15-814 Types and Programming Languages

Course Information

Time: Tue-Thu10:30-11:50
Room: 4303 GHC
Instructor: Robert Harper
Teaching Assistant: Evan Cavallo
Discussion Bboard: Piazza Page
Office Hours
Harper: Tue 13:00-14:00 9207 GHC
Cavallo: Mon 10:30-12:00 6221 GHC


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. Type theory has its orgins in proof theory (the theory of human reason) and is closely related to category theory (the general theory of mathematical structures). The tripartite relationship between type theory, proof theory, and category theory is fundamental to the study of programming languages.


Robert Harper,
Practical Foundations for Programming Languages (Second Edition),
Cambridge University Press, 2015 (to appear).
[Online Preview.]


You are required to achieve a grade of B on each homework assignment, and on the final exam. If you receive a C or D on an on-time submission, you will be given three days 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 at the beginning of lecture 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 in PDF format, and must be typeset. (LaTeX is recommended; we will provide macros).

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. Only one re-do is permitted per assignment.

Final Exam

There will be a 48-hour take-home final examination during the exam period at the end of semester. You will be assigned a letter grade as for homework, but with no possibility of resubmission.

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 must be erased, and you must not transcribe or take with you anything that has been written on the board during your discussion. You must be able to reproduce the results solely on your own after any such discussion.


CS PhD students are assigned a pass/fail grade in the University grading system, but are given an internal letter grade for Black Friday purposes. A final letter grade of B is required to pass this course. To achieve this, you must have (1) completed all homework assignments on-time with a grade of B; and (2) earned a grade of B or better on the final exam.

Undergraduate students and students in other programs will be assigned letter grades according to the same policies used to assign internal letter grades for CS PhD students.

Schedule of Lectures

Date Topic Reading Homework
Sep 8 What is a programming language? PFPL1-7
10 HW1 out
(handout [LaTeX template] [macros])
(corrected 9/15/15)
15 Functions, Products, and Sums PFPL8-11
22 Generic Programming, Inductive and Co-Inductive Types PFPL 14-15
24 HW1 due. (solutions)
HW2 out.
(handout [LaTeX template] [macros])
29 Polymorphic Types, Abstract Types, Parametricity PFPL 16-17, 49
Oct 1
6 Partiality and Recursive Types PFPL 19-20
8 HW2 due. (solutions)
HW3 out.
(handout [LaTeX template] [macros])
13 Dynamic Typing PFPL 22-23
20 Dynamic Dispatch PFPL 26 HW3 due. (solutions)
HW4 out.
(handout [LaTeX template] [macros])
22 (Guest lecture by Dana Scott)
27 Parallelism PFPL 37-38
Nov 3 Stacks and Continuations PFPL 28-30
5 HW4 due. (solutions)
HW5 out.
(handout [LaTeX template] [macros])
(notes on continuations and logic)
10 Modernized Algol PFPL 34
17 References; Benign Effects PFPL 35 HW5 due. (solutions)
19 Dynamic Classification, Exception Values PFPL 33 HW6 out.
(handout [LaTeX template] [macros])
24 Laziness PFPL 36
26 (Thanksgiving)
Dec 1 Concurrency PFPL 39-40
3 HW6 Due 12/6. (solutions)
Dec 8 Modularity PFPL 42-44

Robert Harper
Last modified: Sun Dec 13 00:45:23 EST 2015

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