The following schedule lists the topics we will cover and approximately the number of meetings we will spend on each topic. The schedule is tentative. Most likely, some things will change during the semester, and I will revise the schedule as necessary.

The Reading column lists the assigned reading for the meeting. You should view the readings as an introduction to spark discussion in class.

The Assignment column lists the due date for each assignment.

Date Part Topic Reading Assignment
M 1/12 Welcome and course overview [slides]
W 1/14 Application Model checking and SLAM [slides]
Thomas Ball and Sriram K. Rajamani. The SLAM Project: Debugging System Software via Static Analysis. Symposium on Principles of Programming Languages (POPL), 2002.
Thomas Ball and Sriram K. Rajamani. Automatically Validating Temporal Safety Properties of Interfaces. International SPIN Workshop, 2001.
Sign-up on the course moodle and introduce yourself.
M 1/19 No class, Martin Luther King, Jr. Day
W 1/21 Application Counterexample-guided abstraction refinement [slides] Thomas A. Henzinger, Ranjit Jhala, Rupak Majumdar, and Gregoire Sutre. Lazy Abstraction. Symposium on Principles of Programming Languages (POPL), 2002.
M 1/26 Semantics A simple imperative language and operational semantics [slides]
Winskel, Chapter 2 up to 2.6 (i.e., 2.1-2.5). Section 2.6 is very short, so you may want to read ahead for 1/28.
Keep the forum posts for 1/26 to the Winskel chapter and the class discussion. We will have a separate forum on the Hoare paper.
HW0 Due
W 1/28 Semantics Contextual operational semantics [slides]
Winskel, 2.6
Choose at least one of the following historical articles:
Recent research (optional). Here are some recent papers that use operational semantics. Just skim to the appropriate figure and see if you can recognize the definitions.
Textbook supplement (optional). For some additional background, take a look at Harper, Chapter 10.
Textbook supplement (optional). Here is essentially a textbook on operational semantics. Chapter 2 provides another take on small-step operational semantics (where Winskel left as an exercise).
M 2/2 Semantics Proof techniques: structural induction [slides]
Winskel, Chapter 3
Textbook supplement (optional). For some additional background, take a look at Harper, Chapter 1 (especially 1.4).
More details (optional). Winskel, Chapter 4.
HW1 Due
W 2/4 Semantics Denotational semantics for the spectator [slides] Winskel, Chapter 5 (up to at least 5.4)
M 2/9 Semantics Denotational semantics for the spectator [slides]
Winskel, Chapter 5 (finish)
Winskel, Chapter 8 (read for the general concepts, not the details)
Textbook supplement (optional). For an alternative presentation of partial orders, least upper bounds, monotonic and continuous functions, and least fixed points, take a look at the following report (up to and including Section 2.4):
HW2 Due
W 2/11 Semantics Axiomatic semantics, an introduction (and review of denotational semantics and domain theory) [slides]
C.A.R. Hoare. An Axiomatic Basis for Computer Programming. CACM 12(10), October 1969.
Robert W. Floyd. Assigning Meanings to Programs.
M 2/16 Semantics Axiomatic semantics, an introduction [slides]
Winskel, 6.1-6.4
C.A.R. Hoare. Proof of a Program: FIND. CACM 14(1), January 1971.
HW3 Due
W 2/18 Semantics Axiomatic semenatics, an introduction [slides]
Winskel, 6.5-6.7 and 7.1-7.3
George Necula. Completeness of Axiomatic Semantics (using operational semantics).
M 2/23 Semantics Verification conditions [slides]
Winskel, 7.4-7.6
HW4 Due
W 2/25 Semantics Symbolic execution and applying verification condition generation [slides]
Choose at least one of the following papers on using symbolic execution for automated testing:
Recent research (optional). CUTE is a follow-on project to DART. Both of these projects combine symbolic execution with concrete execution to perform automated testing.
Classic paper (optional). The following is the classic paper on symbolic execution:
M 3/2 Semantics Abstract interpretation, an introduction [slides]
Patrick Cousot. Informal Introduction to Abstract Interpretation. These are some lecture slides that explain the basic concepts of abstraction using a graphics analogy. Browse up to at least slide 52.
Samson Abramsky and Chris Hankin. An Introduction to Abstract Interpretation.
HW5 Due
W 3/4 Semantics Abstract interpretation, an introduction [slides]
Patrick Cousot. Abstract Interpretation Based Formal Methods and Future Challenges. Informatics, 10 Years Back - 10 Years Ahead, 2001.
Ken Thompson. Reflections on Trusting Trust. CACM 27(8), August 1984. This is Ken Thompson's Turing Award lecture.
Classic paper (optional). The following is the classic paper on abstract interpretation:
Su 3/8 Project Proposal Due
M 3/9 Types Lambda calculus and functional programming [slides]
Benjamin Pierce. Foundational Calculi for Programming Languages. (through Section 2)
HW6 Due
W 3/11 Types Lambda calculus and functional programming [slides, lambda.ml (exercise), lambda.ml (solution)]
Textbook supplement (optional). For another take on lambda calculus, take a look at Pierce's TAPL book (e-book). Chapter 5 discusses the untyped lambda calculus, and Chapter 6 discusses de Bruijn notation.
Recent research (optional). Xavier Leroy. Formal certification of a compiler back-end, or: programming a compiler with a proof assistant. Symposium on Principles of Programming Languages (POPL), 2006.
M 3/16 Types Simply-typed lambda calculus [slides]
Luca Cardelli. Type Systems. (through at least Section 3, Section 4 optional).
Textbook supplement (optional). In Pierce's TAPL book (e-book), Chapter 9 gives another presentation of the simply-typed lambda calculus.
W 3/18 Types Monomorphic type systems [slides]
Andrew K. Wright and Matthias Felleisen. A Syntactic Approach to Type Soundness.
Textbook supplement (optional). In Pierce's TAPL book (e-book), Chapter 11 presents the basic monomorphic types.
M 3/23 No class, Spring Break
W 3/25 No class, Spring Break
Su 3/29 Project Status Update Due
M 3/30 Types Subtyping [slides] Textbook supplement (optional). In Pierce's TAPL book (e-book), Chapter 15 discusses the main concepts of subtyping.
W 4/1 Types Types for Imperative Features [slides]
Classic paper (optional). The following is a classic paper on exception handling:
Textbook supplement (optional). In Pierce's TAPL book (e-book), Chapter 13 and 14 talk about reference and exception types, respectively.
Sa 4/4 Midterm Due
M 4/6 Midterm Discussion [slides]
Tu 4/7 Midterm Resubmit Due
W 4/8 Types Recursive Types [slides]
Luca Cardelli. Type Systems. (rest, Section 5 to end).
Textbook supplement (optional). In Pierce's TAPL book (e-book), Chapter 20 discusses recursive types, while Chapter 21 gives more of the mathematical foundation.
M 4/13 Types Polymorphism [slides] Textbook supplement (optional). In Pierce's TAPL book (e-book), Chapter 23 discusses universal types (for polymorphism). Section 22.7 talks a bit about ML-style let-polymorphism and the value restriction. For more advanced topics, Chapter 26 discusses bounded quantification (for both universal and existential types). Chapter 29 and 30 talks about kinding ("a type system for types").
W 4/15 Types Data abstraction and dependent types [slides] Textbook supplement (optional). In Pierce's TAPL book (e-book), Chapter 24 discusses existential types (for modularity and data abstraction). Section 30.5 briefly gives some intuition for dependent types.
M 4/20 Application Automated Theorem Proving and Proof Checking [slides] Greg Nelson and Derek C. Oppen. Fast Decision Procedures Based on Congruence Closure. JACM 27(2), April 1980.
W 4/22 Application Shape Analysis [slides]
Bor-Yuh Evan Chang, Xavier Rival, and George C. Necula. Shape Analysis with Structural Invariant Checkers. Static Analysis Symposium (SAS), 2007.
Textbook supplement (optional). Thomas W. Reps, Reinhard Wilhelm, and Mooly Sagiv. "Shape Analysis and Applications." In The Compiler Design Handbook: Optimizations and Machine Code Generation, Chapter 5, CRC Press, 2008.
M 4/27 Project presentations
W 4/29 Project presentations
W 5/6 Project Paper Due