Abstract: The task of system design is shared by all engineering disciplines, each coming with its own techniques. In spite of their differences in tools, there is large intersection in their conceptual approach to design. In this talk, we exploit this commonality to take an abstract view of systems and their composition. We understand systems and subsystems in terms of their assume-guarantee specifications, or contracts.

Assume-guarantee contracts are formal specifications that state (i) the assumptions that a design element makes on its environment and (ii) the guarantees it delivers when the environment behaves according to the contract's assumptions. Contracts come with a rich algebra that allows us to carry out several design-relevant tasks: obtaining system-level specifications from component specifications, finding specifications of components that need to be added to a design in order to meet an objective, etc. We will introduce the algebra of contracts and discuss how the various algebraic operations relate to system-design tasks. We will then provide a universal characterization of contracts as the adjoint of a well-known functor. Time permitting, we will discuss the application of this methodology and Pacti, a software package that supports system design using contracts, in areas ranging from space-mission design to autonomous vehicles.