On Compilation of Higher-Order Concurrent Programs into First Order Programs Preserving Scope Equivalence

This paper discusses the expressive power of a graph rewriting model of concurrent processes with higherorder communication. As we reported before, it is difficult to represent the scopes of names using models based on process algebra. Then we presented a model of concurrent systems based on graph rewriting. The model makes it possible to represent the scopes of names precisely. We defined an equivalence relation called scope equivalence. Two systems are scope equivalent not only in their behavior but in extrusion of scopes of names also. This paper presents a result that there is no compilation mapping from the higher-order model into the first-order model that is homomorphic wrt input context and full abstract wrt the scope equivalence. As reported, it is possible to compile LHOπ processes into first-order π-calculus processes preserving a behavioral equivalence. In that sense, the first-order calculus is as expressive as the higher-order calculus when we focus on the behavioral equivalence. On the other hand, this paper shows that the higher-order model is strictly more expressive than the firstorder model if we focus on scope equivalence.