An Alvis model is defined as shown in Definition 1.

Definition 1. An Alvis model is a triple $\mathbf{A} = (H,B,\varphi)$, where:

• $H$ is a hierarchical communication diagram,
• $B$ is a syntactically correct code layer,
• $\varphi$ is a system layer.

Moreover, each non-hierarchical agent $X$ belonging to the diagram $H$ must be defined in the code layer, and each agent defined in the code layer must belong to the diagram.

It should be underlined that currently Alvis Compiler supports $\alpha^0$ system layer only.

Before generation of the Haskell model representation models are transformed into equivalent non-hierarchical form. The transformation applies to the communication diagram only. Thus, from the theoretical point of view, we can consider models defined as $\mathbf{A} = (D,B,\varphi)$, where $D$ is a non-hierarchical communication diagram.

Definition 2. A non-hierarchical communication diagram is a triple $D = (A, C, \sigma)$, where:

• $A = \{X_1,\dots,X_n\}$ is the set of agents consisting of two disjoint sets, $A_A$, $A_P$ such that $A = A_A \cup A_P$, containing active and passive agents respectively;
• $C \subseteq P \times P$, where $P$ is the set of all ports, is the communication relation, such that:
  • a connection cannot be defined between ports of the same agent;
  • procedure ports are either input or output ones i.e. ports defined as procedures are used to transfer signals (values) either to or from a passive agent;
  • a connection between an active and a passive agent must be a procedure call;
  • a connection between two passive agents must be a procedure call from a non-procedure port.
• The start function $\sigma$ makes possible delaying activation of some agents.

Each element belonging to $C$ is called a connection or a communication channel.

Names of agents that are initially activated are underlined in a communication diagram.

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