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.
Content
- 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)
- 6th March. Recursively Defined Programs.
Recursion and Fixed Points. Chains and Directed Sets. Lubs and Cpos. Continuity. Fixed Point Theorems.
Notes Recording
- 11th March (in AT2.04). Constructions on Cpos.
Products, functions. Universal properties. The Category CPO. Functors.
Notes Recording
- 13th March. Constructions on Cpos Continued.
Functors: functions, and sums. Strictness.
Same notes as previous lecture Recording
- 18th March. PCF and Compactness.
Typed λ-calculus. Finite Approximations. Compactness.
Notes Recording
- 20th March. Scott Domains.
Algebraicity. Closure Properties. Representation Theorem. Consistent Completeness.
Same notes as previous lecture Recording
- 25th March. Recursively Defined Domains.
Fixed Points for Domain Equations. Colimits. Cocontinuous Functors. Generalising the Fixed Point Theorem. Untyped λ-calculus.
Notes Recording
- 27th March. Non-determinism.
Monads. Powerdomains. Smyth, Hoare, and Plotkin's Constructions. Ideal Completions. Egli-Milner Ordering.
Notes Recording