Multiparty sessions are systems of concurrent processes, which allow several participants to communicate by sending and receiving messages. Their overall behaviour can be described by means of global types. Typable multiparty sessions enjoy lock-freedom.

We look at multiparty sessions as open systems by allowing one to compose multiparty sessions by transforming two of their participants into a pair of coupled gateways, forwarding messages between the two sessions. Gateways need to be compatible. We show that the session resulting from the composition can be typed, and its type can be computed from the global types of the starting sessions. As a consequence, lock-freedom is preserved by composition. Compatibility between global types is necessary, since systems obtained by composing sessions with incompatible global types have locks (or they are not sessions). We also define direct composition, which allows one to connect two global types without using gateways. Finally, we propose a decomposition operator, to split a global type into two, which is the left inverse of direct composition. Direct composition and decomposition on global types prepare the ground for a novel framework allowing for the modular design and implementation of distributed systems.

多方会话是并发过程的系统，它允许多个参与者通过发送和接收消息进行通信。它们的整体行为可以通过全局类型来描述。典型的多方会话享有锁定自由。

通过将多方会话的两个参与者转换为一对耦合的网关，在两个会话之间转发消息，允许多方会话构成多方会话，因此我们将多方会话视为开放系统。网关需要兼容。我们显示了可以对合成产生的会话进行类型化，并且可以从开始会话的全局类型中计算出其类型。结果，通过组合保留了锁定自由。全局类型之间的兼容性是必需的，因为通过将具有不兼容的全局类型的会话组成的系统具有锁（或者它们不是会话）。我们还定义直接组成，它允许一个人在不使用网关的情况下连接两种全局类型。最后，我们提出了一个分解算子，将一个全局类型分为两个，这是直接合成的左逆。对全局类型的直接组合和分解为新的框架奠定了基础，该框架允许模块化设计和分布式系统的实现。