SHF: Small: A Framework for Bijective Data Transformations

SHF：小型：双射数据转换框架

• 批准号: 1018172
• 负责人: Paul Tarau
• 金额: $ 9.75万
• 依托单位: University of North Texas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-08-15 至 2013-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1018172&HistoricalAwards=false
• 关键词: SHF; Small; Framework; Bijective; Data

A relatively small number of universal data types are used as basic building blocks in programming languages corresponding to a few well tested mathematical abstractions. This project is about structuring equivalences between them as bijective data type transformations connecting computational objects widely used by computer scientists and mathematicians, like sequences, sets, trees, logic circuits, graphs. An implementation of these transformations will be built in the form of an open source Data Transformation Library. It is also planned to make available the software in the form of a Java applet and a Mathematica notebook, having as broader impact various teaching applications and support for experimenting with data transformations in an intuitive, visual framework.The PI's recent work has showed that these bijections can be organized naturally as a finite groupoid with objects provided by the data types and morphisms provided by their transformations. The project plans to extend these encodings into a comprehensive data transformation framework providing a uniform view of the basic building blocks of various computational artifacts. It also plans exploring the transfer between data types of inductive definitions of their fundamental operations, opening the possibility to derive interesting new algorithms. As a proof of concept, algorithms performing arbitrary size arithmetic computations using symbolic representations like trees or graphs will be obtained. In a broader sense, the project is likely to bring significant simplifications to the ontology shared by computer science and engineering fields, resulting in better communication and synergy between them.

相对少量的通用数据类型用作编程语言中的基本构建块，对应于一些经过充分测试的数学抽象。这个项目是关于将它们之间的等价结构化为双射数据类型转换，连接计算机科学家和数学家广泛使用的计算对象，如序列，集合，树，逻辑电路，图形。这些转换的实现将以开源数据转换库的形式构建。它还计划提供的Java applet和Mathematica笔记本的形式的软件，具有更广泛的影响各种教学应用程序和支持实验数据转换在一个直观的，可视化的框架。PI的最近的工作表明，这些双射可以自然地组织为一个有限的广群提供的对象的数据类型和态射提供了他们的转换。该项目计划将这些编码扩展到一个全面的数据转换框架中，为各种计算工件的基本构建块提供统一的视图。它还计划探索其基本操作的归纳定义的数据类型之间的传输，从而为衍生有趣的新算法提供可能性。作为概念的证明，将获得使用符号表示（如树或图）执行任意大小算术计算的算法。从更广泛的意义上说，该项目可能会为计算机科学和工程领域共享的本体带来显着的简化，从而使它们之间更好地沟通和协同。