Functional Languages and Category Theory
- 2012 年度版 (2013年度版準備中)
Instructor
Goal and Theme
The concepts of category, functor, and natural transformation are introduced. These concepts place a firm theoretical foundation for functional languages though their applications are not limited to language processors but also spread over other areas in computer science. Each theme below takes two class meetings.
Abstract
We use Mathematica as a programming tool. We will see various abstract concepts through concrete examples. Students must turn in assignments at each class meeting.
Schedule
| 回 | テーマ | 内容 |
|---|---|---|
| 1 | Introduction | We wiil overview the whole topics upcoming. |
| 2 | The Algebra of Functions | Various programming constructs in the functional framework are introduced. |
| 3 | The Algebra of Functions | We will calculate arrow composition tables. |
| 4 | Products and Sums | Products are introduced by examples. We will calculate via universality. |
| 5 | Products and Sums | Sums are introduced. We will compare the sums and the products, and realize the essential difference between them. |
| 6 | Distributive Categories | Distributed categories are introduced. Products are often distributed against sums. We abstract this property from concrete examples. |
| 7 | Distributive Categories | We invent some data structures for the distribution operation. |
| 8 | Data Types | Abstract data types are interpreted in the category framework. |
| 9 | Data Types | We implement various data types with categories. |
| 10 | Categories of Functors | Functors are introduced. They are kind of structure preserving functions between two categories. |
| 11 | Categories of Functors | We will calculate functors between various categories. |
| 12 | Advanced topics in Products | We choose some topics from computer science. |
| 13 | Advanced topics in Products | We choose some topics from abstract algebras. |
| 14 | Computational Category Theory | We will discuss some themes for the term papers. |
| 15 | Computational Category Theory | We will continue the discussion above. |
授業外に行うべき学習活動
Reading and trying all the samples which are to be found at an announced URL.
Materials
Materials at http://cis.k.hosei.ac.jp/~yukita/
References
R.F.C. Walters, "Categories and Computer Science," Cambridge University Press B.C. Pierce, "Basic Category Theory for Computer Scientists," The MIT Press
Evaluation Method
Assignments papers and term papers.
情報機器使用
Laptop PCs and Internet connection in class.
前年度の授業改善アンケートからの気づき
Not applicable.