University of Birmingham > Talks@bham > Theoretical computer science seminar > Inductive-inductive definitions: axiomatisation and categorical semantics

Inductive-inductive definitions: axiomatisation and categorical semantics

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  • UserFredrik Nordvall Forsberg, Swansea University
  • ClockFriday 28 October 2011, 16:00-17:00
  • HouseLG52 Learning Centre.

If you have a question about this talk, please contact Paul Levy.

Induction is a powerful and important principle of definition, especially so in dependent type theory and constructive mathematics. Induction-induction (named in reference to Dybjer and Setzer’s induction-recursion) is an induction principle which gives the possibility to simultaneously introduce a set A together with an A-indexed set B (i.e. for every a : A, B(a) is a set). Both A and B are inductively defined, and the constructors for A can refer to B and vice versa. In addition, the constructors for B can also refer to the constructors for A.

In this talk, we consider some examples of inductive-inductive definitions. We then sketch a finite axiomatisation of the theory, and show how it can be given a categorical semantics similar to the initial algebra semantics of ordinary inductive data types.

This talk is part of the Theoretical computer science seminar series.

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