By contrast, the product for monoidal categories (such as Hilbert space and the vector spaces of functional analysis) is the tensor product. The internal language of such categories is linear logic, a form of quantum logic; the corresponding type system is the linear type system. Such categories are suitable for describing entangled quantum states, and, more generally, allow a vast generalization of the Curry–Howard correspondence to quantum mechanics, to cobordisms in algebraic topology, and to string theory. The linear type system, and linear logic are useful for describing synchronization primitives, such as mutual exclusion locks, and the operation of vending machines.