Monday, Wednesday, Friday: 9:30 - 10:20
Grissom Hall 103
Office Hours: Monday, Wednesday: 12pm - 1pm
Pedro Da Costa Abreu
Wed. 11AM - 12pm, HAAS G072
Srinivasa Arun Yeragudipati
Tues. 2PM - 3PM, HAAS 143
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
languages centers on more universal, foundational
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:
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:
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:
Automated Program Verification