# 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