Abstract
Since the discovery of fully abstract models of PCF in the early 1990s, game semantics has expanded to a wide range of programming paradigms, covering effects like state, control, general references, non-determinism, probability and concurrency. Those models revealed an interesting phenomenon referred to as Abramsky’s cube: starting from the PCF model and relaxing each of its combinatorial conditions, one was led to capture a corresponding impure effect. In this paper we initiate the construction of an analogous cube for nominal games, a strand of game semantics developed in the last ten years that incorporates names as semantic atoms and captures generative effects without using “bad-object” constructors. In particular, we examine the stateful axis of the cube: starting from games for higher-order references we move to full ground references, where strategies respect visibility, and from there to purely functional behaviour and innocent strategies.
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Murawski, A.S., Tzevelekos, N. (2013). Towards Nominal Abramsky. In: Coecke, B., Ong, L., Panangaden, P. (eds) Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Lecture Notes in Computer Science, vol 7860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38164-5_17
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DOI: https://doi.org/10.1007/978-3-642-38164-5_17
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