Prioritise the Best Variation

Abstract

Binary session types guarantee communication safety and session fidelity, but alone they cannot rule out deadlocks arising from the interleaving of di↵erent sessions. In Classical Processes (CP) [53]-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, in Good Variation (GV) [54,39]-a linear concurrent -calculus-deadlock freedom is guaranteed by combining channel creation and thread spawning under the same operation, called fork. In both CP and GV, deadlock freedom is achieved at the expense of expressivity, as the only processes allowed are tree-structured. Dardha and Gay [19] define Priority CP (PCP), which allows cyclic-structured processes and restores deadlock freedom by using priorities, in line with Kobayashi and Padovani [34,44]. Following PCP, we present Priority GV (PGV), a variant of GV which decouples channel creation from thread spawning. Consequently, we type cyclic-structured processes and restore deadlock freedom by using priorities. We show that 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.

Deadlock-free session types in linear Haskell

“…• present a variant of Priority GV [35]-the calculus upon which Priority Sesh is based-with asynchronous communication and session cancellation following Fowler et al [20] and explicit lower bounds on the sequent, rather than lower bounds inferred from the typing environment; and • show that Priority Sesh is related to Priority GV via monadic reflection.…”

“…• in section 2.1, we build a small library of linear or one-shot channels based on MVars [54]; • in section 2.2, we use these one-shot channels to build a small library of session-typed channels [12]; and • in section 2.4, we decorate these session types with priorities to guarantee deadlock-freedom [35].…”

“…These changes preserve subject reduction and progress properties, and give us tighter bounds on priorities. To see why, note that PCP [10] and PGV [35] use the smallest priority in the typing environment as an approximation for the lower bound. Unfortunately, this underestimates the lower bound in the rules T-Var and T-Lam (check fig.…”

“…We briefly revisit the syntax and type system of PGV, but a full discussion of PGV is out of scope for this paper. For a discussion of the synchronous semantics for PGV, and the proofs of subject reduction, progress, and deadlock freedom, please see Kokke and Dardha [35]. For a discussion of the asynchronous semantics and session cancellation, please see Fowler et al [20].…”

“…Recent works by Padovani and Novara [53] and Kokke and Dardha [PGV,35] integrate priorities [32,51] into functional languages. Priorities are natural numbers that abstractly represent the time at which a communication action happens.…”