Type theory

Education facts

Code: MM8036

The course provides an introduction to type theory with simple and dependent types, how it can be used to represent logical systems and proofs, and how proofs give rise to computable functions. The final part of the course covers applications of type theory. The following topics are covered: Type theory: lambda calculus, contexts, forms of judgement, simple types, inductive types. Operational semantics: confluence and normalization. The Curry-Howard isomorphism. Martin-Löf type theory: dependent types, induction and elimination rules, identity types, universes. The Brouwer-Heyting-Kolmogorov interpretation of logic. Meaning explanations. Semantics of dependent types. Explicit substitution. Category theoretical models. One or more of the following areas of application of type theory are covered: homotopy theory, models for (constructive) set theory and proof assistants.

Entry requirements

Admission to the course requires knowledge equivalent to at least 90 credits in mathematics, including the course Logic 7.5 credits (MM7008). English B/English 6 or equivalent.

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Type theory

  Stockholm University

  Stockholm

  Start date: 18 January 2027

  End date: 6 June 2027

  Pace of study: 25 %