Composition: A Fresh Look at an Old Topic

Abstract

Composing separate components is a fundamental design principle for concurrent systems. Composition $A_1\cdot A_2$ of two components $A_1$ and $A_2$ is mostly modeled by “gluing” according elements of the interfaces of $A_1$ and $A_2$. Composition of many components is usually assumed to be associative (i.e. $(A_1 \cdot A_2) \cdot A_3 = A_1 \cdot (A_2 \cdot A_3)$). In this paper we suggest such a composition operator for any kind of graph based structures. The central and new idea exploits the observation that in a composed system $A_1 \cdot ... \cdot A_n$, every component $A_i$ $(2 \le i \le n-1)$ has a left partner $A_{i-1}$ and a right partner $A_{i+1}$. The interface of $A_i$ hence canonically partitions into the left and the right port of $A_i$. To gain $A_1 \cdot A_2$, elements of the right port of $A_1$ are glued with corresponding elements of the left port of $A_2$. We present two instantiations of this framework, modeling synchronous and asynchronous composition, respectively, of components with local states.