FACT: A Domain-Specific Language Based on a Functional Algebra for Continuous Time Modeling

Hybrid and cyber-physical systems create synergy by combining digital modules with analog implementations of signal processing operations typically implemented in the digital domain. We propose a domain-specific language (DSL), so-called FACT – Functional Algebra for Continuous Time, based on the algebraic properties of the General Purpose Analog Computer (GPAC), a theoretical model of computation recently updated as a continuous time equivalent of the Turing Machine. We lift the GPAC to a continuous time dynamics inside a black box semantics for understanding hybrid systems, which allows us to redefine continuous time semantics inspired by the functional reactive programming style. FACT leverages the type class mechanism from the Haskell functional programming language to implement operators that capture the proposed continuous time semantics. An speed-optimized working open-source implementation in the Haskell functional language is provided and was used to demonstrate how the language supports modeling and simulation.