

Theorem: tree-listp-of-lex-*-lexeme.trees

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

Theorem: nat-listp-of-lex-*-lexeme.rest-input

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

Theorem: len-of-lex-*-lexeme

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

Theorem: lex-*-lexeme-of-nat-list-fix-input

(defthm lex-*-lexeme-of-nat-list-fix-input
  (equal (lex-*-lexeme (nat-list-fix abnf::input))
         (lex-*-lexeme abnf::input)))

Theorem: lex-*-lexeme-nat-list-equiv-congruence-on-input

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