Pict correctness revisited

Abstract

machine Fairness Pict a b s t r a c tThe Pict programming language is an implementation of the π -calculus in which executions of π-calculus terms are specified via an abstract machine. An important property of any concurrent programming language implementation is the fair execution of threads. After defining fairness for the π-calculus, we show that Pict abstract machine executions implement fair π-calculus executions. We also give new proofs of soundness and liveness for the Pict abstract machine.

Fair termination of binary sessions

“…But while defining fair runs for session types is doable with little effort (cf. Definition 3.17), the definition of fair runs for the 𝜋-calculus is much more involved [Bidinger and Compagnoni 2009;Cacciagrano et al 2006Cacciagrano et al , 2009Kobayashi 2002]. Besides, none of the available definitions is directly applicable to our language since they are all based on choiceless versions of the 𝜋-calculus with replication instead of recursion.…”

A Hybrid Type System for Lock-Freedom of Mobile Processes

“…A sequence of transitions is strongly fair if, intuitively, any τ -action that is enabled infinitely often will eventually succeed (see [3,11] for a formal definition of strong fairness in the π-calculus). See Appendix A.2 for a note on the difference between weak and strong lockfreedom.…”

“…To define the partial confluence, we assume that each prefix is uniquely labeled (as in [3]), and extend the transition relation to η,S −→ where S is the set of the labels of the prefixes involved in the transition: see [15]. Robust confluence indicates partial confluence after any sequence of transition that conforms to the base type system ST.…”