SHF: Small: A Framework for Bijective Data Transformations

University Of North Texas, Denton TX

Investigators

Abstract

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.