**Organisers**: S Abramsky (*Imperial College, London*), G Kahn (*INRIA, Sophia-Antipolis*), J C Mitchell (*Stanford*), A M Pitts (*Cambridge*)

### Semantics of Computation Seminar

Wednesday 29 November, 11am

#### The Functorial Type System

C. Barry Jay (Sydney UT and Newton Institute)

The functorial type system represents functors (and natural transformations) directly as types, rather than as parametrised types, which suggests new posibilities for functional programming. In particular, mapping for functors is represented by a single, type-free algorithm whose type is polymorphic with respect to functors. Such shape polymorphism is a powerful new extension of parametric polymorphism. The conceptual advance derived from working directly with functors may open up new possibilities.