可执行集理论与Prolog中的算术编码
Executable Set Theory and Arithmetic Encodings in Prolog
摘要：
本文是组织作为一个独立的文学Prolog程序，实现元素的可执行有限集理论，重点是组合生成和算术编码。完整的Prolog代码可以在http://logic.csci.unt.edu/tarau/research/2008/pHFS.zip上找到。首先，在遗传有限集的宇宙中的一些“数学优雅”的数据类型的排名和unranking功能提供的幂集，超图，序数和选择功能的算术编码。在实现了遗传有限集的有向图表示之后，我们定义了{ \em装饰函数}，该装饰函数可以从其相关联的无环有向图的编码中恢复良基集。我们的结论与任意有向图的编码，并讨论了一个概念的对偶诱导的集合隶属关系。在这个过程中，我们发现了令人惊讶的可能性，内部共享同构对象，独立于他们的语言水平的类型和含义。
英文摘要：
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at http://logic.csci.unt.edu/tarau/research/2008/pHFS.zip . First, ranking and unranking functions for some "mathematically elegant" data types in the universe of Hereditarily Finite Sets with Urelements are provided, resulting in arithmetic encodings for powersets, hypergraphs, ordinals and choice functions. After implementing a digraph representation of Hereditarily Finite Sets we define {\em decoration functions} that can recover well-founded sets from encodings of their associated acyclic digraphs. We conclude with an encoding of arbitrary digraphs and discuss a concept of duality induced by the set membership relation. In the process, we uncover the surprising possibility of internally sharing isomorphic objects, independently of their language level types and meanings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
