From -calculus to Higher-order -calculus | and Back

We compare the rst-order and the higher-order paradigms for the representation of mobility in process algebras. The prototypical calculus in the rst-order paradigm is the-calculus. By generalising its sort mechanism we derive an !-order extension, called Higher-Order-calculus (HO). We give examples of its use, including the encoding of-calculus. Surprisingly, we show that such an extension does not add expressiveness: Higher-order processes can be faithfully represented at rst order. We conclude that the rst-order paradigm, which enjoys a simpler and more intuitive theory, should be taken as basic. Nevertheless, the study of the-calculus encodings shows that a higher-order calculus can be very useful for reasoning at a more abstract level.