I now have the compact closed category of open games that I wanted for years... but at what cost? It's built on computable functions, and game theory over computable functions turns out to be pretty weirdpic.twitter.com/ZWcb1o9Bnh
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You're getting fairly close to Dusko Pavlovic's research programme here, to put all of computer security on a better foundation by rebuilding game theory (*not* game semantics) on top of computability
I'm trying to build formally verified decentralized applications. To keep the entire thing tractable, I'm envisioning a tower of implementations (for that see categorical sketch in http://j.mp/FarePhD ). Cryptography will presumably be treated differently at various layers.
Would some kind of substructural types, epistemic logic, or nonstandard analysis, provide a framework that simplifies the handling of cryptography? What about commutative cryptography and other non-free variants of primitives with meaningful equations that imply nontrivial leaks?
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