Contract-based design is a method to facilitate modular design of systems. While there has been substantial progress on the theory of contracts, there has been less progress on practical algorithms for the algebraic operations in the theory. In this article, we present (1) principles to implement a contract-based design tool at scale and (2) Pacti, a tool that can efficiently compute these operations. We illustrate the use of Pacti in a variety of case studies.

Hybrid systems modeling languages that mix discrete and continuous time signals and systems are widely used to develop cyber-physical systems where control software interacts with physical devices. Compilers play a central role, statically checking source models, generating intermediate representations for testing and verification, and producing sequential code for simulation and execution on target platforms. This paper presents a novel approach to the design and implementation of a hybrid systems language, built on synchronous language principles and their proven compilation techniques. The result is a hybrid systems modeling language in which synchronous programming constructs can be mixed with ordinary differential equations (ODEs) and zero-crossing events, and a runtime that delegates their approximation to an off-the-shelf numerical solver. We propose an ideal semantics based on nonstandard analysis, which defines the execution of a hybrid model as an infinite sequence of infinitesimally small time steps. It is used to specify and prove correct three essential compilation steps: 1) a type system that guarantees that a continuous-time signal is never used where a discrete-time one is expected and conversely; 2) a type system that ensures the absence of combinatorial loops; and 3) the generation of statically scheduled code for efficient execution. Our approach has been evaluated in two implementations: the academic language Zélus, which extends a language reminiscent of Lustre with ODEs and zero-crossing events, and the industrial prototype Scade Hybrid, a conservative extension of Scade 6.

Since its 3.3 release, Modelica offers the possibility to specify models of dynamical systems with multiple modes having different DAE-based dynamics. However, the handling of such models by the current Modelica tools is not satisfactory, with mathematically sound models yielding exceptions at runtime. In this article, we propose several contributions to this multifaceted issue, namely: an efficient and scalable multimode extension of the structural analysis of Modelica models; a systematic way of rewriting a multimode Modelica model, based on this analysis, so that the rewritten model is guaranteed to be correctly compiled by state-of-the-art Modelica tools; a proposal for the handling of the consistent initialization of multimode models; multimode structural analysis algorithms that handle both multiple modes and mode change events in a unified framework, coupled with a compile-time algorithm for identifying and quantifying impulsive behaviors at mode changes. Our approach is illustrated on relevant example models, and the performance of our implementations is assessed on a variable dimension large-scale model.