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Li-yao Xia (Nov 30 2021 at 18:35):Game semantics papers surrounding the original full abstraction for PCF result like to refer to "Abramsky's semantic cube", where each dimension is an impure feature one can add to PCF, and each corresponds exactly to a relaxation of the fully abstract game semantics for PCF. Is there a good citation for an overview of that idea/programme?
There is an introduction to game semantics by Abramsky that mentions two dimensions (control and state), while suggesting a third might be nondeterminism. But a full account of this "cube" has been elusive.
Is it a 3d cube like Barendregt's lambda cube, or is this idea meant in a more open ended fashion (I have a hard time believing control+state+nondeterminism are comprehensive in any way)?
Alex Gryzlov (Nov 30 2021 at 18:55):Try
https://arxiv.org/abs/1908.04291 Ghica, [2019] "The far side of the cube"
and
https://arxiv.org/abs/2103.15453 Castellan, Clairambault, [2021] "Disentangling Parallelism and Interference in Game Semantics"
Alex Gryzlov (Nov 30 2021 at 18:56):Both of them suggest that the base of the idea is actually a square, and there are several ways to extend it into a hypercube but many are incompatible.