Requirement patterns in deductive verification of poST programs

Process-oriented programming is one of the approaches to developing control software. A process-oriented program is defined as a sequence of processes. Each process is represented by a set of named states containing program code that define the logic of the process's behavior. Program execution is sequential execution of each of these processes in their current states at every iteration of the control cycle. Processes can interact through changing each other's states and shared variables.
The paper expands a method for classifying temporal requirements for process-oriented programs in order to simplify and automate the deductive verification of such programs. The method consists of the following steps. At the first step, the requirements are formalized in a specialized language DV-TRL, a variant of typed first-order predicate logic with a set of interpreted types and predicate and functional symbols, that reflect specific concepts of control systems in a process-oriented paradigm. At the second step, the formalized requirements are divided into classes, each of which is defined by a pattern — a parametric formula of the DV-TRL language. The correctness conditions generated for process-oriented programs regarding requirements satisfying the same pattern have the same proof scheme. At the third step, appropriate proof schemes are developed. In our paper, we first give a brief introduction to the poST language, a process-oriented extension to the ST language of the IEC 61131-3 standard. Next, the DV-TRL language is defined. We also provide a collection of natural language requirements for several control systems. Then we define patterns that fully cover all the requirements of this collection. For each of these patterns we give an example of a formalized requirement from the collection and describe a scheme for proving the correctness conditions for this pattern. Statistics on the distribution of requirements from the collection across patterns reveals the most popular patterns. We also analyzed related works.