Designing a semantic model for a wide-spectrum language with concurrency

Abstract

A wide-spectrum language integrates specification constructs into a programming language in a manner that treats a specification command just like any other command. The primary contribution of this paper is a semantic model for a wide-spectrum language that supports concurrency and a refinement calculus. A distinguishing feature of the language is that steps of the environment are modelled explicitly, alongside steps of the program. From these two types of steps a rich set of specification commands can be constructed, based on operators for nondeterministic choice, and sequential and parallel composition. We also introduce a novel operator, weak conjunction , which is used extensively to conjoin separate aspects of specifications, allowing us to take a separation-of-concerns approach to subsequent reasoning. We provide a denotational semantics for the language based on traces, which may be terminating, aborting, infeasible, or infinite. To demonstrate the generality and unifying strength of the language, we use it to express a range of concepts from the concurrency literature, including: a refinement theory for rely/guarantee reasoning; an abstract specification of local variables in a concurrent context; specification of an abstract, linearisable data structure; a partial encoding of temporal logic; and defining the relationships between notions of nonblocking programs. The novelty of the paper is that these diverse concepts build on the same theory. In particular, the rely concept from Jones’ rely/guarantee framework, and a stronger demand concept that restricts the environment, are reused across the different domains to express assumptions about the environment. The language and model form an instance of an abstract concurrent program algebra, and this facilitates reasoning about properties of the model at a high level of abstraction.

Encoding Fairness in a Synchronous Concurrent Program Algebra

“…The first point is important for devising a compositional approach to reasoning about the fairness properties of concurrent systems in terms of the fairness properties of their components. The second point allows us to utilise the synchronous concurrent refinement algebra [3,7,8] (which has similarities to Milner's SCCS [14,13]) to encode fairness in an existing theory with no built-in fair-parallel operator. The third point shows that no expressive power is lost compared to starting with a fair-parallel operator, in fact, there is a gain in expressiveness as one can define a parallel composition which imposes fairness on only one of its components: ((c ⋓ fair) skip) d.…”

“…The command term allows only a finite number of program steps but does not rule out infinite pre-emption by its environment. It is defined as follows [6,3], recalling that α = π ⊓ ǫ. term = α ⋆ ǫ ω…”

Some Challenges of Specifying Concurrent Program Components

“…with qu do (guar true) ⋓ qu prefixof qu ′ ⋓ qu: qu ′ = qu ⌢ [v] od = as (guar true) requires no guarantee and q 1 ⋓ x: q 2 = x: q 1 ∧ q 2 with qu do qu: qu prefixof qu…”

“…is introduced, in which the command term only allows any terminating behaviour and for a temporal logic formula t, the command encode t allows just those traces that satisfy t. 2 If the temporal logic formula t holds, terminate t must terminate, but if t does not hold termination is not required, but is allowed. Neither of the specifications of write and read in Fig.…”

“…Such a command can be straightforwardly defined in the semantics for rely/guarantee concurrency presented in[2].…”