## Invited Paper: Cartesian Closed Double Categories, Their Lambda-Notation, and the Pi-Calculus (at LICS 1999)

**Roberto Bruni Ugo Montanari**

### Abstract

We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. Also, inspired by the connection between simply typed lambda-calculus and cartesian closed categories, we define a new typed framework, called double lambda-notation, which is able to express the abstraction/application and pairing/projection operations in all dimensions. In this development, we take the categorical presentation as a guidance in the interpretation of the formalism. A case study of the pi-calculus, where the double lambda-notation straightforwardly handles name passing and creation, concludes the presentation.

### BibTeX

@InProceedings{BruniMontanari-CartesianClosedDoub, author = {Roberto Bruni and Ugo Montanari}, title = {Cartesian Closed Double Categories, Their Lambda-Notation, and the Pi-Calculus}, booktitle = {Proceedings of the Fourteenth Annual IEEE Symposium on Logic in Computer Science (LICS 1999)}, year = {1999}, month = {July}, pages = {246--265}, location = {Trento, Italy}, note = {Invited Talk}, publisher = {IEEE Computer Society Press} }