New methods for building computer algebra systems

这项研究的主要目的是从根本上重新审视目前用于构建计算机代数系统的方法，旨在做出实质性的改进。众所周知，计算机代数系统(CAS)是许多新的编程语言技术(泛型编程、依赖类型、一类类型等)的前沿，并且在它们在主流中流行很久之前就采用了先进的软件工程技术。虽然在过去的几年里，计算机代数领域的新的、更快的算法的发展速度非常快，但工程问题却没有得到太多的关注。然而，在类型理论、名义语言的指称语义、生成式编程和自动测试等领域的最新进展都可以有益地应用于用例的构造。

The main objective of this research is to fundamentally re-examine the methodology currently used to build Computer Algebra Systems, aiming to make substantial improvements. Computer Algebra Systems (CAS) are well-known to be at the forefront of many new programming language technologies (generic programming, dependent types, first-class types, etc), as well adopting advanced software engineering techniques long before they are popular in the mainstream. While the development of new, faster algorithms in the area of Computer Algebra has proceeded at a breakneck pace in the last few years, engineering issues have received less attention. However, recent progress in such areas as type theory, denotational semantics for nominal languages, generative programming and automated testing can all be profitably applied to the construction of CASes.