This paper provides a coalgebraic approach to the language semantics of regular nominal non-deterministic automata (RNNAs), which were introduced in previous work. These automata feature ordinary as well as name binding transitions. Correspondingly, words accepted by RNNAs are strings formed by ordinary letters and name binding letters. Bar languages are sets of such words modulo $\alpha$-equivalence, and to every state of an RNNA one associates its accepted bar language. We show that this semantics arises both as an instance of the Kleisli-style coalgebraic trace semantics as well as an instance of the coalgebraic language semantics obtained via generalized determinization. On the way we revisit coalgebraic trace semantics in general and give a new compact proof for the main result in that theory stating that an initial algebra for a functor yields the terminal coalgebra for the Kleisli extension of the functor. Our proof requires fewer assumptions on the functor than all previous ones.

翻译：本文对先前工作中引入的常规名义上非决定性自动自治语言语言语义学提供了一种结合地格学的方法。 这些自动语义特征既具有普通性,也具有与名称结合的过渡性。 相应的, 由RNNAs接受的单词是普通字母和名称约束字母组成的字符串。 巴尔语是这类单词的组合, 包括modulo $\alpha$- equvalence, 以及对于 RNNA 的每个州, 都与它所接受的条形语言相关联。 我们显示, 这种语义既作为Kleisli- 风格的煤热点痕迹语语词词词典的一例出现, 也作为通过普遍确定性获得的煤热点语言语义词义学的例子出现。 在如何重新审视一般的煤热点痕迹语义时, 并为理论的主要结果提供了一个新的缩略证据, 即真菌师的初始代数能产生 Kleisli 扩展的终端煤值。 我们的证据要求的配方的假设比以前所有的配料要少一些。