arXiv subjects
Publications and source records attributed to Xian Xu.
Levy-Longo Trees and Bohm Trees are the best known tree structures on the λ-calculus. We give general conditions under which an encoding of the λ-calculus into the π-calculus is sound and complete with respect to such trees. We apply these conditions to various encodings of the call-by-name λ-calculus, showing how the two kinds of tree can be obtained by varying the behavioural equivalence adopted in the π-calculus and/or the encoding.
Parameterization extends higher-order processes with the capability of abstraction and application (like those in lambda-calculus). This extension is strict, i.e., higher-order processes equipped with parameterization is computationally more powerful. This paper studies higher-order processes with two kinds of parameterization: one on names and the other on processes themselves. We present two results. One is that in presence of parameterization, higher-order processes can encode first-order (name-passing) processes in a quite neat fashion, in contrast to the fact that higher-order processes without parameterization cannot encode first-order processes at all. In the other result, we provide a simpler characterization of the (standard) context bisimulation for higher-order processes with parameterization, in terms of the normal bisimulation that stems from the well-known normal characterization for higher-order calculus. These two results demonstrate more essence of the parameterization method in the higher-order paradigm toward expressiveness and behavioural equivalence.
Parameterization extends higher-order processes with the capability of abstraction (akin to that in lambda-calculus), and is known to be able to enhance the expressiveness. This paper focuses on the parameterization of names, i.e. a construct that maps a name to a process, in the higher-order setting. We provide two results concerning its computation capacity. First, name parameterization brings up a complete model, in the sense that it can express an elementary interactive model with built-in recursive functions. Second, we compare name parameterization with the well-known pi-calculus, and provide two encodings between them.
This paper studies context bisimulation for higher-order processes, in the presence of parameterization (viz. abstraction). We show that the extension of higher-order processes with process parameterization retains the characterization of context bisimulation by a much simpler form of bisimulation called normal bisimulation (viz. they are coincident), in which universal quantifiers are eliminated; whereas it is not the same with name parameterization. These results clarify further the bisimulation theory of higher-order processes, and also shed light on the essential distinction between the two kinds of parameterization.