Domain Theory 2024

Where and When

Mondays and Wednesdays at 17:30, for about an hour. We are in Appleton Tower 2.11, except for Monday 11th of March, where we will be in AT2.04 instead.


  1. 4th March. First Steps to Scott Domains.
    Denotational Semantics. Recursion. Flat Domains. Pointed Partial Orders. Monotonicity.
    Notes Recording (apologies for the lack of video, will be rectified in future weeks)
  2. 6th March. Recursively Defined Programs.
    Recursion and Fixed Points. Chains and Directed Sets. Lubs and Cpos. Continuity. Fixed Point Theorems.
    Notes Recording
  3. 11th March (in AT2.04). Constructions on Cpos.
    Products, functions. Universal properties. The Category CPO. Functors.
    Notes Recording
  4. 13th March. Constructions on Cpos Continued.
    Functors: functions, and sums. Strictness.
    Same notes as previous lecture Recording
  5. 18th March. PCF and Compactness.
    Typed λ-calculus. Finite Approximations. Compactness.
    Notes Recording
  6. 20th March. Scott Domains.
    Algebraicity. Closure Properties. Representation Theorem. Consistent Completeness.
    Same notes as previous lecture Recording
  7. 25th March. Recursively Defined Domains.
    Fixed Points for Domain Equations. Colimits. Cocontinuous Functors. Generalising the Fixed Point Theorem. Untyped λ-calculus.
    Notes Recording
  8. 27th March. Non-determinism.
    Monads. Powerdomains. Smyth, Hoare, and Plotkin's Constructions. Ideal Completions. Egli-Milner Ordering.
    Notes Recording