Domain theory provides a mathematical foundation for the denotational
semantics of programming languages. It offers mathematical structures
for representing partial information, recursive definitions, and
potentially non-terminating computations.
The course begins with the order-theoretic foundations of domain theory,
including partially ordered sets, complete lattices, directed-complete
partial orders (dcpos), and directed-join-preserving functions. We then
study the Scott topology, continuous and algebraic domains, fixed-point
theory, and recursive domain equations.
In the final part of the course, we turn to applications in computer
science and explore how domain theory provides denotational models for
the lambda calculus and related functional programming languages.
Course Contents
- Partially ordered sets and complete lattices
- Directed-complete partial orders (dcpos)
- Directed-join-preserving functions
- The Scott topology
- Continuous and algebraic domains
- Fixed-point theory and recursive definitions
- Recursive domain equations
- Domain-theoretic models of the lambda calculus and denotational semantics