8 - Linear Pi Calculus with Values

Summary

This chapter introduces a variant of the pi calculus defined in Chapter 2. We drop choice and channel closing, retaining only message passing. To compensate, messages may now carry values other than channel endpoints: we introduce record and variant values, both of which are standard in functional languages. We further introduce new processes to eliminate the new values. We play the same game at the type level: from input/output, external/internal choice and the two end types, we retain only input/output types. In return we incorporate record and variant types, again standard from functional languages. Unlike the input and output types in all preceding chapters, those in this chapter have no continuation. These changes lead to a linear pi calculus with record and variant types. The interesting characteristic of this calculus is that it allows us to faithfully encode the pi calculus with session types, even though it has no specific support for session types. We present an encoding based on work by Dardha, Giachino and Sangiorgi.