15-814 Types and Programming Languages

Course Information

Date / Time: Mon & Wed / 12:00 pm - 1:20 pm
Room: GHC 4303
Instructor: Karl Crary
Teaching Assistant: Yong Kiam Tan
Discussion Board: Piazza Page
Office Hours
Karl Crary: Tue / 3:30 pm - 4:30 pm GHC 9217
Yong Kiam: Thu / 4:00 pm - 5:00 pm GHC 7513


This is an introductory course on the foundations of programming languages. The central organizing principle is the identification of language features with types. The theory of programming languages, therefore, reduces to the theory of types. Type theory is a comprehensive foundational theory of computation, and also corresponds (in a way that can be made mathematically precise) to the vernacular of logic. The course is about the dual interpretations of type theory as programming and as logic, and about the interplay between those interpretations.


Robert Harper,
Practical Foundations for Programming Languages (Second Edition),
Cambridge University Press, April 2016.
[Online Preview]


You are required to achieve a grade of B on each homework assignment. If you receive a C or D on an on-time submission, you will be given extra time in which to revise to achieve a B grade on that assignment. Failure to submit on time, or a failing grade on an assignment, precludes resubmission and will result in a failing grade in the course.

All homeworks are due by 11 pm on the stated due date. No late homeworks will be accepted, unless prior permission is obtained from the instructor, which will be granted only under exceptional circumstances. Homeworks are to be submitted by email to the teaching assistant. Homeworks should preferably be typeset in LaTeX, but can also be handwritten neatly, scanned and submitted as a PDF.

All homeworks are to be submitted by sending the PDF via e-mail to the teaching assistant with "15-814 Homework" as the subject line. No late homeworks will be accepted. Any re-do's must be finished within three days of their being returned to you. One re-do is generally permitted per assignment. You would be allowed more than one re-dos only under exceptional circumstances.

Midterm Exam

There will be a 24-hour take-home midterm examination during the exam period in the mid of semester. You will be assigned a letter grade as for homework.

Final Exam

There will be a 24-hour take-home final examination during the exam period at the end of semester. You will be assigned a letter grade as for homework.

Academic Integrity

Unless explicitly instructed otherwise, all homework and exam work is to be solely your own, and may not be shared with or borrowed from any other person in the course. You are not permitted to draw upon assignments or solutions from previous instances of the course, nor to use course materials (such as assignments or programs) obtained from any web site or other external source in preparing your work.

You may discuss homework assignments with other students in the class, but you must adhere to the whiteboard policy. At the end of discussion the whiteboard (or whatever discussion medium is used) must be erased, and you must not transcribe or take with you anything that has been written on the board during your discussion. In other words, after any such discussion, you must be able to reproduce the results solely on your own.

Tentative Schedule of Lectures

Date Topic Reading Homework
Sep 4 Labor Day (No lecture)
6 Inductive Definitions PFPL 1-3
11 Statics and Dynamics PFPL 4-5 HW1 out
(handout [LaTeX template] [macros] )
13 Type Safety PFPL 6
18 Simply-Typed Lambda Calculus PFPL 8, 21
20 Substitution PFPL 8, 21
25 Contextual and Evaluation Dynamics
Products and Sums
PFPL 5.3, 7
PFPL 10, 11
HW1 due
HW2 out
(handout [LaTeX template] [macros])
27 System T PFPL 9
Oct 2 Definability PFPL 9
4 Polymorphism and System F PFPL 16
9 Existential Types
Data Abstraction
HW2 due
HW3 out
(handout [LaTeX template] [macros])
11 Abstraction Theorem PFPL 48
16 Free Theorems Theorems for free! HW3 due
HW4 out
(handout [LaTeX template] [macros])
18 Curry-Howard Isomorphism
23 PCF and Recursive Types PFPL 19-20 Midterm (available 23 Oct - 27 Oct)
25 State and Effects PFPL 34
30 Modernized Algol PFPL 34-35 HW4 due
HW5 out
(handout [LaTeX template] [macros])
Nov 1 Modernized Algol PFPL 34-35
6 Assignables and References PFPL 34-35
8 Control Stacks PFPL 28
13 Exceptions and Continuations PFPL 29-30 HW5 due
15 Continuations and Classical Logic PFPL 13 HW6 out
(handout [LaTeX template] [macros])
20 Subtyping PFPL 24
22 Thanksgiving (No Class)
27 Higher Kinds PFPL 18
29 Linear Logic
Dec 4 Substructural Logic HW6 due
6 Modal Logic

Yong Kiam Tan

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