Non-alternating innocence in asynchronous games

The notion of innocent strategy was introduced by Hyland and Ong in
order to capture the interactive behaviour of lambda-terms and PCF
programs. An innocent strategy is defined as an alternating strategy
with partial memory, in which the strategy plays according to its
view.  Extending the definition to non-alternating strategies seems
problematic because the definition of views is based on the hypothesis
that Player and Opponent alternate during the interaction. In this
talk, I will take advantage of the diagrammatic reformulation of
innocence developed by Melliès in earlier work on asynchronous games,
in order to extend the definition of innocence to non-alternating
games. I will explain how to construct a *-autonomous category with
asynchronous games as objects, and innocent and non-alternating
strategies as morphisms - and how to recover the usual category of
innocent and alternating strategies as a subcategory. I will conclude
my talk by indicating briefly how first and second order linear logic
is interpreted in this framework.