The eighth meeting of the Wessex Theory Seminar took place on Tu= esday 13th July 2010 at the University of Bath. Talks were held in room 1E2= .4 from 2pm.

=2014.00 Martin Hyland: Varieties of Algebraic Theories

=2014.45 Giuseppe Rosolini: Rem= arks on Realizability (slides)

=2015.30 Coffee Break

=2016.00 Pawel Sobocinski: Rep= resenting Petri-Net Interactions (slides<= /a>)

=2016.45 Guy McCusker: Graph-sty= le models of programming languages

=2017.30 Close.

=20=20

**Remarks on Realizability** (slides<=
/a>)

The full internal category on modest sets in the effective topos is suff= iciently complete to provide an elementary model of polymorphism, i.e. one = where type abstraction is interpreted as products over the collection of al= l types provided the semanticist is prepared to use intuitionistic set theo= ry in place of standard set theory. But that internal category is not compl= ete.

=20Thus Peter Freyd's remark that an internal complete category of a (Groth= endieck) topos is posetal could still hold for any topos - without the pare= nthesized assumption.

=20We show that the 1-category reflection of the 2-category PGRPD of the ef= fective topos consisting of those internal PER-enriched groupoids with a pr= ojective object of objects, with enriched functors and natural transformati= ons, gives a topos with an internal non-posetal category which is complete.= Since it is complete it provides, in particular, another elementary model = of polymorphism, and we believe that that is also parametric.

=20=20

**Graph-style models of programming languages**

Scott's Pw graph model is one of the simplest and oldest models of the l= ambda-calculus. Recently, some similar-looking models have emerged which ar= e capable of handling more sophisticated features, including imperative con= structs and fresh name generation. This talk gives an overview of these mod= els and their properties, and investigates what algebraic structure is need= ed to make them work.

=20=20

**Representing Petri-Net Interactions** (slides)

We introduce a novel compositional algebra of Petri nets, as well as a s= tateful extension of the calculus of connectors. These two formalisms are s= hown to have the same expressive power. A paper is available from Pawel's home page

=20From Bath:

=20- =20
- Ana C. Calderon =20
- Martin Churchill =20
- Guy McCusker =20
- John Power =20

From Cambridge:

=20- =20
- Nathan Bowler =20
- Martin Hyland =20

From Southampton:

=20- =20
- Julian Rathke =20
- Pawel Sobocinski =20

From Swansea:

=20- =20
- Peter Mosses =20

From Genoa (Italy):

=20- =20
- Giuseppe Rosolini =20

From Kent:

=20- =20
- Eerke Boiten =20