Entry requirements

120 credit points and 90 credit points Mathematics and Computer Science

Learning outcomes

In order to pass the course (grade 3) the student should be able to

• use lattice theoretical concepts:
• describe various fixed point theorems and their relation to recursive procedures;
• describe various categories of domains and give an account of common domain constructions such as function space, product, and sum within various categories;
• give an account of the interpretation of simple typed lambda calculus in Cartesian closed categories;
• give an account of the connection between computability and continuity;
• reason in an abstract category with concepts such as product, exponent and monads;
• give an account of data structures as solutions of domain equations or as initial or final algebras;
• solve domain equations and to give a model for untyped lambda calculus;
• give an account of PCF and the relation between its operational and denotational semantics.

Content

Fixed points. Various domain concepts: cpo, algebraic cpo, Scott-Ershov domains. Domain constructions, domain equations and the theory for their solutions. Briefly about topological concepts related to domain theory. Alternative ways to present domains: neighbourhood systems, information systems. Briefly about computable domains, power domains, universal domains and formal topological spaces.

Category theoretical concepts: Adjoints, initial and final algebras, monads, monoidal categories and functor categories.

Models of lambda calculus. Operational and denotational semantics of PCF. Optionally, some elements about game semantics. Semantics for quantum programming languages.

Instruction

Lectures and problem solving sessions.

Assessment

Written at the end of the course combined with assignments given during the course.