This Agda library formalizes the following predicates and relations on dependent session types:

• fair termination of a session type T, namely the property that it is always possible to terminate the protocol T no matter how long it has been carried out;
• fair compliance of a session type R with respect to a session type T, namely the property that any interaction between two processes behaving as R and T can always be extended so as to satisfy the process behaving as R without disrupting the process behaving as T.
• fair subtyping (Padovani 2013, Padovani 2016), a liveness preserving refinement relation for session types. In addition to satisfying the safe substitution principle for session types (Gay Hole 2005), whereby it is safe to use a session endpoint of type T where a session endpoint of type S is expected if T is a subtype of S, it ensures that any process that is fair compliant with T is also fair compliant with S.

The library presents two distinct formalizations of each property: a "semantic" one, given in terms of the labeled transition system of session types, and a "syntactic" one, given as a generalized inference system (Ancona Dagnino Zucca 2017, Dagnino 2019) making use of corules.

The formalization uses a local copy of the library Ciccone Dagnino Zucca 2021 (v1.1). Check release notes for the compatibility with latest Agda and stdlib versions.

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