论文标题
支持集 - 名义集和自动机的新基础
Supported Sets -- A New Foundation For Nominal Sets And Automata
论文作者
论文摘要
目前的工作提出并讨论了支持集的类别，该集合为标称集的各种统一集提供了基础，例如平等对称性，订单对称性和重命名集。我们表明，所有这些不同风味的名义集类别的名义类别都是在受支持的集合上进行的。因此，受支持的集合提供了一种规范有限的方式来表示名义集及其自动机，例如注册自动机。遵循De Bruijn索引的想法，由支持集中的名称绑定在受支持的集合中。该函子在名义集中升至众所周知的抽象函子。与Monadicity结果一起，这产生了一个转换过程，该过程将寄存器自动机的有限表示形式在支持的集合中，并将其转换为标称集中的配置自动机。
The present work proposes and discusses the category of supported sets which provides a uniform foundation for nominal sets of various kinds, such as those for equality symmetry, for the order symmetry, and renaming sets. We show that all these differently flavoured categories of nominal sets are monadic over supported sets. Thus, supported sets provide a canonical finite way to represent nominal sets and the automata therein, e.g. register automata. Name binding in supported sets is modelled by a functor following the idea of de Bruijn indices. This functor lifts to the well-known abstraction functor in nominal sets. Together with the monadicity result, this gives rise to a transformation process that takes the finite representation of a register automaton in supported sets and transforms it into its configuration automaton in nominal sets.
