Representing the Finite calculus in Multi Interaction Nets Concurrency Interaction Non determinism

We extend the Interaction Nets of Lafont with some non determinism capabilities and then show how to implement the nite monadic calculus in that system Introduction The calculus of Milner et al is one of the most popular theoretical tools for the investigation of concurrent computations Its popularity is due to its con ceptual simplicity yet great expressive power However similar to the calculus the calculus leaves some of the basic low level components of computation im plicit namely the distribution of values and synchronization expressed as the global process of substitution Uncovering this ner computational structure and dispensing with the important role that syntactic entities like names play in calculus is the goal of this paper Interaction Nets IN of Lafont are a novel model of parallel compu tation simple and elegant Their essential properties as relating to parallelism are the locality of interaction and the simplicity of the rewriting process We in troduce a version of IN extended with non determinism Multi Interaction Nets and translate faithfully the calculus to MIN Our translation is similar to the nets of Milner and the Interaction Diagrams of Parrow but we represent blocking synchronization in a distributed manner without using boxes We also compare our construction to the Concurrent Combinators of Honda and Yoshida a Interaction Nets and Non Determinism Interaction Nets IN were introduced by Lafont as a simple and elegant model of parallel computation inspired by Linear Logic s Proof Nets and de signed to be useful both as an abstract programming language and as a useful intermediate representation Supported by a University of Alberta Dissertation Scholarship INs are graphs consisting of nodes agents of certain types and undirected edges connecting them The points of contact of edges and nodes are called ports and every node type has a particular signature of ports In conventional INs every node type has exactly one principal port denoted with a bold triangle and every port hosts exactly one edge Computation in INs is governed by interaction rules of the form