On formal reasoning on the semantics of PLC using Coq

Programmable Logic Controllers (PLC) and its programming standard IEC 61131-3 are widely used in embedded systems for the industrial automa-tion domain. We propose a framework for the formal treatment of PLC based on the IEC 61131-3 standard. A PLC system description typically combines code written in different languages that are defined in IEC 61131-3. For the top-level specification we regard the Sequential Function Charts (SFC) language, a graphical high-level language that allows to describe the main control-flow of the system. In addition to this, we describe the Instruction List (IL) language – an assembly like language – and two other graphical languages: Ladder Diagrams (LD) and Function Block Diagrams (FBD). IL, LD, and FBD are used to describe more low level structures of a PLC. We formalize the semantics of these languages and describe and prove relations between them. Formalization and associated proofs are carried out using the proof assistant Coq. In addition to this, we present work on a tool for automatically generating SFC representations from a graphical description – the IL and LD languages can be handled in Coq directly – and its usage for verification purposes. We sketch possible usages of our formal framework, and present an example application for a PLC in a project demonstrator and prove safety properties.