类型论
在最广泛的层面上,类型论(英語:)是关注把实体分类到叫做类型的搜集中的数学和逻辑分支。在这种意义上,它与类型的形而上学概念有关。现代类型论在部分上是响应罗素悖论而发明的,并在伯特兰·罗素和阿弗烈·诺夫·怀海德的《数学原理》中起到重要作用。
在计算机科学分支中的编程语言理论中,类型论提供了设计分析和研究类型系统的形式基础。实际上,很多计算机科学家使用术语“类型论”来称呼对编程语言的类型语言的形式研究,尽管有些人把它限制于对更加抽象的形式化如有类型lambda演算的研究。
类型论体系
活跃
- 正在研究中的同伦类型论
参考文献
- Farmer, William M. . Journal of Applied Logic. 2008, 6 (3): 267–286. doi:10.1016/j.jal.2007.11.001.
延伸阅读
- Andrews, Peter B., 2002. An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof, 2nd ed. Kluwer Academic Publishers.
- Cardelli, Luca, 1997, "Type Systems," in Allen B. Tucker, ed., The Computer Science and Engineering Handbook. CRC Press: 2208-2236.
- Mendelson, Elliot, 1997. Introduction to Mathematical Logic, 4th ed. Chapman & Hall.
- Pierce, Benjamin, 2002. Types and Programming Languages. MIT Press. ISBN 0-262-16209-1)
- Thompson, Simon, 1991. Type Theory and Functional Programming. Addison-Wesley. ISBN 0-201-41667-0.
- Winskel, Glynn, 1993. The Formal Semantics of Programming Languages, An Introduction. MIT Press. ISBN 0-262-23169-7.
外部链接
- Stanford Encyclopedia of Philosophy: Type Theory" -- by Thierry Coquand.
- National Institute of Standards and Technology: Abstract data type
- A summary paper on the formal basis of ADTs, relationship to category theory, and list of good references. Pages 3-4 appear relevant. Reference number [6] looks good, but it may not be available online.
- Constable, Robert L., 2002, "Naïve Computational Type Theory," in H. Schwichtenberg and R. Steinbruggen (eds.), Proof and System-Reliability: 213-259.
- The Nuprl Book: "Introduction to Type Theory."
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