A methodology for programming with concurrency: An informal presentation

AbstractIn this methodology, programming problems which can be specified by an input/output assertion pair are solved in two steps: 1.(1) Refinement of a correct program that can be implemented sequentially.2.(2) Declaration of program properties, so-called semantic relations, that allow relaxations in the sequencing of the refinement's operations (e.g., concurrency).Formal properties of refinements comprise semantics (input/output characteristics) and (sequential) execution time. Declarations of semantic relations preserve the semantics but may improve the execution time of a refinement. The consequences are: 1.(a) The concurrency in a program is deduced from its formal semantics. Semantic correctness is not based on concurrency but precedes it.2.(b) Concurrency is a property not of programs but of executions. Programs do not contain concurrent commands, only suggestions (declarations) of concurrency.3.(c) The declaration of too much concurrency is impossible. Programs do not contain primitives for synchronization or mutual exclusion.4.(d) Proofs of parallel correctness are stepwise without auxiliary variables.5.(e) Freedom from deadlock and starvation is implicit without recourse to an authority outside the program, e.g., a fair scheduler

Formal Derivation of Strongly Correct Concurrent Programs

A method is described for deriving concurrent programs which are consistent with the problem specifications and free from deadlock and from starvation. The programs considered are expressed by nondeterministic repetitive selections of pairs of synchronizing conditions and subsequent actions. An iterative, convergent calculus is developed for synthesizing the invariant and synchronizing conditions which guarantee strong correctness. These conditions are constructed as limits of recurrences associated with the specifications and the actions. An alternative method for deriving starvationfree programs by use of auxiliary variables is also given. The applicability of the techniques presented is discussed through various examples; their use for verification purposes is illustrated as well