SHF: Small: A Framework for Bijective Data Transformations

在与一些经过良好测试的数学抽象相对应的编程语言中，使用数量相对较少的通用数据类型作为基本构建块。这个项目是关于将它们之间的等价性构造为双射数据类型转换，将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、图连接起来。这些转换的实现将以开放源码数据转换库的形式构建。它还计划以Java小程序和数学笔记本的形式提供该软件，具有更广泛的影响，具有各种教学应用程序，并支持在直观、可视的框架内进行数据转换实验。PI最近的工作表明，这些双射可以自然地组织为有限群组，对象由它们的转换提供的数据类型和态射提供。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，提供各种计算构件的基本构建块的统一视图。它还计划探索基本运算的归纳定义的数据类型之间的转换，从而打开了派生有趣的新算法的可能性。作为概念证明，将获得使用树或图等符号表示来执行任意大小算术计算的算法。从更广泛的意义上讲，该项目可能会对计算机科学和工程领域共享的本体进行重大简化，从而使它们之间更好地沟通和协同。

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.