Types and Programming Languages Course ID 15814 Doctoral Breadth Course: Programming Languages - (*) Classes marked with "*" (star) are appropriate for any CSD doctoral or 5th year master's student. Description The course studies the theory of type systems, with a focus on applications of type systems to practical programming languages. The emphasis is on the mathematical foundations underlying type systems and operational semantics. The course includes a broad survey of the components that make up existing type systems, and also teaches the methodology behind the design of new type systems. Key Topics Static and dynamic semantics Preservation and progress Hypothetical judgments and substitution Propositions as types, natural deduction, sequent calculus The untyped lambda-calculus Functions, eager and lazy products, sums Recursive types Parametric polymorphism, data abstraction, existential types K machine, S machine, substructural operational semantics Shared-memory concurrency, session types Required Background Knowledge This is an introductory graduate course with no formal prerequisites, but an exposure to various forms of mathematical induction will be helpful. Course Relevance Enterprising undergraduates and masters students are welcome to attend this course. If you have already taken 15-312 Principles of Programming Languages at CMU, please check with the instructor if this course is suitable for you. Course Goals After taking this course, students will be able to define programming languages via their type system and operational semantics draw from a rich set of type constructors to capture essential properties of computational phenomena state and prove the preservation and progress theorems or exhibit counterexamples recognize and avoid common fallacies in proofs and language design write small programs to illustrate the expressive power and limitations of a variety of type constructors state and prove properties of individual programs based on their semantics or exhibit counterexamples critique programming languages and language constructs based on the mathematical properties they may or may not satisfy appreciate the deep philosophical and mathematical underpinnings of programming language design
