  Contract theories have been proposed to formally support distributed and
decentralized system design while ensuring safe system integration. In this
paper we propose hypercontracts, a generic model with a richer structure for
its underlying model of components, subsuming simulation preorders. While this
new model remains generic, it provides a much more elegant and richer algebra
for its key notions of refinement, parallel composition, and quotient, and it
allows inclusion of new operations. On top of these foundations, we propose
conic hypercontracts, which are still generic but come with a finite
description.
