Deterministic concurrency: A clock-synchronised shared memory approach

Abstract

Synchronous Programming (SP) is a universal computational principle that provides deterministic concurrency. The same input sequence with the same timing always results in the same externally observable output sequence, even if the internal behaviour generates uncertainty in the scheduling of concurrent memory accesses. Consequently, SP languages have always been strongly founded on mathematical semantics that support formal program analysis. So far, however, communication has been constrained to a set of primitive clock-synchronised shared memory (csm) data types, such as data-flow registers, streams and signals with restricted read and write accesses that limit modularity and behavioural abstractions. This paper proposes an extension to the SP theory which retains the advantages of deterministic concurrency, but allows communication to occur at higher levels of abstraction than currently supported by SP data types. Our approach is as follows. To avoid data races, each csm type publishes a policy interface for specifying the admissibility and precedence of its access methods. Each instance of the csm type has to be policy-coherent, meaning it must behave deterministically under its own policy—a natural requirement if the goal is to build deterministic systems that use these types. In a policy-constructive system, all access methods can be scheduled in a policy-conformant way for all the types without deadlocking. In this paper, we show that a policy-constructive program exhibits deterministic concurrency in the sense that all policy-conformant interleavings produce the same input-output behaviour. Policies are conservative and support the csm types existing in current SP languages. Technically, we introduce a kernel SP language that uses arbitrary policy-driven csm types. A big-step fixed-point semantics for this language is developed for which we prove determinism and termination of constructive programs.