A seminar for junior and
senior CS majors and graduate students on programming languages and
software verification, with hands-on exercise in the interactive theorem prover Coq.

Topics: logic; functional programming; inductive datatypes, recursion, and structural induction; operational, denotational, and axiomatic semantics; the simply-typed lambda calculus; the polymorphic lambda calculus; pi calculus; type systems and typechecking; SAT and SMT.

Topics: logic; functional programming; inductive datatypes, recursion, and structural induction; operational, denotational, and axiomatic semantics; the simply-typed lambda calculus; the polymorphic lambda calculus; pi calculus; type systems and typechecking; SAT and SMT.

**Lecture**: MW 3:05pm-4:00pm, ARC 159

**Lab**: F 3:05pm-4:00pm, Stocker 192

**Professor**: Gordon Stewart (gstewart@ohio.edu)

**Office Hours**: W 11:00am-12:00pm, F 1:00pm-2:00pm (Stocker 355), or by
appointment

Two IDEs for Coq are available, the Emacs-based ProofGeneral and CoqIDE (bundled with Coq). I recommend CoqIDE for new Coq users (this is also the IDE we'll be using in class); ProofGeneral is good but requires more setup and some Emacs experience.

Periodically I may assign additional supplementary (optional but recommended) readings from Types and Programming Languages, Benjamin Pierce, and from The Formal Semantics of Programming Languages, Glynn Winskel. Both of these books are available on Amazon.

In addition to the weekly homework assignments, drawn primarily from Software Foundations, there will be a take-home midterm exam (Week 7, approximately 15% of your grade) and a final project (Week 15, approximately 35%). The weekly homeworks and attendance at lecture and lab are worth approximately 50%.

Blackboard will be used only to report grades. Up-to-date information on all other aspects of the course (assignment due dates, etc.) will be posted on this website.

Introduction to functional programming, Coq. Basic proofs.

Reading:
Basics,
Induction,
Lists.

Homework: Assignment 0.

More functional programming: polymorphism, implicit arguments,
higher-order functions. Coq proof strategies, additional tactics.

Reading:
Poly,
Tactics.

Homework: Assignment 1.

Logic in Coq, inductively defined propositions.

Reading:
Logic,
IndProp.

Supplementary Reading:
How to Write a 21st Century Proof, by Leslie Lamport

Homework: Assignment 2.

The little imperative language Imp.

Reading:
Maps,
Imp.

Supplementary Reading:
Winskel, Ch. 2, Secs. 2.1-2.5.

Homework: Assignment 4.

Interlude: More Functional Programming (!) in Coq

Take-home Midterm : due Wednesday, 10/11.

Small-step Operational Semantics.

Reading:
Smallstep,
Auto.

Supplementary Reading:
Winskel, Ch. 2, Sec. 2.6.

Homework : Assignment 7.

Type systems.

Reading:
Types.

Supplementary Reading:
TAPL, Chs. 1 and 8.

Homework : Assignment 8,
Final Project Checkpoint #1 .

Untyped Lambda Calculus, Simply-Typed Lambda Calculus.

Reading:
Stlc.

Supplementary Reading:
TAPL, Chs. 5 and 9.

Homework : Assignment 9.

More STLC: let-bindings, pairs, unit, sums, lists, recursion.

Reading:
StlcProp,
Typechecking
MoreStlc.

Supplementary Reading:
TAPL, Ch. 11.

Homework : Assignment 10.

Denotational semantics of regular expressions

Supplementary Reading:
Winskel, Ch. 5., Regular-expression derivatives reexamined

Homework:
Final Project Checkpoint #2.

Denotational semantics of Imp;
Pi Calculus

- Design and implement inductively defined data types to solve computational problems
- Design and implement recursive functions over inductively defined data types in order to solve computational problems
- Model the behavior of an imperative programming language using operational semantics

(b) An ability to analyze a problem, and identify and define the computing requirements appropriate to its solution. Students will be able to:

- Analyze a type system in order to prove metatheoretic properties like type soundness
- Analyze a program in order to identify specifications (Hoare-logic pre- and post-conditions) that capture the program's expected behavior

(c) An ability to design, implement, and evaluate a computer-based system, process, component, or program to meet desired needs. Students will be able to:

- Use an interactive theorem prover to mechanically prove type soundness for a small arithmetic expression language
- Use an interactive theorem prover to prove type soundness for the simply-typed lambda calculus
- Extend a mechanical proof of type soundness for the simply-typed lambda calculus to support additional features such as products or sums
- Use an interactive theorem prover to build a mechanical Hoare-logic proof of safety for a small imperative program

(j) An ability to apply mathematical foundations, algorithmic principles, and computer science theory in the modeling and design of computer-based systems in a way that demonstrates comprehension of the tradeoffs involved in design choices. Students will be able to:

- Reason about, and recognize the tradeoffs of, various definitions of program equivalence with respect to a language's operational semantics

Instructor/GA | Noninstructor (e.g., Another Student) | |
---|---|---|

You | all collaboration allowed | high-level discussion
(of the problems, not your code!)
allowed but only after you've started the assignment;
must be documented in README as described below |

You **may** discuss the homework with other students in
the class, but only after you've attempted the problems on your own
first. If you do discuss the homework problems with others, write the
names of the students you spoke with, along with a brief summary of
what you discussed, in a README comment at the top of each
submission. Example:

(*
README Gordon Stewart, Assn #1

I worked with X and Y. We swapped tips regarding the use of Coq's "rewrite" tactic. *)

However, **under no circumstances** are you permitted
to share or directly copy code or other written homework material,
except with course instructors.
If I discover that you've cheated on an
assignment, you'll get an automatic 0 along with an immediate
referral to the
Office of Community Standards, which will likely
take disciplinary action against you.
Remember: homework is there to give *you* practice in
the new ideas and techniques covered by the course; it does you no
good if you don't engage!

In general, students in EECS courses such as this one must adhere to the Russ College of Engineering and Technology Honor Code, and to the OU Student Code of Conduct. If you haven't ever read these documents, please do so.