Cartesian Closed Double Categories, their Lambda-Notation, and the Pi-Calculus (1999) [14 citations — 10 self]
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author = {Roberto Bruni and Ugo Montanari},
title = {Cartesian Closed Double Categories, their Lambda-Notation, and the Pi-Calculus},
booktitle = {},
year = {1999},
pages = {246--265},
publisher = {IEEE Computer Society Press}
}
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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 -calculus and cartesian closed categories, we define a new typed framework, called double -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 ß-calculus, where the double - notation straightforwardly handles name passing and creation, concludes the presentation. 1. Introduction The (untyped) -calculus was introduced by Church as a convenient formalism for developing the theory of computable functions. Since then, the -calculus in its various versions has played a central role in bot...
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