Domain Theory 2024

These are resources from a lecture series run by Professor Liam O’Connor in Spring 2024.

Content

1. First Steps to Scott Domains.
   Denotational Semantics. Recursion. Flat Domains. Pointed Partial Orders. Monotonicity.
   Notes Recordings

2. Recursively Defined Programs.
   Recursion and Fixed Points. Chains and Directed Sets. Lubs and Cpos. Continuity. Fixed Point Theorems.
   Notes Recordings

3. Constructions on Cpos.
   Products, functions. Universal properties. The Category CPO. Functors.
   Notes Recordings

4. Constructions on Cpos Continued
   Functors: functions, and sums. Strictness.
   Same notes as previous lecture Recordings

5. PCF and Compactness
   Typed λ-calculus. Finite Approximations. Compactness.
   Notes Recordings

6. Scott Domains
   Algebraicity. Closure Properties. Representation Theorem. Consistent Completeness.
   Same notes as previous lecture Recordings

7. Recursively Defined Domains
   Fixed Points for Domain Equations. Colimits. Cocontinuous Functors. Generalising the Fixed Point Theorem. Untyped λ-calculus.
   Notes Recordings

8. Non-determinism
   Monads. Powerdomains. Smyth, Hoare, and Plotkin’s Constructions. Ideal Completions. Egli-Milner Ordering.
   Notes Recordings