Reactive Processes Sample Clauses

Reactive Processes. Xxx Xxxxxxxx (York). An introduction to a nondeterministic, sequential, reactive programming language. As well as giving many examples of its use, there was also an introduction to CSP tools, with an emphasis on refinement checking with the ProB animator and model checker.

Reactive Processes. 11 2.4 Isabelle/UTP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Reactive Processes. ‌ The theory of reactive processes [29, 9] unifies the semantics of different reactive lan- guages. The two main goals of reactive processes are to (1) embed traces into the re- lational calculus, which is achieved through R1 and R2, and (2) introduce intermediate observations which is acheived through R3. In addition to ok and okj, the theory has three pairs of observational variables wait, waitj : B that determine whether a process (or its predecessor) is waiting for interaction with its environment or else has terminated; tr, trj : seq Event that describes the trace before and after the process’ execution; and ref , ref j : P Event that describe the events being refused during an intermediate state, as required by the failures model of CSP [28]. Our version of reactive processes removes the ref and ref j variables to allow extension to behavioural semantic models other than failures. Moreover, we add st, stj : Σ to explicitly model state as suggested by [5], where Σ is a suitable record type. In our previous work [18] we have shown how the UTP theory of reactive processes can be generalised by characterising the trace model with an abstract algebra, called a “trace algebra”. A T trace algebra ( , ^, s) is a form of cancellative monoid that axiomatises operators for ≤ − trace concatenation (x ^ y), trace prefix (x y), and trace difference (x y). The trace algebra will be discussed in more detail in Section 3. T From these algebraic foundations we have reconstructed the complete theory of reactive processes, including its healthiness conditions and associated laws, in particular those for sequential and parallel composition. We thus generalise the type of tr and trj to be an instance of a suitable trace algebra , and recreate the three reactive healthiness conditions, with some modifications. R1(P) ¾ P ∧ tr ≤ trj R2c(P) ¾ P[(), tt /tr, tr R3h(P) ¾ IIR wait IIR ¾ tt ¾ (trj − tr ) Rs ¾ R1 ◦ R2c ◦ R3 Definition 2.4 (Stateful Reactive Healthiness Conditions). a d j] tr ≤ trj P P ((∃ sat • II)da wait d II) a ok d R1(true) h − ≤ − R1 states that tr is monotonically increasing; processes are not permitted to undo past events. R2c is a version of R2, created to overcome an issue with definedness of sequence difference [18], but semantically equivalent in the window of R1. It states that a process must be history independent: the only part of the trace it may constrain is trj tr , that is, the portion since the previous observation tr . Specifically, if the histor...