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

First Steps to Scott Domains.
Denotational Semantics. Recursion. Flat Domains. Pointed Partial Orders. Monotonicity.
Notes Recordings 
Recursively Defined Programs.
Recursion and Fixed Points. Chains and Directed Sets. Lubs and Cpos. Continuity. Fixed Point Theorems.
Notes Recordings 
Constructions on Cpos.
Products, functions. Universal properties. The Category CPO. Functors.
Notes Recordings 
Constructions on Cpos Continued
Functors: functions, and sums. Strictness.
Same notes as previous lecture Recordings 
PCF and Compactness
Typed λcalculus. Finite Approximations. Compactness.
Notes Recordings 
Scott Domains
Algebraicity. Closure Properties. Representation Theorem. Consistent Completeness.
Same notes as previous lecture Recordings 
Recursively Defined Domains
Fixed Points for Domain Equations. Colimits. Cocontinuous Functors. Generalising the Fixed Point Theorem. Untyped λcalculus.
Notes Recordings 
Nondeterminism
Monads. Powerdomains. Smyth, Hoare, and Plotkin’s Constructions. Ideal Completions. EgliMilner Ordering.
Notes Recordings