Prioritise the Best Variation

Session types are used to specify and verify communication protocols and have been integrated in the {\pi}-calculus and a linear concurrent {\lambda}-calculus -- Good Variation (GV), among others. Session type systems guarantee communication safety and session fidelity, but cannot guarantee deadlock freedom and avoid bad interleaving of different sessions. In Classical Processes (CP), a process calculus based on classical linear logic, deadlock freedom is guaranteed by combining channel creation and parallel composition under the same logical cut rule. Similarly, deadlock freedom in GV is guaranteed by combining channel creation and thread spawning under the same operation, called fork. In both GV and CP, deadlock freedom is achieved at the expense of expressivity as the only communication structures allowed are trees. Dardha and Gay define Priority CP (PCP), which allows for cyclic structures and restores deadlock freedom by adding priorities to types, in line with Kobayashi and Padovani's work. Following PCP, we present Priority GV (PGV), a variant of GV which decouples channel creation from thread spawning, and restores deadlock freedom by adding priorities. PGV has strong ties to linear logic and solves several problems in the original GV. We show our type system is sound by proving subject reduction and progress. We define an encoding from PCP to PGV and prove that the encoding preserves typing and is sound and complete with respect to the operational semantics.