New methods for building computer algebra systems

这项研究的主要目标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，第一类类型等）的前沿，以及采用先进的软件工程技术，早在主流流行之前。 虽然在过去的几年里，计算机代数领域新的、更快的算法的发展以惊人的速度进行，但工程问题却受到较少的关注。 然而，最近的进展，如类型理论，命名语言的指称语义，生成式编程和自动化测试等领域都可以有益地适用于建设的CAS。

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.