We present the mathematical foundations of the contract-based model developed
in the framework of the SPEEDS project. SPEEDS aims at developing methods and
tools to support "speculative design", a design methodology in which
distributed designers develop different aspects of the overall system, in a
concurrent but controlled way. Our generic mathematical model of contract
supports this style of development. This is achieved by focusing on behaviors,
by supporting the notion of "rich component" where diverse (functional and
non-functional) aspects of the system can be considered and combined, by
representing rich components via their set of associated contracts, and by
formalizing the whole process of component composition
