Non-angelic concurrent game semantics

The hiding operation, crucial in the construction of categories of games and strategies and hence the compositional aspect of game semantics, has a tendency, as a side effect, to remove branches of computation not leading to observable results. Accordingly, games models of programming languages are usually biased towards angelic non-determinism, where branches leading to e.g. divergence are forgotten. We present here new categories of games, which do not suffer from this bias. In our first category, we achieve this by avoiding hiding altogether; instead morphisms are uncovered strategies (with neutral/invisible events) up to weak bisimulation. Then, we show that by hiding only certain events dubbed inessential we can consider strategies up to isomorphism, and still get a category – this partial hiding remains sound up to weak bisimulation, so we get a concrete representations of morphisms (as in standard concurrent games) while avoiding the angelic bias. We give a semantics for Affine Idealized Parallel Algol which is adequate for both may and must equivalence within the model.