Theory of Reactive Processes Sample Clauses
Theory of Reactive Processes. Here, we use our trace algebra to provide a generalised theory of reactive processes. We prove the key laws of reactive processes, thus demonstrating the conservative nature of our theory. Many of the properties here have been previously proved [9], but we restate and prove many of them due to our weakening of the trace model and some small differences. Another novelty is that all these theorems have been mechanised in our Isabelle/UTP repository. Following [29, 9] we define the theory in terms of two pairs of observational variables: wait, waitj : B – describe when the previous or current process, respectively, is in an intermediate state; tr, trj : – the trace that occurred prior to and after execution of the current process in terms of a trace algebra (T , ^, s). Our theory does not contain refusal variables ref , ref j, as these are not always necessary to describe reactive processes [51]. We describe three healthiness conditions namely R1, R2c, and R3. R1 and R3 are already presented in [29]; for their R2 we have a different formulation, which we call R2c.
Theory of Reactive Processes. 20 3.4 Reactive Relations and Conditions . . . . . . . . . . . . . . . . . . . . . 23 4 Hybrid Relational Calculus 26 4.1 Core Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2 Derivatives and Ordinary Differential Equations . . . . . . . . . . . . . . 29 4.3 Perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 7 Modelica Semantics 42 7.1 Semantics Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 7.2 Core Language Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . 45 7.3 Modelica Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 7.4 Block Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 7.5 Model Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 A UTP Theory of Generalised Reactive Designs 66 A.1 Healthiness Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 A.2 Unifying Reactive Languages . . . . . . . . . . . . . . . . . . . . . . . . . 71 A.3 Linking with Imperative Specifications . . . . . . . . . . . . . . . . . . . 73 A.4 Recursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 1 Introduction INTO-CPS multi-models are composed of models whose foundations lie in a variety of modelling notations, each of which has its own unique syntax, semantics, and underlying paradigmatic concepts, such as discrete or continuous time. The purpose of a multi-model is assign behaviour to a Cyber-Physical System (CPS) by composing the behaviours of the constituent models. Thus, in order to provide an integrated tool chain for trustwor- thy CPS development, there is a necessity for unification of these underlying semantic models to allow consistent integration of heterogeneous system components. This will then allow us to substantiate statements made about the multi-model with respect to the underlying mathematical core. Hoare and He’s Unifying Theories of Programming [29] (UTP) has been designed as a framework in which the integration of languages, through the common semantic domain of the alphabetised relational calculus, can be achieved. In this deliverable we leverage the UTP to provide the foundations for continuous-time modelling in the INTO-CPS tool chain. Modelling of continuous dynamical systems in the INTO-CPS tool chain is provided by the Modelica and 20-sim ...