15-814 Types and Programming Languages

Course Information

Time: Tue-Thu 12:00-1:20
Room: 4303 GHC
Instructor: Robert Harper
Teaching Assistant: Stefan Muller
Discussion Bboard: Piazza Page
Office Hours
Harper: Tue 14:00-15:00 9207 GHC
Muller: Mon 15:00-16:00, Fri 16:00-17:00 6004 GHC


This is an introductory course on the foundations of programming languages. The central organizing principle of language design 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. (Similar correspondences hold between type theory and category theory (types are objects, programs are maps) and between category theory and proof theory (propositions are objects, proofs are maps), but we shall not consider these in this course.)


Robert Harper, Practical Foundations for Programming Languages, Cambridge University Press, 2013.
[Online preview edition, with corrections.]
[Working draft of second edition, with major revisions.]


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 entails 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 9 What is a programming language? PFPL1-7
11 HW1 out
(handout [LaTeX template] [macros])
16 Products, Sums, Functions PFPL8-9,11-12
18 HW1 due. (solutions)
HW2 out.
(handout [LaTeX template] [macros])
23 Generic Programming, Inductive and Co-Inductive Types PFPL 14-15
30 Polymorphic Types, Encodings, Parametricity PFPL 20-21
Oct 2 HW2 due. (solutions)
HW3 out.
(handout [LaTeX template] [Pt. 3 template] [macros])
7 Abstract Types, Representation Independence; Partiality and PCF PFPL 21, 10
14 Recursive Types; Dynamic Typing PFPL 16; 18-19
16 HW3 due. (solutions)
HW4 out.
(handout [LaTeX template] [macros])
21 Dynamic Typing; Dynamic Dispatch PFPL 25
28 Modernized Algol; Mutable Storage 35-36 Notes
30 HW4 due. (solutions)
HW5 out.
(handout [LaTeX template] [macros])
4 Parallelism PFPL 39
11 Processes and Concurrency PFPL 41-43 Notes
13 Notes
HW5 due. (solutions)
(HW6 cancelled.)
Nov 18 Exceptions and Exception Values PFPL 27-28; 34 Notes
20 Notes
25 Laziness and Eagerness Notes (HW6 cancelled.)
27 (Thanksgiving Break)
Dec 2 Modularity PFPL 44-46 Notes
4 Notes

Robert Harper
Last modified: Tue Nov 18 13:53:58 EST 2014

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