Streamlining progress-based derivations of concurrent programs

Abstract

Abstract. The logic of Owicki and Gries is a well known logic for verifying safety properties of concurrent programs. Using this logic, Feijen and van Gasteren describe a method for deriving concurrent programs based on safety. In this work, we explore derivation techniques of concurrent programs using progress-based reasoning. We use a framework that combines the safety logic of Owicki and Gries, and the progress logic of UNITY. Our contributions improve the applicability of our earlier techniques by reducing the calculational overhead in the formal proofs and derivations. To demonstrate the effectiveness of our techniques, a derivation of Dekker's mutual exclusion algorithm is presented. This derivation leads to the discovery of some new and simpler variations of this famous algorithm.

Deriving real-time action systems with multiple time bands using algebraic reasoning

“…However, unlike Jones, who assumes rely conditions are interleaved with those of the component under consideration, we assume rely conditions are interval predicates that are assumed to hold over the interval in which an action executes. Our derivation method uses enforced properties [15,17], which are formulae that restrict the behaviour of the system under development to those that satisfy the formulae. We first present enforced properties on actions, which allow finer-grained control over the execution of an action system.…”

“…Furthermore, execution of b → y := e ensures each output V not in y is stable and that each variable in V is right stable. By (15), the behaviour of b → F : [p] holds if it is possible for b to hold in some apparent state, followed by an interval in which the framed interval predicate F : [p] V holds. We leave out the guard b if b is true, i.e., we write S for true → S .…”

“…This paper adds to our series of papers on program derivation [16,17,19,20,24,25]. Of these, [16,24,25] consider concurrent program derivation and [17,19,20] consider real-time programs.…”

“…The derivation method builds on our method of enforced properties [15,16,17,19], which uses the verify-while-develop paradigm to incrementally obtain program code from the underlying specifications. Our framework incorporates a logic of time bands [9,10,49], which allows one to formalise properties at different time granularities and define relationships between these properties.…”

“…Of these, [16,24,25] consider concurrent program derivation and [17,19,20] consider real-time programs. Our papers [17,19,20] increasingly consider more realistic assumptions in concurrent real-time systems and the most advanced of these [19] allows one to consider sampling issues and components that operate over multiple time granularities.…”