**Cornell CS 6117: Category Theory for Computer Scientists (Fall 2022)**
- 09/29: Homeworks will now be every other week, rather than every week.
- 08/24: **ROOM CHANGE**: We are moving to **Phillips 407**.
- 08/22: Office hours, readings for first half
- 08/03: Welcome to CS 6117!
Category theory is an abstract theory of structures and transformations. While
originally motivated by pure mathematics, category theory has since found
applications across physics, philosophy, linguistics, logic, and more; the area
is under active development and continues to evolve.
The breadth of applications and high level of abstraction can make category
theory difficult to approach. This course aims to introduce and motivate
category theory by focusing on applications in computer science, and in
particular programming language semantics.
(##) Course Information
This is 3-credit, graduate-level course. Undergraduates are welcome to enroll
with permission of the instructor. The main pre-requisite for this course is CS
6110 or CS 4110.
Although this course is offered in the computer science department, it is a
**purely theoretical course**. There will be no programming involved, and
students will be **required to do proofs for all homework assignments**.
(##) Course Objectives
After completing this course, students should be able to (a) give categorical
semantics to different kinds of programming languages and programming language
features, (b) carry out basic proofs in category theory, (c) learn and explore
further applications of category theory on their own, building on their
familiarity with basic concepts and methods in category theory, and (d) explain
the basic concepts of a wide variety of denotational semantics.
- Lectures: **PHILLIPS 407** ~~Upson 152~~, Tuesdays and Thursdays 1:00 PM - 2:15 PM
- Questions: [Edstem](https://edstem.org/us/join/3EnPQX)
Instructor: Justin Hsu
Syntax, Types, Equations | CfT 3.1-3 | Sep 01 | Algebraic Type Theory
Categorical Semantics and Soundness | CfT 3.4-6 | Due: A01
Out: A02 Sep 06 | Algebraic Type Theory
Categories of Models | CfT 3.7 | Sep 08 | Algebraic Type Theory
Classifying Category | CfT 3.7-8 | Due: A02
Out: A03 Sep 13 | Algebraic Type Theory
Classifying Category | CfT 3.8-9 | Sep 15 | CT: Representable Functors | BCT 4, CT 8.3-4 | Due: A03
Out: A04 Sep 20 | CT: Cartesian Closed Categories
Functional Type Theory: Syntax | CfT 2.8, 4.1-3, CT 6 | Sep 22 | Functional Type Theory
Categorical Semantics and Soundness | CfT 4.4-6 | Due: A04
Out: A05 Sep 27 | Functional Type Theory
Classifying Category | CfT 4.7-9 | Sep 29 | Functional Type Theory
Categorical Gluing | CfT 4.10 | Due: A05 Oct 04 | Functional Type Theory
Proving Conservativity | CfT 4.10 | Oct 06 | CT: Adjoint Functors | BCT 2, CT 9.1-5 | Out: A06 Oct 11 | **FALL BREAK: NO CLASS** | **NO CLASS** | **NO CLASS** Oct 13 | Polymorphic Type Theory
Syntax, Types, Equations | CfT 5.1-2, PFPL 16 | Oct 18 | Polymorphic Type Theory
Types and terms in type context | CfT 5.3-4 | Oct 20 | Polymorphic Type Theory
Type and term substitutions | CfT 5.3-5.4 | Due: A06
Out: A07 Oct 25 | Polymorphic Type Theory
Polymorphic types and terms | CfT 5.3-5.4 | Oct 27 | CT: Limits and Colimits | BCT 5, CT 5.4-6 | Nov 01 | CT: Algebras and Coalgebras
Inductive Types | [#Métayer] | Nov 03 | Initial Algebras
Fixed-Points of Functors | [#Métayer] | Due: A07
Out: A08 Nov 08 | Continuous Functors
Domain Equations | [#Métayer]
[#SP] and [#AMM] | Nov 10 | CT: Monoidal Categories
Linear Logic: Multiplicatives | [#Benton] | Nov 15 | CT: Comonads
Linear Logic: Exponentials | CT 10.4
[#Benton] | Nov 17 | Linear logic: LNL models
CT: Monads, Effects, Kleisli Triples | [#Benton]
[#Moggi] | Due: A08
Out: A09 Nov 22 | CT: More Monads, Kleisli Category
Monadic Metalanguage | CT 10.1-2
[#Moggi] | Nov 24 | **THANKSGIVING: NO CLASS** | **NO CLASS** | **NO CLASS** Nov 29 | CT: Monads and Algebras
Algebraic Effects | CT 10.3
[#Bauer] | Dec 01 | Algebraic Effects | [#Bauer] | Due: A09 **Readings**: [#Métayer]: François Métayer. Fixed points of functors. 2003. [[pdf](https://www.irif.fr/~metayer/PDF/fix.pdf)] [#SP]: Michael B. Smyth and Gordon D. Plotkin. The Category-Theoretic Solution of Recursive Domain Equations. 1982. [[pdf](https://homepages.inf.ed.ac.uk/gdp/publications/Category_Theoretic_Solution.pdf)] [#AMM]: Jiří Adámek, Stefan Milius, Lawrence S. Moss. Fixed Points of Functors. 2016. [[pdf](https://www.sciencedirect.com/science/article/pii/S2352220816301201)] [#Benton]: P. N. Benton. A Mixed Linear and Non-Linear Logic: Proofs, Terms and Models (Extended Abstract). 1995. [[pdf](http://nickbenton.name/cslpaper.pdf)] [#Moggi]: Eugenio Moggi. Notions of Computation and Monads. 1991. [[pdf](https://www.sciencedirect.com/science/article/pii/0890540191900524)] [#Bauer]: Andrej Bauer. What Is Algebraic about Algebraic Effects and Handlers? 2019. [[pdf](https://arxiv.org/pdf/1807.05923.pdf)] # Policies (##) Academic Integrity Cornell University has a Code of Academic Integrity (see [here](https://theuniversityfaculty.cornell.edu/dean/academic-integrity/)). Violations of this code are treated very seriously by Cornell and can have long-term repercussions. In this course, you are encouraged to discuss the content of the course with other students, and you may also discuss homework problems with other students. However: - You must do your own work and write up assignments individually, without shared notes of any kind. - If you discuss a problem with another student, you are expected to document this fact in your write-up. - Unless otherwise stated, you may freely use any of the resources above. However, searching for or copying solutions from other sources is not allowed. (##) Respect in Class Everyone—the instructor, TAs, and students—must be respectful of everyone else in this class. All communication, in class and online, will be held to a high standard for inclusiveness: it may never target individuals or groups for harassment, and it may not exclude specific groups. That includes everything from outright animosity to the subtle ways we phrase things and even our timing. For example: do not talk over other people; don't use male pronouns when you mean to refer to people of all genders; avoid explicit language that has a chance of seeming inappropriate to other people; and don't let strong emotions get in the way of calm, scientific communication. If any of the communication in this class doesn't meet these standards, please don't escalate it by responding in kind. Instead, contact the instructor as early as possible. If you don't feel comfortable discussing something directly with the instructor—for example, if the instructor is the problem—please contact the advising office or the department chair. (##) Special Needs and Wellness It is Cornell policy to provide reasonable accommodations to students who have a documented disability (e.g., physical, learning, psychiatric, vision, hearing, or systemic) that may affect their ability to participate in course activities or to meet course requirements. Students with disabilities are encouraged to contact [Student Disability Services](http://sds.cornell.edu/) at 607-254-4545, or the instructor for a confidential discussion of their individual needs. If you are experiencing undue personal or academic stress at any time during the semester or need to talk to someone who can help, contact the instructor or: - [Engineering Academic Advising](https://www.engineering.cornell.edu/resources/advising/) at 607-255-7414, - [Learning Strategies Center](http://lsc.cornell.edu/) at 607-255-6310, - [Let's Talk Drop-in Counseling](https://health.cornell.edu/services/counseling-psychiatry/lets-talk) at Gannett at 607-255-5155 - [Empathy Assistance and Referral Service](http://orgsync.rso.cornell.edu/org/ears) at 607-255-EARS.