*Semantics Club 04 05 2001*

# Strategies and universal types

### Abstract

I will give some more detail on the theoretical story behind my
recent Lab Lunch talk. In particular, I will define more precisely
the category of types and strategies I have in mind. I arrived at
this category simply as the Karoubi envelope of a certain
lambda algebra, but it turns out to be essentially the same as
Abramsky's category of games and strategies with no innocence or
well-bracketing constraints. I will also consider the expressive
power of the corresponding programming languages, and the
implications of this model for programming language semantics and
logic.

I will also sketch some ideas not mentioned at Lab Lunch: the
use of this category for modelling objects with persistent internal
state (as in object-oriented languages). It appears that the
CCC of strategies is equipped with a natural "state monad",
giving rise to an SMC category of algebras which seems to be
suitable for modelling object-oriented styles of computation.

All this stuff is work in progress and as yet poorly understood.