In this class, we will consider how to use mathematics to specify and analyze models of programs, computer hardware, and physical processes, such as phylogentics and rapid, single-flux, quantum computers. This class will require careful thought as we will be pushing the boundaries of what the academic community considers to be an adequate specification and sufficient confirmation evidence that a program (or process) meets its specification. Typically, some form of testing is the only mechanism that is used to see if a program meets its specification; our focus will be proof-based methods.
We will use proof-based techniques to determine the correctness of models of code, circuits, and digital systems. At first, we will use hand proofs; that is, we will use some informal notation to compare a specification program to an implementation program. We will also convert the behavior of some programs into a form that will allow a mechanical comparison of the behavior of some process and its specification.
This class will be taught in an "inverted" style. That is, we will concentrate class time on examples, working through specifications, proofs, describing challenges, and exploring problems being faced by students. Thus, it is important that you bring your laptop to class. There will be lectures to introduce various topics, but primarily, we will use class time for problem solving, demonstrating how to use various tools, and exchanging information.
Exam(s) and quizzes are open-book, open-notes affairs -- however, no electronic devices (laptops, cell phones, tablets, PDAs, calculators) of any kind are allowed during test and quiz events. As such, you may wish to have a physical copy of any materials that you believe will be helpful during quizzes and exams. Remember, cell phones are not allowed during exams; during quizzes and exams the remaining time will be periodically announced.
Note: this course requires students to program in a subset of Lisp.
For the adventurous student, special projects are possible. The content of a special project is pretty flexible -- so long as it has to do with specification and validation. For instance, I am interested in the development of an ISA model of IBM's Harvest computer (circa 1950s), which was a extension of IBM's Stretch computer. A possible specification project might involve some microprocessor, such as RISC-V. Another project I'm looking for help with concerns booting FreeBSD or Linux on our evolving ACL2-based x86 ISA emulator. I work on rapid, single-flux, quantum computing; there are many questions that formal modeling and proof could help answer. Other independent study projects are possible; please discuss your ideas with the instructor and/or TA.
The value you get from this class will be directly related to the effort you (as a student) put forward. This class will require that you learn to work on your own, and this class may be less structured than many of the classes you have taken. If you have a laptop computer, you should bring it to class. Having a laptop is not a requirement, but it will be very helpful for students to be able to individually access information during class, and when we are discussing proof issues it may be helpful for you to try things immediately. Note, it is possible to checkout a Linux-based laptop from the UTCS Department; check with the instructor if you wish to borrow such a laptop.
Students will be encouraged to give short (five- to ten-minutes) presentations in class on particular topics. When well done, these presentations can serve in place of a missed quiz or homework. In fact, any student may be called upon to give a two- or three-minute presentation on something being discussed in class or on their solution to a homework problem. Please come to class prepared to work; we will sometimes stop for a few minutes to make sure that everyone that has a chance to consolidate their thinking and to help students overcome problems with their understanding or with questions about the in-class presentations.
Our office hours are listed on the main class web-page. In addition, if you need help, you may certainly seek out and visit with the class TA and/or the instructor(s). You may arrange to meet us at other times than those listed, but you will need to send E-mail to arrange a time. If we become too busy during the scheduled office hours, we will expand our office hours to meet the needs of the students. If you cannot come to the scheduled office hours due to conflicts with other classes, let us know quickly so we can make arrangements to meet your needs.
The following gives an outline of what we will discuss. We are open to discussing other related topics of general interest, and we will include some of our own experiences. The syllabus below is approximate; the exact rate at which we will cover some material will vary.
Schedule Below is Approximate, Lectures Dates May Change Slightly
*** NOTE: The Exam date is tentative until September 2, 2021 ***
*** NOTE: Lab assignments and due dates are tentative until assigned ***
Week Class Date Short Description
0 00 Aug 26 Course Content Introduction, Example uses
Course Procedures and UT required disclosures
1 01 Aug 31 Introduction to the ACL2 Logic, Data Types, Terms
1 02 Sep 2 Substitution and Abbreviations for Terms
Finalize course Exam date
Sep 6 Labor Day - Holiday
2 03 Sep 7 Function Definitions, Axioms
2 04 Sep 9 Terms as Formulas
3 05 Sep 14 Definitions, Revisited
3 06 Sep 16 Structural Induction, Structural Recursion
4 07 Sep 21 Definition Problems
4 08 Sep 23 Structural Induction
5 09 Sep 28 Structural Induction
5 10 Sep 30 Example Inductions
6 11 Oct 5 Induction Problem, ACL2 Proof-builder
6 12 Oct 7 Ordinals, ACL2 Proof-builder
7 13 Oct 12 Ordinals, General Definitional Principle
7 14 Oct 14 General Induction Principle
8 15 Oct 19 Student Presentation of Project Ideas
8 16 Oct 21 Student Presentation of Project Ideas
9 17 Oct 26 Relations between Recursion and Induction
9 18 Oct 28 ACL2 Arithmetic
10 19 Nov 2 Lemmas about NTH and UPDATE-NTH, ISORT
10 20 Nov 4 Memory-based ISORT functions and proof
11 21 Nov 9 Specifying and Embedding BDDs in the ACL2 Logic
11 22 Nov 11 Proving Correctness of a BDD package
* 12 23 Nov 16 In-class EXAM
12 24 Nov 18 Rewriting and other ACL2 Features
13 25 Nov 23 Example presentations by Instructors
Nov 24 - 27 Thanksgiving Holiday
14 26 Nov 30 Student Presentations (class 3:30 to 5:30)
14 27 Dec 2 Student Presentations (class 3:30 to 5:30)
There will be six or so homework assignments given (primarily) during the first half of the semester. On most weeks, homework will be assigned on Tuesdays and due nine days later (on Thursdays) by class time. In some cases, 16 days will be given for some assignments. No homework will be assigned during the last five weeks of class. The lowest homework grade will be dropped in the computation of the final homework grade. Homework will not be accepted late.
There will be one, in-class (70- to 80-minute) examination. The material on exam will be cumulative. See the above schedule (marked with a * above) for the date(s). There will no final exam. There will be a number of (five to eight) unannounced "pop quizzes". The lowest quiz grade will be dropped in the calculation of your class quizzes score. The examination must be taken at the scheduled time. Quizzes are offered at random times; each quiz will take 10 to 15 minutes.
The main result of this class will be student projects.
The weighting of the grades for the various aspects of the course are:
Component Percentage of Course Grade
Exam: 20%
Quizzes: 20%
Homework: 20%
Project: 40%
The grading for the entire course will be as follows:
Course Score Grade
[90 -- 100] A
[87 -- 90) A-
[85 -- 87) B+
[80 -- 85) B
[77 -- 80) B-
[75 -- 77) C+
[70 -- 75) C
[67 -- 70) C-
[65 -- 67) D+
[60 -- 65) D
[ 0 -- 60) F
Note the interval marks around the course-score column. For example,
a course grade of B will be assigned if your semester grade is greater
than or equal to 80 and less than 85. This also means that a course
grade of at least 67 needs to be achieved for this course to count
toward a UTCS degree.
This class is a fair amount of work, and it is important to keep current. The material in this class is cumulative; it can be hard to catch up if one falls behind. It is very important to keep doing and turning in your homework. Homework grades are our most reliable indicator of how well a student will do in this class. Note, it is important to show up for class, as pop quizzes will be given, and material not reproduced in any particular book or web page may be discussed.
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