Monday, Wednesday, Friday: 9:30 - 10:20

Grissom Hall 103

Suresh Jagannathan

LWSN 3154J

Ph: x4-0971

email: suresh@cs.purdue.edu

Office Hours: Monday, Wednesday: 12pm - 1pm

Pedro Da Costa Abreu

Wed. 11AM - 12pm, HAAS G072

email: pdacost@purdue.edu

Srinivasa Arun Yeragudipati

Tues. 2PM - 3PM, HAAS 143

email: syeragud@purdue.edu

The field of programming languages is
as old as computing itself, and is central to the way we
transform abstract algorithmic notions to concrete executable
plans. While some aspects of language design entail issues
related to choice of syntax (e.g., Lisp), contain features that
are only relevant to the specific domains in which the language
is intended to operate (e.g., XML), or are centered around
particular methdologies the language designer wishes to promote
(e.g., Javascript), much of the focus in the study of programming
languages centers on more universal, foundational
questions.

Rather than evaluating a programming
language in terms of qualitative judgments (why is
language X better to write
programs in than
language Y ?), we are interested
in pursuing a more substantive line of inquiry centered around
notions
of semantics and correctness -
what are the tools and methods that can be used to rigorously describe what a program does or means, without
injecting subjective bias into our characterization; and, how do
we ascertain from this description, assurance that any execution
of this program will be faithful to the intent of the developer?

More generally, these questions broadly fall under the term *formal methods*, an important branch of
Computer Science that allows us to precisely
reason about programming language features and behaviors using logical principles. Our focus will be to explore core ideas in
programming languages from this perspective. To do so, we will undertake our study using small language definitions
(program calcuii), sufficiently expressive to serve as useful objects of study, but not burdened
with features that, while necessary for practical use, are not semantically interesting.

The course will be centered on tools, techniques, and methodologies that enable better understanding of how we might design, specify, and implement various kinds of language features related to notions of state, modularity, and abstraction. We will also use these mechanisms to help us think about how to gain stronger assurance and confidence that the programs we write do what we expect them to do.

From the above description, you can conclude that this course will not be a survey of existing languages or
a taxonomy of language constructs. Neither will it be a course on compilers or software
engineering *per se*. While implementation principles will be discussed periodically, this will
not be an important focus of the course. Instead, the material we present will be mostly intended to allow us to explore new ways to
understand programming languages, helping us to answer questions such as the
following:

- What is the meaning of a program specification and what role do specifications play in program construction and reliability?
- How do we verify that a program adheres to its specification?
- What are sensible and tractable notions of program correctness? What are the conditions under which we can assert that a program is “safe”?
- How do we prove useful properties about a program; what do we mean by a proof in this context?
- How do we qualify the “expressive power” of a language feature? How do we relate different features found in different languages?
- What is a type and how can they be used to reason about program correctness?
- How foundationally different are various methodologies espoused by different languages (e.g., object-oriented, functional, imperative)?
- How do we reason about the equivalence of programs, or programs and their compiled translation?
- What tools can we bring to bear to help automate the way we reason about a program’s behavior?

To help answer these questions, the
course is designed around several interleaved themes: (1) the
role of logic and related mathematical formalisms to enable
writing rigorous *specifications* of a program's behavior;
(2) formal reasoning devices that
explain the meaning (or *semantics*) of programming language features
and program executions; (3) the use of *types* to define and
specify safety conditions on program executions, and to enrich
language expressivity; (4) characterization of different notions
of *correctness* and development of mechanisms to *verify* that
programs are correct with respect to their specification; (5)
the use of automated *tools* (e.g., proof assistants, program
verifiers) to help validate important theorems that describe
useful program properties.

By the end of the class, students should be comfortable with objectively assessing and comparing superficially disparate language features, understanding how these features impact implementations, be able to distinguish concepts that are truly foundational from those that just appear to be, and be able to critically reason about program correctness and safety. Most importantly, the overarching goal of this course is to equip students to ask better questions about language design, even if the answers themselves are not readily apparent.

It is assumed that students taking this class have had exposure to programming at the undergraduate level, and are comfortable with basic mathematical concepts (e.g., sets, functions, relations, basic rules of logic), and software implementation techniques. There will be a number of programming exercises in the class, using proof assistants (Coq) and automated verification tools (Dafny) but no prior background in any specific programming language is necessary.

Students are encouraged to work together to clarify issues presented in class. However, students are not allowed to collaborate on programming assignments or examinations. We will use Piazza for posting and answering questions about lectures, homeworks, etc.

Grading for the class is as follows:

**Homeworks**: 35%

There will be regular homework exercises; there are 7 planned over the course of the semester. Each exercise will consist of some number of recommended problems that you can use to guage whether have understood the basic concepts of the material covered by the exercise, and some number of required problems that test how well you have assimilated these concepts by applying them in situations different from what we examine in class. Answers will be provided for both classes of problems, but you will only be graded on your submission to the required problems.**Quizzes**: 10%

There will be weekly take-home quizzes. These quizzes will consist of 3 - 5 multiple-choice or short-answer questions posted on Gradescope. These quizzes are intended to test your understanding of lecture material covered in class.**Midterm**: 25%

The midterm will be an evening exam scheduled for Wednesday, March 20, 2024, 8:00pm - 9:30pm, KRAN G016**Final (Cumulative)**: 30%
The final will be take home.

We will use the online textbook **Software Foundations**, available
here
for part of the course. Students should download the text, and install the Coq mechanized proof assistant (see here).
There are a number of IDEs available for Coq: CoqIde (available as part of the
Coq download), or Proof General, a Coq IDE for Emacs users are two popular choices. For those of you
who decide to use Proof General, Company Coq provides additional syntax highlighting and auto complete
features. The textbook is essentially one large Coq program, with explanation provided in comments, so
students are encouraged to bring their laptops to class to interactively explore the material during the lecture. There is extensive documentation
for Coq; see here for the reference manual and here for
a list of available tactics.

In addition, students might find the following texts also useful:

- Certified Programming with Dependent Types, Adam Chlipala, MIT Press, 2013
- Types and Programming Languages, Benjamin Pierce, MIT Press, 2002.

The latter half of the course will also use Dafny, an

*Foundations*

- Functional Programming
- Polymorphism
- Induction Principles
- Logic and Propositions
- Curry-Howard Correspondence
- Relations

*Semantics*

- Program Equivalence
- Denotational and Operational Semantics

*Types*

- Simply-Typed Lambda Calculus
- Subtyping
- System F

*Automated Program Verification*

- Hoare Logic and Axiomatic Semantics
- Verification-Aware Languages (Dafny)

- Readings: Induction
- Lecture slides
- Homework 1: Due: January 29, 2024 (
**updated**)

- Readings: Lists, Polymorphism
- Lecture slides

- Readings: Logic, Inductive Propositions, Tactics and Automation
- Lecture slides
- Homework 2: Due: February 9, 2024

- Readings: Relations, Curry-Howard Isomorphism, Induction Principles
- Lecture slides

- Readings: A Simple Imperative Language, Program Equivalence,
- Lecture slides
- Homework 3: Due: February 23, 2024

- Readings: Smallstep Operational Semantics
- Lecture slides

- Readings: Introduction to Type Systems Simply-Typed Lambda Calculus Properties
- Lecture slides
- Homework 4: Due: March 8, 2024

- Readings: Hoare Logic (Part 1), Hoare Logic (Part 2)
- Lecture slides
- Homework 5: Due: March 29, 2024
**Midterm: Wednesday, March 20, 8-9:30PM, KRAN G016**

**No class: Friday, March 22nd**

- Readings: Chapters 1,2 Program Proofs
- Lecture slides

- Readings: Chapters 3,4,5: Program Proofs
- Lecture slides
- Homework 6: Due: April 12, 2024

- Readings: Chapters 6 - 10, 11 - 14: Program Proofs
- Lecture slides

- Lecture slides
- Homework 7: Due: April 26, 2024